The review register

The review register is the record of how optmat’s data and models were checked. It is the part of the package that makes its other claims verifiable: every value in the curated records can be traced to its page, and the register says what was done with it once it was there.

What it records

• Every transcription:

  • which tables, rows and columns of a paper were taken;

  • in what unit, at what state and in what wavelength medium;

  • with what stated uncertainty, and at what confidence level;

  • how they were checked: against the table image, against the paper’s own derived column, by reproducing a printed value from its formula.

• Every correction of a printed value, with the evidence. The correction itself lives in the source record as an erratum; the register explains it.

• Every decision taken in fitting:

  • a dataset fitted, fixed or kept as a validator;

  • a scale left free;

  • a prior chosen;

  • a range set.

  Each comes with the numbers that motivated it.

• Every finding:

  • two sources that disagree;

  • a formula that does not reproduce its own paper;

  • a published model that departs from the data.

• Every question left open, and its resolution when it comes.

How to read it

Entries are numbered TC-n (“to check”), in the order in which the work was done, and are permanent once integrated into main; branch-only numbers are provisional until integration. Established entries are never renumbered or removed. The code, the data records and this manual cite them by number: when a comment, a record’s notes or a page of this manual says TC-92, the entry of that number holds the evidence. A later entry that corrects or supersedes an earlier one says so. Each entry closes with its status:

Status	Meaning
open	Waiting for a check or a decision; the entry says what is open.
verified (date)	Checked against the primary source.
corrected (date)	An error was found and corrected.
decided (date)	A choice was made, for the reason given. Many transcription entries are “accepted with” an integration entry: the records were reviewed as a set and adopted; anything the entry marks open stays open.

The curation was done by J. C. Travers working with AI agents. Most records were transcribed and checked by an agent at extraction and reviewed by a second curator, an agent or J. C. Travers; the decisions on data, fits and conventions are his. “At extraction” and “a second curator” in the entries refer to this division of the work.

Entries describe the data format of their day. The format was generalised on 2026-09-26 (TC-316), and the package layout settled the same day (TC-317); later entries use the present names.

How entries are added

Instructions for authors are in Maintaining the review register. The register itself is REGISTER.md.

See reconciling concurrent branches.

The register

The entries follow, from TC-1.

TC-1: real-gas densities from the equation of state’s compressibility factor

• Where: optmat.gas.eos.number_density, optmat.gas.eos.compressibility.

• Claim: the real-gas density is formed as p / (Z k_B T) with CoolProp’s Z, not from its mass density, because several CoolProp equations carry older gas constants (argon and nitrogen: R = 8.31451 J/(mol K)) that put their mass densities 5.7e-6 from the CODATA ideal gas at vanishing pressure (measured 2026-09-24 at 10 Pa, 273.15 K: Ar 0.9999944, N2 0.9999943, H2 0.9999988, He 1.0000003).

• Consequence for solprop: solprop.physdata.equation_of_state uses the mass density, so its argon and nitrogen densities carry this 5.7e-6 offset (for the solprop integration).

• Status: open.

TC-2: Edlen 1966 standard-air dispersion formula

• Where: optmat.conditions.standard_air_refractivity.

• Claim: 1e8 (n - 1) = 8342.13 + 2406030 / (130 - s^2) + 15997 / (38.9 - s^2), s the vacuum wavenumber in um^-1, for dry air with 0.03 % CO2 at 15 degrees C and 101 325 Pa (B. Edlen, Metrologia 2, 71 (1966)). Transcribed from memory: the paper is not in the curators’ library (cited by Smith 1976 and Zhang 2008). It is used only to convert standard-air wavelengths (Leonard 1974 Table II, Cuthbertson) to vacuum, where a 1e-7 error in n - 1 moves a wavelength by 1e-7 relative and a refractivity by ~1e-9.

• Status: verified (2026-09-24, source edlen_1966): the package’s formula is Edlen’s Eq. (1) exactly, coefficients, variable and reference state.

TC-3: Huber & Tondello (1974), helium 92-190 nm

• Where: data/sources/huber_1974.toml, tools/extract/huber_1974.py.

• Transcribed: Table I (tbl_6b16f76840f9), 11 rows: the experimental column (primary) and the theoretical column (Victor et al., reproduced), x1e-5, vacuum Angstrom, 0 degrees C and 760 Torr (“NPT”; the reduction method is not stated, so density = "unknown").

• Uncertainty: “the probable error in the best-fit curve is smaller than +-3 %” (p. 391), read as a probable error of 3 % (1.48 x 3 % one sigma). The table lists the smoothed best-fit curve, not the individual measurements.

• Status: open.

TC-4: Bideau-Mehu et al. (1981), Ne, Ar, Kr, Xe 140-254 nm

• Where: data/sources/bideau_mehu_1981.toml, tools/extract/bideau_mehu_1981.py.

• Structural fixes: the captions in the curators’ extraction are wrong for three tables (checked on the images): tbl_804a29eb8dd3 = Table 2 neon, tbl_7062fe0f03a9 (captioned “Table 5 Xenon”) = Table 4 krypton, tbl_7ab7e916e7b3 = Table 5 xenon. The raised dots marking other authors’ extrapolated values, lost in the extracted CSVs, were read from the images and those cells are not extracted; Chashchina & Shreider’s xenon values below 155 nm are also dropped as extrapolations because the text says they stopped measuring at 155 nm.

• Uncertainty: 0.5 % for Ne, Ar, Kr and 0.3 % for Xe (1 % at 149.5 and 148.3 nm), level not stated; the paper gives “about 0.5 % for neon to 0.3 % for xenon”, so Ar and Kr were given 0.5 %, the bound of the stated range. To confirm: this reading.

• Reduction: 0 degrees C, 760 Torr, real gas (van der Waals for Ne, Kr, Xe; Hilsenrath for Ar).

• Erratum: fit_Ne at 253.7 nm, printed 69.60, corrected 68.60 (the formula gives 68.60 and reproduces every other row).

• Formulas: Ne corrected (B1 182.90 -> 1.8290, lambda^-1 -> lambda^-2); Xe corrected (C2 50.578 -> 59.578); Ar reproduces its column; Kr does not (0.1-0.7 % low, no single coefficient explains it; left as printed). The upper ends of the formulas’ ranges (546.1, 567.7, 623.4, 670.8 nm) are the longest wavelengths of the literature data the authors joined, taken from refractiveindex.info’s entries: to check.

• Heddle column: Ref. 19’s argon values (332.0, 336.0 at 184.9, 180.7 nm) are not Heddle et al.’s published 325 and 328 x 1e-6 at 1850 and 1805 A.

• Status: open.

TC-5: Ermolov et al. (2015) helium formula and its reference state

• Where: data/sources/ermolov_2015.toml.

• Transcribed: Table I coefficients from the table image (the header row was lost in extraction): B = 2.16463e-5, 2.10561e-7, 4.75093e-5; C = -6.8077e-4, 5.13251e-3, 3.18621e-3; Eq. (3), rho relative to 1 bar at 273 K (read as 273.15 K).

• Finding: referred to 1 bar as printed, the formula lies 1.3 % above Mansfield & Peck, Borzsonyi and every refractiveindex.info helium entry from the UV to the near infrared; referred to 1 atm it agrees with them (gallery, helium page). solprop’s reading (1 atm) matches the data; the paper’s stated state does not. To confirm (with an author of the paper): which state the fit was made at.

• Status: decided (2026-09-25): follow the data, the formula is a 1 atm fit (an author of the paper cannot recall the fit’s state; the 1 bar in the paper is presumably an error). solprop’s reading stands.

TC-6: Luna legacy fits (argon 56cc3ab, krypton PR #425)

• Where: data/sources/luna_physdata.toml.

• Transcribed: from solprop’s sellmeier.py and a survey of Luna and its pull requests (Luna PhysData.jl modal-fixed 6537a0f; PR #425 via gh): helium JCT, argon Kingston fit (1 bar), krypton Kingston fit at 1 bar (as Luna evaluates it) and at 1 atm (solprop’s reading). Ranges 110 / 130-1000 nm from PR #425’s phase-matching limits.

• Status: open.

TC-7: NIST ASD accuracy grades

• Where: data/external/nist_asd/PROVENANCE.md.

• Claim: the NIST accuracy grades (AAA <= 0.3 %, AA <= 1 %, A+ <= 2 %, A <= 3 %, B+ <= 7 %, B <= 10 %, C+ <= 18 %, C <= 25 %, D+ <= 40 %, D <= 50 %, E > 50 %) are written from memory of the ASD documentation; they will set the priors of the resonance oscillator strengths.

• Status: open.

TC-8 mansfield_peck_1969 (identity unverified)

• Transcribed: Table I tbl_aae92dff687e (extracted cells, no CSV; image checked): 13 fitted He points (experiment, x1e-9, vacuum A, 1 atm 0 C, real gas via White’s virial Z) and the two parenthesised, footnote-a points 9660.434 and 15300.153 A (experiment_excluded). Deviation column not extracted.

• Table II tbl_330bf663e80e (image): 20 oscillator strengths (reproduced; row ids name the upper state; the CSV merges series labels into the sum rows).

• Tables III (Koch 1913, Cuthbertson 1932 at 5462.258 A), IV (Korwin, present calc, Musulin-Epstein, Karplus-Kolker, Migneron-Levinger at 5500 A), VI (six static polarizabilities, x1e-24 cm3): one dataset per author (images checked).

• Uncertainty: per point 0.29e-9 rms (Eq. 4 residual), systematic 0.26 % (the paper’s “liberal” +-0.009e-5 at the green line, taken as one sigma: the level to confirm).

• Erratum: Table II 1s4p wavenumber 19.4195 -> 19.1495 (digit transposition; Rydberg fit to the paper’s n = 5-10 gives 19.150).

• Formulas: Eqs. 1-4 (experiment) reproduce Table I (rms 0.63/0.41/0.53/0.38e-9 vs quoted 0.57/0.42/0.36/0.29); Eq. 3 static limit gives Table VI’s 6.462 exactly (so its “+” is right). Eq. 7 sign misprint (“-” -> “+”) and Eq. 8 missing “+”: corrected forms agree with each other (3.49784 at 5462 A) and give Table VI’s 6.468; the paper’s own 3.4976 (Table IV) is 7e-5 lower, unexplained.

• Doubts: Table I’s deviation column reproduces from no version of Eq. 4 (sign appears flipped); text says (2s,np) sum from n = 7 is 0.00122, table prints 0.00137 (left as printed); Table IV “0.02 %” does not follow from its numbers; Tables V, VII, VIII (derived F values, Becquerel constants, Verdet constants with no power of ten) not extracted. Source id is mansfield_peck_1969, not the <first author>_<year> rule (mansfield_1969).

• Status: open.

TC-9 cuthbertson_1932

• Transcribed: Table II Ne tbl_4ee024d8daf8 and Table III He tbl_01cd89e4e3aa (extracted cells, no CSV; images checked): observed (primary) and calculated (check) columns, 12 Ne and 14 He points, x1e-8, raised decimal point read as a point.

• Errata (22): He wavelengths printed to “four figures” (truncated) corrected to Table II’s full vacuum values for the 11 shared mercury lines, in both He datasets; 3126, 2926, 2753 A stay truncated (up to 1 A).

• State not stated in the paper: 1 atm 0 C assumed (the authors’ 1909-10 convention), density unknown. To confirm.

• The curators’ extracted Markdown drops one of the three He green-line values (3485e-8); page image checked. Uncertainties: per point = rms of obs-calc (Ne 0.29, He 0.15 printed units); systematic Ne 0.03 %, He 0.1 % (spread of absolute values).

• Formulas: ne_1932, he_1932 reproduce the calculated columns to 0.14e-8 with V = 3e10 cm/s (implied, not printed); Koch’s 1913 He formula (reproduced) checked against Koch’s green-line value.

• Status: open.

TC-10 cuthbertson_1910 (Proc. R. Soc. A 84, 13)

• Transcribed: Table I Ar tbl_7e2ecfe6276e (image: header is x10^8, the extraction’s 10^9 is a misreading), Table II He/Ne/Kr/Xe tbl_c0066726ecc8 (extracted cells; image): observed (primary) and calculated (check); all doubled, 2(mu-1): scales include 1/2.

• Structural: Xe columns are x10^7 though headed x10^8 (formula confirms): scale 5e-8.

• Excluded: Ar 5769.5 (authors’ own exclusion); He 5769.5 printed 6963.8 (19.7 below the formula and below the 6438.5 value: misprint for 6983.8 or a one-band miscount; not corrected, excluded).

• Reproduced: Burton (6563, 5896) and Ahrberg (6439, 5461, 4359) argon from the earlier-work table tbl_f8dd6a8e65a1 (image); white-light and “5790-70” rows skipped.

• Wavelengths are air (the Cd/Hg/Ag/Li air values): standard_air. State assumed 1 atm 0 C (stated in cuthbertson_1910b). To confirm.

• Formulas: Table III constants for five gases (doubled) reproduce the calculated columns to <= 0.7 printed units with V = 3e10 and air wavelengths, except Kr at 6707.85 A (85052.5 vs printed 85055); Burton/Ahrberg refits; Burton’s Cauchy argon.

• Status: open.

TC-11 cuthbertson_1910b (Proc. R. Soc. A 83, 149)

• Transcribed: tbl_9757a187853d, three rows collapsed into one cell in the curators’ extraction, split by the script after checking the image: Ne 2(mu-1) x1e6 = 134.02, 134.30, 134.63 at 6438, 5461, 4800 A (air). excluded as superseded by cuthbertson_1910’s remeasurement (dispersion “not trusted to less than 5 per cent”).

• State: “0 C and 760 mm” stated (p. 149).

• Formulas: Ne Cauchy (b’s power of ten not printed; 0.05 low, rounding) and Sellmeier (reproduces the three values); revised Kr, Xe, Cuthbertson-Metcalfe He, Burton He and Ar formulas from the p. 151 table, all doubled though headed “mu - 1”.

• Status: open.

TC-12 smith_1976 (identity unverified)

• Transcribed (all images checked): Table IV He tbl_e2f6e80b5c2b (extracted cells): 25 experiment points (col 3; “Identification” spans two cells), Victor theory (35 rows, reproduced, private communication), Abjean 1970 (6, reproduced, not in the curators’ library), Huber-Tondello (3, reproduced from huber_1974: identical), Bideau-Mehu unpublished 170.2 nm (1, reproduced). Table V H2 tbl_5b5868c91642: 26 experiment, interpolated fit (35, check), Ford theory (35, reproduced), Koch 1913 (5; the four h-marked extrapolated cells dropped), Kirn 1921 (9). Table VI O2 tbl_1bad6e7f544c: 22 points (b marks on 191.85, 184.30 stripped; 1.0 % there). Table VIII Kr tbl_8156b916136f: 28 experiment, interpolated (55, check), Bideau-Mehu (6, identical to bideau_mehu_1981/experiment_Kr), Kronjager/Koch via Leonard (21, reproduced).

• Uncertainties: 90 % confidence from Table III; He uses the “2 atm” row (0.35/0.58 %) because the text quotes +-0.35 to +-0.6 % for the helium data (to confirm: which pressure the He data were taken at is not said explicitly). Kr: 0.10 % > 220 nm, 0.11 % 190-220, 0.13 % < 190 (the 0.25 atm run’s 0.3 % not used).

• Real-gas reduction to 273.15 K, 760 Torr (Hilsenrath Z / Sengers virial). Vacuum wavelengths.

• No formulas (Sellmeier coefficients not printed). CO skipped. Citation (Phys. Rev. A 13, 1422) as supplied with the source list; page numbers counted from 1422.

• Doubt: Table IV’s Delta(%) for other measurements has the opposite sign to its footnote (not used).

• Status: open.

TC-13 stone_2004

• Text values (inline points, pages checked): He A_R(633 nm) = 0.5202634(5) cm3/mol (check; p. 191); n(633 nm, 101325 Pa, 20 C) - 1 = 3.242600e-5 (8e-11) (check; p. 192); reproduced He A_R Achtermann 0.5213(1), Birch 0.5220(3); N2 A_R at 633 nm: this work 4.4454(7) (k = 2, primary), Birch 4.4457(8), Hou-Thalmann 4.4456(6), Montixi 4.4454(5), Achtermann 4.4464(5) (reproduced; levels not stated) (p. 195).

• Formulas: Eq. 5 alpha(omega) (reduced a.u.), Eq. 8 A_R(lambda nm), Eq. 9 B(T), Eq. 10 B_R. Eq. 5 with Eqs. 6-7 gives Eq. 8’s coefficients to all digits; Eq. 8 gives 0.5202634 at 633 nm; the full procedure gives n = 1.00003242604 (printed …426 00(8)); the 4e-11 is the change of k since CODATA 2002.

• Doubt: the N2 reduction cites [15] (Hurly-Moldover, helium) for B(T).

• Status: open.

TC-14 marchetti_2006

• Table 1 tbl_fcf07d146f15 (OCR body; image checked): alpha_P of CO2, N2, O2, He at 10.57 um, 1e-4/atm, 23 C (”@ 296 °C” = 296 K), last-digit errors converted to absolute sigma; stored as refractivity at 1 atm, 296 K, ideal gas (primary).

• Table 2 tbl_a64b03e950d7 (image): alpha_rho = (n-1)/rho in cm3/mol stored as refractivity_per_density with scale 1/N_A: this work (check, = Table 1 x RT), Simmons 1978 (CO2, N2 at 10.59 and 0.633 um), Achtermann 1991 (CO2, N2, He at 0.633), Edlen and Old theory for CO2 (via Ciddor 2002), all reproduced. Structural fix: the cell “7.21973)” is 7.219 with “(73)” wrapped (image). Air skipped.

• To confirm: the per-density storage (scale 1/N_A, state 1 atm 296 K) and the ideal-gas reading of alpha_P.

• Status: open.

TC-15 marchetti_2007

• Table tbl_33adeac1f5b0 (image): 27 CO2 lines, dn in 1e-4/atm at 21 C, wavenumber cm^-1; errors (last digits) as sigma. Refractivity at 1 atm 294.15 K, ideal gas.

• Formula Eq. 4 (parabola in wavenumber) reproduces the table within the errors.

• Consistent with marchetti_2006’s 10.57 um value scaled by T.

• Status: open.

TC-16 liu_1997

• Table I tbl_c824036c5cc9 (image): 16 alpha(omega) values, a.u., omega = 0-0.75 a.u. (hartree), primary (ab initio, nonrelativistic, infinite mass; no uncertainty stated). Table II tbl_936a0db2e146 (image): Im alpha (8, primary), cross sections (check: Eq. 17 of Im alpha, verified to the last digit at all 8 energies), Samson et al. 1994 cross sections (reproduced). Table IV tbl_5f861154394b q = 1 row: |chi_1| in cm3 at ~46 um (stored as 46000 nm), 1064, 532, 248 nm (check).

• FORMAT GAP: the negative real parts of alpha above threshold (Table II) have no quantity (polarizability must be > 0.5 a.u. in the tests); not extracted.

• To confirm: infinite-mass frequency axis (reduced-mass scaling ~1.4e-4 matters near 0.75 a.u.); use = primary for an ab initio theory.

• Status: open.

TC-17 migneron_1965

• Table I tbl_a097df9cffbb (image): 25 n - 1 values at 600-7000 A, 1 atm 0 C, ideal (Loschmidt), x1e-6; use check (semi-empirical, 2-5 %).

• Table II tbl_f60413766558 (image): totals S(-2..2) in Ry^p, one dataset per p with scale 2^-p (a.u.), check; Essen/Johnston S(-2) and Pekeris S(-1..2) reproduced.

• Text: Chan and Dalgarno n - 1 = 36.4e-6 at 2000 A (reproduced, p. A648).

• FORMAT NOTE: cauchy_moment in Ry^p needs a per-p scale, hence five one-point datasets.

• Status: open.

TC-18 berkowitz_1997 (identity unverified)

• Table 1 tbl_989659e9200e (image): He 1 1S -> n 1P oscillator strengths by source: Schiff 1971 (4), Kono-Hattori 1984 (8), Drake 1996 (6), Fernley 1987 (6), Chan 1991 (6, with +- sigma), all reproduced; the author’s parenthesised extrapolation n = 10-20 (11, check). Thin-space digit groups removed. Abscissa = n (index).

• FORMAT GAP: no Rydberg energy unit for the wavelength column (E/R, R = 13.6057 eV); the energies stay in the printed cells.

• Table 2 tbl_2a3db8fd2b0e: f_xs (x1e-4) of the 2snp autoionising series at 60-65 eV (9, check).

• Table 3 tbl_6523ca2ec08b (extracted cells; merged cells read on the image): recommended totals S(-2..2) (check) and exact values (Miller S(-2), Pekeris S(-1..2), reproduced), in Ry^p with scale 2^-p.

• Text: Miller’s alpha printed 0.0204956e-24 cm3 (p. 889) -> erratum 0.204956 (the paper’s own S(-2) = 0.345778 needs it).

• Formulas: Table 4’s seven power-series fits; the five df/d(E/R) fits reproduce Table 3’s partial sums (S(0) IP-120 = 1.4085 as in the text; Bizeau and Samson 120-280 all five S(p); Hino 280 eV-12 keV S(0) 0.0243 vs 0.0242). The 3000-12000 eV (E/R)^2 fit does NOT reproduce (300x too large at 3 keV); no correction found. Salpeter-Zaidi and Samson asymptotic formulas recorded (reproduced).

• Doubt: Table 3’s IP-120 S(-1) for Chan printed 0.4476, text 0.4776 (not extracted).

• Status: open.

TC-19 wang_2021

• Table 2 tbl_d0fc08f74765 (image + page image for footnotes gg-jj, lost in the extracted Markdown): He, Ne, Ar only. Own CCSD(T) (check); quoted Calc. and Expt. values as one-point reproduced datasets with their references (He 1.38319 Yan/Pachucki, 1.38376 Lach 2004, Expt 1.383746(7) Newell-Baird/Grohmann-Luther; Ne 2.666 (82-84), 2.663 Klopper, Expt 2.663 Dalgarno-Kingston (= dalgarno_1960), 2.66110(3) Gaiser-Fellmuth 2010; Ar 11.10 Reinsch-Meyer, 11.085(60) Lupinetti/Hohm, Expt 11.083(2) Newell-Baird, 11.070(7) Johnston et al.).

• To confirm: He convention: 1.38319 matches Stone’s reduced-unit static value, 1.38376 = x (1 + me/m_alpha)^3 (physical 4He). The He “Expt.” 1.383746(7) attributed to 1965 and 1992 papers looks like a modern theory value; kept as printed.

• Status: open.

TC-20 bishop_1989

• Text only (p. 3550): alpha(0) = 1.383192 a.u. (check; infinite mass). Hyper- and quadrupole polarizabilities not extracted. A 1995 erratum exists (not in the curators’ library).

• Status: open.

TC-21 dalgarno_1960

• Table 1 tbl_61824749ae46 (extracted cells; image): He S(k), k = 0, -1, -2, -4, -6, exact and Eq. (18) (check), in Ry^k, scale 2^-k. Table 2 tbl_07f29f0464dd: static alpha of He-Xe in a0^3 (check: derived from Cuthbertson data).

• Formulas: n^2 - 1 Cauchy series for He, Ne, Ar, Kr, Xe (p. 428); static limits reproduce Table 2 to 0.05 % except Ne (2.668 vs 2.663, 0.2 %, unexplained); He gives Cuthbertson’s 3.489e-5 at 5462 A.

• Not extracted: atomic H, Table 3, Verdet formulas.

• Status: open.

TC-22 wheeler_1933

• Text points: resonance-line f = 0.266 (p. 261, check, <= 30 % error) and Vinti’s 0.349 (reproduced), index n = 2.

• FORMAT GAP: Table I (df/dE at 20 energies, Rydberg units) has no quantity (a differential oscillator strength); not extracted. Eq. (12) recorded as a formula; it agrees with Table I within 1.2 % up to E = 4 Rh, 4-6 % at 10-16 Rh.

• Eq. (14) one-term n - 1 recorded; 3.1 % above Cuthbertson’s at 5462 A (checked).

• Status: open.

TC-23 musulin_1964

• No tabulated data; the shielding-approximation formula recorded (check: zeta(0) = 1.640625, n - 1 = 3.130e-5 at 5462 A).

• Doubt: mansfield_peck_1969 Table IV quotes 2.983e-5 for this theory at 5462 A; the formula gives 3.130e-5 (noted in both records).

• Status: open.

TC-24 swift_1988

• Table I tbl_98326ad22a2d (extracted cells; image): alpha (1e-24 cm3) at 4579, 4880, 5145, 6328, 13150 A for He, N2, O2, Ar, CO2, O3, SF6 (5 points each, primary; 2 % bound, O3 10 %). beta = 2 pi alpha N_s checked consistent for all curated cells, not extracted. Skipped: H2O, Cl2, ICl, CF3I, I2, n-C3F7I (not curated; note CF3I’s 6328 A beta is inconsistent with its alpha).

• To confirm: wavelength medium taken as standard air (nominal laser lines).

• Status: open.

TC-25 borzsonyi_2008 (Borzsonyi et al., Appl. Opt. 47, 4856 (2008))

• Transcribed: Table 1 (tbl_15ed1378c327, JSON cells only: the curators’ extraction has no CSV for it; read through the helper tools/extract/_json_table.py), SGD / SGDD / STOD with their +- errors for N2, He, Ne, Ar, Kr, Xe (air skipped): 18 one-point datasets. Compared with the table image: all cells as printed.

• State: 1000 mbar and the per-gas ‘Temperature of Meas.’ (19.4-20.8 C); the caption says ‘20 C’. Density = real (measured at the state, not reduced). Wavelength 800 nm vacuum (omega0 = 2.35 fs^-1, p. 4). Level of the +- errors not stated.

• SGD is the excess over vacuum ((n_g - 1)/c; He 146 fs/m): recorded as parameters.excess_over_vacuum = true. The vocabulary’s group_delay does not say whether 1/c is included: to be defined.

• Doubt, SGD set to use = "check": every SGD is 22-39 fs/m above what the refractivity implies (He 146.0 printed vs about 108 expected from its n - 1 known to 0.1 %). Probably a common additive offset; unverifiable. SGDD kept primary; STOD is an upper limit only (p. 5): check.

• Lorentz-Lorenz constants (m^3/kg) not extracted: their derivation is not given and 2/3 (n - 1)/rho does not reproduce N2’s.

• Formulas: six Sellmeier fits (Eq. 14, Table 2 tbl_8d505c3d8e77, image checked), ideal-gas (p/p0)(T0/T) scaling of n^2 - 1, p0 = 1000 mbar, T0 = 273 K (text) / 0 C (caption). Fitted to three literature n (Leonard / Peck-Khanna / CRC) plus the SGDD only. Checks at 546.2258 nm (0 C, 1013.25 mbar): N2 299.15 (PK 299.14), He 34.88, Ne 67.24, Ar 282.46, Kr 430.71 against Leonard’s Table I. At 800 nm the fits give SGDD N2 19.67 (18.04 measured), He 0.94 (0.82), Ne 1.84 (2.11), Ar 18.14 (17.98), Kr 37.33 (37.32).

• Formula misprint, Xe C1: printed C1 x 10^6 = 12.75 gives n - 1 = 683.7e-6 at 546 nm (Leonard 706.60) and SGDD 1.17 (87.42 measured). C1 = 12.75e-3 um^2 gives 707.09e-6, SGDD 88.54, STOD 41.5 (40 +- 12). Recorded in the formula’s notes (Luna uses the same correction).

• Status: open.

TC-26 shelton_1986 (Shelton & Mizrahi, Phys. Rev. A 33, 72 (1986))

• Transcribed: Table III (tbl_0a217d3795df, image checked): D2/H2 phase-match density ratios, 9 points 476.6-694.5 nm, errors from the parentheses (1.0308(7) -> sigma 0.0007), phase_match_density_ratio, reference H2, harmonic 2; and the ‘calc’ column (Shelton’s evaluation of Rychlewski 1983) as reproduced.

• Definition written into parameters.definition: ESHG, Delta k = 2k_w - k_2w = (4 pi/lambda_w)(n_w - n_2w); equal |Delta k| for both gases, so to first order rho_D2/rho_H2 = [alpha_H2(2w) - alpha_H2(w)] / [alpha_D2(2w) - alpha_D2(w)]; lambda = fundamental, vacuum (the Ar+ lines are printed at vacuum wavelengths: 514.7, 496.6, 488.1, 476.6). Densities are real (virial EOS).

• Cross-check: the ratio of the Table I fits at 694.5 nm is 1.03085 (Table III 1.0308).

• Formulas: 6 x Table I (lambda^3/rho, Eq. 6) and 6 x Table II ((n_w - n_0)_STP,i, Eq. 8, ideal-gas density at 0 C, 1 atm), images checked. Table II recomputed from Table I with rho_STP,i = 44.6150 mol/m^3 and |Delta k|_opt = 1161.5 m^-1: A and B to the last digit or 1e-5; C within 0.2 % (C’ has three digits).

• The phase-match densities of Fig. 2 are not tabulated (figure only).

• Status: open.

TC-27 shelton_1990 (Shelton, Phys. Rev. A 42, 2578 (1990))

• Transcribed: Table I (tbl_5295cecf2a78, JSON only; image checked), rho_B/rho_A at 1319 and 1064 nm with +- errors, 12 curated pairs x 2 points (Ne/He, Ar/He, Kr/Ar, Xe/Ar, H2/He, D2/H2, N2/He, O2/N2, Ar/N2, CO2/N2, SF6/N2, CH4/N2); CF4, C2H6, C3H8, n-C4H10, C4H6 skipped. A duplicate copy in the curators’ library has the identical table: not used.

• Process: ESHG (harmonic 2), not THG: rho_B/rho_A ~ (alpha_2w - alpha_w)_A / (alpha_2w - alpha_w)_B (p. 6), Eq. 4.

• Representation choice to confirm: Table I prints rho_reference/rho_sample. To keep the printed number and match the vocabulary (rho_gas/rho_reference), each ratio is filed under Shelton’s reference B as gas with his sample A as reference_gas (so CO2/N2 is N2/density_N2_over_CO2); parameters.sample_gas and parameters.shelton_reference_gas keep his roles. A ratio constrains two gases: the fitting layer must look up ratios by either gas.

• Wavelengths recorded as standard air (Table III caption: lambda in air; nu 7581 and 9395 cm^-1 in vacuum for these lines).

• Consistency: 19.83 x 0.9282 = 18.406 (Ar/He 18.41) at 1319; 18.525 vs 18.54 at 1064. rho_H2/rho_D2 = 0.9720 / 0.9717 vs 1/1.0290 = 0.9718 from Shelton 1986.

• Not extracted: gamma ratios and Tables II-V (hyperpolarizability).

• Status: open.

TC-28 wilmouth_2020 (Wilmouth & Sayres, JQSRT 255, 107224 (2020))

• No datasets: the measured Rayleigh cross sections (264-297 nm) are figures only. Text values recorded in notes: measured/n-based ratios Ar 1.008, CO2 0.990, SF6 0.959, CH4 0.775 (p. 5); mean 1-sigma 3.1 / 2.1 / 1.9 / 2.1 % (p. 3).

• Vocabulary gap: no quantity for a Rayleigh scattering cross section (needs F_k as a parameter). See also he_2021.

• Formulas (equation images checked): SF6 Eq. 4 and CH4 Eq. 5 (UV only), SF6 Eq. 6 and CH4 Eq. 7 (UV + visible, recommended); 288.15 K, 101325 Pa, N = 2.5469e19 cm^-3 (ideal), F_k = 1 assumed. Check: Eq. 4 vs 6 and 5 vs 7 cross-section differences 0.23-0.26 % mean / 0.46 % max (paper 0.25 / 0.49) and 0.40-0.47 / 0.85 (paper 0.44 / 0.91): approximately reproduced; the maxima do not match exactly (sampling or range).

• Reproduced formulas from Table 1 (image checked): He, N2 (Bates UV branch), Ar (= Peck & Fisher 1964, algebra checked against its abstract), CO2 (Bideau-Mehu 1973 + Alms F_k via Sneep & Ubachs). The curators’ extracted CSV mangles the CO2 cell; the image shows five additive terms, identical to He et al. 2021 Table 1.

• Format extension used: reproduced_from inside [[formulas]] entries (not in the formula schema as then specified): to confirm or reject.

• Status: open.

TC-29 he_2021 (He et al., Atmos. Chem. Phys. 21, 14927 (2021))

• No datasets: Table 2 (tbl_7b887ae8ae76, image checked) holds the measured (‘Exp’) and n-based Rayleigh/extinction cross sections (1e-27 cm^2) of CO2, SF6, N2O, O2, CH4 at 330, 404, 532, 660, 710 nm, but no vocabulary quantity fits. Needs a rayleigh_cross_section quantity (unit cm2, parameter F_k); then a JSON-table extraction is direct. Exp values (for reference, from the image): CO2 96.8, 41.6, 13.3, 5.52, 4.08; SF6 239.4, 105.7, 34.1, 14.2, 10.4; N2O 136.7, 57.9, 18.3, 7.47, 5.48; O2 35.1, 14.8, 4.55, 1.95, 1.41; CH4 85.3, 35.9, 11.3, 4.68, 3.47 (CH4 > 400 nm and O2 include absorption).

• Formulas (checked against the PDF text via pdftotext): CH4 Eq. 7 (UV-only), SF6 Eq. 8, N2O Eq. 9, CH4 Eq. 10; 288.15 K, 1013.25 hPa, N = 2.546899e19 (ideal).

• Reproduced Table 1 formulas (image checked): He, N2, CO2, CH4 (= Wilmouth Eq. 7), N2O (Sneep, Cauchy form), SF6 (= Wilmouth Eq. 6), O2 (Bates, at 273.15 K, N = 2.68678e19; footnote read from the PDF, truncated in the curators’ extraction). Recomputed Table 2’s n-based column from them: O2 exact, others uniformly 0.10-0.15 % high (a density convention difference), confirming the transcriptions.

• Status: open.

TC-30 andrews_2016 (Andrews et al., Opt. Express 24, 14086 (2016))

• Short record, no datasets. The paper’s own data are phase-vs-pressure figures calibrated against literature polarizabilities. Table 1 (tbl_9c65adc46529, image checked, garbled headers) holds only reproductions to 3 digits; the 1532 nm values of Ar (1.74e-40) and N2 (1.95e-40) are below their static values (1.82, 1.96): physically impossible, so not worth keeping even as a check.

• Status: open.

TC-31 orr_1936 (Orr, Trans. Faraday Soc. 32, 1556 (1936))

• Text only (p. 3): n_H2 - n_D2 = (179 +- 2)e-8 at 5462 A (recomputed: 35.0/14.25 x 5462/75 x 1e-8 = 178.9e-8), measured at room temperature and ~atmospheric pressure (neither stated). n_D2 = 1.0001378(7) at 273 K, 760 mm = ICT H2 1.00013966 minus the difference, unscaled. Entered as one inline point, refractivity 137.87e-6, sigma 0.02e-6, use = "check": it inherits the ICT H2 value (0.25 % high per Peck & Huang 1977: 139.304 vs 139.66) and the unscaled room-density difference.

• The independent result (D2 about 1.3-1.4 % below H2 at 546 nm) has no vocabulary quantity (a refractivity difference); noted as open.

• The parenthesised last digit ‘(7)’ read as an uncertain digit, not an error: to confirm.

• Raw drum tables not extracted.

• Status: open.

TC-32 peck_1977 (Peck & Huang, J. Opt. Soc. Am. 67, 1550 (1977))

• Note: the second author is Huang (the curators’ library metadata and the paper), not “Hung”.

• Table I (tbl_7beee2e55930, image checked): 15 fitted points (primary), the two parenthesised rows as excluded, and the Eq. (4) column as check. Structural fixes in the script: thin spaces in wavelengths, parentheses, the one surviving decimal comma (‘137,746’ -> 137.746).

• Erratum: Eq. (4) column at 1.3507884 um, printed 135.305 -> 136.305 (difference column and the formula: 136.3052).

• Uncertainty: absolute 0.0018 (rms of fit, p. 1551), systematic_relative 3.1e-4 (0.017 statistical and 0.04 systematic, e-6, in quadrature over 139.3): a combination made here, to confirm. Real-gas reduction (virial Z, Eq. 2) at 0 C 760 Torr.

• ‘Eighteen wavelengths’ in the text vs 17 rows in Table I (image: none lost).

• Table II (image checked): 6 older values at 546.2 nm, reproduced (Cuthbertson 1933 summary). Table IV (JSON only, image checked): polarizability (au) this work (check), Kirn (reproduced), Kolos-Wolniewicz (static, 1 pt), Ford-Browne (2 pts).

• Formulas: Eqs. 4, 5, 7 checked against Table I (rms 0.0016 / 0.0045 / 0.0022; asymptotes 135.736 / 135.734 as stated); Eq. 6 (fit to SHP’s data) and Koch’s and Kirn’s formulas recorded as reproduced, not checked.

• Status: open.

TC-33 griesmann_1999 (Griesmann & Burnett, Opt. Lett. 24, 1699 (1999))

• Table 1 (tbl_0e295af4655d, image checked): 31 points 149.2119-278.8107 nm, vacuum, x 1e6 at 273.15 K / 101325 Pa (garbled unit row skipped; wave-number column redundant, = 1000/lambda to 5e-7). Absolute 0.2e-6, level 1 sigma (combined standard uncertainty). LL + Peck-Khanna Z: density real.

• Scale tied to Abjean et al. 1970 (optical pressure measurement); no systematic uncertainty set (the paper gives none): whether to set one is open.

• Formula Eq. 5: rms 0.16 vs Table 1, max -0.52 at 149.4169 nm: the paper’s claim of all deviations < 0.2 is not reproduced; a free refit gives max 0.37, rms 0.145, so no misprint. Noted in the formula.

• Addendum (after peck_1966): SGDD is also doubtful. Peck-Khanna’s N2 Eq. 3 at 800 nm, 1000 mbar, 19.4 C gives SGDD 19.84 fs^2/m (printed 18.04 +- 0.15: 9 % low); Peck-Fisher Ar gives 18.38 (printed 17.98 +- 0.11). SGDD left primary with the numbers in the notes: to decide.

• Status: open.

TC-34 peck_1966 (Peck & Khanna, J. Opt. Soc. Am. 56, 1059 (1966))

• Source id peck_1966 (docs convention <first author>_<year>), not peck_khanna_1966 as first proposed: to confirm. Identity unverified in the curators’ library; title/authors/received date in the text match the citation used by Griesmann and Peck & Huang. No DOI recorded.

• Table I (tbl_c2970086b7ad, image checked; ‘Hg^{193}’ is 198Hg): 16 fitted points (primary), 3 parenthesised (excluded), Eq. (3) column (check). Relative values standardised to 28352.40e-8 at 5462.258 A, 15 C, 1 atm: absolute 0.083 (rms of fit), systematic_relative 3.3e-4 (299.14 +- 0.10 ‘realistic’ at 0 C): a reading made here, to confirm. Real-gas Z (old 273.16 K convention noted).

• Table II (tbl_029c38d597ef, image checked): Verdet ratios V/V(5780 A, air), computed (check) and Ingersoll & Liebenberg (reproduced), quantity verdet_constant with unit ‘ratio to the value at 5780 A (air)’: the vocabulary has no relative Verdet quantity; row ‘5460-61’ placed at 5460.5 A (script comment).

• Formulas: Eqs. 3-7 all checked (Eq. 3 reproduces the calculated column to 0.01; rms 0.083 / 0.075 / 0.364 as stated; Eqs. 4, 7 = Eqs. 3, 6 x 1.05507-8 = the Z ratio); reproduced Cuthbertson, Tausz & Gorlacher, Koch (LL function), Wilkinson (plus P&K’s refit in notes). Two formulas have ‘+ sigma^2’ denominators: stored C with a negative sign, explained in notes.

• Status: open.

TC-35 old_1971 (Old, Gentili & Peck, J. Opt. Soc. Am. 61, 89 (1971))

• Identity unverified; the citation (volume/page) is the one supplied with the source list and could not be checked from the record: to verify. Pages cited as pdf pages.

• Table I (tbl_02a196e116e3, image checked): 19 experimental points (primary, all fitted), predicted column (check). Absolute 0.030 (rms of fit), systematic_relative 1.33e-4 (4505.0 +- 0.6 at 546 nm): a reading made here. Real-gas Z, 1 atm 0 C, vacuum.

• Errata (predicted column): 0.9227030: 4434.595 -> 4435.595 (formula, difference column); 0.8777160: 4440.310 -> 4440.332 (formula; the printed difference +0.011 then becomes -0.011) - the second is a judgement: the formula reproduces every other row to 0.001.

• Formula: three-term Sellmeier, LHS (n - 1) 10^5 from the equation image only; reproduces the predicted column, rms 0.029 (paper 0.030), poles and (n^2-1)_inf = 936.

• Table II (Verdet ‘S’ factors, image checked) not extracted: derived, not refractive-index data; non-monotonic at 0.8000 um (probable misprint, unresolvable).

• Status: open.

TC-36 cuthbertson_1914 (C. & M. Cuthbertson, Phil. Trans. R. Soc. A 213, 1 (1914))

• State ‘theoretical density’ D/(d0 76): the molar density of H2 at 0 C, 76 cm (molar volume 22428.8 cm^3, p. 6). Represented as the ideal-gas state 273.15 K, 101258.0 Pa (= R T / 22428.8 cm^3), density ideal: a construction made here, to confirm. Air wavelengths (1912), recorded as standard air.

• O3: Table IX (JSON, image checked) 8 kept + [585] excluded; Table X 5 kept + [495] excluded (structural fix: the curators’ extraction attaches the remarks to experiment 1; the image puts them against the bracketed rows 7 and 3). Both check. Adopted 1.00052 (p. 19) inline as check. Table XI O3 row (dispersion, derived by subtraction with 520 at 5461 assumed) primary: absolute 44e-8 bound (an estimate made here from the 1/200 rule x 100/6.18), systematic_relative 0.0115 (2 % bound as uniform). Recomputed the O3 row from means and O2 row: within 10e-8.

• O2: Table XI O2 row, reproduced from Cuthbertson 1909 (not in the curators’ library).

• N2O: the merged cells of tbl_6f5db40b38bd split into 4-digit values as in the image (5092, 5102 / 5097, 5098, 5099 / 5087, 5091), check; Table XIV (caption lacks the gas; N2O from the text) observed primary (absolute 4.4e-8 bound from ‘error should not exceed 1/200 of the effect’; systematic_relative 0.0012 from ‘1/500 at least’), calculated check.

• Formulas: O3 two-point Sellmeier (52083 at 5461 as stated 52082), N2O one-term (calc column within 1.6 except 2.2 at 5209.1 and 6.7 at 4799.9: rounded constants).

• Not extracted: Mascart’s N2O values (printed as n, 10 % impure gas; no n quantity), the mixture rows, all other species (Cl2, Br2, I2, HCl, HBr, HI, H2O, NH3, NO).

• Status: open.

TC-37 rychlewski_1983 (Rychlewski, J. Chem. Phys. 78, 7252 (1983))

• Theory (variation-perturbation). Extracted (images checked): Table V alpha(D2) at 293 K (16 pts, primary), Table II alpha(D2, J = 0-6) (7 x 16, check, parameters J, v), Table VI column a alpha(H2) 293 K (16 pts, primary; not independent of bishop_1980). Vacuum wavelengths in A (from omega in au), ‘inf’ static.

• Not extracted: HD (not a species), anisotropies gamma (no vocabulary quantity), Table VII non-diagonal elements, Table VI columns b/c (= bishop_1980 Table V).

• Check: thermal average of Table II with spin weights 6/3 and an approximate B = 29.9 cm^-1 (from memory, only for this check) reproduces Table V (5.3637 vs 5.3641 static, 12.391 vs 12.392 at 1215.7 A).

• No accuracy stated; ‘lower bound’ remark and 0.03 % agreement with Bishop & Cheung recorded in notes.

• Status: open.

TC-38 bishop_1980 (Bishop & Cheung, J. Chem. Phys. 72, 5125 (1980))

• Table V (tbl_7b56aafde20c, image checked): 22 vacuum wavelengths (not 23), H2 isotropic alpha (au): thermal 293 K (primary), J = 0-4 (check), Victor & Dalgarno ‘Experimental’ (17, reproduced) and its parenthesised semi-empirical values (5, 1300-1700 A, check with reproduced_from).

• Check: Eq. (23) with Table I’s spacings reproduces the thermal column (5.43388 vs 5.4339; 12.79797 vs 12.7980); Eq. (23) prints ‘(2^J + 1)’ - a misprint for 2J + 1. Table IX static components give iso 5.4192 vs Table V J=0 5.4193.

• Not extracted: anisotropies (Table VI; no quantity), HeH+, Table IX.

• Status: open.

TC-39 kumar_2011 (Kumar & Thakkar, J. Chem. Phys. 135, 074303 (2011))

• Table I (image checked): O2 S_k, k = 2..-8, ‘This work’ (primary; stated +-3/2/1/3 % by k as relative_rows, S_0 exact), Zeiss 1977 and Kumar 1996 (reproduced; ‘…’ cells skipped). Quantity cauchy_moment, wavelength_unit index.

• Table III (image checked): O3 S_k for A, B1, B2, C, D. Judgement: C primary (the authors’ compromise; true values ‘between B1 and C’), B1 and B2 check, A and D excluded (rejected by the authors). No stated uncertainties. k = -2 ‘Other’ values split by footnote letter into six reproduced static polarizabilities (au): CASPT2 18.83, MRCI 18.65 (Andersson 1992), CCSD(T) 19.27 (Maroulis 1999), CCSD(T) 17.12 (Naves 2011), Berkowitz 19.7 (from Cuthbertson refractivity) and 20.2 (dielectric). The ab initio values are electronic only (ZPVC about +1.43 au, p. 074303-4).

• Not extracted: I_k (Tables II, IV; Table IV’s merged cells read from the image and written into the notes), C6 (Table V). The table listed for extraction as ‘static alpha compilations’ (tbl_2ad5924f2ef1) is Table V, the C6 table: nothing to extract.

• The paper is refractivity-constrained: O2 by Smith et al. 2208.7 A and Stoll 9224 A; O3 by Swift et al. (x 0.95 for C) or the Cuthbertsons.

• Status: open.

TC-40 kalugina_2015 (Kalugina & Thakkar, Mol. Phys. 113, 2939 (2015))

• Best estimate alpha_bar = 19.0 +- 0.3 au (text, p. 2941) inline, check, level ‘bound’ (the +- is a method-convergence range); W4 18.86 (Karton & Martin 2010) inline, reproduced. Table 4 (image checked) CCSD/aug-cc-pV6Z Cauchy moments S(0), S(-2), S(-4), S(-6) = 23.96, 19.58, 134.8, 2687 (check).

• All electronic at the equilibrium geometry (no zero-point vibration, about +1.43 au per Naves et al. as quoted by Kumar 2011): that is why they are checks, flagged by parameters.electronic_only. Open: how theory enters O3 fits.

• Tables 1-3 (method/basis convergence) not extracted; their images were not checked.

• Status: open.

TC-41 maroulis_1994 (Maroulis, J. Chem. Phys. 101, 4949 (1994))

• Table IV (JSON only, image checked) mean alpha row: CCD+ST(CCD) 18.95 (check, +-2 % bound from the conclusions, p. 4954), CASPT 18.83 (Andersson 1992, reproduced; also in kumar_2011), ‘Experiment’ 18.90 ‘Referenced by Mack and Muenter’ (reproduced; origin unknown). Electronic only.

• Status: open.

TC-42 maroulis_1999 (Maroulis, J. Chem. Phys. 111, 6846 (1999))

• Identity unverified (observed title ‘Using JCP format’); the text, file name 6846_1_online.pdf, DOI candidate 10.1063/1.479977 and the citations by Kumar and Kalugina agree: to verify; DOI not recorded.

• Table III (JSON only, image checked): CCSD(T) 19.27 (check; ‘vibrational correction neglected’, footnote 20) and ‘Experiment’ 19.33 (U. Hohm, private communication, extrapolated old refractivity; reproduced). Cyclic form and hyperpolarizabilities not extracted.

• Status: open.

TC-43: the helium formula of Wilmouth & Sayres (2020) and He et al. (2021) is a 0 degrees C formula

• Where: he_2021.toml and wilmouth_2020.toml, formula He_table1.

• Claim: both papers list (n - 1) x 10^8 = 2283 + 1.8102e13 / (1.5342e10 - nu^2) as the refractivity at 288.15 K and 1013.25 hPa. It gives 3489.3e-8 at 546.2 nm, which is helium’s refractivity at 0 degrees C (Stone’s formula: 3486.9e-8; Mansfield & Peck 3495.0e-8); at 15 degrees C helium’s is 3305.5e-8. Read at the stated 15 degrees C, the formula is 5.5 % high (the ratio 288.15/273.15), and a Rayleigh cross section computed from it about 11 % high. The formula is recorded as printed (state 1atm_15C); the gallery’s helium page shows the offset. Whether the papers’ helium cross sections carry the error is outside this package’s scope.

• Status: open.

TC-44: Mansfield & Peck (1969) lie 0.25 % above modern helium theory

• Where: gallery, helium page.

• Observation: Stone & Stejskal’s molar refractivity (theory to 1e-6), Liu’s ab initio polarizabilities, Cuthbertson 1932, Smith 1976, Victor’s theory and the static polarizabilities agree with each other; Mansfield & Peck’s absolute scale, the basis of most helium Sellmeier formulas (Borzsonyi fitted to Leonard, who adopted it), is 0.25 % higher, inside its own stated systematic (+-0.009e-5 of 3.4950e-5, 0.26 %). The proposed fits take Mansfield & Peck’s relative dispersion with a free scale.

• Status: decided and closed (2026-09-24/25): the relative dispersion with a free scale.

TC-45: Borzsonyi et al.’s group-delay data

• Where: borzsonyi_2008.toml (TC-25).

• Observation: every SGD is 22-39 fs/m above what the refractivity implies (helium 146 against about 108), so SGD is kept as a check; the SGDD of nitrogen is 9 % below Peck & Khanna’s and argon’s 2 % below Peck & Fisher’s. SGDD is kept primary for now. Question: should Borzsonyi’s SGDD enter the fits (it is the only direct near-infrared dispersion for Ne, Kr and Xe), and with what systematic?

• Status: decided (2026-09-24): SGDD is a validator, not fitted (use = "check").

TC-46: leonard_1974 (Leonard, At. Data Nucl. Data Tables 14, 21 (1974))

• Transcribed: Table I (recalculated absolute (n-1)x1e6 at 5462.258 A vacuum with probable errors; 5 datasets absolute_<gas>, 29 points; recommended_<gas>, 5 points), Table II (dispersion, 27 author-gas datasets, 309 points, standard-air wavelengths, STP 273.16 K / 1 atm / real), Table III (a) absolute Rayleigh (8 single-point datasets), (b) ratios to Ar (5 + inline N2 footnote), (c) Cerenkov (3 points), (d) hook (1), Table IV kappa (4 points in 2 datasets), Table V Verdet (12 datasets, 101 points), Table VI static polarizabilities (11 datasets, 55 points). Total 78 datasets, 521 points.

• Structural fixes (script): Table II re-keyed from the images: values and (except Kr) reference numbers are in the extraction’s reading order; wavelengths assigned from an explicit image-read list (TABLE_II_KEYS), asserted against the extracted reference column (He, Ne, Ar, Xe exact; Kr: extracted refs are the printed sequence minus “1010” / “12” lost at the end of each half) and wavelength column (Ar 4861.327 A is missing from the extraction; image shows 283.9, Ref. 26). Kr: braced values taken from the wavelength cell, merged cells split by the two-decimal pattern. Table I braces (He Refs. 7+18, Ar Ref. 29 x2) restored; Table VI brace (He Ref. 82 x2) restored; Table III header column order read from the image. Starred Table II rows asserted equal to Table I’s underlined values and not extracted twice.

• Errata: damkohler_1934_Xe wavelength 5717.7 -> 5117.7 (out of descending order, value between neighbours); larsen_1934_Ar wavelength 2893.565 -> 2893.595 (same Hg line printed 2893.595 in He/Ne/Kr/Xe); peck_fisher_1964_Ar and mansfield_peck_1969_He wavelength 7425.113 -> 7245.166 (Peck-Fisher’s 7247.163 A vacuum line in standard air via the package’s Edlen conversion; the value 280.2792 is Peck-Fisher’s at that line, and 7425.113 A would give 280.143). All 16 other Peck-Fisher wavelengths of Table II were checked as air equivalents of Peck 1964’s vacuum wavelengths.

• Excluded, not corrected: Larsen Ar 4108.066 A printed 282.853 is 1.26 % low (neighbours within 1e-4 of Peck-Fisher); Larsen’s own value there (Peck 1964 Table II, 2865.41e-7 at 0 C) scaled by Leonard’s Larsen factor 0.99970 gives about 286.45; no single misprint maps one to the other -> own dataset larsen_1934_Ar_4108, excluded. To check against Larsen 1934 if it becomes available to the curators.

• Scale correction (dataset metadata, not an erratum): Table IV is headed “kappa x 10^6” but the values need 10^-4 (kappa = n-1 - lambda dn/dlambda = 2.927e-4 at 5461 A from Peck-Fisher’s formula vs Bennett 2.915); scale = 1e-4.

• Use decisions: authors with parenthesised references excluded (Scheel-Schmidt, Herrmann, Tausz-Gorlacher, Ahrberg, Quarder, Kronjager Xe); Rusch’s 67628.5 A absolute value check; recommended values check (Table II is normalised to them); r.i.-extrapolated polarizabilities check; Cabannes, George et al. and Pery-Thorne Table III values excluded per the text; the rest reproduced.

• Formulas: Chashchina Ar/Kr/Xe three-term Sellmeier (Leonard-adjusted). Verified only indirectly: vs Chashchina’s values reproduced (unadjusted) in Bideau-Mehu 1981, +0.05..0.08 % (Ar), +0.14..0.30 % (Kr; +0.89 % at 213.9 nm), +0.70..0.79 % (Xe); static S(-2) from the Ar formula 11.052 vs Tang’s recast of the original 11.044. Not reproducible to the digit (no values printed).

• Could not verify / to decide: wavelength medium of Tables III(a), IV (ref 46) and V assumed standard air (not stated; 3e-4 effect); Verdet state assumed STP; Xe Damkohler 4588.3 A = 714.42 is 3.5 below its neighbours (read from a graph; left as printed); Table VI’s reference “42” for r.i. extrapolation (list: Shardanand) probably means Ref. 47; Verdet “Ref. 48” is van Vleck’s book in the list; the printed abbreviation of “Verhandl. Deut. Physik” + “Gesellschaft” is expanded to “Physik. Gesellschaft” in the citations (codespell rejects the abbreviation). Whether absolute_<gas> (Leonard’s re-reductions of other authors’ absolute values) should be reproduced or check.

• Status: open.

TC-47: kingston_1964 (Kingston, J. Opt. Soc. Am. 54, 1145 (1964))

• Transcribed: Table I n-1 (x1e4, NTP) Ar 12, Kr 10, Xe 8 points; Table II Verdet (mantissa(power) cells stored as mantissa e power) Ar 12, Kr 11, Xe 10; Table III (JSON) calculated Ar 4 (check), Heddle 3 and Gill 1 (reproduced). All check (theory), density ideal (1.0007e-4 = 4 x 2 pi N_L a0^3).

• Checked: Xe 1900 A = 9.884 in the image (Tang 1974 prints 9.984, erratum there).

• Status: open.

TC-48: langhoff_1969 (Langhoff and Karplus, J. Opt. Soc. Am. 59, 863 (1969))

• Transcribed: Table I as cauchy_moment S(-2..-8) for He, Ne, Ar, Kr, Xe, H2, N2, O2 (8 x 4, check); Table III predictions Ne 11, Ar 11, Kr 9, Xe 8 (check) and Kingston’s columns (reproduced); Table IV Ar: Heddle 3, Gill 1, Marmo 1, Kingston 4, Liggett 1, five Pade columns x 4 (check); Table V N2: Wilkinson 1960 measured 22 (reproduced, original not in the curators’ library) and five Pade columns x 22 (check).

• Formulas: cauchy_<gas> (Eq. 29) and pade22f_<gas> (Eq. 30, Table II) for 8 species. Checks: Table II’s moments reproduce Table I to 0.1 %; [2,2]_f reproduces Table V’s [2,2]_f column (+0.0002..0.0012) and Table IV’s; Cauchy at 5462 A vs Leonard’s recommended: He 0.000 %, Ne +0.03 %, Ar +0.02 %, Kr -0.47 %, Xe -0.16 %.

• Errata: theory_Xe 1600 A 15.640 -> 15.460 (lower bound from Table I moments 15.462; Tang 1974 prints 15.460); pade21f_N2 1874.25 A 4.492 -> 3.492 (bracketed by [1,1]_f 3.464 and [2,2]_f 3.496; neighbours).

• Found: Table III entries are lower bounds only for Ne down to 1400 A, Ar and Kr down to 1900 A; below, means of bounds (text says “last two”). Xe entries all lower bounds (as Tang found). Wavelengths of Table V (Wilkinson) assumed vacuum.

• Status: open.

TC-49: tang_1974 (Tang and Poon, J. Opt. Soc. Am. 64, 1582 (1974))

• Transcribed: Table I moments (Ne, Ar, Kr, Xe(1) reproduced from Langhoff; Xe(2) recommended, check); Tables II-V columns (upper41, Pade (reproduced), mean, Xe lower42, previous: Saxon 1973 interpolated for Ne, Kingston for Ar/Kr/Xe), Table VI (mean from recommended moments, Kingston, Starkschall-Gordon 1971, Abjean et al. 1971 (5), Chashchina-Shreider 1969 (7; 1500 A value dropped as an extrapolation below their 1550 A limit)), Table IX Ar S(-2n) n = 1..18 (check), f1 = 0.1385, f2 = 0.1418 (text, at 0.4272 / 0.4347 hartree, check).

• Erratum: kingston_1964_table6_Xe 1900 A 9.984 -> 9.884 (Kingston’s Table I, Tang’s own Table V, Langhoff’s Table III).

• Could not verify: Abjean et al. 1971 and Chashchina-Shreider values at round wavelengths are presumably formula values; Tables X, XI (bound sequences) and the H atom Tables VII, VIII not extracted.

• Status: open.

TC-50: liggett_1968 (Liggett and Levinger, J. Opt. Soc. Am. 58, 109 (1968))

• Transcribed: Table II mu_-4 (Rydberg units, stored as cauchy_moment with scale 16 -> S(-4) in a.u.; argon Cuthbertson 1.76 x 16 = 28.16 = Langhoff’s S(-4)), four sources x Ne/Ar; Table III delta at Lyman alpha (Ne 3, Ar 5 single-point datasets); text: accepted static polarizabilities Ne 2.70, Ar 11.1 a.u. (reproduced). Table I power-law cross sections recorded as 7 formulas (not refractivity).

• Lyman alpha wavelength: the paper names the line only; 1215.67 A taken from Mahon et al. 1979 (p. 4). Density N of Eq. (1) not stated; NTP assumed.

• Not extracted: Tables IV-V (x-ray delta, all negative); oscillator strengths in the text (no transition wavelengths printed) - recorded in notes.

• Found: Liggett lists Heddle’s 1210 +- 30 A value under Lyman alpha and gives Kingston’s value as 5.20 (Kingston’s own 1216 A value is 5.30).

• Status: open.

TC-51: peck_1964 (Peck and Fisher, J. Opt. Soc. Am. 54, 1362 (1964))

• Transcribed: Table I (JSON): measured 15 C (primary, 17 points, sigma column, reference row sigma 0), measured 0 C (check), fit 15 C (check); Table II fit 0 C (check) and Larsen 1934 measured (reproduced, 8).

• Uncertainty decision: systematic_relative = 1.95e-4 = quadrature of 0.42/2677.08 (std. dev. of mean) and 2e-4 / sqrt(3) (stated systematic bound). To confirm.

• Formulas: peck_15C (reproduces the calc column to 0.001e-7 at 16 of 17 wavelengths; 4679 A: 2694.806 vs printed 2694.832, unexplained), peck_0C (coefficients = 15 C x 1.0551257; reproduces the measured 0 C column within 0.022 except 4679 A); reproduced formulas of Burton 1908, Cuthbertson 1910 (as printed gives 2x argon’s n-1: presumably n^2 - 1; not corrected), Quarder 1924, Larsen 1934 (reproduces Larsen’s Table II values to 0.04-0.08e-7).

• Found: Table II’s “calculated (0 C)” = 15 C formula x 288.16/273.16 (ideal-gas scaling), 2.0e-4 below the paper’s own 0 C formula; Table II wavelength 5677.40 A does not match Leonard’s 5677.17 A (air) = 5678.72 A (vacuum).

• Status: open.

TC-52: gordon_1993 (Gordon et al., J. Chem. Phys. 98, 9481 (1993))

• Transcribed: Table I Ar experiment 4 (primary) and theory 4 (check), H2 experiment 3 (primary) and theory 3 (check); Table II H2 anomalous 8 (check); text: Chashchina Ar 1216 A 5.016 (reproduced), calculated 5.12 (Ar), 3.24 (H2).

• Structural fixes: Table I’s 1109.45 A H2 row merged into the Ar cell (“see Table II” stripped); Table II’s “a” marks belong to R(4), R(2) (no value), not R(5), R(3).

• Dependence: n_3 = measured (n_3 - n_1) + n_1 from the Kumar-Meath (Ar) / Zeiss (H2) DOSD; stated in the record. A duplicate library copy noted, not used.

• Status: open.

TC-53: ferrell_1987 (Ferrell, Payne and Garrett, Phys. Rev. A 35, 5020 (1987))

• Transcribed (text, pp. 9-10, page images checked): Ar 3 points (primary), Kr 2 (check: inconsistent pair, 11 % / 2.7 % from the paper’s own calculation), the paper’s Sellmeier values (Ar, Kr, Xe; check), Chashchina Ar 5 and Kr 1 (reproduced), Chashchina-Shreider Xe 2 (excluded: below their 155 nm limit). All as refractivity_per_density in cm^3 (printed unit “cm^-3” is wrong).

• Erratum: chashchina_1968_Ar wavelength “30” -> 130 nm.

• Found: Bideau-Mehu’s Xe 148.3 nm value quoted as 1.895e-23 should be 1.895e-22 (not extracted: in bideau_mehu_1981); the “blue side” Xe point’s wavelength (140.4 nm) is inferred from the quoted Bideau-Mehu value; Kr 121.6 nm values negative, in notes only; Table I oscillator strengths not extracted (no wavelengths).

• Status: open.

TC-54: heddle_1963 (Heddle, Jennings and Parsons, J. Opt. Soc. Am. 53, 840 (1963))

• Transcribed: Table I (JSON; the curators’ extraction had no CSV): Ar and N2 experiment 3 each (primary, 1 sigma), Larsen-formula (Ar 3) and Wilkinson-formula (N2 2) columns (check).

• Formulas: Larsen 1939 (reproduces the “From Larsen” column and the 4358 A reference 28.52e-5); Dalgarno-Kingston extrapolation, printed “4.32 x 10^32 / lambda^8” (page image), impossible; 4.32e23 likely (coefficient progression); recorded as printed with the note; check against dalgarno_1960.

• Status: open.

TC-55: gill_1963 (Gill and Heddle, J. Opt. Soc. Am. 53, 847 (1963))

• Transcribed: Table I |n-1| at 1216 A: Ar, H2 primary (2 %, bound), N2 reproduced (Heddle’s normaliser), Kr excluded; ratios to Ar: Kr, Xe excluded, H2, N2 check; He 4.27e-5 (text, Dalgarno-Stewart calculation, reproduced).

• Decision to confirm: Xe absolute 172e-4 not extracted (690 a.u. fails the package’s plausibility test; physically not an atomic refractivity); kept as the excluded ratio 30.5. Kr printed 53.1 vs 9.46 x 5.653 = 53.5 (internal inconsistency). The PDF copy in the curators’ library also contains an unrelated paper (Patterson and Vaughan).

• Status: open.

TC-56: mahon_1979 (Mahon et al., IEEE J. Quantum Electron. 15, 444 (1979))

• Transcribed (text p. 4, page image checked): calculated (n-1)/N Ar 5 (incl. Heddle-band averages with spreads), Kr 2, Xe 1 (check); Chashchina Ar 1.87e-23 and Chopra-Heddle Ar 1.90e-23 at 1216 A (reproduced).

• Not extracted (format): Tables I-II (Kr negative contributions; C per atom), the measured C_Kr = -1.13e-17, Bjorklund’s C_Xe = -5.99e-17 and C_Ar = 5.54e-18 (cm^2) - listed in the record notes. Text misprint “(1.26 +- 0.03) +- 10^-23” (page image) read as x 10^-23. Text cites Heddle et al. as [14] and Chopra-Heddle as [13]; the list has them the other way round.

• Status: open.

TC-57: zhang_2008 (Zhang, Lu and Wang, Appl. Opt. 47, 3143 (2008); identity unverified)

• Transcribed: Table 2 (JSON): measured at 800 nm (primary, 1 sigma) and extrapolated at 632.99 nm (check) for N2, O2, Ar, CO2; reproduced columns: Old 1971, Bideau-Mehu 1973, Birch 1991, Simmons 1978 (CO2), Peck-Khanna 1966, Griesmann 1999 (excluded: extrapolation of a 145-270 nm formula), Birch (N2), Birch (O2), Peck-Fisher, Birch (Ar). Air skipped.

• Formulas: own N2, O2, Ar, CO2 (reproduce Table 2 at 800 and 632.99 nm to the printed digits; Ar numerator “12,32158.1” in Table 1 = “1,232,158.1” in Eq. (26)); reproduced Old CO2 (gives +0.13e-7 vs Table 2, unexplained), Peck-Khanna N2 (-0.10..-0.11e-7, unexplained), Peck-Fisher Ar (0.002e-7; = 15 C coefficients x 0.98288).

• No DOI given (unverified identity); citation from the article footer and Kren’s reference list.

• Status: open.

TC-58: kren_2011 (Kren, Appl. Opt. 50, 6484 (2011); identity unverified)

• Transcribed: Birch 1991 O2 1.000255720 +- 0.000000050 at 15 C, 633 nm (text p. 2, the +- is the unmapped glyph; page image checked), stored as n-1 = 0.000255720.

• Formula: kren_O2 (derived, not measured); gives 1.000251323 at 633 nm as printed.

• Status: open.

TC-59: lehmeier_1985 (Lehmeier, Leupacher and Penzkofer, Opt. Commun. 56, 67 (1985))

• Transcribed: Table 1 n-1 at 1.055 um and its third harmonic (0.3516667 um = lambda_1/3, not printed) for He, Ne, Ar, Kr, Xe (reproduced from dalgarno_1960) and N2 (reproduced from Landolt-Boernstein). He n30 carries mark c) (presumably a)).

• Status: open.

TC-60: lhuillier_1990 (L’Huillier, Li and Lompre, J. Opt. Soc. Am. B 7, 527 (1990))

• Transcribed (text p. 4): static polarizabilities Ar, Kr, Xe: experimental (Miller and Bederson 1977, reproduced) and RPA (check). Table 1 (Delta k per harmonic) not extracted (no phase-mismatch quantity); errata paper affects equations only.

• Status: open.

TC-61: drescher_2018 and ackermann_2018

• Records only, no datasets: Drescher (figures and Lorentz-Lorenz simulations only); Ackermann (model index from oscillator strengths, no values).

• Status: open.

TC-62: format gaps met

• Tables with merged cells in the curators’ extraction have no CSV; every script that needs them has a local grid() reading tables/<id>.json (8 copies of the same 10 lines): _library.table could read the JSON.

• A refractivity dataset must imply 0.5 < alpha < 400 a.u. (test): negative n - 1 (x-ray, above a resonance: Liggett Tables IV-V, Mahon Table I, Kr at Lyman alpha) and Gill’s Xe 172e-4 cannot be stored.

• No quantity for a phase mismatch per atom (Mahon’s C, L’Huillier’s Delta k).

• Oscillator strengths need a wavelength; papers that name levels only (Ferrell, Liggett) cannot be stored.

• Per-row use/exclusion is impossible, so single points are split into their own datasets (Leonard’s Larsen 4108 A, Rusch 67628.5 A).

• Status: open.

TC-63 lesiuk_2023 (Ar theory)

• Transcribed: Table XI tbl_cb5cfdf665dc (extracted cells; image) row “Total” only: alpha_0, alpha_2, alpha_4 = S(-2), S(-4), S(-6) = 11.0775(19), 27.976(15), 95.02(11) a.u. (cauchy_Ar, primary, 3 points). The contribution rows were summed and reproduce the totals (11.0775, 27.9755, 95.0182; quadrature 0.00194, 0.0154, 0.106).

• Text: alpha_6 = 382.5 (Eq. (36), p. 13; HF + valence CCSD + CC3 only, 10 % bound; sum of Eqs. (7), (10), (12) = 382.53) as cauchy_alpha6_Ar; Egan et al.’s 11.22431(17) at 632.9908 nm (Eq. (37), reproduced, includes chi_0); Eq. (38) 11.22445(11) (check).

• Table XII tbl_787fa31e3c55 (extracted cells; image): Kumar and Thakkar 2010 (3 moments, reproduced from kumar_2010), Orcutt and Cole, Buckley et al., Gaiser and Fellmuth 2018 (static, reproduced), Pawlowski et al. (3 moments), Lupinetti and Thakkar (static). “This work” not extracted (= Table XI).

• Corrections: all included for alpha_0 (relativistic incl. Breit, D2, spin-orbit; QED leading + one-loop; FNS; FNM for 40Ar); alpha_2, alpha_4 omit D2, SO, FNM. Uncertainty level not stated (quadrature of conservative component estimates).

• Formulas: cauchy_theory (alpha_series, c = 11.0775, 27.976, 95.02, 382.5) and recommended (alpha_series, c = Gaiser’s 11.077183, 27.976, 95.02). The recommended combination plus chi_0 = -2.3004e-4 reproduces Eq. (38) to 5e-6 (11.224455). range_nm = [450, inf] from the paper’s “above roughly 450 nm”.

• DOUBT / format: both formulas give the ELECTRIC polarizability; the refractive index needs alpha + chi_0 (chi_0 = -2.30(2)e-4 a.u., -21 ppm). The form has no slot for it; recorded in notes. Open: whether the models layer adds chi_0 for Ne/Ar (and He).

• Orcutt and Cole 1967 is in the curators’ library without a source record: reproduced_from holds the citation; switch to the id if a record is made.

• Status: open.

TC-64 lesiuk_2020 (Ne theory)

• Transcribed: Table IX tbl_68954d2edbcd (extracted cells; image) row “Total”: 2.66080(36), 2.850(7), 4.932(14) a.u. = S(-2), S(-4), S(-6) (cauchy_Ne, primary). Budget rows sum to the totals.

• Table XI tbl_c9bc797bccfd (extracted cells; image): Chan et al. 1992 (Ne paper, S(-4), S(-6)), “Kumar and Meath [29]” (= Kumar and Thakkar 2010, values identical to kumar_2010’s Ne column: wrong label, noted), Orcutt and Cole 2.658 and 2.663^a (compressibility-corrected; the row label spans both rows, carried down by the script), Gaiser and Fellmuth 2010 (= gaiser_2010) and 2018, Pawlowski (3 moments), Klopper, Larsen. All reproduced.

• Magnetic susceptibility chi_0 = -8.484(19)e-5 a.u. mentioned only (32 ppm of alpha_0).

• Formula cauchy_theory (alpha_series). No dynamic value printed to check against. range_nm = [450, inf] is a choice made here (the paper states only “well below 0.6107 a.u.” and quantifies convergence at 633 nm): to confirm.

• Status: open.

TC-65 gaiser_2010 (Ne DCGT)

• Transcribed: Table 2 tbl_7249e8b90cbe (CSV; image agrees; validation has a TABLE_OCR_REJECTED on the header’s 10^7 only): weighted mean A_eps = 9.94727e-7 m^3/mol (molar_polarizability, primary, molar_refractivity scale 0.1 cm3/mol, u_r 10.6 ppm 1 sigma); the seven per-temperature values (check, relative_rows); the mean’s alpha_0 = 2.66110 a.u. (check; a CODATA-2006 conversion, reproduces to 2e-6).

• Weighted mean recomputed: 9.947271 (reproduces). Its 10.6 ppm is larger than the 8.5 ppm of an independent average because ~8 ppm type-B is common.

• Text values: Christiansen 1998 9.943(37) (reproduced), the authors’ rescalings of Klopper 2004 9.950(08) and Franke 2001 9.956(22) (checks), all x1e-7 m^3/mol.

• No dielectric virial coefficient is reported (inside the unreported A_2, A_3).

• FORMAT GAP: optmat.datasets.Uncertainty.stated ignores relative_rows; with relative_rows alone the standard uncertainty is NaN. Worked around with a fallback relative = 290e-6 (the largest row) that no row uses.

• wang_2021’s gaiser_fellmuth_2010_Ne note says the original is not in the curators’ library: it now is (gaiser_2010); its reproduced_from can become [“gaiser_2010”].

• Status: open.

TC-66 kumar_1985 (Ne-Xe constrained DOSDs)

• Number notation: “2.875(-1)” = 2.875e-1 (power of ten), then “(66)” = reference number; the script tells them apart (exponent: one signed digit directly after the mantissa; reference: 2-3 digits or STOBBE) and writes e-notation; printed cells kept.

• Transcribed: Tables 8-11 (cells files; images) “Adopted DOSD” column only: integrated oscillator strengths per energy interval, Ne 22, Ar 28, Kr 24, Xe 28 rows (dosd_*, check). Each column sums to Z (10.0003, 17.9994, 35.9987, 53.9976): transcription verified. Input-data columns (one reference per cell) not extracted.

• FORMAT GAP: no quantity for an oscillator strength integrated over an energy interval. Stored as oscillator_strength with wavelength_unit = "index" (row position) and the interval in eV as the row id (“21.47-21.57”, “discrete:16.67-21.48”, “100000-inf”). Proposal: an integrated_oscillator_strength quantity with low/high energy columns.

• Table 12 tbl_1b74f66df9be (cells file; image): S_k, k = 2 … -10 incl. half-integers (-0.5, -1.5, -2.5), adopted (16 per gas, moments_*, check: superseded by kumar_2010) and Leonard and Barker (11 per gas, reproduced). L_k not extracted.

• Erratum: leonard_barker_Kr S_-4 printed “5.665” (no power of ten, image checked) -> 5.665e1.

• Uncertainty: <~1 % for -6 <~ k <~ 0, S_1 ~2 %, S_2 ~3 % (p. 1628); nothing stated below k = -6 (I used the 1 % default there: to check).

• Text: the molar-refractivity constraints of Table 8-11 captions (2 per gas, reproduced from cuthbertson_1932 non-ideal-corrected, Coulon 1981, smith_1976, bideau_mehu_1981). Vacuum wavelengths inferred from the values (Ar 6329.9/4766.2 A: He-Ne and Ar+ lines).

• NO PSEUDO-SPECTRUM in this paper (“will be presented elsewhere”, p. 1628: Kumar and Meath, Mol. Phys. 54, 823 (1985), not in the curators’ library). No formula recorded.

• Table 12 footnote misprints (not extracted): CI S_2(Ne) “2.599” for 2.599(4); HF S_1(Ne) “1.514(3)” for 1.514(2) (kumar_2010 Table III: 151.4).

• HF, HCl, HBr skipped (not species).

• Status: open.

TC-67 kumar_2010 (Ne-Xe constrained DOSDs revisited)

• Transcribed: Table I tbl_2e89f4a65bc0 (CSV; image): S_k, k = 2 … -10 incl. -0.5 and -1.5, 15 per gas (moments_*, PRIMARY, following the kumar_2011 precedent); uncertainties from the caption (3 % k=2, 2 % k=1, 1 % 0>k>=-6, 3 % -7..-10).

• DOUBT: the S_k (k<0) are constrained to refractivities also in the database (cuthbertson_1932, smith_1976, bideau_mehu_1981; Coulon 1981 and Hohm 1994/1996 not in the curators’ library): fitting both double counts. Which constraints were used per gas is only in the supplementary material (not in the curators’ library). To decide: primary or check.

• Tables II-IV (S_2, S_1, S_-1; CSV; checked on PDF page 5): 27 one-point reproduced datasets (HF, CI, MRCI, Olney DOSD, TDMP2, Bethe-Goldstone); rows repeating Table I or kumar_1985 skipped (identical, checked).

• Text p. 074301-5 (PDF page checked; the curators’ extracted text has unmapped +- glyphs): Thakkar and Lupinetti’s recommended static polarizabilities, experimental (Huot and Bose 1991: Ne 2.6669(8), Kr 16.782(5), Xe 27.078(5); Johnston et al. 1960: Ar 11.078(10)) and theoretical (Klopper Ne 2.661(5), Lupinetti Ar 11.085(60), Nakajima and Hirao Kr 16.80(13), Xe 27.06(27)): 8 reproduced datasets. Huot and Bose’s Ne is 0.2 % above gaiser_2010 (far outside both uncertainties): flag.

• NO PSEUDO-SPECTRUM in the paper: the ten-term pseudospectra (reproducing S_k, 2 >= k

  = -17) are supplementary material only (Ref. 84), not in the curators’ library. No formula.

• Cross-checks: lesiuk_2023’s Table XII Kumar-Thakkar Ar row and lesiuk_2020’s “Kumar and Meath” Ne row equal these Table I values (rounded).

• Codespell flags the second author’s surname of Olney et al. (Chem. Phys. 223, 59 (1997); C-a-n-n) as a misspelling; the citations in kumar_2010 are shortened to “Olney et al. (with G. Cooper and C. E. Brion)”. Add the name to the codespell ignore list and restore the full author list.

• Status: open.

TC-68 chan_1992 (Ar, Kr, Xe dipole (e,e) oscillator strengths)

• Continuum: Tables I-III with continuations (CSV; all six images checked cell by cell against the CSV): df/dE, 10^-2 eV^-1, differential_oscillator_strength unit 1/eV scale 1e-2, wavelength_unit = "eV", primary, 5 % (not stated level): Ar 450, Kr 287, Xe 251 points. Rows numbered in reading order (column by column).

• Erratum: Ar continuation prints “208.0” for 308.0 eV (row 333; image checked); with it the Ar energies are strictly increasing (checked).

• Discrete: Tables IV-IX (cells files; images checked): 87 datasets (present work per gas primary: Ar 15, Kr 13, Xe 12 lines; the rest reproduced per source; summed theory values and “Total to ionization” as index-abscissa datasets; present totals as check). Every printed ratio column agrees with its row except Lewis [70] Xe (values identical to Anderson’s row, ratio differs): DOUBT, kept as printed.

• Errata: present_total_Ar sigma (0.0043) -> 0.043 (Kr and Xe totals are exactly 5 %); wiese_1969_Ar 3d’ (14.304 eV) 0.0106 -> 0.106 (note c: reanalysis of Lawrence, whose value is 0.107(0.015)). Both to check (the second rests on the table’s own evidence).

• DOUBT: present Ar 7s (15.186 eV) and 5d(underlined) (15.190 eV) both print 0.0426(0.0043): one fitted value for an unresolved pair printed twice, or a misprint. Similar repeated values in Geiger [82] Kr (b) and Delage and Carette Xe (b) (blends). Kept as printed; the fitting layer should not treat them as independent lines.

• Excluded: Delage and Carette Xe 10.401 eV (note c: normalised to Geiger).

• Upper limits not extracted: present Xe “<0.001” at 10.979, 11.495, 11.583 eV; Geiger [83] Ar “<0.0025” at 13.864 eV.

• Sums in the text (a1+a2 = 0.331, b1+b2 = 0.407) reproduce from the table values (0.0662 + 0.265 = 0.3312; 0.214 + 0.193 = 0.407).

• No sum rules (S_k) in this paper.

• Status: open.

TC-69 chopra_1974 (Lyman-alpha Rayleigh scattering; identity unverified)

• Transcribed: Table 2 tbl_6ff9e885d7c3 (CSV; image): Rayleigh cross sections at 1216 A (barn -> cm2, scale 1e-24): present Ar 5.47, N2 5.37, Kr 16.3 (primary), H2 2.28 (= Dalgarno et al.’s calculation, the normalisation: reproduced); Shardanand and Mikawa 1967 (H2, Ar, N2) and Gill and Heddle 1963 (H2, Ar, N2; Kr, Xe excluded: resonance lines in the detector range) reproduced. Molecular Xe2 (17.1 Mb) skipped.

• Table 4 tbl_d63bbf88a338 (CSV; image): Ar 10^4 (n-1) = 5.2 (check, derived), Heddle 1963 5.6 at 1210 A, Gashchina (Chashchina) 1968 5.0, Kingston 1964 5.3 (reproduced). Text p. 2426: Kr (n-1) = 8.8e-4 (check, beyond_resonance, sign unknown).

• Normalisation: to Dalgarno, Ford and Browne’s (1971) calculated H2 cross section, 2.28 b (<1 %). Table 1 ratios (Ar/H2 2.40(2), N2/H2 2.34(2), Kr/N2 3.05(6)) are the actual measurement; FORMAT GAP: no quantity for a ratio of cross sections (recorded in notes only). Relative uncertainties of the absolute values derived from those +- (Ar 0.0083, N2 0.0085, Kr 0.021), systematic 0.01 (the H2 normalisation): to check.

• SIGN: Rayleigh scattering gives (n-1)^2. Ar positive (below 11.62 eV). Kr: Lyman alpha (10.20 eV) lies between Kr 5s (10.03) and 5s’ (10.64 eV): sign undetermined; the paper’s contribution estimate (Table 5) can be of either sign.

• Erratum: refractivity_Ar 5.2 -> 5.1 (the paper’s relation with its 5.47 b gives 5.12e-4; Kr reproduces; Mahon 1979 quotes 1.90e-23 N = 5.11e-4).

• DOUBT: N2 5.37 is not 2.34 x 2.28 = 5.34; Kr (16.3) uses 5.34, Xe2 (17.1 Mb) uses 5.37.

• Formula: (n-1)^2 = 4.8e16 sigma at 1216 A (recorded, no form; constant reproduces 4.77e16 with Loschmidt’s number).

• Not extracted: Xe attenuation cross sections (Table 3; no quantity for absorption below threshold: FORMAT GAP), Table 5 (model contributions).

• mahon_1979/chopra_heddle_1974_Ar and ferrell_1987’s Chopra quotes can now point reproduced_from at chopra_1974.

• Status: open.

TC-70 rusch_1923 (argon, visible and 6.76 um; German)

• Gases: ONLY air and argon were measured (“air and argon were chosen as the test gases”, p. 374). No H2, N2, O2, CO2 data; air skipped.

• Transcribed: the argon Tabelle 7 tbl_1f78cf25d43e (cells file; image checked): observed (nu_0 - 1) x 10^7, visible 4 points (standard air: 656.30, 579.05, 576.95, 546.10 nm as printed) and infrared 1 point (6763.2 nm vacuum), primary; “ber. I” and “ber. II” as checks (split the same way). Tabelle 5 duplicates (prints 567,95 for 576,95: noted, not extracted).

• Conditions: nu_0 at 760 mm Hg and 0 C via Loria’s Eq. (2), Gladstone-Dale plus the ideal gas equation, with the gas’s pressure coefficient alpha in (1 + alpha t) (alpha* disputed in sign); Delta p reduced to 0 C and 45 deg latitude. density “ideal”. Probable errors 0.3-0.4 x 1e-7 (argon, 15 measurements), error limit of means 0.02 %.

• Why Leonard says the value “cannot be properly corrected to STP”: the paper gives no gas temperature t and no absolute pressures, only the ideal-gas/Gladstone-Dale reduced nu_0; the real-gas reduction cannot be redone (non-ideality ~0.1 % at 1 atm vs the claimed 0.02 %). Also the infrared wavelength: calcite reststrahlen centroid 6763.2 +- 0.4 nm at room-temperature plates, vacuum (calibration includes the vacuum correction, footnote p. 377), but it grows to 6.78-6.82 um with heated plates (Tab. 2), and the plates are irradiated continuously during the refraction measurement.

• Formulas: hk_II_Ar (C = 4.216e27, n_0^2 = 15177e27, n = 3e10/lambda Hz) reproduces “ber. II” exactly; hk_I_Ar (Tabelle 6: 2C = 9.0942e27, n_0^2 printed 18 348) reproduces “ber. I” and the printed static 2781 only with n_0^2 = 16 348: correction recorded (formulas.corrections). The implied c = 3e10 cm/s is not stated. No form fits (frequency-squared single oscillator; a form may be added). Reproduced Tabelle 6 constants of Cuthbertson, Burton, Ahrberg recorded (Burton’s static limit 2792.8 vs printed 2799: unexplained).

• Comparison: IR value = alpha 11.104 a.u. (+0.24 % vs modern 11.078), 546 nm +0.45 %.

• Leonard’s Table II lists Rusch’s IR point at 67628.5 A standard air, not Rusch’s 6763.2 nm vacuum converted: unexplained, to check in leonard_1974.

• Translations of the relevant passages (reduction formula and definitions, error budget, alpha* dispute, vacuum-wavelength footnote, temperature dependence of the reststrahlen, argon purification) are in the record’s notes.

• Missing: the 1928 erratum (Ann. Physik (4) 85, 581), which may change these values.

• Status: open.

TC-71: refraction measures alpha + chi_0; theory and dielectric data give alpha alone

• Where: optmat.gas.fitting; raised from Lesiuk et al. 2020 and 2023.

• Claim: at optical and microwave frequencies n^2 = eps mu, so a refractivity measures the electric polarizability plus the (diamagnetic) magnetic susceptibility chi_0 of the atom, while an ab initio alpha(omega) and a dielectric-constant (capacitance, DCGT) measurement give the electric polarizability alone. Lesiuk gives chi_0 = -2.30e-4 a.u. for argon (-21 ppm of alpha) and -8.484(19)e-5 a.u. for neon (-32 ppm); helium’s is of order -2e-5 a.u. (-1.5e-5 of alpha; value to be taken from Puchalski et al. 2016). The fits model the refractive polarizability alpha + chi_0 and add chi_0 to every electric-only value (theory, dielectric) before fitting; each such dataset is marked in its fit configuration. At the level of Borzsonyi or Bideau-Mehu (1e-3) this is invisible; at the level of Puchalski, Lesiuk, Gaiser and Peck & Fisher it is not.

• Status: open (to be implemented in the fits).

TC-72: Kumar & Thakkar (2010) dipole sums are fitted to refractivity data already here

• Where: kumar_2010.toml.

• Claim: the DOSDs were constrained by refractivities from Cuthbertson 1932, Smith 1976, Bideau-Mehu 1981 (in this package) and Hohm, Coulon (not), so fitting their S(k) beside those datasets would count the same data twice. The S(k) datasets are therefore used as validators (check) in the fits, not as data (a reversible decision).

• Status: open.

TC-73: argon’s absolute level: Peck & Fisher +3.5e-4 and Zhang +2.6e-4 above theory and metrology

• Where: data/gas/fits/Ar.toml, fit/Ar.

• Observation: Lesiuk & Jeziorski’s ab initio moments (S(-2) to 1.7e-4), the dielectric (DCGT) static polarizability of Gaiser & Fellmuth (2.4e-6, via Lesiuk) and Egan’s refractometry at 632.99 nm (1.5e-5, via Lesiuk) agree with each other, and Birch 1991 at 633 nm lies -53 ppm from them. Against that level, Peck & Fisher’s 17 points lie a uniform +353 ppm high (their stated systematic <= 2e-4) and Zhang et al.’s 800 nm comb value +265 ppm (stated 2.3e-5). The fit takes Peck & Fisher’s shape with a free scale (their shape residuals are at their 4e-6 rms) and Zhang as a validator. The Borzsonyi-family argon formulas, fitted to Leonard’s (Peck-based) level, are 0.1-0.15 % high in the visible; Luna’s legacy Kingston fit rises several per cent above the fit below 150 nm.

• Status: confirmed (2026-09-25): Peck & Fisher’s shape with a free scale, Zhang a validator.

TC-74: argon vacuum-ultraviolet sources used as validators

• Where: data/gas/fits/Ar.toml.

• Observation: Gill & Heddle’s Rayleigh value at 121.6 nm is 11 % above the fit, and Heddle et al.’s Cerenkov values -2 % (180, 185 nm) and +8 % (121 nm); Chopra & Heddle (Rayleigh, 121.6 nm, normalised to a calculated H2 cross section) -1.6 %; Ferrell’s third-harmonic values +0.1 to -1.7 %. All are validators, not fitted: broad bandpass (Cerenkov), sign-blind and normalised (Rayleigh), or no stated per-point uncertainty (Ferrell). Bideau-Mehu (140-254 nm, 0.5 %) and Gordon (111-115 nm, 5 %) are fitted and agree within their errors. Chashchina’s smoothed values (via Bideau-Mehu) lie 0.05-0.5

• Status: open.

TC-75 puchalski_2016

• Units: true atomic units (a0^3, t0 = hbar^3/(m_e e^4)), never reduced units (p. 3); vacuum wavelengths, lambda[A] = 455.633525275/omega[au].

• Transcribed (images checked):

  • Table VII (tbl_f97b1bb8eafc, cells file): alpha = static total 1.38376077(14) and alpha(6329.908 A) = 1.39181197(14), 4He, nonrelativistic (finite mass exact) + 1/c^2 (infinite mass) + 1/(M c^2) recoil + 1/c^3 QED (static complete, dispersion Pachucki-Sapirstein approximation) + static one-loop 1/c^4 + finite nuclear size; use primary. Also alpha_piszczatowski_2015 1.39181164(14) and alpha_bhatia_drachman 1.391780800 (reproduced; the latter is Puchalski’s own evaluation of BD’s corrected coefficients, not printed by BD).

  • Table II (tbl_047bf9b3647c): nonrelativistic alpha_k^(0), k = 0-6, 4He finite mass, stored as Cauchy moments S(-2)..S(-8) (alpha_k = S(-k-2)); use check (no relativistic/QED). BD column as reproduced moments (from BD 1994 and BD 1997).

  • Text p. 7: alpha_8..alpha_14 = S(-10)..S(-16), 4.39500532(1), 6.7725956(1), 10.622083(1), 16.86118(1) (pdf text checked).

  • Table IX (tbl_a088e2718911, cells file): A_eps (= package molar refractivity) present 0.51725413(6) static, 0.52026369(6) at 6329.908 A (check: same as alpha); reproduced Lach 2004 0.51725419(10), Schmidt 2007 0.5172535(47), Achtermann 1991/1993 0.5213(1), Birch 1991 0.5220(3). Note b of Table IX read on the pdf text (the extracted Markdown lost part of it).

  • Text p. 12: static B_eps(273.16 K) = -0.0506 cm^6/mol^2 (Rizzo et al. 2002, interpolated), reproduced refractivity_virial_coefficient.

• Formulas: nonrelativistic_series (form alpha_series, Table II + text coefficients) reproduces Table VII’s nonrelativistic rows to all printed digits at 6329.908 A; range_nm [150, inf] is my choice (truncation < 1e-7), the paper evaluates 6329.908 A only. recommended (unstructured: sums of printed components of Tables II, IV, VII, VIII) gives 1.391811967 at 6329.908 A vs Table VII 1.39181197(14), and alpha(lambda) - alpha_0 = 0.008051197 vs 0.00805120(3). table6_total (A_k in a0^3 A^k, no QED) reproduced from Tables II and IV via f^k. A_eps(0), A_eps(6329.908) reproduced from alpha with CODATA 2010 N_A to 1e-9; the loader (CODATA 2018 N_A) gives alpha 1e-7 higher from them.

• Not extracted: Tables I, III, V (convergence; V is 3He); Table IV and VIII components (in notes); Table X a_r (= A_eps + A_mu), b_n, c_n (no quantity; values in notes). I computed b_r = (2/3) b_n - a_r^2/4 = -0.0518 cm^6/mol^2 (273.16 K, 6329.908 A), not printed.

• Added: cauchy_total (primary, inline, computed here): S(-2) = the Table VII static total 1.38376077(14); S(-4), S(-6), S(-8) = alpha_k^(0) + alpha_k^(20) + alpha_k^(21) + alpha_k^(30) = 1.54323951046, 2.04277705405, 2.9306867380 with quadrature sigmas of the printed components and 10 % of the QED terms (6.2e-6, 1.17e-5, 2.17e-5); S(-10..-16) = nonrelativistic alpha_8..alpha_14 with sigmas = printed + the omitted correction extrapolated linearly in k from the relative corrections at k = 4, 6 (1.31e-4 … 2.38e-4 relative: 5.8e-4, 1.1e-3, 2.2e-3, 4.0e-3); the series reproduces Table VII’s total at 6329.908 A to 3e-9. To check: the arithmetic and the extrapolation choice. alpha (Table VII totals) changed to check (the same information). The one-loop 1/c^4 dispersion components are not included (as in the paper).

• chi_0 = -0.000021194(1) a0^3 (Bruch and Weinhold 2002, p. 11; A_mu = -0.0000079224(4) cm^3/mol) recorded in the notes only: no quantity for a magnetizability (format gap).

• Doubts: uncertainty level not stated (estimates; I used “not stated”); the static and 6329.908 A uncertainties are fully correlated (0.14 u a0^3 from the 1/c^4 allowance). Refractometry measures alpha + chi (A_mu/A_eps = -1.53e-5): the package’s Lorentz-Lorenz treatment has no magnetic term; at the 1e-5 level helium n - 1 from alpha alone is 1.5e-5 too high.

• Status: open.

TC-76 piszczatowski_2015

• Transcribed: Table I (tbl_df068b216aa3, cells file; image checked): static total 1.383 760 77(14) and alpha(632.9908 nm) 1.391 811 64(14), 4He, as puchalski_2016 but without the dispersion QED term alpha_2^(30) omega^2 (0.32 u a0^3); use check (superseded).

• Misprints noted (no dataset affected): the abstract’s ‘1.39181141 a.u.’ (pdf text) vs Table I 1.391 811 64 (confirmed a typo by puchalski_2016 Table VII note e); Table II note e’s ‘n - 1 = 34.895(10) x 10^-4’ should be x 10^-6 (and puchalski_2016 says the value is a theoretical one cited by Leonard); Table II row ‘302 K’ vs note f ‘303 K’.

• Not extracted: Table II (a_r including A_mu; b_n, c_n); in notes, including a second theoretical wavelength a_r(546.2268 nm) = 0.521 297 25(6).

• Status: open.

TC-77 lach_2004

• Transcribed: Table IV (tbl_81cac1358e95) Total 1 383 760.79(23) x 1e-6 a.u., static 4He (nonrelativistic with nuclear motion + alpha^2 + alpha^3 QED incl. the field derivative of ln k0 + recoil and alpha^4 estimates); check (superseded by puchalski_2016). Text p. 4: molar polarizability 0.517 254 19(9)(4) cm^3/mol (page image checked; the extracted Markdown’s parentheses are unmapped glyphs); sigma stored = the theoretical (9).

• The CSV of Table IV lost minus signs and parentheses: only the intact Total cell is extracted; the other rows are in notes, read from the image.

• Doubt: the uncertainties are called ‘error bounds’ (level not stated; stored as not stated).

• Status: open.

TC-78 bhatia_1998

• Units: reduced Rydberg units and reduced Bohrs up to Eq. (13) (4He, K = 2.741493e-4); a0^3 and lambda in A from Eq. (15); no QED; no uncertainties.

• Transcribed (text, page image checked): Eq. (15) static term 1.383 729 930 a0^3 (check); Eq. (17) values 34.886 46 (5462.258 A) and 34.816 73 (6329.9 A) x 1e-6 at Loschmidt density (ideal, 1 atm 0 C; check; the printed +- is the last term, not stored); Verdet 0.661 22 (5000 A), 0.254 816 (8000 A) (check); reproduced Leonard 34.895 +- 0.01 (leonard_1974 recommended_He), Achtermann 1993 34.887 +- 0.007 (state assumed 1 atm 0 C, not stated), Leonard/Ingersoll-Liebenberg Verdet 0.637, 0.246.

• Formulas: Eq. (12) and Eq. (13) consistent with the generalized polarizabilities (checked). Eq. (15): A2 and A6 wrongly converted ((1 + m_e/m_alpha)^(3+2k) instead of ^3; reproduced both ways), A4 a misprint (neither conversion gives 8.822907e10); corrected values 3.2036675e5, 8.8032341e10, 2.621934e16 (Puchalski 2016 Table VI BD column, reproduced here from Eq. 13). Eq. (17) reproduces the printed n - 1 values (and so inherits the errors: corrected values 2.3 and 1.7 ppm lower); Eq. (18) reproduces the printed Verdet constants. No form fits (reduced units; lambda^-2 series in A); the corrections are in the formula notes (no form, so no corrections entries).

• Cross-check with stone_2004: Stone’s Eq. (5) dynamic coefficients are BD’s Eq. (13) exactly; Stone’s Eq. (8) lambda^-2 coefficient 1197.5410 matches Puchalski’s nonrelativistic + relativistic A_2 in cm^3/mol nm^2 to 4e-7, so Stone converted correctly and is not affected by the Eq. (15) error; its lambda^-4 and lambda^-6 coefficients differ from Puchalski’s by -3.8e-5 and -2.2e-5 (BD’s less accurate alpha_4 and missing relativistic alpha_6).

• Not extracted: the generalized polarizabilities alpha_1..eta_1 (reduced units; the conversion to au per moment, c_k 4^k (1 + m_e/m_alpha)^(3+2k), checked against Puchalski’s BD column, is not one dataset scale); they are in the notes.

• Status: open.

TC-79 schmidt_2007

• Transcribed: text pp. 1, 3: measured A_eps = 0.517 253 5 (47) cm^3/mol, 273.16 K, one standard uncertainty (primary; microwave 2.7-7.6 GHz stored as static, the dispersion to f = 0 being 1e-11); parentheses are unmapped glyphs in the curators’ extracted text, value checked on the pdf text and against puchalski_2016’s reproduction. Table I (tbl_db1498b084c8, cells file; image checked): Lach’s A_eps 0.517 254 19 (10) (reproduced).

• The measured quantity is A_eps + A_mu; A_mu = -0.000 008 03 (17) (Bruch and Weinhold 2000) subtracted by the authors. Dielectric virial b = -0.098(04) cm^3/mol is in notes only (B_eps = A_eps b is not printed).

• Status: open.

TC-80 velsko_1986

• No datasets: the paper measures Delta n = n(532 nm) - n(1064 nm) (at 1 amagat, ideal-gas scaling) and c = d(phase)/(dP dl) in mrad/(psia cm); the format has no quantity for either (format gap). Tables I and II transcribed into notes from the CSV (images checked): 13 and 12 gases, of which He, Ne, Ar, Kr, Xe, H2, N2, O2, CO2, CH4 (and SF6 in Table I only) are species.

• Checks: l_c = 2 pi/(c x 14.696 psia) for every gas; Table II vs Table I’s c agree to +-0.1 % only (not an exact conversion); caption 24 C vs text 25 C for l_c. Helium Delta n from puchalski_2016’s series: 2.150e-7 vs measured 2.160e-7 (0.5 %, inside the 2 % at 95 %).

• Status: open.

TC-81 birch_1991

• Transcribed (images checked; cells files only): Table 1 (tbl_6072c809ac8e) per gas (N2, O2, Ar, CO2, Ne, He, N2O, Kr): alpha-bar in A^3 at 632.99 nm (primary, relative 2.0e-4, N2O 2.5e-4, at 99 %) and the per-run [R] (check, scale 3/(4 pi) to A^3; each run’s T, p, n - 1, density in the printed cells). Table 2 (tbl_10576f9abc2b): Birch’s own n - 1 at 101 325 Pa, 15 C (check, real gas, +- at 99 %) and 17 reproduced values (Kerl 1982 x5, Peck-Khanna, Cuthbertson 1910 x4 [printed 1911], Peck-Fisher, Edlen (CO2 ‘predicted by Edlen’, derived by Birch), Simmons, Cuthbertson 1932 x2, Mansfield-Peck, Hey et al. 1988); their state is Birch’s caption, density unknown.

• Checks: every run’s [R] reproduces from its n - 1 and density to 1e-4 except He: the printed He densities 0.17071, 0.17070 should be 0.17081, 0.17080 (they reproduce the printed [R] and the virial density); density is not extracted, so no erratum, but to check. Means, alpha-bar and Table 2 own values reproduce.

• Format gap: the 99 % level is not in the vocabulary (stored as “not stated”; to one sigma divide by 2.576). No refractivity virial coefficients in this paper (some were expected). He [R] is 3.4e-3 above theory (known, stone_2004, puchalski_2016).

• Status: open.

TC-82 achtermann_1991

• Transcribed (images checked; cells files only): Table II (tbl_dffe72791eb0 and its continuation tbl_5293ebc0b026) for CH4, CO2, SF6, H2, N2, He, Ar: A_R (34 datasets, rows by temperature) and B_R (47 datasets, one per temperature, parameters. temperature_k; “…” temperatures stored as row “unknown” without the parameter); this work primary (A_R +-: level not stated; B_R +-: “three standard deviations … as well as errors due to cell distortion and adsorption”: stored as not stated, format gap), others reproduced (orcutt_1967 by id, the rest by citation), Table III’s literature B_eps (static, 8) reproduced and the authors’ 4 extrapolations (mark a) as check. C2H4, C2H6 skipped.

• Structural: the continuation table’s first row (B = 0.036, Theory Ref. 36, no gas) is H2’s (caption); Kirouac and Bose’s “a” mark stripped; CH4 A_R printed twice (323 and 373 K rows, identical) - the 323 row is excluded_rows (A_R fitted at 373.15 K, Fig. 2 caption).

• Wavelengths per the caption: 632.99 nm except Olson and Diller 546.2 nm, Orcutt and Cole and Kirouac and Bose static; theory B_R rows (DID estimates) stored at 632.99 nm (not stated), Dacre’s He B_eps static.

• Not extracted (format gap: no C_R/D_R quantity): C_R, D_R values, in notes.

• Doubts: Ar A_R ‘4.196 +- 0.0002’ (digits); CH4 B_R at 323 K 6.08 (Table II) vs 6.11 +- 0.10 (Table III); the A_R of the Theory rows are said to be computed from Landolt-Boernstein (whose, unclear). He B_R = -A_n^2/9 only (Delta K = 0); He A_R = A_eps + A_mu; judged 10 sigma off theory by puchalski_2016.

• Status: open.

TC-83 newell_1965

• Transcribed: Table III (tbl_601dafe76d7c, cells file; image checked): per gas (Ar, CO2, He, H2, N2, O2; air skipped) the cylindrical (primary) and Fabry-Perot (check) values and the reproduced Maryott-Buckley, Essen 1953, Essen-Froome 1951, Froome 1955 values; 29 single-point datasets at 0 C, 760 Torr, 2 sigma (Newell’s and the two the paper equates to 2 sigma), level not stated for Essen and Froome.

• Wavelengths: vacuum c/f in m computed from 47.736 GHz (6.2802 mm) and the nominal 9, 24, 72 GHz; Maryott-Buckley stored at inf (means over rf to optical).

• Density: ideal for He, H2 (Eq. 7), real for N2, O2, Ar (Barrell-Sears), CO2 (Berthelot), by the earlier convention; but the values were measured near 1 atm and 20 C and only scaled in temperature, so they are close to the real-gas n - 1 at 0 C: with “ideal” the loader’s He polarizability is biased by Z = 1.0005 (to check: the convention for such reductions).

• O2 excluded (paramagnetism and the 60 GHz band); Froome’s 72 GHz O2 marked beyond_resonance. CO2’s static value includes the vibrational polarizability (noted).

• He 34.51 is 0.26 % below the ab initio static value 34.598 (computed here with puchalski_2016’s A_eps and a real-gas density), beyond the stated 2 sigma.

• Pages: pdf page N is journal page 3749 + N (checked on the pdf).

• Status: open.

TC-84 orcutt_1967

• Transcribed: Table II (tbl_f6b30fa838e4, cells file; image checked): A_eps this work (primary, static, He/Ne/Ar/Kr/H2/N2), Newell and Baird’s (reproduced newell_1965, converted by the authors) and NBS (Maryott-Buckley) values; B_eps (corr) this work (primary, parameters.temperature_k 322.15), literature (Johnston et al. 1960 He, Ar; Orcutt and Cole 1965 Ar; N2 mark e unidentified), the authors’ fluctuation-induced B_tf (check). The Ar literature cell holds two values (split by marks c, d; image). Table III CO2 34 C at 5461 A (Phillips 1920 via the authors’ fit): A_n and B_n (reproduced; 5461 A taken as air).

• Not extracted: Table I (per-run, before the capacitance correction; merged cells; values in notes), Table III rows averaged over 4471-6678 A (no single wavelength; in notes), the quadrupole-induced B.

• Doubts: temperature 49 C (Table II text, abstract) vs ‘kept at 40.0 C’ (apparatus, p. 698) vs 50 C (figure captions); Table III B_n unit printed cm^3/mole^2 (for cm^6/mole^2); Table II note e missing (N2 literature B unidentified).

• Status: open.

TC-85 samson_1994

• Transcribed (images checked): Table 1 (tbl_95893c11a7e1) 129 rows 24.587-280 eV in Mb, split into measured (to 120 eV, 97 rows, relative 1 % / 1.5 % / 2 % by energy range per the text, relative_rows) and extrapolated (125-280 eV, 32 rows, fit to Watson and Denne, uncertainty not stated); Table 2 (tbl_168a48a2c629) 38 rows 280-8000 eV in barns (scale 1e-6; the 280 eV row excluded as a repeat of Table 1), +-10 % stored as a bound. All primary.

• Formulas: Eq. (2) 403 E^-3.05 (reproduces Table 1 140-280 eV to +1.3/-0.7 %), Eq. (3) 410 E^-3.5 (reproduces Table 2 at 3-8 keV), text 335 E^-3.25 (700-1800 eV, to 1.2 %).

• Doubt: Table 3’s f(120-280 eV) = 0.1053 is not reproduced by integrating Table 1 (0.113, trapezoid); the other ranges and the total agree to 1-2 %. Not extracted (no quantity for range-integrated oscillator strengths).

• Status: open.

TC-86 chan_1991

• Transcribed (images checked): Table II (tbl_bd7d4d0ec5c7) 153 low-resolution df/dE values 24.6-180 eV in 1e-2/eV (differential_oscillator_strength, primary, uncertainty not stated); Table III (tbl_ae85cd966ffd, cells file) discrete f for 1 1S -> n 1P, n = 2-7 (index n; no energies printed): present work primary (scatter column + 5 % scale as systematic_relative), 8 theory and 12 experiment columns reproduced (Backx and De Jongh: n = 2 excluded as their normalization points; Korolyov and Odintsov’s two n = 2 values as rows 2-1, 2-2).

• Errata: Green, Johnson and Kolchin 7 1P 0.0525 -> 0.00525; Schiff and Pekeris 2 1P 0.02762 -> 0.2762 and 3 1P 0.00734 -> 0.0734 (decimal misprints; evidence in the record).

• Misprints noted, not data: Lassettre et al. cited as ‘Ref. 30’ in the table (Ref. 39 in the text and reference list); the text calls Table II ‘Table I’ (p. 196); resonance energy ‘63,655’; the total 0.431 printed ‘(0.0006)’.

• No sum rules S(k) are given besides the TRK normalization; berkowitz_1997 reproduces the present f column (its n = 3 as 0.074).

• Status: open.

TC-87 edlen_1966 (identity from the pdf cover: Metrologia 2, 71)

• No datasets (air is not a species). Eq. (1), p. 76, recorded verbatim in the notes and checked on the page image: (n - 1)_s x 10^8 = 8342.13 + 2406030 (130 - sigma^2)^-1 + 15997 (38.9 - sigma^2)^-1, sigma the vacuum wavenumber in um^-1; standard air dry, 15 C, 760 torr, 0.0003 CO2 by volume (pp. 72, 79). Check: Eq. (1) reproduces Table 2’s printed ‘1965-1953’ column at all 53 wavelengths to 0.1e-8.

• Closes TC-2: optmat.conditions.standard_air_refractivity agrees exactly (coefficients, variable, reference state 15 C / 101 325 Pa / 0.03 % CO2); the formula was typed from memory there and is now confirmed from the paper.

• Also recorded verbatim in notes: Table 4 approximations, Eqs. (12), (15), (17), (21)-(23); and two CO2 formulas as [[formulas]] (Eqs. 16, 18: CO2 relative to standard air, from Koch 1914 and the Cuthbertsons 1920, normalized to 42676e-8 at 5462 A, 15 C, 760 torr; consistent with that normalization to 1e-8 and 6e-8).

• Doubt: none on Eq. (1). Eq. (13) is garbled in the curators’ extracted Markdown (‘t + 0.003671 t’); not used.

• Status: open.

TC-88 henke_1993 (scanned pdf, OCR text)

• Short database record, no datasets (the package keeps the CXRO .nff files). Citation from the title page and running footer (ADNDT 54, No. 2, July 1993, pp. 181-342).

• Sign convention (Eq. 3, p. 184, page image): n_r = 1 - delta - i beta = 1 - (r0/2 pi) lambda^2 sum n_q f_q(0), f = f1 + i f2: n = 1 - r_e lambda^2 N (f1 + i f2)/(2 pi). The package’s data/external/henke/PROVENANCE.md writes (f1 - i f2) (the other time convention): inconsistent with the paper’s sign; to check and fix there.

• Validity quoted: > about 50 eV and outside threshold regions (pp. 183, 202); f1 undefined near edges (p. 201); tabulated 50-30 000 eV.

• Comparison with the .nff files (He, Ne, Ar, Kr, Xe at 49.3, 91.5, 108.5, 524.9, 1011.7 eV; the paper tabulates at x-ray line energies, not round values): identical to the printed digits for He, Ne; all within 0.2 % above 500 eV and in f2 everywhere except Kr at its 3d edge (91.5 eV: f1 1.52 vs -0.92, f2 5.41 vs 5.67); Ar f1 1.1 % lower in the files at 91.5-108.5 eV, Kr f1 4 % higher at 108.5 eV (CXRO revisions near the M/N edges). The paper tables used (tbl_ba3aa8cd984a He, tbl_6d4aad08e4c2 Ne, tbl_a9ecc4b5c66d Ar, tbl_ad86e348703a Kr, tbl_dfb608127b3a Xe) were identified by Z (edges, conversion factors, the high-energy limit of f1); Kr’s image checked.

• Status: open.

TC-89: Mansfield & Peck’s helium dispersion departs from ab initio theory by 1e-4

• Where: data/gas/fits/He.toml.

• Observation: with its level fitted free (1.002283, the +0.23 % of TC-44), Mansfield & Peck’s 13 points lie +108, +110 and +69 ppm (480-546 nm) and -18 to -47 ppm (0.72-2.06 um) from the model built on Puchalski et al.’s coefficients: their relative dispersion between 480 and 546 nm is about 2 % off theory, where theory is good to 1e-5. They are fitted with a 1e-4 allowance added to their 8e-6 stated precision, which leaves them without influence on a model fixed by theory.

• Status: open.

TC-90: classical helium refractometry scatters by +-0.3 % about theory

• Where: data/gas/fits/He.toml validators.

• Observation: against the model (Puchalski + Schmidt): Birch 1991 +0.32 % (stated 7.8e-5 at 99 %; its printed densities found suspect, TC-81), Cuthbertson 1910 +0.24 %, Achtermann 1991 +0.20 % (Puchalski et al. flag it), Orcutt & Cole +0.34 % (dielectric, 0.19 %), Newell & Baird at 47.7 GHz -0.30 % (0.07 %), Cuthbertson 1932 +0.07 % (inside its 0.1 % systematic), Smith 1976 within its 0.2 %. Only Schmidt et al.’s microwave value (9 ppm) agrees with theory to its uncertainty. All but Cuthbertson 1932, Smith, Huber, Swift and Marchetti are validators.

• Status: open.

TC-91: the helium model in the vacuum ultraviolet

• Where: fit/He.

• Observation: below 90 nm the model rests on Puchalski’s high-order coefficients (S(-10) … S(-16) are nonrelativistic, with estimated correction allowances) and the NIST 1s2p and 1s3p lines; its stated uncertainty is 3 ppm at 83 nm, 24 ppm at 70 nm and 0.08 % at 61 nm. Liu’s independent (infinite-mass, nonrelativistic) calculation departs smoothly from it, -411 ppm at long wavelength (the mass and relativistic correction) to -0.16 % at 65 nm and -0.8 % at 60.75 nm, the growth the shift of the resonance pole implies. The fitted 1s2p oscillator strength is 0.2767(8) (NIST 0.27625, AAA).

• Status: open.

TC-92: neon’s dispersion: experiment against ab initio theory (2.5 sigma)

• Where: data/gas/fits/Ne.toml, fit/Ne (reduced chi-squared 2.5).

• Observation: Lesiuk et al.’s S(-4) = 2.850(7) and S(-6) = 4.932(14) (with S(-2) = 2.66080(36)) give less dispersion than every experiment-constrained source: the fit to the Cuthbertsons’ visible shape alone wants S(-4) = 2.868; Kumar & Thakkar’s DOSD (constrained by refractivities) has 2.875 with S(-2) = 2.669, Langhoff & Karplus 2.863; relative to the static term the experiments’ S(-4)/S(-2) is 0.6 % above theory’s. Bideau-Mehu’s VUV values lie +1 to +2 % above the theory-constrained model at 140-152 nm (sigma 0.5 %). For argon, theory (Lesiuk 2023) and Peck & Fisher’s shape agree. The fit keeps every stated uncertainty and scales its band by the reduced chi-squared. Question: trust the ab initio dispersion (inflate the old data’s errors) or the experiments (inflate the theory’s dynamic terms)?

• Status: decided (2026-09-25): keep the ab initio backbone; the two experimental routes (refractometry above, photoabsorption below, TC-126) bracket it; the working estimate 0.3 % covers the spread.

TC-93: helium and neon refractometry systematically high (a contamination hypothesis)

• Observation: against theory-anchored fits, classical values for the light gases lie high: helium Birch +0.32 %, Cuthbertson 1910 +0.24 %, Mansfield & Peck +0.23 %, Achtermann +0.20 %, Orcutt & Cole +0.34 %; neon Birch +0.14 %, Orcutt & Cole +0.33 %, Cuthbertson 1932 +0.32 %; for argon Birch is -0.01 %. A trace of a heavier gas raises a light gas’s refractivity strongly (0.03 % of air in helium adds about 0.24 % to its n - 1), which would explain the sign and the size. A hypothesis only; it is why the fits take these values’ shapes, not their levels.

• Status: open.

TC-94: krypton and xenon rest on single static anchors and old dispersion data

• Where: fit/Kr, fit/Xe.

• Observation: the curators’ library has no ab initio dispersion for Kr or Xe; their levels rest on dielectric static polarizabilities (Huot & Bose 1991 as reproduced by Kumar & Thakkar 2010, Orcutt & Cole 1967 for Kr) and Birch’s 633 nm value (Kr), their shapes on Smith 1976 (Kr), Bideau-Mehu 1981 and the Cuthbertsons (level free). Both fits have reduced chi-squared below 0.7. Leonard’s recommended 546 nm values lie +0.05 % (Kr) and +0.14 % (Xe) above the fits; Huot & Bose’s Kr value is 2.8 sigma from Orcutt & Cole and Birch. The magnetic susceptibilities are not in the curators’ library and are neglected (about -25 ppm of alpha). Useful additions: ab initio dispersion coefficients for Kr and Xe, their chi_0, Hohm & Kerl 1990 and Hohm & Thakkar 2012 (static values).

• Status: open.

TC-95: the molecular fits (N2, H2, D2, O2)

• Where: data/gas/fits/{N2,H2,D2,O2}.toml.

• N2 (reduced chi-squared 1.1): Griesmann’s VUV (level free, calibrated on Abjean), Peck & Khanna, Birch, Stone, Achtermann, Zhang, Newell, Orcutt & Cole and Marchetti agree to their uncertainties; effective oscillators only (N2 has no infrared-active mode).

• H2 (reduced chi-squared 0.8, Newell a validator): the absolute level is contested at 1e-3. Relative to the fit, Rychlewski’s ab initio thermal average is -450 ppm and Bishop & Cheung’s -200 ppm (the two theories differ by 0.17 %, which is the allowance given to theory), Peck & Huang -1000 ppm (their scale is fitted with its 3.1e-4 prior: -3.3 sigma), Achtermann +140 ppm (reliable for Ar and N2, 10 sigma high for He), Orcutt & Cole +744 ppm, Newell -1370 ppm (a validator). The temperature dependence of H2’s rotationally averaged polarizability is not modelled (theory at 293 K, data at 273-323 K). A modern ab initio H2 alpha(omega) with its uncertainty would settle it.

• D2: Rychlewski’s theory, and since TC-96 Shelton’s D2/H2 and H2/D2 ratios; Orr’s 1936 value (+0.2 %) inherits an outdated H2 refractivity.

• O2 (reduced chi-squared 0.2): above the Schumann-Runge bands only (195 nm); Zhang’s 800 nm value is -482 ppm (12 sigma; Kren’s A-band criticism). Kumar & Thakkar’s sums (constrained by Smith’s and Stoll’s refractivities) against the fit with Shelton’s N2/O2 ratio (TC-96): S(-2) -0.03 %, S(-4) +0.55 %, S(-6) -6 %, S(-8) -1 % (before the ratio: -0.01, -0.7, -3.1, +3.1 %); the high moments hang on the lowest pseudo-oscillator (155 nm, the Schumann-Runge region) and two oscillators do not fix them.

• CH4, SF6, N2O are not fitted: the curators’ library holds no direct dispersion data for them beyond single visible or 633 nm values (Achtermann, Birch, Swift, Cuthbertson 1914 for N2O) and Rayleigh-derived formulas; their infrared bands need band intensities (HITRAN) that are not curated. The papers that would supply them are not in the curators’ library.

• Status: decided (2026-09-25): put hydrogen on theory: Raj et al.’s 293 K average fitted with a 0.1 % allowance (the spread of the three calculations), the experiments’ levels free or prior-limited (TC-101).

TC-96: Shelton’s phase-matching density ratios as fit observations

• Where: optmat.gas.fitting._ratio, data/gas/fits/{Ne,N2,H2,D2,Kr,Xe,O2}.toml, optmat.gas.crosschecks.

• What: each ratio rho_gas / rho_ref = Delta alpha_ref / Delta alpha_gas (Delta alpha = alpha(2 omega) - alpha(omega)) is fitted in the gas whose dispersion it constrains, with the partner held at its recommended model (fits are run in dependency order: He and Ar first, then Ne, N2, H2, Kr, Xe, then O2 and D2). Resulting reduced chi-squared: Ne 2.6 (He/Ne 1.4 and 1.6 sigma, the TC-92 tension again), N2 1.15 (He/N2), H2 0.76, D2 0.25, Kr 0.80, Xe 0.68, O2 0.19.

• Argon against Shelton: Shelton’s ratios are self-consistent to 0.02 % (He/N2 x N2/Ar = He/Ar), but the argon model (Lesiuk & Jeziorski’s ab initio moments) gives a He/Ar ratio 0.31 % and 0.32 % below Shelton’s (1.9 and 1.2 sigma). Fitted in N2, the 0.02 % N2/Ar ratio drags nitrogen onto that difference (reduced chi-squared 1.1 to 1.76, Peck & Khanna’s chi-squared 16 to 26), so N2/Ar is a validator of fit/N2 (-0.11 %). To check: whether Shelton’s He/Ar (or the whole argon-referenced set: Ar/Kr, Ar/Xe) carries a 0.3 % systematic, or the argon dispersion at 1.3 um does.

• D2 needed 20 starting points ([model] starts, new): with the default six, one effective oscillator stayed at zero strength (chi-squared 8605). The other fits give the same minimum with 20 starts (He and Ar lower by 0.13 and 0.03 in chi-squared).

• Status: open.

TC-97: Borzsonyi’s group-delay dispersions against the fits

• Where: optmat.gas.crosschecks.group_delay_dispersions, borzsonyi_2008/sgdd_* (validators).

• Observation: at 800 nm the fits give, relative to the measured GDD: He +21 % (1.3 sigma), Ne -12 % (2.6 sigma), Ar +2.2 % (3.6 sigma), Kr +0.4 %, Xe +0.6 % (2.9 sigma), N2 +10 % (12 sigma). The fits’ near-infrared dispersion rests on data an order of magnitude more precise (Peck & Khanna and Shelton’s He/N2 for N2; ab initio moments for He, Ne, Ar), so the spread is taken as Borzsonyi’s; it confirms the decision to keep these values as validators. To check: the state Borzsonyi’s GDDs are quoted at (1 bar and room temperature as curated) and whether N2’s value is misread.

• Status: open.

TC-98: the published CH4, SF6 and N2O formulas fail the near-infrared ratios

• Where: he_2021/{CH4,SF6,N2O} (the defaults for want of fits), optmat.gas.crosschecks.

• Observation: against Shelton’s N2/SF6 ratio the formula predicts -28 % at 1319 nm and -2.5 % at 1064 nm; against N2/CH4, -3.4 % and +0.2 %. The measured ratios change by 35 % (SF6) and 25 % (CO2) between the two wavelengths: in a difference of polarizabilities the infrared vibrational term matters, and Old’s CO2 formula (with its infrared terms) reproduces the CO2 change to 0.2 %. The He et al. formulas have no infrared term. Shelton’s printed values are confirmed against the table (TC-27). These gases need vibrational poles from band intensities (HITRAN) before they can be fitted.

• Status: open.

TC-99: the extreme-ultraviolet distributions’ approximations

• Where: optmat.gas.euv, data/gas/euv/{He,Ar,Kr,Xe}.toml, docs/euv.md.

• Approximations to review:

  • Ar, Kr, Xe: the autoionising region between the 2P3/2 and 2P1/2 limits is not tabulated by Chan et al. (only plotted); its density is taken flat at the first tabulated value. Without it the constraint scales would be 1.006, 1.10 and 1.30 instead of 0.980, 0.994 and 1.0005.

  • The unlisted Rydberg members below the 2P3/2 limit enter as one pseudo-line just below the limit (their total from Chan’s “total to ionization”).

  • TRK sums: He 1.979 (2), Ar 18.49 (18), Kr 34.51 (36), Xe 50.85 (54). Where the argon excess and the krypton and xenon deficits sit (the Chan-Henke join, the inner shells, the autoionising fill) has not been established.

  • No line widths: between the first line and the threshold the index is given between the lines only.

  • Neon: built from chan_1992_neon and NIST’s lines (TC-126).

• Status: open.

TC-100: parity with solprop’s gas formulas

• Where: tests/test_solprop_parity.py, tests/data/solprop_sellmeier.json (from solprop by tools/solprop_parity.py; re-recorded 2026-09-26 against the public solprop, values unchanged).

• What: each of solprop’s 18 gas formulas (air excluded) is matched to a model here and reproduces solprop’s refractivity at its reference state to 1e-11, except Bideau-Mehu Ne, Ar and Kr (Luna’s premultiplied, rounded coefficients: at most 3.3e-6). To confirm the mapping: solprop’s peck H2 is Peck & Hung’s Eq. 7 (not Eq. 4), its D2 is the same hydrogen formula (Orr), its zhang O2 is Kren’s corrected coefficients, and its ermolov helium is Luna’s full-precision coefficients read at 1 atm.

• Refresh: re-run the tool when solprop’s sellmeier.py changes.

• Status: open.

TC-101: robustness of the fits (leave one dataset out) and their near-degenerate minima

• Where: tools/fit/robustness.py, data/gas/models/robustness/*.json, gallery Robustness.

• Single-dataset levels: hydrogen’s level rests on Achtermann’s 633 nm value alone (without it the fit moves -870 ppm, 18 sigma of the stated 47 ppm, towards Peck & Hung and the ab initio values; TC-95), and oxygen’s on Birch’s (-840 ppm, 10 sigma of 79 ppm). The stated uncertainty band reflects that one measurement, not the spread of the levels. Open question: widen those values’ allowance (or add a level uncertainty to the model), or accept the metrology as it stands.

• By design: the backbones move their models by many sigma when dropped (helium’s Puchalski moments 2151 sigma, neon’s DCGT 20, argon’s Lesiuk moments 9 and DCGT 6, deuterium’s Rychlewski 49, xenon’s Bideau-Mehu 16 near its range’s short end, oxygen’s Smith 114 at 205 nm); every other dataset moves its model by less than 4.3 sigma, most by less than 2.

• Minima: the fits’ cost has near-degenerate minima (a far effective oscillator enters only through f/E^2). More starting points find slightly lower ones: helium chi-squared 37.97 against 38.10 with its fourth oscillator driven to infinity (its covariance then singular), argon 19.60 against 19.63, neon 52.55 against 54.65 with an oscillator on the first resonance. They differ from the stored fits by at most 0.44 sigma of the model anywhere in range, so the stored fits stand; a global search (variable projection over the effective energies) would make the minimum unique. The robustness refits start from the full solution (fit(..., start=)) so that they measure the dataset.

• Status: decided (2026-09-25): hydrogen’s level moves to the ab initio calculations (TC-95); oxygen’s is resolved by Egan 2026 (TC-147).

TC-102: independent second read of the errata and formula corrections

• Where: a second reading of every erratum; the source records it touched.

• What: all 44 errata and the six formula corrections were re-read against the table images or rendered pages by a second reader (an AI model, 2026-09-25), with every cited calculation recomputed: none is wrong (37 + 2 confirmed, 7 + 4 confirmed with a slip in the reason or evidence text), and every erratum’s row holds exactly the printed string. The text slips were fixed in the source records (Bideau-Mehu’s “to the last digit”, page and line labels; Chan 1991’s page; Langhoff’s Pade bound now computed; Leonard’s Damkohler, Larsen and Mansfield & Peck evidence; Old’s argument; Borzsonyi’s xenon STOD 42.6, recomputed here with linear density scaling: 42.64; Mansfield & Peck’s static value). No value changed.

• Also noted: Mansfield & Peck’s Eq. 8 operator and Bideau-Mehu’s neon lambda^-2 are applied through the formula’s terms and form without a corrections record, so the loader does not check them against the print; Rusch 1923’s Burton row (not used) gives 2793 against the printed 2799.

• Status: open (a spot check of the second read).

TC-103: the dispersion uncertainty of the fits, statistical against empirical

• Where: optmat.gas.models.fitted.FittedModel.dispersion_sigma_relative, optmat.gas.models.oscillator.OscillatorModel.dispersion_au, docs/accuracy.md (its table checked by tests/test_accuracy_page.py), gallery Dispersion uncertainty, the GVD shifts added to data/gas/models/robustness.

• Finding: the covariance-propagated GVD uncertainty is a lower bound. Adding Shelton’s ratios (TC-96) moved the 800 nm GVD of krypton by +1.0 % (8 statistical sigma), oxygen +0.95 % (6), deuterium +0.42 % (26) and xenon +0.35 % (3); leaving one dataset out moves nitrogen’s and hydrogen’s GVD by 0.2 % (17 and 8 sigma). A ratio-fitted gas also inherits its partner’s uncertainty, which its covariance lacks.

• Working estimates: the page’s “working estimate” column (He < 0.01 %, Ne 0.3 %, Ar 0.05 %, Kr 1 %, Xe 0.4 %, N2 and H2 0.2 %, D2 0.3 %, O2 1 % at 800 nm) is a judgement from both measures. At 800 nm solprop’s formulas for neon, hydrogen and oxygen lie within these estimates of the fits, those for krypton close to it, the others well outside.

• Also: the assessment’s formula table rows for Ne, Kr and Xe were stale (from before the ratio refits) and were recomputed.

• Status: decided (2026-09-25): the working estimates accepted; columns at 343 and 1800 nm to be added.

TC-104: infrared band strengths from HITRAN, checked against Shelton’s ratios

• Where: tools/hitran/band_strengths.py, data/external/hitran/ (with PROVENANCE.md), optmat.gas.infrared, tests/test_infrared.py.

• What: band strengths of CH4 and N2O summed from HITRAN2024 line lists (0-11000 cm^-1, all isotopologues), and of SF6 integrated from HITRAN’s measured cross-sections (Ref. [1164], 560-6500 cm^-1; its nu3 window agrees with Ref. [1638] to 1 %). Static vibrational polarizabilities: SF6 13.94, N2O 2.63 (1.19 once the pure rotational bands are left out, TC-156), CH4 0.240 a.u.

• Check: Shelton’s N2/SF6 and N2/CH4 ratios at 1319 and 1064 nm are consistent with a single scale on the electronic formula’s dispersion only if the infrared term is right: the scale on HITRAN’s strengths that makes them consistent is 1.007 (SF6) and 0.88 +- 0.08 (CH4). With HITRAN’s strengths the ratios require the electronic dispersion of He et al. 2021’s formulas times 0.770 and 0.768 (SF6: 23 % too high) and 0.968 and 0.972 (CH4: 3 % too high).

• To check: the conversion f = S / (pi r_e) and HITRAN’s intensity definition (per molecule of the natural mixture, 296 K); the SF6 windows (560-700, 700-1100, 1100-6500 cm^-1); that the near-infrared overtone bands of CH4 and N2O (to 11000 cm^-1) are not meant to be represented near resonance.

• Next: fits of CH4, SF6 and N2O with these bands fixed and effective electronic oscillators fitted to the curated papers (Watson, Cuthbertson 1920, Vukovic, Alms, Sneep & Ubachs, Ityaksov) and to Shelton’s ratios.

• Status: open.

TC-105 raj_2018 (Raj, Hamaguchi & Witek, J. Chem. Phys. 148, 104308 (2018))

• Transcribed (tables checked against their images): supplement Table T1 (H2, tbl_b0cae9bc8235) and T5 (D2, tbl_3f331311ba2d), the diagonal columns <0,0|alpha|0,0> and <1,0|alpha|1,0>, 53 rows each (52 laser wavelengths in nm and “Static”); main Table II (tbl_aa58a97e916a, JSON), the H2 293 K thermal average “Our”, 15 rows. Inputs read (not stored): Tables T26 (tbl_8f44df72c173 S0/O1, tbl_db455a894d4d Q1/S1) and T29 (tbl_7c62aa367012), the “Our” transition energies.

• Computed, not printed: the authors’ own module rovibME.py (SHA-256 75823f2e…, files dated 24 Jan 2018, from a local copy of the authors’ GitHub repository H2-PolarizabilityMatrixElements) run unmodified by tools/extract/_raj_2018_program.py in a pinned uv script environment (Python 3.11.16, NumPy 1.24.4, SciPy 1.10.1) because it fails under NumPy 2 and calls scipy.integrate.quadrature (removed in SciPy 1.15). Per-state <0,J|alpha|0,J>, J = 0-10, H2 and D2, at T1’s 53 wavelengths: 22 files raj_2018__program_J*.csv (raj_2018.py --program, about one minute). Then normal H2 / normal D2 averages at 273.15, 293.15, 296.15 K (6 files, extract()).

• Decisions:

  1. Normal gas = spin species in the high-temperature ratio (H2 para:ortho 1:3, D2 ortho:para 2:1), each Boltzmann within its own levels; so only energies within each parity chain are needed (T26/T29’s S0 give them; no S0 connects odd and even J). Equilibrium at 293.15 K differs by at most 1.4e-5 a.u. for H2 (HITRAN E(J=1)).

  2. D2 spin weights 6:3 have no directly stated numeric source for D2: the curators’ library has “the spin of the D nucleus is I_N = 1, so that for the D2 molecule, even j states are twice as populated as odd j” (an unverified copy, Chen et al. 2007 by its file name, PDF p. 15; the same page wrongly says H2 even j are 3x odd) and “equals 6 for even j and 3 for odd j” for two spin-1 nuclei (Borysow et al. 2019, 14N2, PDF p. 8). HITRAN has no D2. The 6:3 weights also reproduce Rychlewski’s D2 average (rychlewski_1983 notes). H2 1:3: Bishop & Cheung (1980) text after Eq. (23) and HITRAN’s g’’ (HITRAN API 2026-09-25, isotopologue 103).

  3. v = 0 only (v = 1 population < 5e-7 at 296.15 K from Q1(0)); J <= 10 (D2 J = 9 holds 1.7e-5 of its species at 296.15 K, J = 10 1.3e-6).

  4. use: normal_293K primary (H2 and D2), the other temperatures and everything else check. For H2 it is a third ab initio set beside Rychlewski and Bishop.

  5. The environment for the authors’ module is a tool environment (uv inline script metadata, pinned old NumPy/SciPy), not a project dependency.

• Checks passed: every computed <0,0|alpha|0,0> rounds to T1/T5’s printed value (106 values, asserted in extract()); S0 agrees with S1 - Q1 and Q1 - O1 of the same tables to 7e-4 cm^-1 (asserted to 1e-3); the paper’s own Table II average reproduced to 4e-5 a.u. at all 15 wavelengths; five states identical in a second, independent environment (Python 3.9, NumPy 1.21, SciPy 1.7.3).

• Comparison at 293 K (raj_2018.py --compare, T = 293.0 K, the program’s range 182.25-1320.7 nm only): Bishop & Cheung H2, 16 wavelengths: -0.015 % (static) to +0.146 % (185.46 nm), mean +0.043 %; Rychlewski H2, 14: +0.007 to +0.057 %, mean +0.030 %; Rychlewski D2, 14: +0.015 to +0.055 %, mean +0.031 %.

• D2/H2 dispersion: the ESHG phase-match density ratio D2/H2 computed from these averages (295.15 K; one-off program run at the 9 fundamentals and harmonics, not stored) is 1.0317-1.0345 against Shelton & Mizrahi’s measured 1.0301-1.0319 (shelton_1986/ratio_D2_H2): 0.0009-0.0026 high (1.3-10 times the printed errors), like Rychlewski’s 1.0310-1.0347. Fitting H2 and D2 to Raj’s values would conflict with that ratio.

• Accuracy: “accurate to about 10^-3” (PDF p. 10), datasets carry 1e-3 a.u. absolute, level not stated; the package README says +/-1e-4 numerical.

• Not extracted: gamma, off-diagonal elements, T17, Table I; Table II’s Bishop and Victor-Dalgarno columns (identical to bishop_1980’s alpha_293K and victor_dalgarno at all 15 wavelengths, checked); Bridge & Buckingham 632.8 nm (reproduced; D2’s alpha and gamma rows printed swapped: alpha “2.0254”, gamma “5.4514”, image checked). T29 D2 O1(8) Delta^a “0.893” looks misprinted (neighbours 0.025-0.109); not used.

• Could not verify: that the GitHub snapshot is the version the paper used (the paper cites the repository “accessed 18-01-2017”; the files are dated 24 Jan 2018).

• Status: decided (2026-09-25): the pinned regeneration environment is accepted. The D2 spin weights 6:3 are accepted on the evidence above, noted as indirectly sourced. Resolved (2026-09-25): murphy_1934 states the ratio directly (g_s/g_a = 1.97 +- 0.03 measured, ‘the theoretical ratio of 2’, spin 1, even J symmetric; TC-173), and teal_1935 confirms the alternation (TC-174); raj_2018’s notes now cite them.

TC-106 Rychlewski 1983, second copy in the curators’ library (no record)

• The curators’ library holds another download of the same article (7252_1_online.pdf, current AIP cover page; the curated copy is an older Scitation download), 9 pages each. All seven tables are cell-for-cell identical (Table V differs only in header markup, \text{HD} against HD); the body text is identical apart from the cover page. Nothing to change in rychlewski_1983.

• Status: open.

TC-107 kolos_1967 (Kolos & Wolniewicz, J. Chem. Phys. 46, 1426 (1967))

• Transcribed (JSON tables, images checked): Table III (tbl_008b76c50f4e) static alpha_{vJ,vJ} of H2 and D2, 40 states each (v = 0, J = 0-31; J = 0, v = 1-8), one dataset per gas with rows by state (v<v>J<J>, all at inf); Table VI (tbl_3187f42a4fee) the 293 K rotational average 0.8045 A^3 (second value of a merged cell, footnote d), 1 point.

• Erratum: D2 v0J14 printed “9.8344” (image) -> 5.8344 (second differences of the column 0.0042-0.0043 with it; 4.0 and -8.0 without).

• Structural: the curators’ extracted JSON marks the experimental 0.8056 with “^{e}”; the image prints c (Reference 19, Schueler and Wolf). Not extracted.

• Formula: Eq. (17), Schueler and Wolf’s two-term formula in frequency (s^-1), reproduced; static limit 1.36000e-4 and 0.80564 A^3 reproduce the printed 1.3600e-4 and 0.8056. State 1 atm 0 C ideal inferred from Kolos’s N0; no form (converted coefficients would be needed).

• Check: Table VI’s 0.8045 A^3 is reproduced (0.80450) by the normal-H2 average of Table III at 293 K with Raj’s energies.

• Format need: per-state static values have no wavelength axis; stored as rows by state at inf (not a wavelength series).

• Status: open.

TC-108 ford_1973 (Ford & Browne, Phys. Rev. A 7, 418 (1973))

• Transcribed (images checked): Table VII (tbl_8218ee3b07f5, JSON) alpha(omega) “This work” 293 K, 24 wavelengths (1215.7 A to static) and the Victor-Dalgarno “Semi-empirical” column, 22 (reproduced); Table VII continued (tbl_f90a64648330) Cauchy coefficients alpha_k, k = 0-3, “This work” and “From experimental refractive index data”, stored as cauchy_moment S(-2k-2) (4 + 4); Table II (tbl_8a57694d1337) static J = 0-4 (5, rows by state) and the 300 K average (1); Table XI (tbl_31dd70cf3437) Lyman-alpha alpha_00 at 300 K (1) and the Rayleigh cross sections Q_00^c and Q_00^T (1 + 1, rayleigh_cross_section, scale 1e-24).

• Oddities, not corrected (not extracted or only noted): Table VII’s footnote reference numbers do not match the reference list (b “Reference 20” = Golden & Crawford, but the text names Dalgarno & Victor, Ref. 17; g “Reference 12” = Nelissen et al. for the “experimental” Cauchy coefficients, origin unresolved). Table II’s KW column prints 5.4292 at J = 4 (the column’s 300 K average) where kolos_1967 has 5.5096. Table XI alpha_00(Lyman alpha) = 12.538 at 300 K against Table VII’s 12.603 at 293 K, unexplained.

• Checks: Table VII “Expt.” identical to bishop_1980/victor_dalgarno (16 values); the five semi-empirical values at 1300-1700 A identical to bishop’s. Cauchy series at 6328 A: 5.4815 (this work, 0.0275 below Table VII, the static offset) and 5.5450 (refractive, against 5.554).

• Uncertainty: “generally in agreement with experiment to approximately 1%” (p. 424); Table VII’s this-work column carries 1 % relative, level not stated.

• Status: open.

TC-109 zeiss_1977 (Zeiss, Meath, MacDonald & Dawson, Can. J. Phys. 55, 2080 (1977))

• Identity: unverified record in the curators’ library; identified by its printed citation line (p. 2080) and as Margoliash & Meath’s Ref. 4. No DOI recorded.

• Transcribed: Table 3 (tbl_81ed6f008ff0, JSON) S_k, k = 2, 1, 0, -1/2, …, -3, -4, -6, …, -14 (15 rows) for H2, N2, O2 from the curators’ extracted table and N2O read from the image (15), cauchy_moment, rows by k in decimals.

• Structural fixes: the curators’ extracted table lost its last column (N2O): values listed in the script from the image. The extracted table misreads Li S_-4 as 3.504(3) (image 3.504(4)); Li not extracted.

• Checks: Margoliash’s pseudospectra (fitted to these sums) reproduce H2, N2, O2 and the image-read N2O values to <= 0.05 % for integer k = 0 to -14.

• use = check: DOSDs constrained to refractivities (Smith 1976, Peck & Khanna 1966, Koch, Ladenburg & Wolfsohn, Watson & Ramaswamy); not independent of them (as TC-72).

• Uncertainty: Table 5’s alternative-DOSD differences for N2 and O2 (0.0-4 %) quoted in the notes, not stored; none stated for H2 and N2O; “several percent” for k > 0.

• Status: open.

TC-110 margoliash_1978 (Margoliash & Meath, J. Chem. Phys. 68, 1426 (1978))

• Recorded: five [[formulas]], ten-term pseudospectra from Table I (tbl_0daae09a7a5d, JSON, image checked) for H2, N2, O2, N2O (form oscillator, energies in hartree, terms in e-notation with the printed digits) and CH4 (no form: its E0, needed for the range, is only in Thomas & Meath 1977, not in the curators’ library). No datasets: the paper tabulates no S(k).

• Range: range_nm = hc/(0.95 E0) rounded up, with E0 from Zeiss et al. (H2 11.18, N2 12.50, O2 6.12, N2O 5.35 eV): 116.8, 104.5, 213.3, 244.0 nm; “up to 0.95 … E0 with a maximum error of 0.02%” (p. 1429).

• Checks: tools/extract/margoliash_1978.py asserts that the terms equal the curators’ extracted table (no data file). S_0 = 2.00000, 13.99935, 16.00000, 22.00014, 9.99999; S_-2 = 5.4279, 11.7377, 10.5901, 19.6957, 17.2661; alpha(632.8 nm) within 0.13 % (H2), 0.01-0.02 % (N2, O2), 0.09 % (N2O) and 0.45 % (CH4) of the package’s default models.

• Doubt: N2’s S_0 = 13.99935 (0.005 % low) against the others’ 1e-5; a published erratum exists (listed on the cover page) and is not in the curators’ library.

• Status: open.

TC-111 mizrahi_1985_h2d2 (Mizrahi & Shelton, Phys. Rev. A 32, 3454 (1985))

• No datasets: the paper’s data are chi(3) ratios (H2/He at 19, H2/D2 at 9 wavelengths; Table I) and static chi(3) comparisons (Table III); the phase-match densities, the only linear-dispersion information, are not tabulated. The record describes Tables I-III for the later chi(3) work (lambda in air, nu in vacuum).

• Duplicate copy in the curators’ library: Tables I-III cell-for-cell identical; not used.

• Status: open.

TC-112 chan_1992_neon

• Chan, Cooper, Guo & Brion, Phys. Rev. A 45, 1420 (1992), part II (neon) of the series whose part III is chan_1992. TRK-normalised dipole (e,e): the absolute scale is independent of optical data (8.34 = 8 + 0.34 Pauli, 17.6 % above 250 eV, pp. 3, 6).

• Transcribed (images checked, every cell):

  • Table I + continuation (tbl_66ad40730b41, tbl_b252935d2cb5, CSV): df/dE in 10^-2 eV^-1, 21.6-250 eV, 220 points, continuum_Ne (primary). Rows are the energies (unique; no misprint found). No uncertainty stated in the paper.

  • Tables II-IV (tbl_3545e6ef35ab, tbl_bbf7e53a7149, tbl_f0fb0b7927fd, cells files): present work present_Ne (f_1 0.0118(6), f_2 0.159(8); primary), present_higher_Ne (12 lines 4s … 5d’; primary), present_total_Ne (0.292(15), total to ionization up to 21.616 eV; check); 40 reproduced datasets for 31 literature sources / variants (theory and experiment), as in chan_1992.

• Format need / structural choice to confirm: the Ne table headers print no transition energies (unlike part III). Only f_1 = 16.671 eV and f_2 = 16.848 eV are in the text (p. 2); so the resonance lines are <src>_Ne (eV) and the lines of Tables III-IV are <src>_higher_Ne with an index abscissa (1 = 4s, 2 = 4s’, 3 = 3d, 4 = 3d’, 5 = 5s, 6 = 5s’, 7 = 4d, 8 = 4d’, 9 = 6s, 10 = 6s’, 11 = 5d, 12 = 5d’) and rows by label. To use them as lines they need energies from Moore’s tables (Ref. [66], not in the curators’ library). The 3s’ energy: 16.848 eV (p. 2) vs 16.850 eV (calibration, p. 6).

• Structural: the note-a sums (Amus’ya, Kelly, Cooper) are printed centred between the pair’s columns; the cells put them under f_2 (Table II) or under the unprimed line (Tables III, IV). They go to <src>_sum_Ne (index 1 = 3s+3s’ … 7 = 5d+5d’). Table II’s uncertainties are on the row below the value; attached by the script. “0.003 30(0.000 30)” digit-group spaces removed.

• 2P3/2 nd[1/2] and nd[3/2] were fitted as one peak (p. 10): the “3d”, “4d”, “5d” values are the sum of both.

• Labels misprinted in the tables (data unaffected): “Amusy’ya”, “Bhaskar and Luiro” (Lurio), “Lawrence and Liszt (1960)” (1969), “Klose (1970) [34]” (Ref. 34 is 1969), “Jongh and Eck”. Lewis’s f_2 uncertainty (0.002) on 0.168 looks too small (kept as printed; same pattern as in chan_1992’s argon).

• S(k) not in this paper. Lesiuk et al. 2020 (Table XI) quote S(-4) = 2.938, S(-6) = 5.137 as “Chan et al. [89]” citing this paper; the paper prints no moments. lesiuk_2020/chan_1992_Ne should not be treated as a reproduction of values in chan_1992_neon; its origin is unknown.

• Not extracted: Figs. 1-3; autoionising resonance energies (p. 12, text); West and Marr’s discrete total 0.4 (p. 12, text).

• Status: open.

TC-113 gaiser_2018

• Gaiser & Fellmuth, Phys. Rev. Lett. 120, 123203 (2018), DCGT at the TPW.

• Transcribed (images checked):

  • Table III (tbl_a15621c7c166, cells file): A_eps (cm^3/mol, static) “This work” He 0.5172544(10), Ne 0.9947114(24), Ar 4.140686(10) (molar_polarizability_<gas>, primary, standard uncertainties); literature, reproduced: Orcutt & Cole He/Ne/Ar (orcutt_1967, uncorrected low-pressure values), Buckley et al. 2000 He/Ar, Schmidt 2007 He (schmidt_2007), Piszczatowski/Puchalski He theory, Gaiser 2010 Ne (gaiser_2010), Klopper/Larsen Ne theory, Lupinetti & Thakkar (+ relativistic correction) Ar theory.

  • Table II (tbl_ec04560e1d2e): A_eps/R x 10^8 m^3 K/J per capacitor, per_capacitor_<gas> (check), scale = R x 1e-2 with R = k N_A = 8.31446261815324 J/(mol K); relative_rows from Table I “Sum” (ppm, typed from the table image).

• Checks (2026-09-25): Table II weighted means x R reproduce Table III to 0.15 ppm; Table III uncertainties = the correlated 1.9/2.4/2.4 ppm of Table I. In a.u.: He 1.3837616, Ne 2.6610571, Ar 11.0771845 (Lesiuk 2020: 2.661057(7); Lesiuk 2023: 11.077183(27), last digit differs by the constants).

• Electric polarizability only: add A_mu (magnetic) for refractive-index comparisons.

• Supersedes the reproductions lesiuk_2020/gaiser_2018_Ne (2.661057(7) a.u.) and lesiuk_2023/gaiser_2018_Ar (11.077183(27) a.u.), and the alpha_0 inside lesiuk_2023’s Eq. (38) formula/dataset (uses 11.077183).

• Status: open.

TC-114 rourke_2021

• Rourke, J. Phys. Chem. Ref. Data 50, 033104 (2021): review, recommended values.

• Transcribed (Table 3, tbl_9524b9b87512, cells file; image checked): A_eps He 0.51725408(5) (Puchalski et al. 2020, not in the curators’ library; reproduced), Ne, Ar (= gaiser_2018; reproduced); A_R at 632.9908 nm He 0.52025565(5) (Rourke’s assembly of Puchalski 2016 + 2020 + Pachucki retardation; check), Ne, Ar, N2 (= egan_2019; reproduced); B_R N2 0.81(20) cm^6/mol^2 at 302.919 K (Achtermann via Egan 2016; reproduced). Text (pp. 12-13): Ne A_R 1.000249(14) at 632.9908 nm and 0.9956018(34) at 1550 nm (Rourke’s derivation; check); Egan 2016 N2 A_R 4.446139(16) at 302.919 K (reproduced).

• Format needs: A_mu / chi_0 (He -7.921(4)e-6, Ne -3.1713(71)e-5, Ar -8.09(57)e-5 cm^3/mol), C_R (Ar -85.4(20) at 303 K; N2 -89(10) at 302.919 K; text: Ar -86.6(20) at 323 K, -79(10) at 298 K; N2 -85(10) at 298 K), the C_eps linear fits and Table 4, D_eps, density virials: recorded in notes only.

• 632.9908 nm assumed vacuum (not stated). All uncertainties standard (p. 4).

• Status: open.

TC-115 egan_2019

• Egan, Stone, Scherschligt & Harvey, J. Vac. Sci. Technol. A 37, 031603 (2019).

• Transcribed (Table III, tbl_6d3145de2fcf, CSV; image checked): A_R at 632.9908 nm, 293.1529 K, this work Ne 1.000211(16), Ar 4.195685(64), Xe 10.39081(16), N2 4.446107(68), CO2 6.64343(11), N2O 7.49921(12) (primary); 25 literature values, reproduced (Egan & Stone 2011 as adjusted by +19.3e-6: check). Text p. 12: Ne 1.00028(6), Ar 4.1956(6) (the authors’ dispersion-corrected Gaiser values; check).

• Structural fix: the CSV merges each gas’s rows into one cell (values run together, references run together); the script splits on the uncertainty parentheses and “(Ref. n)” and checks the counts; image checked.

• Formulas: Eq. (3) with Table I c_1, c_2, c_3 per gas (six, no form: a pressure-refractivity relation, not dispersion). Check: 2RT/(3 c_1) reproduces Table III to 4e-7 for all six gases.

• Literature stored at 633 nm (caption wording) without temperatures (matters for N2). Egan treats all literature uncertainties as standard; Achtermann’s may be 3 sigma.

• Supplementary n - 1, p, T data are not in the curators’ library.

• Status: open.

TC-116 egan_2011

• Egan & Stone, Appl. Opt. 50, 3076 (2011) (UNVERIFIED in the curators’ library; citation from egan_2019’s Ref. 50 and the pdf name).

• Transcribed (Table 2, tbl_7d11225de36b, cells file; image checked): (n - 1) x 10^8 at 100 kPa, 20 C: this work N2 27368.2 +- 0.9, Ar 25838.9 +- 0.9 (k = 2, p. 7; primary); Birch, Hou & Thalmann, Achtermann rows (the authors’ conversions of those A_R; reproduced, level not stated). Text p. 7: A_R N2 4.44585, Ar 4.19545 cm^3/mol (U = 1.2e-4, k = 2; check).

• Wavelength choice to confirm: the paper says “632.8 nm” (the He-Ne air label); stored as 632.9908 nm vacuum on egan_2019’s statement (p. 12) that the 2011 work was “at the same wavelength”.

• Known bias: Egan et al. 2019 revise these A_R by +19.3e-6 (T - T_90 and a blundered helium-permeation extrapolation) and say 2019 supersedes 2011. The refractivities presumably share the bias (about 5e-9 in n - 1, inside U = 9e-9); kept as printed and primary: to decide whether to scale them or demote them.

• Check (2026-09-25): the package’s real-gas conversion of the refractivities gives alpha within 8 ppm (N2) and 16 ppm (Ar) of the paper’s A_R (different virials).

• Status: decided (2026-09-25): demoted to check, superseded by egan_2019.

TC-117 yang_2018

• Yang, Li & Wei, Sci. Rep. 8, 16447 (2018). No datasets: ambient air only (group index at 1530.8 nm, figures only). Record with notes; nothing to verify beyond that.

• Status: open.

TC-118 hohm_2012

• Hohm & Thakkar, J. Phys. Chem. A 116, 697 (2012) (UNVERIFIED; volume/page from the pdf download stamp, DOI candidate 10.1021/jp2094438).

• Transcribed (Table 1 continued, tbl_9ebc9ba30435, cells file; image checked): static alpha_lit (a.u.) He 1.3832(1) exp / 1.383191(1e-6) theory; Ne 2.66110(3) exp (= gaiser_2010) / 2.661(5); Ar 11.078(10) / 11.085(6); Kr 16.782(5) / 16.80(13); Xe 27.078(5) / 27.06(27). All reproduced (Thakkar & Lupinetti 2006 TL-2/3/4, not in the curators’ library; Ne exp from gaiser_2010). Error-estimate level not stated.

• Structural: the second (theory) row of each atom has an empty atom cell (label carried down); the group label “18” sits on the At row in the cells (image: on He); unused.

• Nothing original here for the noble gases (the paper’s model is a crude 101-element fit).

• Status: open.

TC-119 kumar_2010_supplement

• Supplementary material of Kumar & Thakkar, J. Chem. Phys. 132, 074301 (2010) (the curators’ library record is UNVERIFIED and untitled; page 1 names the paper).

• Transcribed (Table I, tbl_8fedf8f12d10, CSV; image checked, every cell): IDOS per interval [E_j, E_j+1] (eV), idos_<gas> Ne 31, Ar 27, Kr 29, Xe 32 intervals, and the discrete sums discrete_<gas> (0.2800, 0.7623, 1.092, 1.597); all check (constrained DOSD, tied to refractivity data). Discrete + IDOS = 9.99956, 18.0006, 35.9994, 53.9990 (S(0) = N).

• Format need: an interval-integrated oscillator strength has no quantity; oscillator_strength at the interval’s lower edge is used.

• Formulas: four ten-term pseudospectra, form oscillator, energy_unit hartree. Columns swapped in the original (checked on the pdf page image): the column headed “f” holds the energies (hartree) and “E” the strengths. Evidence: “E” sums to N; only this reading reproduces kumar_2010’s S(k) for integer k = 2 … -10 to <= 4e-4 (Table I rounding). The record’s terms are relabelled accordingly (every coefficient as printed). The Kr list is not an extracted table in the curators’ library (extracted as a line of text); checked against the pdf page image. range_nm lower bounds (81, 116, 136, 162 nm = 1.1 x the lowest pole’s wavelength) are the extractor’s choice.

• Refractivity constraints and initial-data sources per gas (Table I notes a-d) recorded in the source notes: Ne 302.2, 546.2 nm (cuthbertson_1932); Ar 325.1, 633.0 nm (Hohm 1994, not in the curators’ library); Kr 177.1, 263.2 nm (smith_1976); Xe 170.2, 253.7 nm (bideau_mehu_1981).

• Status: open.

TC-120 reinsch_1985

• Reinsch, J. Chem. Phys. 83, 5784 (1985); omega in hartree, alpha in a.u.

• Transcribed (cells files; images and pdf pages checked): Table I He (this work SCF excluded, MC-SCF check; Chung, Starkschall & Gordon, Pade “Expt” reproduced; 11/11/ 11/11/8 points); Table III Ne (MC-SCF standard and extended basis, check, 9 points each; “Expt” reproduced, 4 points); Table V CH4 (MC-SCF check; “Exp” from Landolt-Bornstein two-term fits, reproduced; 7 points each); Table VI Ne static (this work’s 2.567 excluded as a duplicate; Werner & Meyer SCF, PNO-CI, CEPA reproduced); Table V note f CH4 PNO-CI/CEPA 16.39/16.53 (inline, reproduced).

• Structural / typed from the image: Table II’s lower block (H2 mean at R = 1.4 bohr, vibrationally averaged v = 0 components and mean, v = 1, 0-1 transition, experiment) is missing from the curators’ extracted table; its values are entered inline, read from the table image and the pdf page (p. 5789). Check: every printed mean equals (alpha_par + 2 alpha_perp)/3 of its printed components to the last digit. Datasets: v0_mean_H2 (check), langhoff_karplus_v0_H2 (reproduced), kolos_wolniewicz_v0_H2 (note f, reproduced), mean_R14_H2, victor_browne_dalgarno_R14_H2, v1_mean_H2 (excluded). The upper block (fixed-R tensor components) is not extracted.

• All of this work’s values are checks (errors 1 % He, 4-9.5 % Ne/CH4 by the author’s account); to decide whether to promote He MC-SCF.

• Ne “Expt” source ambiguous: Table III note a “as cited by Ref. 20” (Starkschall and Gordon) vs the text “as given by Langhoff and Karplus (Ref. 21)”.

• Status: open.

TC-121 shelton_1982

• Shelton & Buckingham, Phys. Rev. A 26, 2787 (1982). No datasets (format need): the linear-dispersion data are phase-match densities rho_opt at |Delta k|_opt = 2465.0 +- 0.5 m^-1 (Table II at 514.5 nm: He, Ar, H2, N2, CO2, CH4, SF6; rho_3K of CH4 at 7412.4 m^-1; Table III: He and CH4 at seven wavelengths, the 694.3 nm values from Finn & Ward 1971 and Miller & Ward 1977). No quantity holds a density at a stated |Delta k|; no ratios are printed. All values are transcribed in the record’s notes from the CSV cells (images checked).

• Wavelengths are argon-ion air wavelengths (514.5 …), not vacuum.

• Status: open.

TC-122 shelton_1986_krxe

• Shelton, J. Chem. Phys. 84, 404 (1986). No datasets: hyperpolarizability ratios only; no phase-match densities or coherence lengths are printed. gamma ratios and fits in the notes (image checked) for later.

• Status: open.

TC-123 shelton_1989

• Shelton, Phys. Rev. Lett. 62, 2660 (1989).

• Transcribed (Table I, tbl_96462ca3eb80, cells file; image checked): Delta alpha_Ne / Delta alpha_He = rho_He/rho_Ne (phase_match_density_ratio of He, reference Ne, as in shelton_1990, TC-27), rows by vacuum wavenumber: present work 7581, 9395 cm^-1 (check: identical to shelton_1990/density_He_over_Ne, the same measurements); Shelton & Lu 1988 at 16817, 19430, 20487 cm^-1 (reproduced; original not in the curators’ library); Finn & Ward 1971 at 14399 cm^-1 (excluded: computed from literature refractive indices).

• Misprint (no erratum needed): lambda “488.8” for the 20487 cm^-1 row (nu and nu_L^2 = 6 nu^2 = 25.183e8 both give the 488.0 nm argon line); wavenumbers are the abscissa.

• Double counting to settle: shelton_1989/present and shelton_1990/density_He_over_Ne are the same measurement; 1990 kept primary, 1989 check.

• Status: open.

TC-124 mizrahi_1985_arn2o2

• Mizrahi & Shelton, Phys. Rev. Lett. 55, 696 (1985) (UNVERIFIED; citation from the curators’ reading list and Shelton 1986’s Ref. 15). No datasets: nonlinear-susceptibility ratios only. Table III’s omega_0 (one-pole fits of Landolt-Bornstein linear-dispersion data, He 206, Ar 138, H2 113, D2 115, N2 126, O2 119) recorded in notes; header “10^13 cm^-1” is a misprint for 10^3 cm^-1. Table I prints Ar 20.99(16) at 600.0 nm, presumably 30.99 (not refractive data; noted for later).

• Status: open.

TC-125 Other records affected by TC-105 to TC-146 (not edited)

• Reproductions now superseded by the originals transcribed here: lesiuk_2020/gaiser_2018_Ne (2.661057(7) a.u.) and lesiuk_2023/gaiser_2018_Ar (11.077183(27) a.u.) by gaiser_2018/molar_polarizability_Ne|Ar; lesiuk_2023/egan_2019_Ar (11.22431(17) a.u.) by egan_2019/A_R_Ar; lesiuk_2023’s Eq. (38) formula and its alpha_theory dataset use Gaiser’s alpha_0.

• lesiuk_2020/chan_1992_Ne (S(-4) = 2.938, S(-6) = 5.137) cites Chan et al. PRA 45, 1420 (now chan_1992_neon), but the paper prints no moments: origin unknown.

• wang_2021/lupinetti_hohm_Ar (11.085(60)) cites Hohm & Thakkar 2012 (hohm_2012/ theory_Ar, itself Thakkar & Lupinetti’s TL-3).

• shelton_1990/density_He_over_Ne and shelton_1989/present_He_over_Ne are the same measurement (identical values): 1990 kept primary, 1989 check.

• Notes now out of date: kumar_2010 (pseudospectra not in the curators’ library -> now kumar_2010_supplement), chan_1992 (the neon part II not in the curators’ library -> now chan_1992_neon), the register’s TC-99 (neon EUV oscillator strengths now available).

• Status: open.

TC-126: neon’s extreme-ultraviolet distribution, and what it says about TC-92

• Where: data/gas/euv/Ne.toml, optmat.gas.euv._lines (NIST lines may now take a total and a pseudo_line_ev), tests/test_euv.py, docs/euv.md.

• Construction: NIST’s 17 ground-state lines with f (sum 0.246); a pseudo-line of 0.046 at 21.55 eV for the unlisted higher members (Chan’s discrete total 0.292(15) to 21.616 eV less the NIST sum; placed just below that midpoint, a choice to review); Chan’s TRK-normalised continuum 21.6-250 eV; Henke’s f2 above; scaled by 1.054 to Lesiuk’s S(-2) = 2.66080.

• Results: S(0) = 9.72; below threshold 0.01-0.02 % from fit/Ne in the infrared and visible, -0.34 % at 120 nm. S(-4) = 2.826 and S(-6) = 4.765, 0.8 % (3.4 sigma) and 3.4 % below Lesiuk’s ab initio values. So the photoabsorption route puts neon’s dispersion below theory, while the refractometry puts it above (TC-92): two independent experimental routes on opposite sides of the theory. The sensitivity of S(-4) to the pseudo-line position, the 5.4 % scale and the NIST line strengths (grades A-D+) is not yet quantified.

• Also (TC-125): lesiuk_2020/chan_1992_Ne attributes S(-4) and S(-6) to Chan et al. 1992, but that paper prints no S(k); the values are presumably Lesiuk’s own integration of Chan’s data. The record is left as reproduced; to review.

• Status: open.

TC-127: Kumar & Thakkar’s 2010 pseudospectra against the fits

• Where: kumar_2010_supplement/pseudospectrum_* (formulas), docs/accuracy.md.

• Numbers (pseudospectrum over fit, electric against refractive, the magnetic term below 40 ppm): level +0.31 % (Ne), +0.015 % (Ar), +0.18 % (Kr), +0.32 % (Xe), rising towards the ultraviolet (Xe +0.75 % at 150 nm); GVD at 800 nm +0.49, -0.25, +0.34, +0.71 %. The level differences follow the classical refractometry Kumar & Thakkar constrained to (Cuthbertson, Smith, Bideau-Mehu), which the fits scale freely (TC-93); for xenon the GVD difference exceeds the fit’s working estimate (0.4 %).

• Status: open.

TC-128 alms_1975

• Transcribed: Table I (tbl_24841f218204, cells file only; image checked), mean polarizability alpha (A^3) of N2 (4579, 4880, 5148->5145, 6328 A, inf), N2O and CO2 (4579, 4880, 5145, 5682, 6471 A, inf): 5 + 6 + 6 points. The inf rows are in the files but in excluded_rows (electronic zero-frequency extrapolation, method not stated). Table V (tbl_e60dab9bc511, image checked): Stuart’s (1952) static electronic alpha for N2 1.76, N2O 3.00, CO2 2.65, as reproduced/excluded single points.

• All Table I alphas of the curated gases are Landolt-Bornstein’s refractive indices converted with n - 1 = 2 pi N alpha (p. 3): use reproduced, reproduced_from the LB volume (not in the curators’ library). Uncertainty: “0.5%-2.0% from the smaller to the larger molecules” (p. 3): 0.5 % for N2 (not stated level), 2 % bound for N2O, CO2 (my reading of the range).

• Structural: nitrogen’s alphas print the last digit as a subscript (guard digit); the cells read it as an ordinary digit, kept. Molecule name only on the block’s first row (row span).

• Erratum: alpha_N2 row 5148, wavelength 5148 -> 5145 (the Ar+ line; every other molecule prints 5145; image shows 5148).

• Wavelengths: laser lines to 1 A, recorded as standard air.

• Not extracted: depolarization ratios (Tables I, II; no quantity), anisotropies and tensor components (for later), Table III band oscillator strengths (3x the orientationally averaged f of Lawrence 1968 / Rabalais 1971: reproduced, rescaled), Table IV static anisotropies.

• Duplicate copy in the curators’ library: text identical but for figure ids/descriptions; Table I cells identical (checked programmatically).

• Status: open.

TC-129 cuthbertson_1920

• Not doubled: unlike cuthbertson_1910, the tables are mu - 1 itself (Table I 45,050e-8 at 5461 A = text’s mean 4505e-7 for CO2; CH4 44,150e-8 = 4415e-7). The expected “2(mu - 1) convention as in cuthbertson_1910” does not apply; to confirm.

• Transcribed (images checked): Table I (tbl_475eaffb74ab) CO2 observed + calculated, 8 + 8; Table III (tbl_ae9680fa9a81) CH4 observed + calculated, 8 + 8; earlier CO2 values at 5461 A (tbl_b6b36b76ac3b), six reproduced single-point datasets (Mascart 4554, Perreau 4515, Walker 4510 +- 5, Stuckert 4511, Grueschke 4512, Koch 4505). Thousands commas dropped. Columns 5-6 of Table I (hydrogen-density scale, column 2 x 0.99246) not extracted. Earlier CH4 values (no wavelength stated) not extracted.

• State: CO2 at 0 C, 76 cm, reduced with Chappuis’s (1 + 0.00371 t) and Leduc’s compressibility: density real. CH4: state and reduction not stated; 1 atm 0 C assumed, density unknown.

• Uncertainty: rms of calc - obs (CO2 2.2, CH4 0.71 x 1e-8); scale: half-range of the absolute values (CO2 0.10 %, CH4 0.057 %). My choices (paper states none).

• Wavelengths printed to 1 A (5770 = Hg 5769.6): standard air, as printed.

• Formulas: co2_1920 reproduces the calculated column only to 1.6e-8 (not rounding; a best one-pole fit to the column itself leaves +-1.2, so no single coefficient correction); ch4_1920 reproduces to 0.7e-8 (V = 3e10). Reproduced 1909 formulas for H2, O2, N2 (Proc. R. Soc. 83, 151; not in the curators’ library) recorded, unchecked.

• Skipped: CO (not curated), carbon-atom formulas, lambda_0 tables.

• Status: open.

TC-130 watson_1936

• State: (mu - 1) at 25 C, 760 mm, reduced to the ideal gas with each gas’s measured compressibility (p. 7): state {1 atm, 25 C}, density ideal. Vacuum wavelengths (p. 3). 0 C values (Tables V, VI) = 25 C x 1.09157.

• Transcribed (images checked): Table II (tbl_56f6683d6c06 + tbl_5065fe5949d9) CH4, SF6, CO2 at 6440.24, 5462.25, 5087.23, 4801.25, 4359.56 A, 5 points each (primary). Structural: value and the second-line difference (calc - obs x 1e8) run together in the cells (“402·94-7”, “411·130” = 411.13 / 0); parsed as value with two decimals. Table III (tbl_97d70f8c24f3): own N2O 463.4, N2 274.1 (primary, 1 point each); Cuthbertson’s O2 248.7, N2O 464.6, N2 274.5 as recalculated to 25 C ideal (reproduced; O2/N2 from the 1909 paper, N2O from cuthbertson_1914). Table V (tbl_23af967b0794): Tausz & Hornung CH4 442.40 (compressibility-corrected by W&R, density ideal), Friberg CH4 443.56, Klemm & Henkel SF6 771.1 (reproduced, density unknown); W&R’s own CH4 443.07, SF6 765.8 (check). Table VI (tbl_06bdd0f09e6a) CO2 447.3, N2O 507.4, N2 299.2 (check). Table VII (tbl_d67d2c70949c): P_A + P_E (dielectric static molar polarization, cm3/mol, wavelength inf) for H2, CH4, SF6, O2, CO2, N2O, N2, He, Ne, Ar (“A”), Kr, Xe (reproduced from W&R’s earlier dielectric papers, revised). CH4 printed twice in Table VII (identical), taken once.

• Uncertainty: 0.06e-6 absolute from “accurate to 0.1 band” with the 1 m tube (my conversion; reading precision only; purity dominates, p. 11).

• Formulas mu - 1 = A/(B - n^2), c = 2.9986e10: sf6 and co2 reproduce the green and violet values and the printed differences to 0.6e-8. ch4 does not: 405.919 at 5462.25 vs printed 405.90; differences -3.5/+3.0/+3.9 vs printed -7/-2/+3; no single misprint explains it (405.90 is what Table V uses). n2, n2o, o2 (Table III): W&R’s A with Cuthbertson’s B; reproduce the green values and A/B.

• Flag: Table VI N2O 507.4 is neither 463.4 x 1.09157 (505.8) nor 464.6 x 1.09157 (507.1); no correction (check dataset).

• He dielectric P_A + P_E = 0.54 is 4 % above the curated A_eps (puchalski_2016); the others agree with orcutt_1967/gaiser_2010 to <1 %.

• Not extracted: Table I (C2H2), Table IV (compressibilities, listed in notes), P_E and P_A (derived), B of Table V, non-curated gases.

• Status: open.

TC-131 vukovic_1996

• Transcribed (images checked): Tables 1 (tbl_dc762adbe049) and 2 (tbl_786fca828745), SF6 only (SOF2 skipped): refractivity x 1e6 at 25 C, 101 325 Pa (632.99 nm 702.96 +- 0.5, 1300 nm 694.0 +- 1; primary, 2 points), at the measurement temperature (708.05 at 22.9 C; 698.7 at 21.8 C; check, one dataset each), A_R (11.336 +- 0.008, 11.18 +- 0.016 cm3/mol; check). Table 3 (tbl_d5adcde5ec76): Buckingham & Graham A_R 11.34, B_R 29 +- 3 at 299 K; St-Arnaud & Bose A_R 11.348 +- 0.021, B_R 36 +- 1.8 at 323 K (reproduced; also in achtermann_1991, which prints B&G’s B_R as 29 +- 5).

• Density real (n - 1 = A p/RT + B (p/RT)^2 of the real gas); vacuum wavelengths (Eq. 6).

• Choice to confirm: the three quantities come from one fit per wavelength; the 25 C refractivities are primary, the others check.

• Flag: the 1300 nm “698.7 at 21.8 C” disagrees with the printed A, B at 21.8 C (701.4) but matches them at 22.9 C (698.75); not corrected. Table 3’s A_R header “10^-5” should be 10^-6.

• Formulas (density expansions at one wavelength, not dispersion): virial_632 reproduces 708.05 and 702.96 (703.00); virial_1300 reproduces 694.0 (693.8) only.

• Status: open.

TC-132 sneep_2005

• Transcribed: Table 2 (tbl_f4af3ec06557, cells only; image checked) at 18 788.4 cm^-1 (532.2 nm): measured sigma (1 sigma) Ar 4.45(0.3), N2 5.10(0.24), CO2 12.4(0.8), CH4 12.47(0.23), N2O 15.90(0.08), SF6 32.3(0.5) x 1e-27 cm2 (primary, king_factor = Table 2’s F_k); n-based column (check). Text p. 15: O2 sigma_R = 4.50 +- 0.15 from the three-component (CIA) fit, inline (primary). CO skipped. Wavelength-resolved Ar/N2/CO2 data are figures only.

• Formulas (all checked against Table 2’s (n - 1), F_k and n-based sigma, which Eq. (2) reproduces to 0.15 %): ar_eq9 (= peck_1964 15 C, exact), n2_eq10 (= peck_1966 0 C formula x 273.15/288.15 ideal: B exact, A 6498.34 vs printed 6498.2), n2_eq11 (Bates), n2_king_eq12, co2_eq13, co2_king_eq14, ch4_eq18 (fit to Hohm 1993), n2o_rho_eq19, n2o_eq20 (fit to alms_1975 = Landolt-Bornstein), sf6_eq21 (fit to vukovic_1996), o2_eq23, o2_king_eq24, and the Table 1 power laws (6).

• Misprints found (formulas are unstructured, so recorded in the check text, not as corrections): Eq. (13) scale 1.1427 x 10^6 must be 10^3 (gives Table 2’s 427e-6); Table 1 sigma_bar unit 10^-47 must be 10^-45; Table 1 N2 delta_n-based 0.974 must be 0.0974 (reproduces Table 2’s 5.30 exactly); Eq. (23) numerator lacks x 10^12 (he_2021 quotes 2.480899e13); Eq. (24) last term nu^2 presumably nu^4; the n-based O2 sigma “4066 x 10^-27” (page image) presumably 4.066, and it is not reproduced by Eqs. 23/24 with any N tried (2.96, 5.18, 4.66). O2 state of Eq. 23 taken from he_2021 (0 C).

• Status: open.

TC-133 ityaksov_2008

• Transcribed: Table 1 (tbl_0ec99fd2f68e, cells only; image checked), extinction cross sections x 1e-25 cm2, +- 1 sigma, 197.70-270.15 nm: measured N2 7, CH4 6, SF6 7 points (primary; king_factor 1 for CH4 and SF6, none for N2, whose Bates F_k varies); predicted N2/CH4/SF6 8 points each (check). Dashes skipped. Wavelengths taken as vacuum (not stated; < 200 nm must be vacuum).

• Formulas: n2_eq8 (their Sellmeier fit to griesmann_1999 “scaled to 293 K”; lambda unit not stated, only Angstrom works), n2_king_eq9 (Bates with 1.03 vs sneep’s 1.034), ch4_eq10 (= sneep eq18), sf6_eq11 (= sneep eq21, 4.996 -> 5), Table 2 power laws (3).

• Checks: the predicted CH4 and SF6 columns are reproduced exactly with N = 2.5469e19 (288.15 K), not the 293 K lab density (3.4 % high). N2 predicted reproduced to 0.5 % with the same N. Doubt: Eq. 8 as printed is 0.944-0.946 x griesmann_1999’s 273.15 K values everywhere, not the stated 293 K scaling (0.932) nor 288.15 K ideal (0.948).

• Text misprint: epsilon(N2) = 0.543 (p. 6) vs 0.534 (Table 2, Fig. 1 caption).

• Status: open.

TC-134 ityaksov_2008_co2

• CO2 deferred: all datasets use = “check”.

• Transcribed: the table (tbl_d53eeed0ae27; image checked), 22 wavelengths 197.70- 270.15 nm: measured extinction (+- 1 sigma) with the 16 rows below 202 nm in excluded_rows (absorption onset; fit range 202-300 nm), 6 kept; calculated Rayleigh sigma (22).

• Check: the calculated column is reproduced to its printed 0.1 at all 22 wavelengths with sneep_2005’s unrounded Eq. 13 (scale 10^3) and Eq. 14 and N(288.15 K); this paper’s Eq. 4 repeats the misprinted scale 1.1427 x 10^6 (must be 10^3) and rounds the poles; Eq. 3 rounds 1.1364 to 1.14.

• Formula power_eq6 (sigma_bar 1.78e-46, epsilon 0.625; 202-300 nm) recorded.

• Status: open.

TC-135 wilkinson_1960

• Transcribed: Table II (tbl_12497a3674f3; image checked), N2 (n - 1) x 1e7 at 0 C, 760 mm (ideal gas, p. 2), 22 vacuum wavelengths 1649.1918-2042.484 A (primary). Uncertainty: rms of the printed obs - calc, 5.9e-7 (the “+-0.13 %” of the abstract is the mean absolute obs - calc).

• Formula eq7 reproduces obs - calc to 1.1e-7 at 19/22 lines; off at 1938.890 (+1.9 vs +7), 1824.2994 (+3.5 vs +1), 1649.1918 (-11.7 vs -3): unresolved. koch_eq8 (reproduced, Koch 1912-24, “+ nu^2” as printed).

• Supersedes langhoff_1969/wilkinson_1960_N2 (22 values; identical except 1938.89 A: Langhoff 3.445e-4 vs original 3455e-7, image checked). heddle_1963 wilkinson_formula_N2 and peck_1966 formula wilkinson_1960 reproduce Eq. 7.

• Status: open.

TC-136 ingersoll_1954

• Transcribed (images checked): Table I (tbl_794626e36b6c) Verdet constants, micro-arcmin/(Oe cm), gas at 76 cm and 0 C (perfect gas), 13 filter wavelengths 3635-9875 A: He 12, Ne 13, H2 13, D2 13, N2 13, O2 13 points; Table III (tbl_b0f0c3f0522a) the same curves at 4360, 5460, 5780, 5893 A (4 each), de Mallemann’s values for Ne, H2, N2, O2 (3 each, reproduced) and Bizette-Tsai He at 5460 (1, reproduced). Butane skipped.

• All Ingersoll datasets excluded: the 1956 paper says the 1954 scale is 0.94 % low (multiply by 1.0094) and republishes the six gases. Checked: 1954 x 1.0094 agrees with 1956 to 0.25 % at the four visible lines and 0.4 % over 3635-9875 A, except O2 at 3635 A (0.9 %), D2 at 3635 A (0.44 %) and He at 9000 A (1 %) (second reading, TC-157).

• Not extracted: Table II (derived ratios), Table IV (pressure effect, same scale error).

• Wavelength medium not stated: standard air as leonard_1974.

• Status: open.

TC-137 ingersoll_1956

• Transcribed (images checked): Tables I (tbl_67fd0411dc50: He, Ne, Ar, Kr, Xe), II (tbl_321e7af15c60: CH4 only), III (tbl_de2fd916f64f: H2, D2, N2, O2, N2O, CO2, SF6; CO and freon-12 skipped). Per gas: dispersion_<gas> = the lower part (relative to 5780 A, 17 wavelengths 3635-9875 A; He 16) as printed with scale = V(5780) of the upper part (primary); absolute_<gas> = the upper part, 4 lines (check).

• Format workaround to confirm: no quantity for a relative Verdet constant, so the scale carries the printed V(5780) (numbers typed from the extracted upper-part file; the generator read them from the CSVs). The product equals leonard_1974’s Table V for the noble gases.

• Uncertainty: relative 0.5 % (mean departure of measurements from the smoothed curves, p. 2), systematic 1 % probable error -> 1.48 % one sigma. My reading.

• CO2 9000 A relative value 0.373 excluded (breaks the smooth curve; N2 with the same neighbours has 0.403); presumably a misprint, not corrected.

• Supersedes leonard_1974 verdet_ingersoll_liebenberg_{He,Ne,Ar,Kr,Xe} (reproduced there) and ingersoll_1954 (scale x 1.0094).

• Status: open.

TC-138 shelton_1985_sf6

• Transcribed: the table (tbl_72ec8b2e57c2; image checked), Delta alpha_SF6 / Delta alpha_N2 = rho_N2/rho_SF6 at 670.0, 650.0, 620.0, 514.5, 488.0, 457.9 nm (+-0.003), 6 points, filed as N2 with reference_gas SF6 (shelton_1990 convention, TC-27). 694.3 nm row (gamma only) skipped.

• Wavelength medium not stated: standard air assumed (the 1986 papers of the series say “wavelength in air”; Ar+ lines as quoted).

• Not extracted: gamma values and gamma fit.

• Status: open.

TC-139 shelton_1986_ch4

• Transcribed: Table I (tbl_9090f1c5cfc2; image checked), Delta alpha_CH4/Delta alpha_N2 = rho_N2/rho_CH4, 12 points 476.5-671.7 nm; row id the air wavelength, abscissa the printed vacuum wavenumber (cm-1). Error bars “may be too pessimistic by as much as a factor of 7” (kept as printed).

• Formula misprint: Fig. 2 fit C = 1.69e-20 cm^4 (page image) must be 16.9e-20: as printed it misses the data by 0.016-0.063; with 16.9e-20 all 12 within 0.0018. Recorded in the formula’s check (unstructured formula).

• Status: open.

TC-140 shelton_1986_co2

• Transcribed: Table I (tbl_ba9d1caa914e; image checked), Delta alpha_CO2/Delta alpha_N2 = rho_N2/rho_CO2, 5 points 488.0-692.9 nm, abscissa vacuum wavenumber. Error bars “may be too pessimistic by as much as a factor of 5”.

• Formulas: vibrational_eq14 (+0.70e-34 nu^-2), n2_eq15 (Delta alpha_N2 from shelton_1986, reproduced), electronic_fit (Fig. 3), electronic_eq16a, landolt_eq16b (LB-derived, reproduced). electronic_fit + Eq.14/Eq.15 reproduce the 5 ratios to 0.0006; Eq.16a/Eq.15 agrees with electronic_fit to 0.3 %.

• Not extracted: Table III (IR transition moments, Raman polarizabilities; alpha 293.3e-42 SI at 632.8 nm from LB), gamma data.

• Status: open.

TC-141 stoll_1922 (German)

• Transcribed (images checked): means and calculated columns of Table V (electrolytic O2, 24 + 24), Table VII (gasometer N2, 24 + 24), Table IX (cylinder CO2, 24 + 24); means of Tables VI (cylinder O2, 96 % O2 + 4 % N2; excluded) and VIII (cylinder N2, ~0.5 % O2; excluded), 24 each; Koch’s 4 CO2 values (reproduced). (n0 - 1) x 1e7 at 0 C, 760 mm; gas-specific expansion coefficients: density real. Air (Tables I-IV, IIIa/b) skipped; no argon gas data (argon only as a line source).

• Wavelengths: the gas tables’ rounded labels mapped to Table II’s full air wavelengths (row id = label); the formulas reproduce the calc columns only with those (air) wavelengths.

• Structural (misreads in the curators’ extracted table, fixed in the script with the image): Table IX 6678 A calc 4473,91 -> 4473,31; Table VIII 7065 A 2951,82 -> 2951,32.

• Text misprint: “0 C und 750 mm Hg” (p. 5) for 760.

• N2 excluded (judgement): dispersion 4388-9224 A 91.1e-7 vs peck_1966 65.7e-7 (+0.10 %, -0.37 %, -0.76 % at 4388, 5876, 9224 A); Stoll’s air Cauchy coefficient 16.17 is below both his N2 22.65 and O2 20.07 (impossible for the mixture); Wilkinson 1960 remarks the same. To confirm.

• Formulas: o2, n2, co2 (checks in the record; calc-column discrepancies at O2 4713, 7273 A and CO2 5015, 8521, 8667 A are the author’s arithmetic), reproduced Scheel N2, Cuthbertson O2 (Stoll quotes n0^2 = 12807e27; cuthbertson_1920 quotes 12,804e27), N2, CO2.

• Uncertainty: relative 0.01 % bound; systematic 0.02 % bound -> 0.0115 % one sigma.

• Status: decided (2026-09-25): gasometer N2 excluded as proposed; electrolytic O2 a validator (TC-147).

TC-142 essen_1953

• Transcribed: the table (tbl_648ebcc40786, cells only; image checked): present (n - 1) x 1e6 at 0 C, 760 mm: O2 266.2, N2 294.1, H2 136.0, D2 134.8, He 35.0 (one point each, primary, sigma = “limits of error including systematic errors”, level bound); Essen & Froome 1951 at 24 GHz: O2 266.4 +- 0.2, N2 294.1 +- 0.1 (reproduced). Water vapour and air skipped.

• Density: O2, N2 real (Barrell & Sears equation); H2, D2, He ideal (p. 4).

• Frequency: text/abstract 9200 Mc/s, table header “9000 Mc/s”: 9200 taken; the wavelength column is c/f in m, computed in the script (newell_1965 convention).

• O2’s microwave n includes its paramagnetism (not separated).

• Supersedes newell_1965 essen_1953_{He,H2,N2,O2} (which use nominal 9 GHz).

• Status: open.

TC-143 zhang_2011

• One-page reply to kren_2011; no values, no corrected coefficients. Short record, no datasets; its cautions on zhang_2008’s O2 formula (valid 740-860 nm only; NBS compressibility; synthetic-air O2 content) quoted in notes. Citation from the page footer (unverified record): Appl. Opt. 50, 6486 (2011).

• Status: open.

TC-144 ciddor_2002

• No datasets. Formulas: edlen_co2 (Eq. 4) and old_co2 (Eq. 5, = old_1971 x 1000). Eq. 4 is stated at 0 C but its coefficients are Edlen’s 15 C air formula + CO2 correction (42426e-8 at 633 nm vs Old’s 44794e-8 at 0 C; x 288.15/273.15 gives 44756e-8, the text’s “< 3e-7” agreement): recorded with state 15 C; the constant 22822.1 is 5.0 below 8342.13 + 14485 (unexplained).

• Virials: only N2’s B_R rho0 / A_R ~ 8e-6 and “~10 %” uncertainty quoted (notes).

• Citation volume/page from marchetti_2006’s reference list (unverified record).

• Status: open.

TC-145 egan_2026

• Inline (text): A_R (A_303, 303 K) of CO2 6.64337 / 6.50541 cm3/mol and O2 4.027716 / 3.968990 at 632.9908 / 1542.383 nm (vacuum); combined u 4.6e-6 and 7.2e-6 relative (1 sigma). A_theta values in notes.

• Formulas: o2_sellmeier (structured dn_sigma2, 20 C, 100 kPa, density real; through the package’s CoolProp density it returns A_303 to 6e-6; A_theta ignored, a 2e-5 effect); b_R(sigma, T) formulas for CO2, O2, N2, Ar (unstructured; B_R = A_R b_R).

• Not extracted: B_rho tables (equation of state), N2+O2 mixtures, dry air, water (Table 5), Table 6 beta (values listed in notes; no vocabulary quantity).

• Format need: a quantity for the dispersion of B_R (Egan’s beta, or b_R^(2)), and for A_theta (the temperature dependence of A_R).

• Status: open.

TC-146: the CH4, SF6 and N2O fits (with the infrared bands)

• Where: data/gas/fits/{CH4,SF6,N2O}.toml, data/gas/models/fitted, data/gas/defaults.toml (the fits are now the recommended models), docs/accuracy.md.

• CH4 (reduced chi-squared 0.23): the Cuthbertsons’ 1920 and Watson & Ramaswamy’s visible dispersion (free scales), Achtermann, Shelton’s 14 ratios to nitrogen; two effective oscillators; HITRAN bands below 4500 cm^-1 (1.8 % of the infrared strength left out). Reinsch’s MC-SCF theory is -12 % (his stated 1-10 %).

• SF6 (4.15): Swift, Vukovic, Achtermann, Shelton 1985 (6) and 1990 (2) ratios. Watson & Ramaswamy’s dispersion is a validator: chi-squared 135 for 5 points even with a free scale. One effective oscillator sits at its lower energy bound (0.25 hartree, a modelling choice) with f = 0.006, and is needed (chi-squared 509 without it). The two Shelton sets prefer HITRAN’s SF6 strengths times 1.036 +- 0.009 (chi-squared 21 against 50 at 1.0); HITRAN’s own two cross-section sets differ by 1 %. The strengths are kept at HITRAN’s (an independent measurement); to decide. SF6’s GVD crosses zero near 1.2 um (the infrared term); He et al.’s formula gives +55 % at 800 nm.

• N2O (3.36): the Cuthbertsons’ 1914 dispersion (shape) and the 633 nm metrology (Birch, Egan); two effective oscillators with the TRK sum S(0) = 22 +- 2.2 as a prior (without it one runs to 6.9 hartree with f = 661 at the same chi-squared). The electronic S(-2) = 19.72 against Zeiss et al.’s DOSD 19.70. Watson & Ramaswamy’s 546 nm value (+0.09 %, 7 sigma) is a validator. The dispersion rests on one visible dataset.

• Status: decided (2026-09-25): keep HITRAN’s SF6 band strengths fixed; record the 3.6 % tension; revisit once the Rayleigh data can be fitted.

TC-147: the N2 and O2 fits with the data of TC-105 to TC-146

• Where: data/gas/fits/{N2,O2}.toml; O2, CH4 and SF6 refitted after N2 (their ratio partner).

• N2: Egan et al.’s 2019 633 nm value added (chi-squared 0.28); the Wilkinson validator now uses the original (wilkinson_1960, 0.5 % above the fit in the VUV) and Essen’s microwave value is a validator (+0.13 %).

• O2: Egan et al.’s 2026 molar refractivities at 633 and 1542 nm added (chi-squared 0.03 for both, Birch 0.02): the level no longer rests on Birch alone (the O2 half of TC-101 is resolved), and the two wavelengths fix the near-infrared dispersion (largest leave-one-out GVD shift 0.07 %, was 0.94 %). Stoll’s 1922 dispersion is a validator: it arches +-250 ppm about the fit (chi-squared 125 for 24 lines with a free scale); Egan’s A_R is at 303 K (the format has no temperature for A_R; its temperature dependence, A_theta, is 2e-5, below its effect here).

• Status: open.

TC-148: the CO2 fit (taken up 2026-09-25)

• Where: data/gas/fits/CO2.toml, data/external/hitran/CO2_bands.csv (HITRAN2024, 540624 lines, 0-11000 cm^-1), data/gas/defaults.toml (now fit/CO2), docs/accuracy.md.

• Fit (reduced chi-squared 3.4): Old, Gentili & Peck 480-1600 nm (shape, 7 ppm), the Cuthbertsons (1920), Watson & Ramaswamy, Swift, Birch, Achtermann, Egan 2019 and 2026 (633 and 1542 nm), Zhang, Shelton’s ratios (488-1319 nm), Marchetti’s CO2-laser values (9.2-10.7 um); two effective electronic oscillators; HITRAN bands below 7000 cm^-1.

• The infrared strength is what the data want: a scale of 0.97 or 1.03 on it raises chi-squared from 520 to 6900 and 2200 (Newell’s microwave value and Old’s near infrared pin it). The combination bands at 4978-6972 cm^-1 are needed (cutoff 4500 cm^-1 leaves Old’s 1.3-1.8 um points off); Old’s 1695 and 1817 nm points, just above the 2 um bands, are outside the fit (one pole per band does not represent a band edge).

• Validators: Stoll 1922 (as for O2), Newell & Baird’s microwave value (+523 ppm, 6.6 sigma; as for H2), Old’s formula and Watson’s 0 C value.

• Remaining tension: Old’s shape (+-20 ppm, 3 of their sigma), Marchetti (+1.7 sigma each), Egan 2026 (26.7 for 2), Zhang (-723 ppm).

• Missing for CO2 (not in the curators’ library): Bideau-Mehu et al. 1973 (the ultraviolet), Simmons 1978, Willetts & Harris 1982 (10.6 um).

• Status: open.

TC-149 willetts_1982

• Transcribed: Table 2 (JSON only; image checked), the three pure gases’ measured (n - 1) x 10^6 at 10.59 um: He 34 +- 2, N2 275 +- 10, CO2 407 +- 10; mixtures and the Gladstone-Dale constants not extracted.

• State: the text’s 103 kPa and 19 C (p. 10); the caption’s “1.03 kPa” is a misprint (the values are of order 1 atm refractivities). Ideal gas (not stated; immaterial at this precision). 10.59 um taken as vacuum.

• Against the fits: He +3.4 % (0.6 sigma), N2 -1.5 % (0.4 sigma), CO2 -3.4 % (1.4 sigma); validators of fit/He, fit/N2, fit/CO2 (use = check: 2.5-6 %).

• Status: open.

TC-150: Rayleigh scattering as an observable, and what it shows

• Where: optmat.gas.fitting._rayleigh (quantity rayleigh_cross_section, parameters.king_factor), tests in tests/test_fitting.py; validators added to fit/{Ar,N2,CO2,CH4,SF6,N2O}.

• Conversion checked: Sneep & Ubachs’s index-based cross sections equal those from the fits to 0.2 % for Ar and N2 (1.5-3 % for CO2, N2O, SF6, whose index formulas differ).

• Against the fits (alpha, measured over model): at 532 nm (Sneep) Ar -1.1 %, N2 -1.8 %, CO2 -2.7 %, SF6 -1.2 % (each about 1 sigma); N2O -5.8 % (23 sigma), where Sneep’s King factor (1.225) is the likely cause (his index-based value agrees with the fit); CH4 +5.3 % (5.8 sigma). In the deep ultraviolet (Ityaksov, 198-270 nm): SF6 +5 % (about 1 sigma per point); CH4 +12 to +20 %, and Ityaksov’s own index-based prediction is +10-14 % while Sneep’s is +14 %. Three refractometry sets fix methane’s level at 633 nm to 0.03 %; the scattering data disagree with them for CH4 by an amount not explained here (not a King factor: CH4 is a spherical top).

• Decision: scattering determines alpha to 1-10 %, against 0.01-1 % from refraction, and carries King-factor systematics; it is used as a validator, not fitted. It does not narrow the ultraviolet working estimates, and it is insensitive to SF6’s infrared strength (TC-146: 1.5e-4 of alpha at 250 nm).

• Not usable yet: Ityaksov’s N2 and CO2 (wavelength-dependent King factors given only as formulas), Chopra’s N2 (no King factor).

• Status: open.

TC-151 zhao_2026 (Zhao, Nie, Wang & Hu, Metrologia 63, 025007 (2026))

• Transcribed (images checked, cells agree): Table 3 (tbl_5032bd285fb3) static A_eps of CH4 and O2, “This work”, RI, DP, DOSD (CO skipped); Table 1 (tbl_632ce5af228b) S(-4), S(-6), S(-8) of CH4 (Olney 1997) and O2 (Kumar & Thakkar 2011; identical to kumar_2011/o2); Table 2 (tbl_72bc6d72934f) the uncertainty budget (used, not stored). Text p. 7: May et al.’s O2 values at 293 K 3.9582(2) and 323 K 3.95824(7) cm^3/mol (inline may_2008_O2).

• Reconstructed, not printed: the paper prints only static values. A_R_1566_CH4 (primary) and A_R_1566_O2 (check) invert the authors’ Eqs. (2)-(3): A_R(1566) = A_eps + (4 pi/3) N_A a0^3 [S(-4) w^2 + S(-6) w^4 + S(-8) w^6] + A_mu, w = 45.56397823/1566. CH4 6.460091(286), O2 3.972719(144) cm^3/mol, uncertainties = Table 2 without S(i) and A_mu (44.3 and 36.3 ppm). To confirm: (1) this reading of Eq. (2) (A_eps + A_mu from n); (2) omitting (1 + m_e/m_w)^3 (< 0.5 ppm); (3) the nominal “1566 nm” as the vacuum wavelength (+-0.5 nm = +-2 ppm).

• What the static values include: electronic only, and still carrying the infrared response at 1566 nm (CH4: -0.029 au, -0.17 %, HITRAN); no static vibrational part.

• Doubt, O2: the reconstruction with A_mu (870 ppm of the value) is 1026 ppm above egan_2026’s 3.968990(7) at 1542.383 nm; without A_mu, 157 ppm. Either Zhao et al.’s n for O2 is 0.1 % above Egan et al.’s, or A_mu was not in fact removed. Hence A_R_1566_O2 is only a check.

• Paper inconsistencies (no erratum: none touches an extracted value): “CO2” for CO in Table 3’s caption and p. 5; the CO/O2 uncertainties (46/49 ppm) and figure panels (f)/(e) swapped in sections 3.2-3.3; O2’s printed (20) is 50.5 ppm, Table 2 says 46; Eq. (2)’s second-order bracket looks garbled.

• Levels: Table 3’s literature parentheses taken as “not stated”.

• Status: decided (2026-09-25): accepted when the records were merged; points marked open or to confirm above remain open.

TC-152 kirouac_1973 (Kirouac & Bose, J. Chem. Phys. 59, 3043 (1973))

• Transcribed: Table I (tbl_18fe8b762246, image checked) A_eps (3 rows, 279.65/303.25/348.25 K from 6.5/30.1/75.1 degrees C) and B_eps (one dataset per temperature); text p. 3 alpha_0 = 3.03e-24 cm^3, mu_0 = 0.18 D.

• Uncertainty level: read as “3 sigma” from “Our estimated error is 3 times the standard deviation given by a least square fit” (p. 3), which follows the B_p discussion; to confirm that it covers Table I.

• What A_eps includes: electronic + vibrational + orientation (mu_0^2/3kT, 7-8 %): stored as a check, not a polarizability. alpha_0 (Debye intercept) is electronic + vibrational; check: a line through Table I gives 3.036e-24 cm^3 and 0.1805 D.

• B_eps excluded: orientation-dominated (B_ind = 0 +- 2 cm^6/mol^2, p. 4).

• Finding for the N2O fit (see TC-156).

• Status: decided (2026-09-25): accepted when the records were merged; points marked open or to confirm above remain open.

TC-153 sharipov_2017 (Sharipov, Loukhovitski & Starik, J. Phys. B 50, 165101 (2017))

• Transcribed: Table A1 (tbl_6536153eecc8, tbl_5c6a04a7a846, images checked) alpha_e(MP4) of CO2, O3, CH4, SF6 (A^3), check. O3’s “2.801a” mark stripped (MP4(SDTQ)).

• Not extracted, quoted in notes: B97-2 alpha_e, ZPV, PV, b, c (Table A1) and the other works of Table 2 (p. 9). Format need: no quantity for a vibrational correction (ZPV, pure vibrational PV): the polarizability quantity would read them as totals, and the test’s 0.5 au floor rejects CH4’s.

• Doubt, O3 PV: Table A1 0.312 A^3 (the digits of the CO2 row above) vs Table 2 0.208 “This work”. Probably Table A1 misprinted; not an erratum since not extracted.

• Comparisons (au): PV vs HITRAN static: CH4 0.236 vs 0.240 (-1.5 %), CO2 2.106 vs 2.121 (-0.7 %), SF6 12.77 vs 13.94 (-8.4 %). alpha_e + ZPV vs fit electronic static: CH4 17.30 vs 17.26 (+0.19 %), CO2 17.74 vs 17.53 (+1.2 %), SF6 31.64 vs 30.07 (+5.2 %).

• Status: decided (2026-09-25): accepted when the records were merged; points marked open or to confirm above remain open.

TC-154 van_duijnen_1998 (van Duijnen & Swart, J. Phys. Chem. A 102 (1998))

• Identity: curators’ library record UNVERIFIED; journal, volume, issue from pdf p. 1; DOI 10.1021/jp980221f inferred from the pdf file name (jp980221f.pdf), not printed; page range not in the text. To confirm.

• Transcribed: Table 1 (tbl_3b0fee402144, JSON) exp of H2, N2, O2, CH4; Table 11 (tbl_737b997b82b0, tbl_f45b9a639abe, JSON) exp of CH4 (17.86), CO2, SF6, N2O (H2, N2, O2 equal Table 1’s, asserted). Images checked.

• Not static: “The values obtained at 5893 A are used throughout this article” (“usually at 5893 A”, p. 4); stored at 5893 A standard air. No per-value sources. All excluded (scatter -4.0 to +1.2 % against the fits at 589 nm).

• CH4 17.68 (Tables 1, 3, 9) vs 17.86 (Table 11): each table’s own deviations reproduce its value, so no erratum; both stored.

• Status: decided (2026-09-25): accepted when the records were merged; points marked open or to confirm above remain open.

TC-155 topfer_2023 (Töpfer et al., J. Chem. Phys. 158, 144302 (2023))

• Transcribed (text p. 4): N2O 2.998 A^3 and Xe 4.005 A^3 (Olney 1997), SF6 4.49 A^3 (Gussoni 1998), CCSD/aug-cc-pVTZ N2O 2.85 and Xe 2.96 A^3. All excluded (force-field inputs; static/optical and electronic/total not stated). No tables, no refractive data.

• Status: decided (2026-09-25): accepted when the records were merged; points marked open or to confirm above remain open.

TC-156 Finding: HITRAN’s N2O “vibrational” static polarizability includes orientation

• data/external/hitran/N2O_bands.csv contains pure rotational bands (upper = lower vibrational state, 51 bands, the largest “0 0 0 0 <- 0 0 0 0” at 18.71 cm^-1). They contribute 1.448 au of the 2.634 au static “infrared” polarizability; the vibrational bands give 1.186 au. The rotational part is the orientation polarization mu^2/3kT at 296 K (1.448 au corresponds to mu = 0.162 D); it scales as 1/T and is not a polarizability. CH4: rotational 0.0004 au; CO2: none.

• Evidence: Kirouac’s A_eps(T) agrees with fit/N2O’s electronic static (19.718 au) + 1.186 + 1.448 x 296/T to -0.20, -0.34, -0.53 % at 279.65, 303.25, 348.25 K (the slope differs: Kirouac’s mu = 0.18 D against HITRAN’s implied 0.162); Watson (1936) Table VII gives N2O P_A + P_E = 7.77 (watson_1936/dielectric_N2O), P_E = 7.36, P_A = 0.41 cm^3/mol: an atomic (vibrational) polarization of 1.10 au, close to 1.186, not 2.63; and fit/N2O electronic + HITRAN vibrational bands only = 7.814 cm^3/mol (+0.6 % on 7.77), with the rotational bands 8.355 (+7.5 %).

• Consequence: fit/N2O’s static value (22.35 au) is the 296 K dielectric A_eps with orientation, not the static polarizability (about 20.90 au). At optical frequencies the rotational terms are negligible (-f/w^2 with tiny f).

• Action (2026-09-25): optmat.gas.infrared.infrared_bands leaves out pure rotational bands (upper and lower vibrational quanta equal); N2O’s static vibrational value is now 1.186 a.u. (CH4 0.2401, SF6 and CO2 unchanged); fit/N2O and fit/CH4 refitted. The optical-frequency effect of the rotational bands was negligible (f ~ 1e-8).

• Status: decided (2026-09-25): accepted when the records were merged; points marked open or to confirm above remain open.

TC-157: independent second read of the corrections of TC-105 to TC-146

• Where: the records it touched.

• What: all 39 of these corrections (2 errata, 21 corrections of printed formulas, units, states or labels, 16 structural fixes in the extraction scripts) re-read against the images and pages by a second reader (an AI model, 2026-09-25): 32 confirmed, 7 confirmed with a slip in the text, none disputed. The slips were fixed: Alms’s 3 A effect (4e-5, not 4e-4 A^3), Sneep’s CO2 Eq. 13 rounding, Ciddor’s Eq. 4 evidence (Fig. 2 settles the state), Egan 2026’s Eq. 8 reading (not established), Essen’s frequency (two statements against two), Ingersoll’s 1954-1956 agreement (0.25-0.4 %), Stoll’s damaged 5015 A cell. No value changed.

• Status: open (spot check pending).

TC-158: conventions of the photoabsorption records (TC-159 to TC-165)

• Quantity. Absorption coefficients are stored as photoionization_cross_section (unit Mb), the quantity the noble-gas photoabsorption records use, although every O2 and CO2 value here lies below the ionisation limit (absorption into bands and dissociation continua). The vocabulary lacks a photoabsorption cross section (format need, reported).

• Conversion. The printed k (cm^-1, natural log, layer “reduced to NTP”) is kept as printed; scale turns it into Mb: scale = 1e18 / n0. Metzger & Cook state n0 = 2.69e19 cm^-3 (scale 0.037174721). The others state no conversion: n0 = 101325 / (k_B 273.15) = 2.6867801e19 cm^-3 (scale 0.0372192721), the ideal-gas Loschmidt number, matching Weissler & Lee’s explicit ideal-gas reduction to 0 C and atmospheric pressure. NTP is not defined by Watanabe et al. or Inn et al.: 0 C and 1 atm assumed (same group, same convention as Bethke’s “1 atm at 0 C” and Metzger’s Loschmidt number). The real-gas O2 density at NTP differs by 0.1 %; irrelevant at these uncertainties.

• Integrated continuum f values (Watanabe 0.161, Metzger 0.142, Weissler about 6, Inn 0.0043/0.0053/0.12) are oscillator_strength datasets with an index abscissa and use = "check" (as chan_1992’s totals); their integration ranges are in the row labels or notes. Format need: a quantity for an oscillator strength integrated over a stated energy range.

• Band oscillator strengths (Bethke, Matsui) use the index v’ as abscissa (Bethke prints no band positions).

• Status: open (the conventions to confirm; a photoabsorption quantity is a format need).

TC-159 watanabe_1953 (Watanabe, Inn & Zelikoff, J. Chem. Phys. 21, 1026 (1953))

• Figures only for k (Figs. 3-5); Table I (relative band intensities, 12-0 = 100, image checked) not extracted (quoted in notes).

• Transcribed from the text (p. 1030, p. 1029): lyman_alpha 0.27 cm^-1 (the zero-pressure extrapolation); sr_maximum 380 cm^-1 “at about 1420A” (5 %, the stated “experimental error (about 5 percent)”); sr_continuum_f 0.161 (5.7e4-7.8e4 cm^-1).

• Doubt: the Lyman-alpha wavelength is not printed by Watanabe; 1215.7 A is taken from metzger_1964 Table 1 (to confirm this cross-source use).

• Resolution 0.85 A; wavelength readings “occasionally … in error by as much as two angstroms”.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-160 weissler_1952 (Weissler & Lee, J. Opt. Soc. Am. 42, 200 (1952))

• Transcribed: Table I (tbl_56bc106d3886 + tbl_3c7b2b7dceeb, cells files, both images checked cell by cell), 76 rows in print order, 74 used: row 1 excluded (k = 7 cm^-1, below the 20 cm^-1 the paper says it cannot measure), row 24 excluded (the paper prints OI 990.797 twice, identical). Table II (tbl_3deee1da1d4e, image checked): first and second order, 4 rows each, both check. Text: continuum_f f approximately 6.

• Structural: abscissa = the source-line wavelength (A, vacuum); the wave-number column (1e8/lambda) kept in printed; the x 10^2 factor in scale (3.7219272080).

• Erratum: Table I row 54 wavelength 660.380 -> 660.280 (Table II prints 660.280; the row’s wave number 151450 = 1e8/660.280).

• Erratum (moderate confidence): Table II OII 644.188 -> 644.148 (Table I’s OII line is 644.148 with wave number 155244 = 1e8/644.148; but Table II’s second-order k, 670, differs from Table I’s 690, while the other three rows equal Table I’s).

• Not corrected, to check: 13 more rows where the printed wave number and 1e8/lambda disagree beyond rounding (listed in the record’s notes: rows 4, 8, 15, 17, 18, 32, 33, 38, 48, 52, 63, 68, 71, 74). Rows 18 and 74 are digit transpositions of the wave number; row 33 (OI 886.618 A against 113815 cm^-1 = 878.62 A) is 8 A apart and cannot be decided from the paper. A line list would settle which column is wrong.

• Paper inconsistencies (no data affected): text p. 202 “k = 550 cm^-1” at 303 A against the abstract’s and Table I’s 530; Table II’s percent difference 7.8 for 640/670 (4.6 %).

• Uncertainty: 10 % (k > 100 cm^-1), 15 % (k <= 100, rows 2, 3, 5, 7, 8, 11, 12, 13, 15, 18), level not stated.

• Doubt, use: the values above about 1000 A are far above the photoelectric values of Watanabe (1953) and Metzger (1964) (e.g. 1206.4 A: 872 cm^-1 here, Metzger’s band B at 1205 A 430 cm^-1; 1217.645 A: 54 cm^-1 here, Metzger’s Lyman-alpha window 0.28 cm^-1 2 A away). Kept primary; to decide whether to exclude the rows above about 1000 A, or the in-band rows (band location in the printed column).

• Formula ladenburg_wolfsohn (reproduced, text p. 200): the three resonance wavelengths and f values of Ladenburg & Wolfsohn (1932). Read as a per-molecule oscillator model, it reproduces the stored fit/O2 to 0.24-0.45 % (static to 200 nm). The equation itself is not printed.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-161 metzger_1964 (Metzger & Cook, J. Quant. Spectrosc. Radiat. Transfer 4, 107 (1964))

• Transcribed: Table 2 (tbl_cbf80ad2566e, CSV, image checked): bands_windows (13 rows: bands A-F, windows 1-7) and sr_maximum (1 row), split because only the maximum has a stated uncertainty (a per-row relative_rows would give the other rows zero uncertainty in standard_uncertainty, see format needs). Text p. 115: sr_continuum_f 0.142 (5.71e4-7.41e4 cm^-1).

• Structural: raised decimal points (“1215·7”) read as full stops.

• Erratum: S-R maximum 420 -> 402 cm^-1 (abstract, Fig. 2 legend p. 109 and text p. 114 give 402 +- 20; 402/2.69e19 = 1.49e-17 cm^2 as the text states; pdf pages 3 and 8 rendered and checked).

• Conversion: the paper’s n0 = 2.69e19 (p. 115); its printed “sigma = … = k n0” must be k / n0 (the numbers show it).

• Paper oddities: the cross section is printed “1.49 +- 1 x 0.10^-17 cm^2” (read (1.49 +- 0.10) x 10^-17); “n_1 = Loschmidt’s number” for n0; the maximum’s wavelength 1422 A (Table 2, text) and 1420 A (Fig. 2).

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-162 matsui_2003 (Matsui et al., J. Mol. Spectrosc. 219, 45 (2003))

• Transcribed: Table 5 (tbl_0c3259b06159, CSV, image checked): present (6), reproduced lbc (5), yfep (1), ggmbl (6), hcmk (6), bethke (6), all in 1e-5.

• Structural: the second header line merged into the (12,0) cells (“Present2.38”); the LBC and YFEP columns merged into one (“LBCc YFEPd2.44 2.43”): the script takes the trailing number(s).

• Erratum: reproduced Bethke (17,0) 2.95 -> 2.94 (Bethke’s Table I prints 2.94; his K_0 = 699 gives 2.938e-5).

• Check: the extended integrated cross sections x 1/(pi r_e) reproduce the printed f to rounding (2.372 vs 2.38 at (12,0), the others within 0.005).

• Not taken: line lists (Tables 1a, 1b, 2, 4a, 4b) and constants (Table 3); the band origins T(v) quoted in notes from Table 3 (tbl_60e4f321647c, image checked).

• Uncertainty: “less than 5 %” on the integrated cross sections, stored as a bound.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-163 bethke_1959 (Bethke, J. Chem. Phys. 31, 669 (1959))

• Transcribed: Table I (tbl_172bb90e7da2, cells file, image checked): band_f (v’ = 2-17, 16), remainder (v’ >= 18, 1, index 18), total (check, index 2), ditchburn_heddle (reproduced, excluded: 80-140 times too large per Bethke).

• Structural: “(-5)” exponents checked and moved to the scale; footnote marks stripped (the cells give “c” where the image prints “e” on the D&H remainder, not extracted); (9,0) “1.07” with a subscript guard digit 1 kept as 1.071.

• Check: Eq. (2), f = 4.203e-8 K_0 / F(v’’), reproduces every f within the rounding of K_0 (at most 0.2 %); bands + remainder = 31.38 against the total 31.4 (1e-5).

• Uncertainty: 8 %; (4,0) 12 %, (3,0) 18 %, (2,0) 30 %; overlap errors not included; the 3Pi_u continuum (up to 15 %) not subtracted (true band sum 0.00027-0.00031).

• Not extracted: K_0, q (Jarmain et al.), f_el (0.163 +- 10 % in notes).

• Doubt, index abscissa: the remainder’s and total’s indices (18 and 2) are labels of their first band, not band positions.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-164 gurtler_1977 (Gürtler, Saile & Koch, Chem. Phys. Lett. 48, 245 (1977))

• No datasets: the N2 absolute cross section (Figs. 1-2) and band oscillator strengths (Fig. 3) are figures only; no table, no stated uncertainty. The text’s quantum defects and autoionisation widths are recorded in notes. To confirm that no number of the figures is wanted by digitisation (the rules forbid it here).

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-165 inn_1953 (Inn, Watanabe & Zelikoff, J. Chem. Phys. 21, 1648 (1953))

• Figures only for k (Figs. 1-3); Table 1 is dissociation energetics (not optical).

• Transcribed from the text: lyman_alpha k = 1.97 cm^-1 at “Lyman alpha (1216A)” (p. 1649), primary; band_peak_1119 about 4350 cm^-1 at about 1119 A (p. 1650), check; continuum_f 0.0043, 0.0053, 0.12 (continua at 1475, 1332, 1121 A), checks.

• Doubts: NTP not defined (0 C, 1 atm assumed); the f formula is “that of Part I”, not printed here; the continua’s integration limits are not stated (symmetrical extrapolation).

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

Agreement between the O2 sources (computed 2026-09-25)

• Schumann-Runge continuum maximum: Watanabe 380 cm^-1 at about 1420 A; Metzger 402 +- 20 at 1422 A (Table 2’s 420 is the misprint); both 20-25 % below Ladenburg & Van Voorhis’s and Ditchburn & Heddle’s 490 at 1450 A (reproduced in text only). 380 and 402 differ by 5.5 %, within the combined 5 % + 5 %.

• Continuum oscillator strength: Watanabe 0.161 (57 000-78 000 cm^-1), Metzger 0.142 (57 100-74 100 cm^-1, a narrower range); Bethke’s f_el 0.163 +- 10 % from the bands; Ladenburg & Van Voorhis 0.193, Ditchburn & Heddle 0.215, Ladenburg & Wolfsohn’s dispersion f2 = 0.202 (quoted).

• Lyman alpha: Watanabe 0.27 (zero pressure), Metzger 0.28 (window 1), Preston 0.28 (quoted): agree to 4 %.

• Weissler against the photoelectric data: see TC-160 (not consistent above 1000 A).

• Band oscillator strengths (12,0)-(17,0): Matsui below Bethke by 15, 17, 17, 18, 24, 28 %; below LBC by 2-9 %; YFEP (12,0) 2.43 against Matsui 2.38 (2 %); HCMK 21-47 % above Matsui. Bethke’s stated 8 % does not cover the difference above (12,0), which Matsui attributes to band blending at low resolution, as Bethke himself foresaw (overlap errors “not included”).

TC-166 abjean_1971 (Abjean, Mehu & Johannin-Gilles, Opt. Commun. 3, 45 (1971))

• Transcribed (images checked): Tables 1 (Xe, tbl_84f9d5968312) and 2 (Kr, tbl_00feebf8a634), measured and calculated columns, 6 lines 1807-2537 A; Tables 3 (Xe, tbl_30db947f05b2) and 4 (Kr, tbl_9e525b4dedbd, uncaptioned in the curators’ extracted tables), JSON cells, 2500-1800 A: the paper’s formula column and the reproduced Kronjager, Koch, Chashchina-Shreider (only cells marked “a) Experimental values”), Kingston and Langhoff-Karplus columns.

• Erratum: fit_Kr 1807 A printed 507.7 -> 570.7 (the row’s own difference 0.0, meas. 570.7; formula 570.74).

• Formula corrections (both formulas): prefactor printed 1.2055 x 10^-6 -> 1.2055 x 10^-4 (numerators are 100 f: the text’s f = 0.187, 0.193 are printed 18.7, 19.3); Xe first numerator printed “-25.60” (a dash before the fraction in the equation image eq_af918dee2bd1.jpg) -> +25.60. With both, Table 1/2 calc columns reproduce to 0.4e-6 (better at the lines’ vacuum wavelengths) and Tables 3/4 “present work” to 0.05e-6. To check on the equation image: is the dash a printed minus?

• Structural: Table 3’s heading prints “(n-1) . 10^3” (image checked); scale 1e-6 used (Table 1’s note for the same gas, and the formula).

• Krypton withdrawn: every Kr dataset excluded (bideau_mehu_1976, p. 188: ‘our previous values were incorrect’; about 4 % high; smith_1975 concurs).

• Wavelength medium: vacuum, inferred from the calc columns (856.7 at 2288 A needs 2288.7 A, 1029.4 at 1849 A needs 1849.5 A). Those vacuum line wavelengths are quoted from memory (NIST); to verify.

• Uncertainty: largest stated standard deviation per gas (Xe 6e-6, Kr 3e-6) taken as 1 sigma for all rows; whether it is of single measurements or of the mean of ~20 is not said.

• Doubt: Table 3’s Langhoff-Karplus xenon column (868.3 … 1021.7) does not match langhoff_1969/theory_Xe (879.5 … 1105.8); the krypton column does. State reduction of the 1971 values is not stated (density unknown).

• Reproductions of these originals elsewhere: bideau_mehu_1981/experiment_Xe rows 253.7-180.7 nm (= Table 1 meas.); tang_1974/abjean_1971_Xe (= Table 3’s formula column, 2200-1800 A: formula values, not measurements, yet a validator of fit/Xe); bideau_mehu_1976/abjean_1971_Kr and smith_1975/abjean_1971_Kr (withdrawn Kr). leonard_1974 does not reproduce Abjean 1971 (checked).

• Against fit/Xe: experiment_Xe -0.12 % mean (-0.28 … +0.12 %); fit_Xe -0.11 %; formula_table_Xe -0.08 %. Withdrawn Kr +3.7 %.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-167 bideau_mehu_1973 (Bideau-Mehu et al., Opt. Commun. 9, 432 (1973)), CO2

• Transcribed (images checked): Table 1 (tbl_9f56a49e9efd) present work, 7 lines 1807.310-2537.281 A; Table 2 (tbl_9bf7f917ab3a) calculated column (37 rows) and the measured values marked [4] (Koch 1914, 15) and [5] (Old et al., 15); the * rows repeat Table 1 and are not extracted twice.

• Erratum: experiment_CO2 2062.300 A printed 53.07 -> 52.07 (Table 2 prints 52.07 with calc - meas = -0.07; 53.07 breaks the monotonic column).

• Formula (read from the page image, pdf page 2; the curators’ extracted equation blocks are fragments): printed without brackets, 1205.5 multiplies every term (as printed only the first). Correction B5 printed 1.218145e-4 -> 1.28154e-4 = Old et al.’s 0.154489/1205.5 (the paper keeps Old’s 4.13 um term; old_1971 gives f = 1.28e-4). With it Table 2’s calculated column is reproduced at all 37 wavelengths, rms 0.0034 (as printed, rms 0.008, 0.027 off at 16945 A). Evidence is strong but the corrected digits are a derivation: check.

• Sneep and Ubachs’s corrected form (sneep_2005/co2_eq13): same poles, numerators x 1000, prefactor 1.1427e3 = 1.2055e3 x 273.15/288.15 (their 15 C rescaling), i.e. the “typographical error” they correct is the bracket; but their infrared numerator 0.1218145e-4 is 10^4 below this paper’s (0.1218145 expected), making the infrared term vanish (0.53e-5 off at 1.69 um). A misprint in Sneep’s copy, to record there. ityaksov_2008_co2/eq follows Sneep.

• Koch’s formula (reproduced, no form): Table 1’s Ref. [4] column is its right-hand side (55.696, 52.089, 48.945 against 55.69, 52.09, 48.94).

• Not extracted: Table 1’s extrapolated formula columns of refs. 2, 4, 5. The quoted Cuthbertson formula 6914.45/(156.85 - sigma^2) differs from cuthbertson_1920’s frequency form rewritten (about 6905/(156.63 - sigma^2)); unexplained.

• Reproductions elsewhere: sneep_2005 (co2_eq13), ityaksov_2008_co2, he_2021 (CO2 formula citing this paper). bideau_mehu_1973/old_1971_CO2 is old_1971 rounded.

• Against fit/CO2 (fit range 250-1400 nm, so the UV is an extrapolation): experiment_CO2 +0.15 % mean (-0.14 … +0.32 %), the formula column +0.06 %.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-168 bideau_mehu_1976 (Bideau-Mehu et al., Opt. Commun. 16, 186 (1976))

• Transcribed (images checked; both tables uncaptioned in the curators’ extracted tables, JSON cells): Table 2 (tbl_3c940398bc8b) He 170.2, Ne/Ar/N2 164.1 and 170.2, Xe 170.2 nm; Table 3 (tbl_d8d2bb41dadd) Kr new values 164.1-228.8 nm and the reproduced columns (Abjean old values, Smith et al., Kronjager-Koch adjusted by Leonard, Chashchina).

• Uncertainty: ‘from about 0.5% for helium to 0.1% for xenon’; Ne, Ar, N2, Kr given 0.5 % as the bound.

• Doubt: the ‘old values’ at 184.4 (563.3) and 206.2 nm (528.8) are not in abjean_1971 (which has 562.4 at 1849 A and nothing near 206 nm).

• Kr comparison: every value of this paper recurs unchanged in bideau_mehu_1981 (experiment_Kr 228.8-164.1 nm; Ne, Ar 170.2/164.1; Xe 170.2). The bideau_mehu_1981 Kr formula is 0.2-0.8 % below these revised values (0.81 % at 170.2 nm) and 0.15-0.28 % below Table 3’s Smith column, and equals the BM1981 ‘our formula’ column only at 170.2 nm: the revision does not explain that formula’s failure.

• Reproductions of these originals: bideau_mehu_1981/experiment_{Kr,Ne,Ar,Xe} at the rows above; smith_1976/bideau_mehu_1981_Kr (six values identical to this Table 3). To decide: whether to mark those rows reproduced (bideau_mehu_1981 is primary in fit/Xe and fit/Kr).

• Against fits: He -0.01 %; Ne +0.33/+0.54 %; Ar -0.25/-0.12 %; Xe -0.16 %; N2 +0.53 % (164.1), +0.07 % (170.2); Kr -0.14 … +0.47 % (mean +0.10 %).

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-169 smith_1975 (Smith, Parkinson & Huber, Opt. Commun. 14, 374 (1975))

• Transcribed (image checked, JSON cells): Table 3 (tbl_bb31b7ebfefd) this work (27 points, 168.46-288.24 nm), the three-term interpolation (54), Abjean’s data (6), Kronjager-Koch as adjusted by Leonard (21).

• Superseded: smith_1976 says its krypton supersedes these (improved drift correction; differences up to 0.4e-6): experiment and interpolation excluded.

• State: not stated in the paper; recorded 0 C, 1 atm (agreement with smith_1976 and Leonard). Probable error 0.1 %.

• Reproductions of this paper: bideau_mehu_1981/smith_1975_Kr and bideau_mehu_1976/smith_1975_Kr (the ‘calc.’ interpolation at the Brest lines, e.g. 488.8 at 228.8 nm). Both point at the 1975 paper; the fit should use smith_1976.

• Against fit/Kr: experiment -0.03 % mean (-0.10 … +0.07 %).

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-170 burns_1986 (Burns, Graham & Weller, Mol. Phys. 59, 41 (1986))

• Transcribed (images checked, JSON cells, raised decimal points turned into ‘.’): Table 2 A_R at 632.8, 514.5, 488.0, 457.9 nm for He, Ne, Ar, Kr, Xe, CH4, CO2, N2, SF6 (this work, and the literature value in parentheses); Table 3 B_R for Ne (2 lines), Ar, Kr, Xe, CH4, CO2, N2, SF6 with the +- column and the literature values (refs 9, 12, 14, 15, single points); Tables 6 and 12 calculated B_R at 632.8 nm, 298.2 K.

• Temperature 298.2 K from Tables 6/12 captions only; Tables 2/3 state none.

• Wavelength medium: standard air (laser labels; the He-Ne vacuum 632.99 nm is quoted from memory). Affects A_R by ~1e-5 of itself.

• Uncertainty: A_R ‘standard deviation less than 0.1 per cent’ as 1 sigma; B_R’s +- is a sum of three uncertainties (level ‘not stated’).

• Refs: [21] printed ‘Proc. R. Soc. A 88, 13 (1910)’ taken as cuthbertson_1910 (volume 84); [20] printed 1913 = cuthbertson_1914. Check.

• Reproductions of these originals (to switch to reproduced): achtermann_1991 A_R_burns_1986_{CH4,CO2,SF6,N2,Ar}, B_R_burns_1986_298_{CO2,SF6,N2,Ar}, B_R_burns_1986_unknown_CH4, B_R_theory_burns_1986_298_{CH4,CO2,SF6,N2,Ar}; egan_2019 burns_1986_Ne, burns_1986_Xe; hohm_1990/burns_1986_* (Table 1, converted).

• Against fits (A_R): He +0.03 %, Ne -0.11 %, Ar -0.06 %, Kr -0.13 %, Xe -0.10 %, CH4 -0.10 %, N2 -0.02 %, SF6 -0.18 %, CO2 -0.28 % mean but -0.80 % at 632.8 nm (Burns’s own 6.590 against the 6.650 he quotes from Buckingham and Graham).

• B_R against refractivity_virial.toml’s choices (achtermann_1991 at 323 K unless noted): Ar 1.57(58) vs 1.76(5); N2 0.74(65) vs 0.89(6); CH4 7.76(132) vs 6.08(10); CO2 4.75(130) vs 1.9(2) (Burns’s other lines 0.73-1.27); SF6 27.3(52) vs 22.7(5) (373 K); Ne -0.14(14) vs orcutt’s static -0.30(10); Kr 6.23(155) vs orcutt 5.6(3); Xe 25.5(29) (the table has no Xe entry). These are the first optical B_R for Ne, Kr and Xe in the package’s data.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-171 hohm_1990 (Hohm & Kerl, Mol. Phys. 69, 803 (1990))

• Transcribed (image checked, JSON cells): Table 1 noble-gas polarizabilities at 632.99 nm (10^-30 m^3 = A^3), this work with standard deviations, and the literature rows (Burns, Kerl, Koide, Buckingham-Graham, Koch, Kumar-Meath, Bridge-Buckingham).

• Formulas (no form): Eq. (18) H2, Eq. (19) N2, Eq. (20) O2 and CH4 with parameters: the empirical alpha(T) fits at 632.99 nm, 300-1100 K (equation images checked); each reproduces the text’s per-1000-K increase. The molecular alpha(T) data exist only as figures.

• Doubt: Kerl’s helium 0.2106 A^3 (2 % high; transposed 0.2061?), reproduced, not corrected (Kerl 1982 not in the curators’ library).

• Format need: a polarizability at a stated temperature (alpha(T)); a parameters.temperature_k for polarizability datasets would let the Eq. (18)-(20) data (if tabulated) or these fits be used.

• Reproductions elsewhere: egan_2019/hohm_kerl_1990_Ne; pawlowski_2005/ other_s-2_Ne cites it but prints 2.663 au, which is not in this paper (0.39682 A^3 = 2.678 au at 632.99 nm).

• Against fits (632.99 nm): He -0.08 %, Ne +0.07 %, Ar -0.03 %, Kr +0.08 %, Xe +0.17 %.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-172 hohm_1994 (Hohm, Chem. Phys. 179, 533 (1994))

• Transcribed (image checked, JSON cells): Table 2 mean polarizabilities (au) at 632.990, 611.971, 594.096, 543.516, 325.130 nm (the table note’s wavelengths, hard-coded in the script): input rows for H2 (primary: ‘unpublished results’, first published here), O2, N2O, CO2 (reproduced from ‘Mol. Phys. (1993), in press’, not in the curators’ library, so fittable); calculated rows (check). Depolarization ratios not extracted.

• Formulas (no form; Table 1): the two-term alpha(omega) = (1/3)(f_par/(w_par^2 - w^2) + 2 f_perp/(w_perp^2 - w^2)); each reproduces Table 2’s calculated row to 1e-5 au (1e-4 for N2O, CO2). Format need: an oscillator form taking squared energies and a strength factor, or accepting derived (f/3, 2f/3; sqrt(w^2)) terms.

• Uncertainty: relative 1e-5 (the dispersion, relative to alpha(632.99)) with a systematic 1e-3 taken from hohm_1990’s apparatus statement: an assumption, check.

• Against fits: H2 +0.016 % (325-633 nm); O2 +0.21 %; N2O +0.16/+0.18 % in the visible, -0.19 % at 325.13 nm (below fit/N2O’s 450 nm range); CO2 +0.04 %.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-173 murphy_1934 (Murphy & Johnston, Phys. Rev. 46, 95 (1934)) — D2 spin weights

• No datasets. States (p. 95 abstract, p. 98 conclusion): g_s/g_a = 1.97 +- 0.03 (probable error, weighted mean of 4 plates, Table II), ‘the theoretical ratio of 2’, nuclear spin 1, even rotational levels more intense, Bose-Einstein statistics; Eq. (2), p. 97: g_s/g_a = (i + 1)/i; even J symmetric, odd J antisymmetric. It does not print 6 and 3, only their ratio 2 : 1, which is all the thermal average uses. This closes the “indirectly sourced” note of TC-105 for the ratio.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-174 teal_1935 (Teal & MacWood, J. Chem. Phys. 3, 760 (1935)) — D2 spin statistics

• No datasets. States (p. 764): alternation of the D2 pure rotational Raman lines, even states more intense; Einstein-Bose statistics, spin non-zero; semi-quantitative agreement with Placzek’s theory for Murphy and Johnston’s spin 1. No ratio printed. Raman shifts (Tables I, II), Delta G_1 and Table III constants left for later.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-175 pawlowski_2005 (Pawlowski, Jorgensen & Hattig, Adv. Quantum Chem. 48, 9 (2005))

• Transcribed (images checked; JSON cells): Tables 2-4, S(-2) … S(-10) of Ne (d-aug-cc-pV6Z), Ar (6Z), Kr (5Z) for CCS, CC2, CCSD (check), CC3 (primary), and the reproduced DOSD (kumar_1985, identical) and ‘Other’ columns. The curators’ extracted table reads the minus sign of k as ‘K’ in Tables 3-4 (restored in the script).

• Volume 48 taken from the DOI (the curators’ library has none).

• Doubt: the ‘Other’ moments cite Chan et al. (chan_1992_neon, chan_1992), which print no moments; the Ne S(-2) 2.663 cites Hohm and Kerl, which has 2.678 au at 632.99 nm and no static value.

• Accuracy: Ne S(-2) left-out effects net -0.004 au; nothing stated for Ar, Kr.

• Against the fits’ moments (data/fit - 1): Ne CC3 +0.15, -0.08, +0.19, +0.66, +2.44 % (k = -2 … -10); Ar CC3 +0.22, +0.09, -0.17, +2.77, +4.15 %; Kr CC3 +0.58, -0.14, -0.46, -5.64, -11.9 % (Kr CC3 falls below the DOSD with |k|, as the paper says; the first ab initio Kr dispersion, TC-94, but not converged per the authors). For reference the reproduced DOSD against the fits: Ne +0.3 … +7.0 %, Ar 0.0 … +6.6 %, Kr +0.15 … -1.3 %.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-176 simmons_1978 (Simmons, Opt. Commun. 25, 211 (1978))

• Transcribed (image checked, JSON cells): the table’s LL function at 300 K (cm^3/mol, primary) and refractive index at NTP (stored as n - 1 by exact decimal subtraction, check) at 22002, 15803, 944 cm^-1 for N2 and CO2 (propane skipped).

• Doubts: NTP undefined, read as 0 C, 1 atm (the LL values give 0.2-1 % agreement there, 5-7 % off at 15-20 C). Abstract and table disagree at 944 cm^-1 (N2 4.32(9) vs 4.30(10); CO2 6.37(9) vs 6.42(10)); the table’s taken. The visible wave numbers are inverted air wavelengths (15803 = 1/632.8 nm), stored as vacuum (format has no air wave number: format need); error ~1e-5 of the values.

• Against fits: LL_N2 -0.53 % (454.5 nm), +0.09 % (632.8 nm), -1.98 % (10.6 um; N2 has no infrared-active band, so a 2 % drop is not expected: Simmons’s 944 cm^-1 value is one stated uncertainty (0.10) low); LL_CO2 +0.05 % (454.5), -1.71 % (632.8), -2.51 % (10.6 um, outside fit/CO2’s 250-1400 nm; the 10.6 um value includes CO2’s infrared bands). The 632.8 nm CO2 value is 1.7 % low: an outlier.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-177 Gordon 1993 duplicate (no record)

• A second copy in the curators’ library (publisher’s “9481_1_online.pdf”, sha256 81bd3bf1…) against the curated copy (sha256 6b79fab8…, with an older AIP cover page): same DOI 10.1063/1.464379, 7 pages each; the three tables’ cells are identical (Table I tbl_d009cc88bfad = tbl_99cea2681cb3, Table II tbl_c084e004c082 = tbl_0bf8e5436a95, Table III tbl_a3a6f7bc5f42 = tbl_3c63e6842989) and the article text is identical; only the cover pages differ. gordon_1993 needs no change; the second copy adds nothing.

• Status: decided (2026-09-25): accepted with the integration of TC-178 and TC-218; points marked open or to confirm above remain open.

TC-178 Integration into the fits (2026-09-25)

• Copies switched to their originals: bideau_mehu_1981 experiment rows now excluded where they reprint bideau_mehu_1976 (Ne, Ar 170.2/164.1 nm; Kr 228.8-164.1 nm; Xe 170.2 nm) or abjean_1971 (Xe 253.7-180.7 nm), and the originals fitted instead (values identical, checked); smith_1976/bideau_mehu_1981_Kr now reproduced_from = bideau_mehu_1976 and dropped from the Kr validators; tang_1974/abjean_1971_Xe now reproduced_from = abjean_1971 and dropped from the Xe validators; the Burns copies in achtermann_1991 and egan_2019 now name burns_1986.

• Fitted: Kr gains bideau_mehu_1976, burns_1986 A_R (chi2 10.0 for 4) and hohm_1990; Xe gains abjean_1971, bideau_mehu_1976, burns_1986 A_R (6.1 for 4) and hohm_1990; CH4 and SF6 gain burns_1986 A_R (SF6: 14.2 for 4; the level moves -186 ppm, between Burns’s -0.18 % and Achtermann); O2, N2O and CO2 gain hohm_1994 (shape 1e-5 with a free-within-1e-3 scale; chi2 33.6, 4.8 and 31.8 for 5, 4 and 5 points: after the scale, O2 and N2O residuals about 1e-5 but 612 and 594 nm of O2 at 3-4 sigma; CO2 about 4e-5).

• N2O range extended to 320 nm (was 450): Hohm’s 325.13 nm point fits within 1e-5 of the visible shape (chi2 +1.4); the GVD moves +3 % at 800 nm, +7 % at 1030 nm and -6 % at 1800 nm against the previous fit, which rested on the Cuthbertsons’ 1914 shape alone (its chi2 rises from 14 to 32 for 8: Hohm’s precise shape disagrees with it by about 1e-4).

• CO2: Hohm’s 325 nm point raises the ultraviolet (+370 ppm at 250 nm, GVD +0.7 % at 343 nm, 2 of the old sigma), toward bideau_mehu_1973 (mean deviation +0.15 % -> +0.06 %). bideau_mehu_1973 fitted with the range extended to 180 nm was tried and rejected: its residuals jump by 0.34 % between 185 and 194 nm (-0.19, -0.27, +0.09, +0.17, +0.24, +0.26, +0.10 % at 181-254 nm), several times its stated 0.08 %, which no smooth dispersion follows (chi2 42 for 7 fitted against 44 as a validator). Validator; range kept at 250 nm.

• Validators added: pawlowski_2005 CC3 moments (Ne, Ar, Kr), burns_1986 A_R (He, Ne, Ar, N2, CO2), hohm_1990 (He, Ne, Ar), bideau_mehu_1976 (He, N2), hohm_1994/input_H2, simmons_1978 (N2, CO2).

• Refractivity virial: Xe gets its first pair term (burns_1986/B_R_Xe, first row, 25.5(29) at 632.8 nm; the other lines 14.9-18.6: known to about 30 %). Ne and Kr keep Orcutt & Cole (Burns agrees, less precise).

• Sneep’s CO2 formula: the infrared-numerator misprint recorded in sneep_2005’s notes; with the term restored the formula reproduces Sneep’s Table 2 value (427 at 18 788.4 cm^-1), which resolves the rounding doubt in that formula’s check.

• D2 spin weights: TC-105 resolved by murphy_1934 (TC-173).

Page numbers are journal pages unless marked “pdf”. Ozone absorption (the checks on the high-resolution data files fetched separately) and ozone theory.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

Conventions common to the ozone records (to confirm)

• Quantity. Every ozone absorption value is an absorption_cross_section with its temperature in parameters.temperature_k where the paper states one (omitted, and said in notes, where it does not).

• Conversion of absorption coefficients. A printed coefficient (cm^-1, layer reduced to NTP or to 0 C and 760 mm Hg) is kept as printed; scale turns it into Mb: scale = 1e18 / n0 for a natural-log coefficient, ln(10) x 1e18 / n0 for a decadic one, with n0 = 101325 / (k_B 273.15) = 2.6867801e19 cm^-3 (ideal gas), as in watanabe_1953 (scale 0.037219272080).

• Integrated band strengths (f of a continuum, a band) are oscillator_strength datasets with an index abscissa and use = "check", as in the earlier records.

TC-179 ogawa_1958 (Ogawa & Cook, J. Chem. Phys. 28, 173 (1958))

• Identity checked on the first page (pdf p. 2): the curators’ library’s observed title lost the “3” of O3.

• Transcribed: Table I (tbl_987cd6327574, image checked row by row), 24 lines, 526-1305 A: absolute (mu, cm^-1, 0 C and 760 mm Hg; primary; 20 % bound) and relative (Lyman alpha = 500, the printed +- as sigma; check; scale = 614/500 x 1e18/n0).

• Structural fixes (OCR, in the script): absolute cells llh -> 1112 (703 A) and 100. -> 1008 (645 A), and 1191 (718 A): the image prints the last digit as a subscript (119_1, 111_2, 100_8); the letter O for zero in 41O (879 A) and 1O.2 (539 A).

• Absolute scale: not measured; the whole column is scaled to 614 cm^-1 at Lyman alpha “as estimated from Tanaka’s graph” (tanaka_1953, whose text gives no Lyman alpha value; their error “as high as 10 percent”).

• Unresolved inconsistencies (no erratum): 1243 A: 288 / 232 = 1.241 against 614/500 = 1.228 for every other row (232 x 1.228 = 285); percent-error column at 1305 A (5.8/190 = 3.1 %, printed 3.3) and 617 A (22.0/762 = 2.9 %, printed 2.7).

• Temperature not stated (the atlas’s 295 K is not in the paper); wavelengths “approximate”, vacuum.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-180 tanaka_1953 (Tanaka, Inn & Watanabe, J. Chem. Phys. 21, 1651 (1953))

• Identity checked (pdf p. 2): Part IV of the Watanabe series.

• Figures only (Figs. 1 and 3). Transcribed from the text (images of pp. 1651 and 1653 checked): text, k = 8 (minimum, about 2015 A), 23 (maximum, about 1725 A), 20 (O2 crossing, about 1700 A), 35 (1600 A), 420 cm^-1 (maximum, about 1330 A); use = "check" (approximate readings of their own curve); 10 % bound (“combined experimental error would be as high as 10 percent”, p. 1652).

• Doubt: NTP taken as 0 C, 1 atm (Part I’s convention); temperature “room”.

• The OCR reads the corrections as “O2, CO2 and CO2”; the image prints “O2, CO, and CO2”.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-181 inn_1953_ozone (Inn & Tanaka, J. Opt. Soc. Am. 43, 870 (1953))

• Identity checked (pdf p. 1). PDF p. 4 is another paper (Richardson et al.).

• Figures only for alpha (Figs. 1-3; “over 200 different wavelengths” measured, no table). Decadic coefficient at NTP (“I = I0 10^(-alpha x)”, p. 871; axes “cm^-1, base 10”), 27 C.

• Transcribed from the text (p. 872, image checked): f_hartley 0.088 (the Hartley continuum) and f_chappuis_continuum about 2e-5 (the weak continuum under the Chappuis bands), both checks. Not extracted: alpha_max = 0.055 cm^-1 (Chappuis, no wavelength stated).

• Wavelength medium not stated (a Cary reads air wavelengths presumably; within the +-1 A (UV) and +-5 A (visible) reading uncertainty).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-182 mason_1996 (Mason et al., J. Phys. B 29, 3075 (1996))

• Identity checked (pdf p. 2).

• Cross sections in figures only (Figs. 5-7, 110-354 nm, Mb against eV); the Mainz atlas’s Mason set is a digitisation of Fig. 5 (not a paper table).

• Transcribed: Table 3 (tbl_cf055268b405, cells, image checked), interval oscillator strengths: present (8 intervals, check) and 12 reproduced rows (Johnstone, Davies, Tanaka, Brion 1984, Inn & Tanaka, Molina & Molina; theory Borowski, Tsuneda (2 values), Hay & Dunning, Thunemann, Nordfors, Padial). Abscissa = lower edge in eV (format need as kumar_2010_supplement).

• Structural fixes (script): note a (Present, last interval ends at 11.25 eV, not 11.30) in the row id; the Tsuneda cell’s two values (CASPT2(g2), MRMP) split into two rows.

• Check: the present contiguous intervals 3.75-11.25 eV sum to 0.3692.

• Doubt: the “Tanaka et al” row: tanaka_1953 prints no f values (integrated from their figure by someone; marked reproduced from tanaka_1953). The Borowski and Nordfors references are cited as printed (Borowski’s volume and page run together, “23 7195”).

• Absolute scale: O2 removed by normalising at its 9.96 eV band; partial pressure reconfirmed by normalising at 253 nm to Mauersberger et al. (1987). Uncertainty for ozone not stated (“<= 5 %” agreement for other molecules). Temperature not stated; sampling 0.05 nm; resolution not stated.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-183 daumont_1992 (Daumont et al., J. Atmos. Chem. 15, 145 (1992))

• Identity checked (pdf p. 1).

• Transcribed: Table III (tbl_d67497d2c571, CSV, image checked): present (5 Hg lines, check: points of the BDM spectrum), reproduced molina_1986, bass_paur_1984 (renormalised to Mauersberger by Daumont, note a), yoshino_1988, and mean (+- RMS, check). Text (p. 152, p. 148): dew_point_254 112.6 +- 2.0 (method 2, primary), reproduced mauersberger_1987 113.6 +- 0.5 and hearn_1961 114.7 +- 2.4.

• Unit inferred: Table III prints no unit; 1e-19 cm^2 from the text’s 253.65 nm value (113.05 x 10^-19 cm^2). The last row’s cells carry “x 10^-2” each (e-notation).

• Air wavelengths (calibration “in air”, p. 150): standard_air (laboratory air in fact; the difference is negligible).

• Facts: 295 K; 0.01 nm steps; resolution not stated; total error 1.3 % Hartley, 1.3-2.5 % Huggins (Table II; level not stated); absolute by the pressure during decomposition (method 1), not normalised; the data set was “on floppy disk … on request” (superseded by malicet_1995 and the Reims files).

• Doubt: the uncertainty of present at 334.15 nm set to the Huggins upper bound 2.5 %.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-184 malicet_1995 (Malicet et al., J. Atmos. Chem. 21, 263 (1995))

• Identity checked (pdf p. 1).

• Transcribed: Table III (tbl_b1fba2648b6c, cells, image checked), 253.65 nm against temperature, one dataset per temperature: this work t295_253 (reproduced from daumont_1992), t243_253, t228_253, t218_253 (check, +- as sigma); Barnes and Mauersberger 297, 273, 253, 221 K (reproduced). Table IV (tbl_418f10b3b9e9, CSV, image checked): t228 (13 wavelengths, check) and yoshino_1988_228 (reproduced).

• Format need: a per-row temperature (Table III); worked around with one-point datasets per temperature.

• Duplicates: t228_253 = t228 row 253.65 (check both, never fitted together); Barnes and Mauersberger’s 297 K 113.6 equals Mauersberger et al.’s 113.6 quoted by daumont_1992 (two papers of 1987; same measurement? unverified).

• Facts: 295, 273 (300-345 nm only), 243, 228, 218 K; bandwidth 0.01-0.02 nm; wavelength medium not stated (daumont_1992’s calibration is in air: recorded as standard_air, to confirm); systematic 1.3-1.5 % Hartley, 1.3-3.5 % Huggins, random 0.3-2.0 %; data “on a floppy disk, available on request”. The quadratic temperature parametrisation’s coefficients are not printed.

• Doubt: the Huggins rows of t228 (315-344 nm) given 3.5 %, the upper bound.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-185 brion_1993 (Brion et al., Chem. Phys. Lett. 213, 610 (1993))

• Identity checked (pdf p. 1). A letter announcing the BDM temperature set (full account: malicet_1995). No table.

• Transcribed from the text (p. 611): t295_253 113.0 +- 1.1 x 10^-19 cm^2 at 253.65 nm, reproduced from daumont_1992 (their 113.05 rounded).

• Facts: 218, 228, 243, 295 K (195-345 nm) and 273 K (300-345 nm); bandwidth about 0.01 nm, steps 0.01 nm; the text says both “195-345” (p. 610) and “190-350 nm” (p. 612) for the files’ range; total error 1.3 % Hartley, 1.3-2.5 % Huggins; medium not stated.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-186 brion_1998 (Brion et al., J. Atmos. Chem. 30, 291 (1998))

• Identity checked (pdf p. 1).

• Transcribed: Table II (tbl_cc4f708ad271, CSV, image checked; decimal commas converted, one cell “4,634 +- 0.070” mixes comma and point as printed): present (6 lines, check), reproduced anderson_mauersberger_1992 (5) and hearn_1961 (1). Text (pp. 291, 294, page images checked): text maxima 4.83 (575 nm) and 5.23 x 10^-21 (603 nm), minimum 4.4 x 10^-24 cm^2 at 377.5 nm (check).

• Deviation column (not extracted) off by 0.02 and 0.06 % at 543.516 and 594.096 nm (unrounded values presumably).

• Facts: 295 K (350-830 nm), 218 K (515-650 nm); 0.02 nm FWHM, 0.01 nm steps; systematic about 1.5 % (420-830 nm), 1.5-4 % (350-420 nm); temperature effect below 1 % in 515-650 nm.

• Doubt: wavelength medium not stated; recorded as standard air (the group’s calibration in air; Table II’s He-Ne and Hg lines look like air values).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-187 burrows_1999 (Burrows et al., JQSRT 61, 509 (1999), GOME FM)

• Identity checked (pdf p. 1); “GOME-2” in the title is part 2 of a series.

• Transcribed: Table 1 (tbl_0aa25c60f740, CSV, image checked; the header cells read “¹ (K)” and “pO3” for T (K) and sigma_O3; reference numbers run into the names): t293_253 1150 (check) and six reproduced one-point datasets (Hearn 295 K, Bass and Paur 298 K, Molina 298 K, Mauersberger 297 K, Yoshino 1993 295 K, Daumont 295 K), 1e-20 cm^2. Table 2 (tbl_7b7a151c331a, CSV, image checked): t293_visible (4 lines, check) and reproduced Ref. 26 (Anderson and Mauersberger) and Ref. 27 (Burkholder and Talukdar), 1e-24 cm^2.

• Attribution conflict: Table 2’s Ref. 27 row (3075, 4569, 4633, 3383) equals brion_1998’s “Anderson and Mauersberger” column; Burrows’s Ref. 26 row (3092, 4674, 4427, 3313) differs (its 4427 at 611.971 nm is also odd against every other value near 4630-4700). Anderson and Mauersberger cited as 19, 923 here and 19, 933 in Brion. gorshelev_2014 Table 6 sides with Brion (its A&M column is Brion’s), so Burrows’s Ref. 26/27 labels are most likely swapped; the datasets keep the printed labels. Needs the originals (not in the curators’ library).

• Facts: 293, 273, 241, 221, 202 K; resolution about 0.2 nm (< 400 nm), 0.3 nm (> 400 nm), up to 0.6 nm at 312-321 nm; absolute scale by NO titration at 293 K (300-480 nm, lab spectrometer), GOME 293 K scaled in 300-330 nm, other temperatures by the integrated cross section over 231-794 nm (assumed temperature-independent, < 2 %); 2.6 % in the Hartley and Chappuis maxima; files “as ASCII files upon request”.

• Doubt: wavelength medium not stated in the paper; table points recorded as standard air (labelled by the Hg and laser lines as in the other papers); the data file’s medium must come from its header.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-188 gorshelev_2014 (Gorshelev et al., Atmos. Meas. Tech. 7, 609 (2014), Part 1)

• Identity checked (pdf p. 1).

• Transcribed: Tables 4-7 (tbl_102450bc135d, tbl_8eb4cf894101, tbl_a995b8119c7a, tbl_6fa5f0d2dae8; CSV; images checked), one dataset per source column, 29 datasets: this_work_uv (7), this_work_380 (3), this_work_vis (6), this_work_nir (16) as checks at 293 K; reproduced Orphal (uv 4, vis 6), Hearn (4), BMD (uv 7 from daumont_1992, 380 3, vis 6, nir 8 from brion_1998), Burrows (uv 7, 380 3, vis 6, nir 6 from burrows_1999), Bogumil (7, 3, 6, 16), Petersen Hearn/BMD-scaled (3 each), Burkholder and Talukdar (1, 6, 3), Axson (3), Anderson and Mauersberger 1992 (5), Anderson 1993 (12), El Helou (5, 8). Vacuum wavelengths (the vacuum value of “vacuum (air)” cells).

• Structural fixes (script): the stray “e” before 302.24 (printed so); Petersen’s “Hearn/BMD” cells split into two datasets; Table 5’s FWHM in parentheses and Orphal’s “+- %” kept in printed only.

• Errata (6): Table 4 row 248.32 nm printed a factor ten low in every column (this work 105.1 -> 1051, BMD 103.8 -> 1038, Burrows 106.3 -> 1063, Bogumil 106.3 -> 1063, Petersen 106.1 -> 1061 and 104.5 -> 1045): the neighbours are 946-965 (244.06 nm) and 1107-1129 (257.34 nm). To confirm against the Bremen file at 248.32 nm.

• Not extracted (format need): Table 3’s band-integrated cross sections (cm^2 nm), quoted in notes; its Wulf limits 633-1000 nm against “663-1000 nm” in the text.

• Facts: vacuum wavelengths (echelle air converted with Edlen; FTS wavenumbers); resolution 0.015-0.025 nm (echelle), 1 cm^-1 / 2 cm^-1 (FTS: 0.01 nm Huggins, 0.02-0.06 nm Chappuis, 0.12-0.24 nm Wulf); published on a 0.01 nm grid by linear interpolation; absolute by pure-O3 pressure in 310-335 and 450-780 nm, the rest relative and scaled; systematic 1.3 %, statistical 1-3 %, “better than three percent” overall, 20-30 %+ in the 380 nm minimum and beyond 1000 nm; file on the IUP Bremen website.

• Doubt: uncertainties assigned: 3 % (uv, vis, nir), 20 % (Table 5), 30 % at 991.841 and 1046.766 nm; levels not stated.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-189 serdyuchenko_2014 (Serdyuchenko et al., Atmos. Meas. Tech. 7, 625 (2014), Part 2)

• Identity checked (pdf p. 1).

• Transcribed: Table 4 (tbl_75e505961474, CSV, image checked; the split header “El Helou et a | l. (2005)” is one heading over two columns), x 10^-22 cm^2, vacuum wavelengths: this_work_223 (13, check), reproduced el_helou_2005_223 (10; printed “222-223 K”, recorded 222.5 K), el_helou_2005_150 (8), burkholder_talukdar_1994_220 (7), bogumil_2003_223 (13), bmd_218 (5, from brion_1998).

• Suspect value (no erratum): Burkholder and Talukdar at 779.416 nm, 1.541, half the others (3.15-3.33) and outside their 407-762 nm range (Table 1).

• Not extracted (format need): Table 3’s band-integrated cross sections at five temperatures (this work’s rows quoted in notes).

• Facts: eleven temperatures 193-293 K; 0.02-0.24 nm FWHM; vacuum wavelengths; each temperature calibrated absolutely on its own (310-335 and 450-780 nm); systematic below 1.2-2.6 % (temperature-dependent), statistical below 1-2.2 %, up to 30 % in 350-450 nm and beyond 900 nm; the quadratic temperature parametrisation (Eq. 1, T in C) holds to 1.5-2 % in the Huggins band, coefficients not printed; files on the IUP Bremen homepage with “updates … expected” (the version fetched is to be recorded).

• Doubt: 3 % and 30 % (beyond 900 nm) assigned to this_work_223; levels not stated.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-190 naves_2011 (Naves, Castro & Fonseca, J. Chem. Phys. 134, 054315 (2011))

• Identity checked (pdf p. 2).

• Transcribed: Table III (tbl_a5631d2a2b1a, cells, image checked), the mean polarizability rows only: ccsd_opt, ccsd_expt, ccsd_t_expt (4 frequencies each: 0, 0.0239, 0.0428, 0.0656 hartree); Table II (tbl_6e45fd86f96d, image checked): ccsd_relaxed_static 16.74; text (p. 054315-7): best_estimate 18.55. All checks, electronic except the best estimate.

• The ZPVA (key): Table IV (image checked) gives zpva = [ ]^{1,0} + [ ]^{0,1} = 1.43 + 0.03 = 1.46 a.u. static (1.45+0.03, 1.51+0.03, 1.63+0.03 at the three frequencies) and pv = 1.41 a.u. static (-0.08, -0.02, -0.01, 0 at infinity). Kumar & Thakkar’s “1.43 au” is the [ ]^{1,0} term alone, as is Naves’s own best estimate (17.12 + 1.43 = 18.55; with 1.46 it would be 18.58). Sharipov’s Table 2 quotes Naves as ZPV 0.216 A^3 = 1.46 a.u. (the total), PV 0.209 A^3 = 1.41 a.u.; Sharipov’s own ZPV is 0.088 a.u. (0.013 A^3), from DFT geometries with MP4, and they call their O3 treatment inadequate. Bearing on the factor 16 (not a resolution): Naves’s corrections are CCSD at the CCSD geometry, CCSD frequencies 6-15 % high (the curvature term scales as 1/omega_a), CCSD far from converged for O3 (orbital relaxation alone -15 %, triples matter), and the authors expect “some inaccuracy” in the zpva. Needs an independent calculation.

• Format need: a quantity for a vibrational correction to the polarizability (zpva, pv); Table IV’s values are in notes only.

• Inference to confirm: the dynamic zpva uses the orbital-unrelaxed analytical CCSD response (not stated).

• To do: kumar_2011/static_i (17.12) now has its original here (naves_2011/ccsd_t_expt, row 0): switch its reproduced_from to naves_2011.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-191 kumar_2011_supplement (Kumar & Thakkar 2011, supplementary material)

• Identity checked on the supplement’s first page (curators’ library status UNVERIFIED; the paper kumar_2011 VALIDATED).

• Transcribed: O2 IDOS (tbl_528da2c47d04, cells, image checked): idos_O2 (33 intervals, j = 4-36) and discrete_O2 (2.862e-4); O3 IDOS (tbl_4d1cc5fd6d9e, CSV, image checked): idos_A, idos_B1, idos_B2, idos_C, idos_D (39 intervals each; A and D excluded as the authors reject them, B1, B2, C checks). Abscissa = lower edge E_j in eV (format need as kumar_2010_supplement).

• Formulas: pseudospectrum_O2, pseudospectrum_O3_B1, pseudospectrum_O3_C (oscillator form, hartree; columns “E f” as printed, NOT swapped, unlike the 2010 supplement). They reproduce kumar_2011 Tables I and III for every integer k (O2 2 to -8, O3 2 to -6) to 4e-4. range_nm lower bounds (191 nm O2, 988 nm O3) are the extractor’s 1.1 x lowest-pole convention; the O3 lowest pole (898 nm, f = 7e-8) stands for the Wulf band.

• Checks: O2 discrete + IDOS = 15.99982; O3 IDOS sums 23.9991-24.0016; the 12-20.6 eV interval ratios reproduce the paper’s scale factors (B1/A 1.359 = 1.34/0.986; D/A 1.026; C/A 1.193 against 1.18/0.986 = 1.197, the rounding of 1.18).

• Reference-number offset: the supplement’s O3 source numbers (and O2’s Henke, Chantler) are 9 higher than the paper’s list; names used.

• Structural: the page-4 line “j=14-15: Mason et al.” is lost from the extracted Markdown (an unclassified block); page image checked.

• Discrepancy (no correction): the paper’s text attributes 12-20.6 eV to Ogawa & Cook and Cook; the supplement assigns j = 18 (12.00-20.60 eV) to Cook alone and Ogawa & Cook to j = 19 (20.60-23.57 eV). Relevant to the ozone model’s “12-20.6 eV scale”.

• To do: kumar_2011’s notes “The DOSDs themselves are supplementary material, not in the library” are now out of date.

Page numbers are journal pages unless marked “pdf”. Carbon monoxide (now curated), static and vibrational polarizabilities, refractivity virials.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-192 smith_1976, CO added (Table VII)

• Transcribed (script, tbl_a6e86bb4461b, image checked): experiment_CO 28 points (the unmarked “This expt.” cells, 167.20-288.24 nm), interpolated_CO 10 points (the cells marked d, “computed from three-term Lagrange fit to our data”, use = "check"), koch_1914_CO 10 points (the “Prev. expt.” column, Koch 1914 as listed in the ICT, reproduced; 237.9-289.4 nm).

• Structural fix: the d marks print as ^{\text{d}}, which the script’s existing _MARK pattern does not match; a separate pattern strips them and routes the ten marked cells to interpolated_CO. The image shows the d marks on exactly the ten rows that carry a Koch value.

• Uncertainty: 0.10 % above and 0.58 % below 220 nm (Table III, 90 % confidence; the photographic 100-Torr runs below 220 nm, normalised to the 1 atm data).

• Doubt: Koch’s wavelengths are printed to 0.1 nm under the table’s “lambda_vac” heading; whether Smith et al. converted the ICT’s (presumably air) wavelengths is not said. The air-vacuum difference here is 0.08 nm.

• Doubt: the paper warns that its fit is inaccurate “in the region of the bands belonging to the fourth positive system” but does not say which measured rows lie near bands. A model should not over-trust the points below 220 nm.

• Delta (%) column not extracted (derived; sign ours minus literature).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-193 cuthbertson_1920, CO added (Table II, earlier-work table, formula)

• Transcribed: experiment_CO and fit_CO 8 points each (Table II, tbl_5e46be9ef072, cells file only, image checked; thousands comma dropped); mascart_CO, perreau_CO, koch_CO, grueschke_CO 1 point each at 5461 A (tbl_fe180e2332d2, image checked; reproduced, no references given in the paper).

• Reduction: the CO absolute value is reduced with the ideal-gas formula (mu - 1) 76/P T/273 (p. 4), so density = "ideal", unlike the CO2 values (real).

• Uncertainty (not stated): rms of calc - obs, 1.2 units x 10^-8; scale half-range of the four absolute determinations (3362-3365), 0.045 %.

• Formula co_1920: mu - 1 = 3.64067e27/(11,124e27 - n^2). With V = 3e10 it exceeds the calculated column by 0.6-1.4 units; with V = 2.99796e10 within 0.6 at all eight lines; the best single V (2.998e10) leaves +-0.54. Not an exact evaluation (as for co2_1920). lambda_0 = 899 A checks (p. 5).

• Doubt: koch_CO’s original is presumed to be Koch, Ark. Mat. Astron. Fys. 10 (1914), the same work as smith_1976’s koch_1914_CO; the paper gives no reference.

• Not recorded: the “carbon atom” formula from CO (p. 7), as for CO2; the lambda_0 comparison table (derived).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-194 watson_1936, CO added (Tables III, VI, VII)

• Transcribed (script; images of Tables III, VI, VII checked): green_CO 307.9e-6 (25 C, ideal gas, primary), cuthbertson_CO 308.1e-6 (reproduced from cuthbertson_1920, recalculated to 25 C with compressibility), zero_celsius_CO 336.1e-6 (check; = 307.9 x 1.09157), dielectric_CO P_A + P_E = 4.98 cm^3/mol at inf (reproduced from the authors’ earlier dielectric papers).

• Checks: cuthbertson_1920’s 336.4e-6 / 1.09157 / (1 + 0.0004) = 308.06 (printed 308.1); P_E from (mu - 1)_inf = 299.56e-6 is 4.886 (printed 4.89).

• Formula co (A = 33323e23, B = 111240e26, Cuthbertson’s B): 307.901e-6 at 5462.25 A and A/B = 299.560e-6, both as printed.

• Doubt: CO is weakly polar; for polar gases the dielectric P_A + P_E comes from a Debye extrapolation to infinite temperature (p. 12). Whether CO was treated so is not stated; if not, the 4.98 includes a (tiny) orientation term.

• Table IV’s compressibility of CO (100 L = 0.04) added to the not-extracted list.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-195 velsko_1986, CO note only

• The record has no datasets for any gas (no quantity for an index difference n(532) - n(1064)); CO’s values were already transcribed in the notes (Table I c = 54.27 mrad/(psia cm), l_c = 7.876 cm; Table II Delta n = 73.61e-7 against Cuthbertson’s 71.6e-7; images checked). Only the “CO, air: not curated” sentence is changed. CO’s measured/calculated gap, 2.8 %, exceeds the stated 2 % (95 %).

• Format need (repeated): a refractivity_difference quantity.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-196 sneep_2005, CO added (Table 2, Eq. 17)

• Transcribed (script, Table 2, image checked): rayleigh_CO 6.19(0.4)e-27 cm^2 (primary, king_factor 1.016), n_based_CO 6.82e-27 cm^2 (check), at 18 788.4 cm^-1.

• Formula co_eq17 (the authors’ fit to Smith et al.’s 38 CO values, 15 C, 1013 hPa, ideal-gas scaling). Misprint: the numerator “(0.456 +- 0.01) x 10^12” (equation image checked) gives n - 1 = 229.5e-6 at 532 nm, not Table 2’s 325e-6, and 231.5e-6 at 167.2 nm against Smith’s 532e-6 (15 C). With 10^14 it gives 324.53e-6 at 532 nm and follows smith_1976 (scaled 273.15/288.15) to -0.83 … +0.26 % over 167-288 nm. Correction recorded in the formula’s check, not applied. The n-based 6.82e-27 needs 325.1e-6 (324.53e-6 gives 6.80e-27, 0.3 % apart; rounding of the printed coefficients).

• F_k = 1.016 checks from rho_p = 0.0048 (Bridge and Buckingham 1966) through Eq. 7.

• Doubt: the 38 points include Smith’s ten Lagrange-interpolated cells.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-197 zhao_2026, CO added (Tables 1-3)

• Transcribed (script; images of Tables 1-3 checked): static_CO 4.88146(24) (check), hohm_2013_ri_CO 4.88(26) (reproduced), tsankova_2018_dp_CO 4.888(45) (check: Zhao’s reduction of Tsankova et al.’s dielectric data to the electronic part at 297 K), kumar_meath_1994_dosd_CO 4.89(53) (reproduced), all cm^3/mol; kumar_meath_1994_moments_CO S(-4), S(-6), S(-8) = 48.26(48), 292.9(29), 2308(64) au (reproduced, 3 points).

• Reconstructed A_R_1566_CO = 4.896795(185) cm^3/mol at 1566 nm, 297.53 K (primary): static + 0.015351 (dispersion) - 15.65e-6 (A_mu); uncertainty 37.8 ppm (Table 2’s CO column without S(i) and A_mu). The CO total 49 ppm checks as the root sum of squares (48.9).

• Doubt: the RI and DOSD uncertainties print as 0.26 and 0.53 cm^3/mol (5 %, 11 %), implausible; possibly 4.8826 and 4.8953 misprinted as value(uncertainty). Taken as printed; needs Hohm 2013 and Kumar & Meath 1994.

• Doubt: which literature values received Bishop and Cheung’s vibrational subtraction (20(1)e-43 C^2 m^2/J = 0.1213 au) is not said (the DP value at least).

• Not extracted: CO’s B_eps 7.97(40) cm^6/mol^2 and B_T -8.5(2) cm^3/mol (Table 1; sources [32-36] unassigned per gas), noted in the record.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-198 van_duijnen_1998, CO added

• table1_CO 13.16 au (Table 1 ‘exp’, image checked; Table 11 repeats 13.16, not written twice), use = "excluded" like every value of this record. 0.8 % above zhao_2026’s static 13.059 au, about 1.5 % below the 589 nm electronic value that zhao_2026’s moments imply (13.36 au).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-199 ingersoll_1956, CO added (Table III column 7)

• dispersion_CO 17 points (relative to 5780 A, scale V(5780) = 11.03, primary) and absolute_CO 4 points (check), micro-arcmin/(Oe cm), 1 atm, 0 C, ideal gas. Image checked; the column is smooth (no outlier like CO2’s 9000 A value).

• Doubt: the sample was only 93.7 % CO (H2 3.5, N2 2.4, CO2 0.2, O2 0.2 %); “correction has been made … for the impurities in CO” (p. 2), method not stated.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-200 simmons_1978, CO note only

• CO appears only in Fig. 3 (no printed value); the note now says so.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

Records searched for CO with nothing to add

zeiss_1977, margoliash_1978, alms_1975, kumar_1985, hohm_1990, hohm_1994, burns_1986, essen_1953, sharipov_2017 (CO only cited, [36]), gordon_1993 (a CO line used as a wavelength for argon), inn_1953 (CO + O dissociation limits), achtermann_1991 and ingersoll_1954 (impurity analyses), ciddor_2002 (mention only): no CO data. Every other curated source’s paper was scanned for “CO” and “carbon monoxide” (markup stripped).

TC-201 christiansen_1998 (new; CO, N2, Ne)

• Transcribed (script, Table X only, image checked): electronic_CO 5 points (static 13.06, 457.9-632.8 nm), total_static_CO 13.18, werner_meyer_CO 13.08 (reproduced), bridge_buckingham_CO 13.34 at 632.8 nm (reproduced), electronic_N2 5 points, alms_N2 5 points (reproduced from alms_1975), bridge_buckingham_N2 11.92, electronic_Ne 2.66, experiment_Ne 2.669 (reproduced, source doubtful). Theory datasets are use = "check", uncertainty 0.03 a.u. (“a few hundredth”, level not stated).

• Checks: Table IX’s estimates 1, 2 and final values recompute from their rows (CO, N2, Ne). Table X’s dynamic values = estimate 1 static mean + Table VII’s k > 0 Cauchy moments, to 0.005 a.u.; the CO pure vibrational terms of Table X from Table VIII.

• Formulas: co_cauchy, n2_cauchy (Table VII components), co_vibrational (Table VIII, CCSD(T)).

• Misprints (formula checks, not data errata): Table VIII CCSD(T) CO omega_1 printed 0.09785 for 0.009785 (image checked; only 0.009785 gives Table VI’s 0.37 and Table X’s optical values); Table VII headers S_zz(6), S_zz(8) for S_zz(-6), S_zz(-8); Table IX’s MP2 and CCSD(T) previous-calculation rows printed shifted one column pair left; BH estimate 2 20.090 for 20.909 (BH not curated). CO total static 13.18 vs recomputed 13.19 (rounding).

• Doubts: Table X’s footnotes are inconsistent: neon’s experimental 2.669 cites Ref. 57 (Muenter’s HF paper); N2’s anisotropy 4.69 is marked g (Ref. 49) but the text says Ref. 56. Christiansen’s Alms values at 632.8 nm and static (11.88, 11.74) do not match alms_1975’s Table I converted to a.u. (11.92, 11.76); the others do. Wavelength medium of Table X not stated (theory recorded as vacuum, experiment as air).

• Not extracted: Tables II-V (benchmarks, dipole moments), the anisotropies, HF, BH, CH+.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-202 bishop_1982 (new; Bishop and Cheung, vibrational polarizabilities)

• No datasets (no quantity for a vibrational polarizability; format need, as for sharipov_2017). Six formula entries (co, co2, n2o, o3, ch4, sf6) hold each curated molecule’s printed omega_n, A_n, P_n and total alpha (10^-40 C^2 m^2 J^-1), from the table images (Tables 1, 2, 4, 6).

• Checks: every P_n = 1e5 A_n/(3 pi^2 omega_n^2) and every total = 0.441 sum P_n reproduce the printed digits.

• HITRAN comparison (optmat.gas.infrared): CO2 -17 %, N2O -8 %, CH4 -4 %, SF6 +8.7 % (Bishop and Cheung relative to HITRAN). CO (0.1213 au) and O3 (0.788 au) have no HITRAN bands yet; christiansen_1998’s ab initio CO value is 0.1246 au.

• Doubt: footnote letters differ between tables (CH4’s d = 5 % in Table 4, but d =

  10 % in Tables 1-2; SF6’s b = 5 % in Table 6). Checked on the page images. The authors say their error classes should be at least doubled.

• O3’s 0.13e-40 (0.117 A^3) is 40-60 % below sharipov_2017’s and Naves et al.’s computed values (relevant to the ozone model).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-203 may_2008 (new; O2 static polarizability and magnetic susceptibility)

• Transcribed (text, inline points, pp. 2, 3, 11): recommended_O2 A_eps,273K = 3.9576(8) cm^3/mol (primary); eq18_O2 3.9578(2), 3.9582(2), 3.95824(7) at 273, 293, 323 K (primary; the 273 K row excluded as averaged into the recommended value); alpha_e_O2 1.7456(3)e-40 F m^2 (check, = recommended); reproduced: Schmidt and Moldover 2003 1.7461e-40 (273 K), Younglove 1972 1.7447e-40 (liquid, 100-140 K), Minaev 2004 1.7329e-40 and Wheatley 2007 1.7477e-40 (ab initio, 0 K).

• Checks: 3 eps0 A_eps/N_A = 1.74563e-40 (printed 1.7456).

• Reproductions: zhao_2026’s may_2008_O2 (293 and 323 K) are this paper’s Eq. (18) values and may_2008_297K_O2 their interpolation: their reproduced_from can now name may_2008 (zhao_2026’s O2 entries not edited here). rourke_2021 has no O2.

• Finding (for zhao_2026, not changed): zhao_2026’s O2 A_mu, 3449e-6 cm^3/mol, equals the CRC chi_M 43.34e-9 m^3/mol divided by 4 pi (3.4489e-3: a cgs molar susceptibility), whereas the A_mu of the working equation is chi_M/3 (SI) = 14.45e-3 (May’s own chi_M00 gives 14.31e-3). nie_2025, same group, uses the chi_M/3 convention (Ar -80.9e-6 = rourke_2021’s). If zhao_2026 used the cgs value for CH4 (-17.4e-6) and CO (-15.65e-6) too, their A_mu are 4 pi/3 too small in magnitude (a < 10 ppm effect there); for O2 the reconstructed A_R_1566_O2 and the static value move by 2800 ppm depending on the convention and on whether the paramagnetic term belongs at optical frequency at all. Open.

• Not extracted (no quantity): chi_M00 = 42.92(6)e-9 m^3/mol, b_mu = -1.8(5) cm^3/mol, Table I’s historical chi_M00 values, Table III (epsilon_r, mu_r at 2 kHz and 2.6-7.2 GHz), the Eq. (19) fit’s b_eps = 0.16, c_eps = -50 (no physical significance per the authors).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-204 nie_2025 (new; H2, N2, Ne at 1566 nm)

• Transcribed (script; Tables I, II images checked): static_{N2,Ne,H2} 4.38705(16), 0.994742(46), 2.031027(71) (check); literature (Table II): egan_2019_N2 4.38679(7) (check, Nie’s conversion), gaiser_2018_Ne 0.9947114(24) (reproduced), hohm_kerl_1990_H2 2.033(4) (reproduced; not a number printed in hohm_1990), olney_1997_N2 4.3887(18), lesiuk_2020_Ne 0.99470(13), sun_2021_H2 2.03080(12) (reproduced); olney_moments_{N2,Ne,H2} 3 points each (reproduced).

• Reconstructed A_R_1566_{N2,Ne,H2} = 4.396554(155), 0.995627(45), 2.037359(66) cm^3/mol at 1566 nm, 297.53 K (primary), inverting Eq. (3) as for zhao_2026; the (1 + m_e/m_N)^3 factor applied to H2 with the proton mass (+5 ppm), omitted for N2, Ne.

• Checks: budget totals are root sums of squares; H2 static 26 ppm above raj_2018’s 296.15 K average; Ne 31 ppm above gaiser_2018; Ne A_R 44 ppm above rourke_2021’s 1550 nm value moved to 1566 nm.

• Doubts: the whole scale is calibrated on argon’s A_eps from gaiser_2018 (not independent). Lesiuk’s neon as quoted (0.99470) is 86 ppm above lesiuk_2020’s alpha_0 converted (0.994615). The reduced-mass factor’s “nuclear mass” is ambiguous for a molecule (5 ppm for H2). Table II’s confidence level is not printed (k = 1 assumed).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-205 yang_2025 (new; two-colour refractometry, Ne, Ar, N2, He)

• Transcribed (script, Table I, image checked): A_eps_{Ne,Ar,N2} 0.994709(8), 4.14070(3), 4.38692(3) cm^3/mol (primary, static, about 303 K); literature rows (reproduced): Ne lesiuk_2020 0.9946(1), gaiser_2018 0.994711(2); Ar lesiuk_2023 4.1408(7), gaiser_2018 4.14069(1); N2 Kumar and Meath [22] 4.388 (no uncertainty), Schmidt and Moldover 2003 4.3877(2); He theory 0.51725408(5), gaiser_2018 0.517254(1).

• Formulas (A_2 has no quantity): ne_cauchy, ar_cauchy, n2_cauchy (A_eps, A_2 of Eq. 4) and he_A2. A_2 converted to S(-4) (computed): Ne 2.84906 (lesiuk_2020 2.850), Ar 27.9486 (lesiuk_2023 27.976, -0.10 %), N2 30.1086 (Olney 30.11), He 1.543206.

• Doubts: the static A_eps depend on assumed A_4, A_6, A_mu (not printed); the authors themselves prefer capacitance values of A_eps; whether A_eps should be primary beside gaiser_2018 (Ne, Ar) is open. N2’s A_eps is 3.9 sigma below Schmidt and Moldover’s capacitance value and 0.8 sigma below nie_2025. Ref. 22’s citation is truncated in the curators’ extracted text (volume/page taken as christiansen_1998’s Ref. 50, presumed the same paper). Temperatures “near 303 K” only.

• Also confirms the nie_2025 doubt: Table I quotes lesiuk_2020’s neon as 0.9946(1), consistent with 2.66080 au, not nie_2025’s 0.99470(13).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-206 st_arnaud_1976 (new; CH4 refractivity virial)

• Transcribed (script; the one table, image checked): B_R_this_work 6.60(38) cm^6/mol^2 at 6328 A, 302.87 K (primary, one standard deviation); A_R_this_work 6.533(2) cm^3/mol (EXCLUDED: 0.62 % below the curated CH4 dispersion at 632.99 nm and 1.0 % below Buckingham and Graham; the authors note it matches the static dielectric value); reproduced: Buckingham and Graham A_R 6.600(2), B_R 7.15(35) (buckingham_1974), Olson 1975 A_R 6.614(2) at 5462 A, B_R 5.5(1.0); B_R_kirkwood_theory 6.11 (check, ‘inf’).

• Doubt: the table prints 302 K, the text 29.72 C (302.87 K) and the theory 302.7 K. The exclusion of A_R is a curation judgment (to confirm).

• Not extracted: B_P -42.0(4) and Olson’s -44.0(3.0) cm^3/mol (no quantity).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-207 st_arnaud_1979 (new; CO2 and SF6 refractivity and dielectric virials)

• Transcribed (script; Tables I-III, images checked): per gas, A_R_this_work (CO2 6.658(21), SF6 11.348(21) cm^3/mol, 6328 A, 323 K, 3 sigma, primary; both 0.23 % above the curated fits), B_R_this_work (CO2 3.3(3.6), SF6 36.0(1.8) cm^6/mol^2, primary), B_R_theory (6.9, 24.8, check), Buckingham and Graham A_R (6.650, 11.34) and B_R (3.2(1.6), 29.0(5.4)) reproduced from buckingham_1974, and the dielectric A_eps (CO2 7.350(6), Bose and Cole 1970; SF6 16.543(17), Hosticka and Bose 1974) and B_eps (50.7(9), 63.3(2.8)) reproduced (static; include vibrational terms).

• Doubt: the dielectric B_eps are stored as refractivity_virial_coefficient at ‘inf’ (the vocabulary’s “dielectric, for a static value”), but they contain B_FIR and B_IR besides the electronic pair term; the dielectric A_eps include the vibrational polarizability. The Buckingham-Graham wavelength (6328 A) is assumed from st_arnaud_1976 (see buckingham_1974).

• Not extracted: B_P; Landolt-Bornstein A_R and Refs. 7, 8, 9 (no wavelength); B_FIR, B_IR.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-208 buckingham_1974 (new; Buckingham and Graham, refractivity virials)

• Transcribed (script; Tables 1, 4-5, images checked): Table 5 for Ne, Ar, N2, CO2, CH4, SF6 at 633.0 nm (in vacuo), 299-300 K: B_R_<gas> (primary; sigma = the “estimated uncertainty” column), B_F_theory_<gas> (check), A_R_<gas> (EXCLUDED: 0.10-0.40 % above the curated dispersion for all six, beyond the stated +-0.2 % worst case); Table 1: Bose and Cole 1970 argon A_eps 4.1397(6), B_eps 0.72(12) (reproduced).

• Checks: Table 1’s other curated rows equal orcutt_1967 (not extracted again).

• Misprint (header, no data effect): Table 5’s B_R unit “m^6 mol^-3” for m^6 mol^-2.

• Citation: volume 337 (curators’ copy, JSTOR cover, vukovic_1996), cited as 336 by st_arnaud_1979, burns_1986, achtermann_1991, hohm_1990.

• Reproductions to relink (not edited): achtermann_1991 (A_R and B_R at 299 K, theory at 298 K), burns_1986 (literature A_R and B_R), hohm_1990 (Table 1), vukovic_1996 (SF6) name B&G by citation; they can now name buckingham_1974.

• Doubts: the measurement wavelength is inferred from the text’s example (lambda_0 = 633.0 nm, He-Ne); the exclusion of A_R is a curation judgment; the “estimated uncertainty” is a sum of three terms (stored as sigma, level not stated).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-209 bridge_1964 (new; depolarization letter)

• Transcribed (script, Table I, image checked): alpha_<gas> for Ar, Xe, SF6, H2, N2, O2, CO2 (A^3 at 6328 A), reproduced from Landolt-Bornstein refractive indices (as the authors state). Agree with the curated fits at 632.99 nm to -0.06 … +0.28 %, except SF6 (+0.71 %).

• Structural fix: the curators’ extracted cells lost the gas column and headings; rows assigned in the printed order (image). The depolarization ratios and anisotropies are not extracted; several depolarization cells are misread in the curators’ extraction.

• A letter, not the 1966 Proc. R. Soc. paper that sneep_2005 and christiansen_1998 cite (not in the curators’ library).

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-210 lewis_1933 (new; D2 spin, short record)

• No datasets. States the even-J-stronger alternation in the D2 Fulcher bands and spin 1 (“2/2”), qualitatively; no ratio. The curators’ copy interleaves an unrelated letter.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-211 farkas_1934 (new; D2 ortho-para conversion, short record)

• No datasets. PRINTS the nuclear statistical weights (t + 1)(2t + 1) (ortho) and t(2t + 1) (para) (p. 482), ortho = even J for Bose-Einstein statistics (p. 486), spin 1 most probable (p. 487, with the caveat that spin 1/2 is not excluded by these data), and n-D2 = 2/3 o-D2 + 1/3 p-D2 (p. 488): the 6 : 3 weights of raj_2018 (TC-105), which murphy_1934 gives as a ratio only.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

CO: what is now curated (summary)

• Refractivity, 167.2-288.2 nm (vacuum, 0 C, real gas): smith_1976 experiment_CO 28 points, 0.10 % (> 220 nm) / 0.58 % (< 220 nm), 90 %; plus the paper’s Lagrange values (check) and Koch 1914 via the ICT (237.9-289.4 nm, reproduced).

• Refractivity, 480-671 nm (air, 0 C, ideal): cuthbertson_1920 experiment_CO 8 points (rms 1.2e-8, scale 0.045 %), formula co_1920; four older values at 546.1 nm (reproduced).

• 546.2 nm (vacuum, 25 C, ideal): watson_1936 green_CO 307.9e-6 (primary), formula co (A from Watson, B from Cuthbertson).

• 532.2 nm: sneep_2005 Rayleigh 6.19(0.4)e-27 cm^2 (F_k 1.016) and the n-based value; formula co_eq17 (fit to Smith, numerator misprint).

• 1566 nm: zhao_2026 A_R_1566_CO 4.896795(185) cm^3/mol at 297.53 K (reconstructed, primary, 38 ppm): the most accurate CO datum.

• Theory: christiansen_1998 electronic_CO (static 13.06 au and 457.9-632.8 nm) with its Cauchy moments (formula) and pure vibrational oscillators (formula).

• Static anchors: electronic 13.059 au (zhao_2026 static, still containing the 1566 nm infrared response), 13.06 au (christiansen_1998 theory), 13.08 au (Werner and Meyer, reproduced); dielectric (electronic + vibrational) 4.98 cm^3/mol (watson_1936, reproduced) and Tsankova et al. reduced by Zhao 4.888(45) cm^3/mol; vibrational 0.1213 au (bishop_1982) and 0.1246 au (christiansen_1998).

• Dipole sums: Kumar and Meath S(-4), S(-6), S(-8) = 48.26, 292.9, 2308 au (via zhao_2026); christiansen_1998’s CCSD means 47.33, 274.7, 2267 au (computed).

• Faraday: ingersoll_1956 Verdet constants 363.5-987.5 nm (17 + 4 points).

• Gaps: 290-450 nm (no measurement; theory from 457.9 nm only), below 167 nm (the Gallagher et al. photoabsorption, TC-212), the infrared (no CO bands in data/external/hitran).

Page numbers are journal pages (journal page = PDF page + 7) unless marked “pdf”.

TC-212 gallagher_1988 (Gallagher, Brion, Samson & Langhoff, J. Phys. Chem. Ref. Data 17, 9 (1988)): no numerical data

• Main finding: the paper holds no numerical cross sections and no recommended values. Tables 2-19 list the data sources per molecule; every cross section is a point or line in the figures. Section 5 (p. 28): “A tabular listing of all data presented in the figures is available in JILA Data Center Report No. 32”. That report is where the numbers are (not available to the curators). Recommended tabulated values were expected; there are none. The record has no datasets; nothing was digitised from the figures.

• Identity checked against PDF page 2 (journal p. 9): title, authors, volume and year agree. The curators’ library’s author-check failure comes from the publisher’s cover sheet (PDF page 1).

• Stated accuracy of sigma_abs^T (p. 28), quoted in the record: better than +-10 % “in almost all cases”, better than +-5 % for N2, CO, O2, NO, CO2, N2O, H2O, NH3, CH4, H2S, CS2, COS; “a few data sets may be less accurate than +-10% … particularly in the immediate threshold region”. Level not stated. H2 and SF6 are not in the 5 % list.

• Method statements quoted with pages: photon I0/I 1-2 % (pp. 19-20), manometer “a few percent” (p. 20), TRK “better than ~5%” (p. 23), partials +-15 % and +-10 % (p. 29), Eq. 2.22 sigma[Mb] = 109.75 df/dE[eV^-1] (p. 17).

• Extraction faults in the curators’ library (none affect data, since none were taken): the reference list in the extracted Markdown numbers C. E. Brion and K. H. Tan, J. Electron Spectrosc. 23, 1 (1981) as 149 (the page image, p. 151, shows 148), so 149 appears twice; the markdown of Table 3 (N2) drops the row “a Adam 1983 E P — beta B 28-38” (it is in the image and the table note); the extractor’s table labels are shifted (Table 4, O2, is “unlabelled”).

• Per gas, the total-photoabsorption source rows (“Abs” ticked) were compared with the table images and their citations with the reference-list page images (pp. 149-153). All agree with the markdown except as noted.

• Format note: codespell flags the surname Wight (G. R. Wight, refs. 99, 138, 256) and a codespell:ignore comment cannot sit inside a multi-line TOML string, so the record writes it Wight (a TOML escape; the loaded notes read “Wight”). An alternative is adding wight to codespell’s ignore list in pyproject.toml.

CO (Table 5, p. 47; Fig. 24, p. 48)

Six measured sets: Lee 1973 (208, photon, AB, 20-70 eV), Watson 1975 (253, photon, AB, 20-35), Wight 1976 (256, dipole (e,e), TRK, 18-70), de Reilhac 1977 (170, photon, AB, 25-118), Cole 1978 (164, photon, AB, 36-83), Samson 1984 (236, private communication, photon, AB, 14-125). All six are in the figure legend. Stated accuracy better than +-5 %. Qualitatively (figure image): Wight’s (e,e) points above the photon sets at 20-30 eV; strong scatter of Samson’s points below ~19 eV. None of the six originals is in the curators’ library or curated.

N2 (Table 3, p. 34; Fig. 13, p. 35)

Seven measured sets: Denne 1970 (172, photon, AB, 150-525 eV), Lee 1973 (208, AB, 19-70), Watson 1973 (254, AB, 17-33), Wight 1976 (256, (e,e), TRK, 18-70), de Reilhac 1977 (170, AB, 24-125), Cole 1978 (164, AB, 35-250), Samson 1986 (236, private communication, AB, 15-107). All seven are in the legends (Watson only in panel a, Denne only in b). Stated accuracy better than +-5 %. Fig. 13(b)’s axis ends at 250 eV, so Denne’s 250-525 eV values (Table 3’s range) are not shown: check against Report No. 32 or Denne. Close agreement of all sets above ~19 eV (figure image). None of the originals is in the curators’ library. Compare with the curated N2 photoabsorption gurtler_1977 (figures only, 12-30 eV) when numbers become available.

O2 (Table 4, p. 40; Fig. 18, p. 41)

Eight measured sets: Denne 1970 (172, AB, 150-525 eV), Lee 1973 (208, AB, 17-70), Watson 1973 (255, Phys. Lett. A 44, 293; AB, 20-30), de Reilhac 1977 (170, AB, 24-124), Cole 1978 (164, AB, 36-250), Mehlman 1978 (219, AB, 36-207), Brion 1979 (149, dipole (e,e), TRK, 5-275), Samson 1984 (236, private communication, AB, 12-107). All eight in the legends (Watson only in a, Denne only in b; b ends at 280 eV, so Denne’s 280-525 eV is not shown). Reference 149 verified on the page image (the markdown’s reference list also gives the number 149 to ref. 148). Stated accuracy better than +-5 %. Structure from threshold (about 12.1 eV) to ~24 eV. Overlaps the curated weissler_1952 (Table 1, 303.8-1306 A = 9.5-40.8 eV): to compare when numbers exist. None of the originals is in the curators’ library.

CO2 (Table 7, p. 62; Fig. 37, p. 63)

Five measured sets: Lee 1973 (208, AB, 17-70 eV), Watson 1975 (253, AB, 19-33), de Reilhac 1977 (170, AB, 24-125), Hitchcock 1980 (195, Chem. Phys. 45, 461; (e,e), TRK, 8-80; printed “Hitchock”), Samson 1984 (236, private communication, AB, 14-107). All five in the legends (Watson only in a). Stated accuracy better than +-5 %. CO2 is the deferred gas (as ityaksov_2008_co2); the curated inn_1953 covers CO2 below the ionisation threshold only. None of the originals is in the curators’ library.

N2O (Table 8, p. 69; Fig. 43, p. 70)

Five measured sets: Lee 1973 (208, AB, 17-70 eV), de Reilhac 1977 (170, AB, 25-120), Cole 1978 (164, AB, 36-250), Brion 1978 (147, Chem. Phys. 34, 141; (e,e), NM, 17-60), Hitchcock 1980 (195, (e,e), TRK, 8-74). All five in the legends. No Samson/Haddad set for N2O. Stated accuracy better than +-5 %, although the figure shows Cole’s points visibly below the (e,e) and Lee sets at 36-50 eV and de Reilhac’s 25 eV point far below (qualitative, from the image; to quantify from Report No. 32). Brion 1978’s normalisation reference is not stated in this paper. None of the originals is in the curators’ library.

CH4 (Table 11, p. 89; Fig. 60, p. 90)

Five measured sets: Lee 1973 (208, AB, 19-68 eV), Backx 1975 (99, J. Phys. B 8, 3007; (e,e), TRK, 14-80; method printed “DIF”, read as a poorly printed “DIP”), de Reilhac 1977 (170, AB, 28-100), Lee 1977 (209, J. Chem. Phys. 67, 1237; AB, 17-24), Samson 1984 (236, private communication, AB, 13-124). All five in the legends (Lee 1977 only in a). Doubt: the stated accuracy is better than +-5 %, but in Fig. 60 Lee 1973 and Backx lie visibly above Samson from about 24 eV, by tens of percent at 30-70 eV (qualitative reading of the image; not digitised). Any CH4 model above ~24 eV must choose between the two groups; Report No. 32 or the originals, and the later dipole (e,e) CH4 work of Brion’s group (not in the curators’ library), are needed to decide. None of the originals is in the curators’ library.

SF6 (Table 17, p. 130; Fig. 95, p. 131)

Five measured sets: Sasanuma 1971 (reference “a”, a conference paper; “Data taken from Lee et al., Ref. 209”: reproduced via Lee 1977), Blechschmidt 1972 (141, Chem. Phys. Lett. 14, 33; 15-50 eV), Lee 1977 (209, 16-65), Hitchcock 1978 (196, J. Phys. B 11, 3245; (e,e), TRK, 5-230, plotted only at about 160-230 eV), Hitchcock 1979 (197, J. Phys. B 12, 2153; (e,e), TRK, 5-63). Photon normalisation printed “Ab”. Figure-legend misprint: Sasanuma is labelled “*211”, but ref. 211 is Lucchese and McKoy’s CO calculation; the table’s note says the data come from ref. 209 (not an erratum: no value depends on it). SF6 is not in the +-5 % list; the figure shows Blechschmidt’s curve far above the others at 16-22 eV and below them above ~38 eV (qualitative). The HITRAN SF6 infrared and the Shelton phase-matching tests are unaffected (these are > 15 eV).

H2 (Table 2, p. 30; Fig. 10, p. 31)

Five measured sets: Cook 1964 (166, J. Opt. Soc. Am. 54, 968; AB, 16-22 eV; a different paper from the curated O2 metzger_1964), Denne 1970 (172, AB, 150-280), Backx 1976 (138, J. Phys. B 9, 315; (e,e), TRK, 10-70), Lee 1976 (207, J. Quant. Spectrosc. Radiat. Transfer 16, 873; AB, 17-70), Samson 1985 (236, private communication, AB, 15-124). All five in the legends. Not in the +-5 % list. Close agreement above ~18 eV (image). D2 is not in the compilation.

O3 and the other curated gases

O3 is not among the 21 molecules; neither are D2 and the noble gases. NO, H2O, NH3, the hydrogen halides, H2S, CS2, OCS, SO2, Cl2 and CCl4 are not curated species.

What remains untranscribed

Everything numerical: every cross section is in the figures (total photoabsorption Figs. 10, 13, 18, 24, 37, 43, 60, 95 for the curated gases; partials and fragments Figs. 11-12, 14-17, 19-23, 25-29, 38-42, 44-48, 61-63, 96-103). The numbers need JILA Data Center Report No. 32 or the original papers (not available to the curators). A digitisation of the figures as a stopgap would be a separate decision (the rules take numbers from tables).

Page numbers are journal pages unless marked “pdf”. Vacuum-ultraviolet photoabsorption of O2 and N2O (and the CO2 values of the 1952 letter), for a later complex-index model of the molecules.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

Conventions common to the vacuum-ultraviolet photoabsorption records (to confirm)

• Quantity. Total photoabsorption is recorded as the new absorption_cross_section (unit Mb, or cm2 where the paper prints a cross section); the earlier records (watanabe_1953, weissler_1952, metzger_1964, inn_1953) still use photoionization_cross_section for the same kind of value and were not changed. parameters.temperature_k is omitted everywhere: none of the five papers states the gas temperature (room temperature; Ditchburn & Heddle’s line analysis assumes 20 C).

• Conversion. The printed absorption coefficient (cm^-1, natural log, at 1 atm and 0 C) is kept as printed; scale = 1e18 / n0 gives Mb. Where the paper states its n0 it is used: Ditchburn & Heddle N = 2.705e19 (scale 0.0369686), Ladenburg & Van Voorhis N = 2.706e19 (0.0369549). These are 0.67-0.71 % above the ideal-gas Loschmidt number 2.6867801e19, so the stored cross sections are 0.7 % below alpha / n0 (to decide: paper’s conversion, as metzger_1964, or the physical n0). Watanabe et al. and Zelikoff et al. state no conversion: n0 = 2.6867801e19 (scale 0.0372192721), as watanabe_1953 and inn_1953.

• Integrated continuum f values are oscillator_strength datasets with an index abscissa and use = "check", as in the earlier records.

• Band oscillator strengths use the index v’ as abscissa.

TC-213 ditchburn_1953 (Ditchburn & Heddle, Proc. R. Soc. A 220, 61 (1953))

• Identity checked against the first page (pdf 2): correct.

• Table 1 (tbl_9b71613fa0c5, cells file only; image checked cell by cell, all agree): 21 group means means (nu mean, alpha mean, +- as sigma, probable error), 15 single-line values of the 205 cm path long_path and 44 of the 0.043 cm path short_path (both check: the same observations as the means). The script checks that each group’s bracketed observation counts add up to column 6 (all 21 do).

• Conversion with the paper’s N = 2.705e19 (reproduces its 1.81e-17 cm2 from 490 cm^-1); 0.68 % below alpha / 2.6868e19.

• Doubt (group mean): the group 64060-63810 cm^-1 (306 (7), 307 (6), 228 (3)) has the observation-weighted mean 63919 cm^-1, 291.8 cm^-1; the table prints 64108 and 277 +- 16. A mean wave number above all its lines is impossible, so the printed row is inconsistent; no single misprint explains it; kept as printed, no erratum. The other 20 groups reproduce (the 69484 group gives 69500 in nu, alpha exact).

• Doubt (errors): the text states the errors are 60 n^-1/2 cm^-1 (probable error); the printed ones are about 80 n^-1/2 (20 for n = 15-17; 16 for the n = 16 group above). Kept as printed.

• Text values: maximum 1.81 +- 0.1e-17 cm2 at 69000 cm^-1 (p. 67, check); continuum_f 0.215 +- 0.020 (note added in proof, p. 70, check).

• Comparison: about 20 % above the photoelectric maxima (watanabe_1953 380, metzger_1964 402 +- 20 cm^-1); the authors blame scattered light in Watanabe et al.’s work. Which to weight is for the model step.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-214 ditchburn_1954 (Ditchburn & Heddle, Proc. R. Soc. A 226, 509 (1954))

• Identity checked against the first page (pdf 2): correct (pdf 14 continues with Skyrme’s next paper).

• Table 1 (tbl_2b2a1247ae97, CSV; image checked, all 21 cells agree): band oscillator strengths f(v’, 0), v’ = 0-20, band_f, each cell with its own power of ten (value in E notation). v’ = 1, 18, 19, 20 extrapolated (p. 514) as excluded_rows.

• Text: band_sum 0.044 (p. 515), total_f 0.259 (abstract; < 20 %, p. 515).

• All excluded: bethke_1959 finds the band strengths 80-140 times too large (pressure-broadened photoelectric measurement; matsui_2003 within 15-28 % of Bethke). Kept for the record.

• Reproduction found: bethke_1959/ditchburn_heddle (Table I column six) reproduces all sixteen values v’ = 2-17 exactly, and its remainder 2276e-5 and total 4450e-5 are the sums of this table (checked 2026-09-25). Its reproduced_from should become ["ditchburn_1954"].

• Not extracted: Table 2 (collisional deactivation cross sections Q per (v’, J’), italic measured / roman calculated, typeface lost), not optical data.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-215 ladenburg_1933 (Ladenburg & Van Voorhis, Phys. Rev. 43, 315 (1933))

• Identity checked against the first page: correct.

• Table I (tbl_0010b8557526, CSV; image checked, agree): Ladenburg & Wolfsohn’s (1932) (n - 1) x 10^7 at eight round wave numbers 52084-25000 cm^-1 extracted as lw_refractivity (reproduced, original not in the curators’ library; “accurate to within one unit”, bound). State assumed N.P.T. = 1 atm, 0 C (the paper’s C uses N at N.P.T.); L-W’s own reduction not described. Wave numbers: vacuum assumed (irrelevant at 1e-7).

• G, H, I columns (continuum contribution, remainder, one-term fit) are in the notes only (no vocabulary quantity; format need: a partial refractivity, useful as the check of a Kramers-Kronig integral of the S-R continuum). H = (n - 1) - G exactly.

• Formulas: lw_1932 (L-W’s three-resonance formula, reproduced) and continuum_plus_one_term (Eq. 4 with f_s = 7.143, lambda_s = 501.3 A). Doubt: both reproduce the table only with C = 1.2096e6 cm^-2, 0.30 % above N e^2 / 2 pi m c^2 from footnote 15’s constants (1.2060e6): the one-term I to 0.5e-7, the three-term (n - 1) to 3e-7. The origin of the 0.30 % is not identified.

• Text: sr_maximum about 490 cm^-1 at 69000 cm^-1 (N = 2.706e19; 10 % bound from “5-10 percent”); continuum_f 0.193 (check). The abstract’s position 6.8e4 cm^-1 against the text’s 69000 (= 1450 A): rounding, not corrected.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-216 watanabe_1952 (Watanabe, Inn & Zelikoff, J. Chem. Phys. 20, 1969 (1952))

• Identity: the curators’ copy is the 1952 letter (pdf 2, received 13 October 1952), titled without a part number. It is the series’ preliminary communication, not Part I: Part III (inn_1953) refers to “Part I of this series” for the method, i.e. the O2 paper watanabe_1953; Part II is zelikoff_1953.

• OCR: the curators’ extracted text of this page is poor (“10SQ-2S00A”, “14S0A”, “0.8SA”); every value was read from the rendered page images (pdf 2-3).

• Gases: O2 (Fig. 1, figure only) and CO2 (text only).

• Transcribed from the text: o2_sr_maximum 380 cm^-1 at 1420 A (check: the same measurement as watanabe_1953/sr_maximum); o2_lyman_alpha 0.33 cm^-1 (excluded: pressure-dependent, about 75 mm Hg); co2_lyman_alpha 2.0 cm^-1 (check: inn_1953 gives 1.97); co2_continuum_maxima about 14 cm^-1 at 1475 A and 18.5 cm^-1 at 1335 A (primary: the only printed k of these maxima; inn_1953 has them only in figures).

• Doubts: the reference state of k is not stated in the letter (NTP assumed, as the full papers); the Lyman-alpha wavelength 1215.7 A is taken as in watanabe_1953. Whether preliminary values should be primary when the full paper gives the maxima only in figures is open.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

TC-217 zelikoff_1953 (Zelikoff, Watanabe & Inn, J. Chem. Phys. 21, 1643 (1953))

• Identity checked against the page image (pdf 2): Part II, nitrous oxide, correct.

• Figures only for k (Figs. 1-4, 1080-2100 A).

• Transcribed from the text (checked against the page images, pdf 3-5): continuum_b_maximum 3.82 cm^-1 at 1820 A (p. 1646); continuum_c_maximum 147 cm^-1 at 68940 cm^-1 (p. 1646; the continuum under the bands); continuum_d_maximum 2465 cm^-1, position 1285 A from the abstract (p. 1645; includes a sharp Rydberg band); band_1178 3010 cm^-1 at 84900 cm^-1 (check, band peak); continuum_f 0.0015, 0.0211, 0.367, about 0.1 with the stated integration limits (checks).

• Reproduced: romand_mayence 118 cm^-1 (1450 A) and 3.13 cm^-1 (1840 A), from Romand & Mayence (1949), not in the curators’ library; reference state not stated.

• Not extracted: Table I (band positions and relative intensities of transition C; image checked, the cells agree), Eqs. 1-3 (spectroscopic formulas).

• Doubts: NTP assumed 0 C, 1 atm; the region D maximum’s wavelength is the abstract’s, the text gives only the value.

• Status: decided (2026-09-25): accepted with TC-218; points marked open or to confirm above remain open.

Reproductions found in curated records

• bethke_1959/ditchburn_heddle reproduces ditchburn_1954 Table 1 (v’ = 2-17, all equal) and its sums: set reproduced_from = ["ditchburn_1954"].

• watanabe_1953/sr_maximum (380 cm^-1 at 1420 A) is the same measurement as watanabe_1952/o2_sr_maximum (kept as a check in the letter’s record).

• inn_1953/lyman_alpha (1.97 cm^-1) supersedes watanabe_1952/co2_lyman_alpha (2.0, check).

• Values quoted only in the notes of earlier records, now curated: Ladenburg & Van Voorhis’s 490 cm^-1 maximum and f = 0.193 (ladenburg_1933; quoted in watanabe_1953, weissler_1952, bethke_1959), Ditchburn & Heddle’s 490 cm^-1 at 1450 A and f = 0.215 +- 0.02 (ditchburn_1953; quoted in metzger_1964, bethke_1959). No dataset of those records holds them, so nothing changes.

TC-218 Integration: ozone and carbon monoxide (2026-09-25)

• Interface (decision 3):

  • optmat.gas.models.base.Model.complex_polarizability, optmat.gas.models.base.Model.refractive_index and optmat.gas.models.registry.refractive_index added. Transparent models return a zero imaginary part.

  • The real-part methods of an absorbing model warn (ModelAbsorptionWarning) where |Im alpha / Re alpha| > 1e-4.

  • A species without an equation of state (ozone) takes the ideal-gas density in the model methods.

• Ozone data:

  • Thirteen files from the MPI-Mainz UV/VIS atlas are committed gzipped and byte for byte, with SHA-256s and the atlas’s citation, in data/external/mainz_uvvis/PROVENANCE.md.

  • The atlas asks to be cited; it states no redistribution terms. Check: is committing the data files acceptable (as for Henke’s files), or should only derived tables be kept (as for HITRAN)?

• Measured-absorption term (optmat.gas.absorption, data/gas/absorption/O3.toml):

  • The windows are Serdyuchenko 293 K for 213.33-1100 nm, Yoshino 1993 for 185-213.33 nm (0.0135 nm, on an absolute scale at 12 lines; the paper is not in the curators’ library), Mason 1996 for 110.2-185 nm (the atlas’s digitisation of Fig. 5) and the curated Ogawa & Cook Table I for 103.3-110.2 nm.

  • Gaussian smoothing is 50 cm^-1 FWHM in wavenumber (decision 1). The Kramers-Kronig transform is an FFT principal value, checked against a direct midpoint sum to 2e-4.

  • The Hartley-band strength is 0.0766, against Kumar & Thakkar C’s 0.0787 (-2.7 %: the newer cross sections).

• The ozone fit (fit/O3):

  • The model is the absorption term, plus kumar_2011_supplement/idos_C above 20.6 eV as fixed poles (fixed_intervals), plus one fitted oscillator for 12-20.6 eV (at Ogawa & Cook’s effective 16.15 eV), plus HITRAN below 2500 cm^-1.

  • It is fitted to swift_1988 (10 % bound), cuthbertson_1914/ozone_adopted (1-2 %) and kalugina_2015/best_estimate with correction_au = [1.46, 0.4]: Naves et al.’s full zero-point correction ([ ]^{1,0} + [ ]^{0,1}, TC-190).

  • Result: f(12-20.6 eV) = 2.55 +- 0.07 (A 1.83, C 2.18, B1 2.48); chi2 3.6 for 6 dof.

  • Check the ZPVA choice. Sharipov’s 0.088 a.u. would lower n - 1 by 2.5 %. Sharipov calls his own treatment inadequate for O3, and Naves’s value is 1.46. With Naves’s value, theory and the refractivity data agree; with Sharipov’s they do not (the prototype’s chi2 rose to 17 for the static point).

• The Cuthbertsons’ ozone dispersion (Table XI) is a validator, not fitted:

  • Its 480/670.8 nm ratio is 1.0498. The model, and every variant of it considered, gives 1.041-1.042.

  • Replacing their 1909 O2 dispersion (subtracted with a factor of 15) by the modern O2 fit explains 0.28 % of the difference (1.0498 -> 1.0469).

  • The rest (0.6 %) is about 6 times their stated 1/200 accuracy of the dispersion.

  • Fitted with its stated uncertainty, it would drag the remote strength to 2.11 at chi2 193 for 8 points.

  • Open: possibly ozone decay during the measurement series.

• Ozone GVD (decision 1):

  • Replacing Serdyuchenko by Bogumil or Brion changes beta2 at 343 and 800 nm by 16-52

  • Working estimate 50 % at 343 and 800 nm; 1 % at 1800 nm.

  • n - 1 is known to about 2 %.

• Temperature (decision 2): 293 K only. The T243 variant of the absorption configuration gives the sensitivity.

• Vibrational static polarizabilities:

  • CO: HITRAN 0.1223 a.u. against Bishop & Cheung’s 0.1213 (+0.8 %).

  • O3: HITRAN 0.869 against Bishop & Cheung’s 0.788 (+10 %) and Naves’s pure vibrational 1.41 (ab initio). This does not affect the optical range; open for the static limit.

  • Other gases: Bishop & Cheung against HITRAN is CO2 -17 %, N2O -8 %, CH4 -4 %, SF6 +8.7 %. The fits’ infrared terms stay on HITRAN, whose strengths the phase-matching data support (TC-104, TC-146).

• The CO fit (fit/CO):

  • It is fitted to smith_1976/experiment_CO, cuthbertson_1920/experiment_CO (level free), watson_1936/green_CO and zhao_2026/A_R_1566_CO (reconstructed, TC-197), with HITRAN below 5000 cm^-1. Reduced chi2 0.37.

  • Effective oscillators: f = 0.185 at 147 nm (the A-X system) and 4.27 at 73.6 nm.

  • Christiansen’s electronic values lie -0.18 % from the fit.

  • Zhao’s derived static value lies -0.11 % (23 sigma): its reduction from 1566 nm differs. Open.

• Record links: kumar_2011/static_i now reproduces naves_2011, and zhao_2026/may_2008_O2 reproduces may_2008; bethke_1959/ditchburn_heddle reproduces ditchburn_1954.

• Not done:

  • The Buckingham & Graham citation strings in achtermann_1991, burns_1986, hohm_1990 and vukovic_1996 are not converted to buckingham_1974: each needs its values checked against that record first.

  • zhao_2026’s O2 A_mu convention (a cgs susceptibility over 4 pi, not chi_M/3) is not changed. No fit uses Zhao’s O2 values; the effect on CH4 and CO is below 10 ppm. Open.

• Format needs reported during the curation and not implemented:

  • an interval oscillator strength;

  • a wavelength-integrated cross section;

  • a vibrational polarizability or correction;

  • a per-row temperature;

  • a refractivity difference;

  • a Cauchy coefficient A_2;

  • a magnetic susceptibility;

  • a partial refractivity.

• Status: decided (2026-09-25): all accepted. The Mainz atlas files stay committed, with citation. Naves’s zero-point correction is used. The Cuthbertsons’ ozone dispersion is a validator. The fits stay on HITRAN rather than Bishop & Cheung. Zhao’s CO static value remains a validator. The format needs are deferred.

Page numbers are PDF pages of the curators’ copy unless marked otherwise.

TC-219 sakamoto_2010 (Sakamoto et al., NIFS-DATA-109, 2010): Berkowitz’s distributions

• Source of the extracted values: the NIFS text files, not the curators’ extracted cells (accepted 2026-09-26, TC-223). tools/extract/sakamoto_2010.py reads the discrete tables from the committed data/external/nifs_photoab/<gas>_table.txt.gz. The curators’ extracted tables of this report are OCR of sideways pages: reversed strings (20+E0056 .7), merged tables (Ar, CO pages) and misread digits (He Table I: 2.4425E+01, 6.8800E-04, 6.416E+01 and a repeated 6.5181E+01 where the page prints 2.4452E+01, 6.6800E-04, 6.4816E+01, 6.5108E+01), while passing the extraction’s grid checks. Data rule 2 says “from the library’s tables” (the curators’ library); the NIFS files are the report’s own electronic tables, checked against the PDF as below.

• Check of the committed NIFS files against the PDF (all 12 species, every row). pdftotext -layout of the curators’ PDF copy, pp. 14-258: every numeric row of every file (102 He, 96 Ne, 226 Ar, 326 H2, 289 N2, 741 O2, 352 CO, 1217 CO2, 682 N2O, 540 O3, 285 CH4, 487 SF6: discrete, interval and continuum rows) is one run of cells on one printed line, and the multisets of all numbers agree exactly per species: no difference. By eye (page images): every discrete table (pp. 14, 28, 37, 42-44, 47, 53, 65, 120) and a continuum page per species (pp. 15, 29, 39, 44, 47, 53, 60, 65, 110, 120, 173, 190, 254), rows compared with the files: all agree. The NIFS text drops the footnote marks (He Table I a); Ar Table I a-f) and the rules that split tables into groups; the script restores both (marks in printed, groups as separate files).

• Internal consistency of every row (E x lambda = hc to 2e-4; sigma_a = 109.76097 df/dE and mu_m = sigma_a N_A / M_A to 3e-4): all pass except helium’s df/dE column, 1.25e4-1e5 eV (17 rows), printed ‘.80404E-10’ … ‘.62035E-13’: a factor 10 too small (the PDF prints the same). sigma_a and mu_m are right there (sigma_a matches the printed high-energy formula to 1e-5). A loader of He_table.txt.gz must use sigma_a (or df/dE x 10) above 1e4 eV. Not an erratum here (the continuum is not a dataset).

• Datasets (all oscillator_strength vs eV, use = "reproduced": Berkowitz’s book values; He Table I from berkowitz_1997; 22 datasets, 443 rows): He discrete_He 20 (row I-20 = sum n >= 21), excess_He 18; Ne discrete_Ne 19, resonance_2s_Ne 6, k_edge_Ne 4; Ar discrete_Ar 21 (series sums a-c, e-f and the inter-threshold continuum d as single rows), window_Ar 7 (negative f: window resonances to subtract from the continuum), k_edge_Ar 1; H2 lyman_H2 37, werner_H2 14, b_prime_H2 9, d_H2 16, rydberg_H2 20, predissociation_H2 17, autoionization_H2 146; N2 discrete_N2 47, k_edge_N2 3; O2 intervals_O2 11 (interval integrals, abscissa the lower edge), k_edge_O2 1; CO discrete_CO 19, k_edge_CO 2; N2O intervals_N2O 5 (interval integrals). CO2, O3, CH4, SF6 have no discrete table.

• Erratum: discrete_Ar row I-6, energy printed 1.3606E+01 (lambda 911.27 A) for the first nd-series line (3d); corrected 13.864 eV from chan_1992 (Moore). 13.606 eV is the Rydberg energy and the hydrogen Lyman limit (p. 11). To confirm with the book.

• Doubt (not corrected): Ar energies differ from chan_1992’s by 10-50 meV for 7s (15.159 vs 15.186), 5d (15.170 vs 15.118) and 4d’ (14.984 vs 15.004 eV).

• Formulas (12): tail_He (Ry units, above 13 600 eV; reproduces the table’s sigma_a at 2e4 and 1e5 eV to 1e-5), tail_H2 (2.888 x the hydrogen formula above 10 keV; reproduces 12.5 keV-100 keV to 6e-5; the book’s 10 keV point is 27 % below it), and the hydrogenic K-shell formula above 1e5 eV for Ne, Ar, N2, O2, CO, CO2, N2O, O3, CH4, SF6 (chi = sqrt(E_K/(E-E_K)), image checked), each 0.5-5 % off the table’s 1e5 eV row (a step at the join). For N2 and O2 the text omits “of each atom”; only the two-atom sum joins the table.

• Sums computed here, not printed (the report prints no totals and no polarizabilities; nothing to transcribe as cauchy_moment). S(-2) [Ry^-2] (alpha = 4 S(-2) au) / S(0) vs Z, from lines + intervals + trapezoid on the printed grid + tails: He 0.3490 (1.396) / 1.9958; Ne 0.6469 (2.588) / 9.693; Ar 2.7493 (10.997) / 18.031; H2 1.3184 (5.274) / 1.960; N2 3.0037 (12.015) / 14.031; O2 2.7135 (10.854) / 16.004; CO 3.3152 (13.261) / 14.027; CO2 4.3584 (17.434) / 22.205; N2O 4.8519 (19.408) / 22.309; O3 4.3474 (17.390) / 22.163 (Z 24); CH4 4.1977 (16.791) / 9.903; SF6 7.6052 (30.421) / 69.042. The grid trapezoid reproduces the report’s printed corrected partial moments to 0.03 % (CO2 S(2)), 0.6-1 % (Ar 243-253 eV), 3.5-4 % (CO IP-17.712 eV; Ar S(1) 500-929.7 eV). **S(0) misses TRK by 7.7 % for O3, 3 % for Ne, 2

  Glass-Maujean’s dissociation continua, but no table holds a df/dE below 15.426 eV, and the continuum has only two points between 15.426 and 17.5 eV. O3: the 527-560 eV (K-edge) region integrates to 0.22 against O2’s 0.32 (1.5 x O2 would be 0.47), and 108.5-300 eV to 2.1 x O2. O2 lacks the Schumann-Runge bands (below 7.125 eV). These totals are for comparison with the fits, not data.

• Partial moments printed (the corrections to the book, pp. 6-7): Ar 243.0-253.0 eV S(1) = 3.5471, S(2) = 64.8246; Ar 500-929.7 eV c = 8315.576, S(1) = 111.9896; CO IP-17.712 eV S(-2..2) = 0.6587, 0.7582, 0.8771, 1.0195, 1.1908; CO2 35.93-107.08 eV S(2) = 145.296. In notes, not datasets: format need, no quantity for a partial moment of an energy interval (nor for an interval-integrated f; the interval tables follow kumar_2011_supplement’s lower-edge convention).

• Joins and reproductions in the continuum are in the record’s notes (per species); for the loader of the NIFS files: Ar 243-336 eV reproduces chan_1992; N2 107-200 eV and N2O 455-506 eV henke_1993; O3 1.65-3.54 eV brion_1998, 3.54-6.70 eV mason_1996. Slips in the sources tables kept as printed: Ar “Table 2.35 p.35” (p. 90), “Cham et al.” (Chan), H2 “a.3 p.128”, “b.4 p.131”; CO “Chan et al., Can. J. Phys. 43 (1965) 1706” for IP-26.84 eV.

• Identity ASSERTED (the curators’ BibTeX), confirmed against the title page (p. 3). Copyright (PROVENANCE.md “Check”): the report is a NIFS preprint with the usual photocopying notice (p. 2); no statement on the electronic tables.

• Status: decided (2026-09-26): accepted with TC-223; points marked open or to confirm above remain open.

TC-220 berkowitz_2008 (Berkowitz, Int. J. Mass Spectrom. 271, 8 (2008)): ozone

• No tabulated cross section: all total and partial cross sections are figures (Figs. 2-5, not digitised). Table 1 (p. 10, image checked) holds photoelectron band areas and CI configurations only (quoted in notes, not extracted).

• Cook’s calibration (quoted in notes): p. 11, Cook’s 1968 calibration ‘preferred by sum rule analysis [24]’ (the book, p. 228) ‘leads to an enhancement in cross section by a factor 1.4’ over his 1970 figure; p. 12, the 1968 abstract’s 42 Mb at 725 A is ‘about 40% higher than shown in the 1970 figure’; the working total is Cook 1970 x ~1.4. Compare kumar_2011’s scale factors for 12.00-20.60 eV (B1 1.34, C 1.18, A 0.986) and check whether sakamoto_2010’s O3 continuum 11.24-20.66 eV (book Fig. 5.12) carries the 1.4.

• Datasets (inline points, absorption_cross_section, Mb): hartley_maximum 11.73 Mb at 2555 A (p. 8; no source, temperature or medium stated; vacuum assumed, check); cook_1968_maximum 42 Mb at 725 A (p. 12; reproduced from Cook 1968, Trans. Am. Geophys. Union 49, 736A).

• Ionisation and appearance energies (notes only, no quantity in the format; all reproduced from Willitsch et al., Weiss et al., Merkt et al., Moore, Taniguchi et al.): adiabatic IP 12.52495(6) eV (p. 9), vertical 12.7500 eV, A 2B2 12.66004(7) eV, AP O2+ 13.1322(4) eV, AP O+ 14.6802(4) eV, 2O + O+ 19.7668(2) eV (p. 12), PES peak energies (p. 10). Checked in the pdf text layer.

• Status: decided (2026-09-26): accepted with TC-223; points marked open or to confirm above remain open.

TC-221 sharipov_2022 (Sharipov, Loukhovitski & Loukhovitskaya, SpringerBriefs, 2022)

• Datasets: alpha_el_mp4_{CO2,O3,CH4,SF6} (Table 3.4, p. 61, tbl_268cb2f58193, image checked), use = "reproduced" from sharipov_2017 (the values are identical: 2.611, 2.801, 2.464, 4.665 A^3). Script tools/extract/sharipov_2022.py.

• What supersedes 2017: nothing numerically. New: the PP thermal coefficients b^PP, c^PP (CO2 27.71/-4.07, O3 21.17/-2.88, CH4 140.07/-22.39, SF6 57.94/-6.11; x1e-6 A^3/K, x1e-9 A^3/K^2), the diatomic ZPV/PV corrections of Loukhovitski et al. 2016 (Table 3.1, p. 44: ZPV H2 0.037, N2 0.021, O2 0.016, CO 0.006; PV CO 0.020 A^3) and the Eq. 3.22/3.24 fit parameters to more digits (p. 62). All in notes (no quantity for a correction: format need, as in 2017).

• O3 PV inconsistency carried over: Table 3.3 (p. 56) prints 0.208, Table 3.4 0.312 (the CO2 row’s digits), exactly as the 2017 paper (Table 2 vs Table A1). 0.208 agrees with Naves et al. (0.209); Table 3.4’s 0.312 is probably the misprint. Not corrected (not extracted).

• Stated reason O3 ZPV is below Naves et al.’s (p. 55, quoted in notes): the O3 ground state’s “severe multireference nature”; the DFT (B97-2) treatment “is not capable to describe adequately the electronic structure of the ground state ozone”, Naves et al. used coupled cluster. 0.013 vs 0.216 A^3 (0.088 vs 1.46 au): factor 15.

• Section 6.1 summarised in notes (two-level model Eq. 6.1; dissociation trend Delta alpha_d/alpha_mol = 3.7e-4 Delta H_d^298 in kJ/mol, Fig. 6.2; O2 behind a Mach-8 shock: O atoms ~2.5 % of n - 1, excited states 1.5 %, K^GD’s temperature dependence up to 1.5 %). The printed “by 0.002 A^3 per one O2 molecule decay” (p. 92) looks small against Fig. 6.2’s Delta alpha_d/alpha_mol of about 0 for O2 (consistent) but is not checkable here.

• Computed here (in notes): the thermal corrections at 296 K from b, c (UP: CO2 0.026, O3 0.012, CH4 0.028, SF6 0.080 au; PP: 0.053, 0.041, 0.267, 0.112 au) and the diatomic corrections in au.

• Reproductions quoted in Tables 3.1/3.3 (notes only): kolos_1967 (H2 ZPV 0.035), christiansen_1998 (N2 ZPV 0.007, CO ZPV 0.007 and PV 0.018), bishop_1982 (CO2 PV 0.26), naves_2011 (O3 ZPV 0.216, PV 0.209).

• Status: decided (2026-09-26): accepted with TC-223; points marked open or to confirm above remain open.

TC-222 gallagher_1988 vs its second library copy (no new record)

• The same scan of the same article (J. Phys. Chem. Ref. Data 17, 9-153 (1988), DOI 10.1063/1.555821 in both): the table images are pixel-identical in layout, fonts and defects (the same clipped last digit of “172” and “218” in Table 4). Copy 1 (146 pp) is AIP’s online PDF: an OCR text layer (Adobe Paper Capture) and an added publisher cover page, so journal page = pdf page + 7 (as the gallagher_1988 record says). Copy 2 (145 pp) is image-only (no text layer) and has no cover: journal page = pdf page + 8, every table one pdf page earlier.

• The curators’ extractions: both have 20 tables, 264 references, 111-112 figures; copy 1 also has machine-generated figure descriptions (hence 591 KB of Markdown against 200 KB). Running text: the same decimals except the cover’s DOI and one misreading in copy 1 (Eq. 3.14’s factor read as K^{2.48}, the superscript reference 48 merged into the exponent; copy 2 reads K^{2}.^48 correctly).

• Tables 2-19 compared cell by cell (the source lists the gallagher_1988 record uses): identical except (a) layout (copy 2 keeps the caption as a first row in Tables 2 and 9; row-shifted, same content), (b) notation (O^+ vs 0^+, subscript braces, 16-22 vs 16- 22), and (c) one real difference, Table 4 (O2), McCoy 1978: copy 1 reads reference 216, copy 2 reads 218; the reference list gives 218 (D. G. McCoy, J. M. Morton and G. V. Marr, J. Phys. B 11, L547 (1978)) and the image shows a clipped “21?”: copy 2 is right. The gallagher_1988 record does not quote this row.

• Recommendation: keep gallagher_1988 on copy 1 (it has the text layer and the record’s page convention); note copy 2 as a duplicate; neither holds a numerical cross section.

• Status: decided (2026-09-26): accepted with TC-223; points marked open or to confirm above remain open.

TC-223 Integration (2026-09-25)

• NIFS tables (data/external/nifs_photoab, fetched from dpc.nifs.ac.jp):

  • Checked number for number against the report’s PDF (TC-219).

  • He df/dE above 1e4 eV is printed ten times too small in the report and the file. Any loader must use the cross-section column there.

  • Copyright: the report asks for copyright inquiries to the NIFS Research Information Office. The files are committed as the Mainz files were (TC-218). Check.

• TC-219: the extraction reads the committed NIFS text, not the curators’ extracted table cells. The curators’ OCR of the sideways tables is corrupt. The reading was checked cell for cell against the page images. Accepted as an exception to data rule 2 (confirmed below).

• Ozone (with fit/O3, TC-218):

  • Berkowitz’s recommended distribution (NIFS) has f(12-20.6 eV) = 2.25 by integration here. That is Kumar & Thakkar C (2.18) to B1 (2.48), and below the fitted 2.55.

  • Its total S(0) is 22.2, 7.7 % short of 24: no data at 1.31-1.65 eV, and missing strength that could not be located (TC-219). Its S(-2) (17.4 au) is therefore not a usable static value.

  • Berkowitz 2008 states that Cook’s 1968 calibration, preferred by sum rules, lies a factor 1.4 above Cook’s 1970 scale, the one that Kumar & Thakkar’s A distribution rests on (1.83). The fit’s 2.55 is 1.39 times that. This is independent support for the fitted strength, which came from the refractivity and the static value alone. fit/O3 is not changed.

• Static polarizabilities from the NIFS distributions

  • The integration of TC-219 gives He 1.396, Ne 2.588, Ar 11.00, H2 5.27, N2 12.02, CO 13.26, CO2 17.43, CH4 16.79 and SF6 30.42 au.

  • Against the fits’ electronic static values they differ by -2.9 % (H2) to +2.5 % (O2) (He +0.9, Ne -2.8, Ar -0.7, N2 +2.4, CO +1.4, CO2 -0.5, N2O -1.5, CH4 -2.7, SF6 +1.2 %), the level of Berkowitz’s evaluations. O3 is -12.6 %: see the S(0) shortfall above. No fit uses them. They are candidate validators, and the starting data for extreme-ultraviolet models of the molecules (later work).

• Sharipov 2022 adds nothing that replaces a 2017 value. It confirms that its O3 zero-point correction is unreliable (multireference character): fit/O3’s choice of Naves stands.

• Status: decided (2026-09-26): the extraction from the committed NIFS text (TC-219) and the committed NIFS files are accepted.

Every value was read from the curators’ extracted table cells (JSON or CSV) by the source’s extraction script and compared with the table image, or typed from the text with its page (inline points). Pages are the journal’s.

TC-224 shelton_1994 (Shelton & Rice, Chem. Rev. 94, 3 (1994))

• Transcribed (script tools/extract/shelton_1994.py, JSON cells, each compared with its image; footnote marks checked cell by cell by the script):

  • Table IV (p. 9): static gamma_0 of He, Ne, Ar, Kr, Xe, correlated and SCF (5 datasets, 2 rows each). Reproduced (bishop_1989, Voegel 1979, Rice et al. 1992, rice_1991).

  • Table V (p. 10): 21 ab initio static gamma_0 of Ne (one dataset; the “8, 65” VPT cell split into two rows).

  • Table VI (p. 11): He absolute dc Kerr (4) and THG (1) experiments; Bishop & Pipin’s dc Kerr (2 distinct rows; the 632.8 nm value repeated three times kept once) and THG (1) values.

  • Table VIII (p. 15): gamma^v of H2, D2, N2, O2 and gamma^R of H2, N2 by process (static, dc Kerr, DFWM = kerr, ESHG, THG; T = 295 K): 30 one-point datasets. Notes h and i (H2 gamma^R DFWM/ESHG/THG; N2 gamma^R) are the review’s own calculations, primary; the rest reproduced (bishop_1991, Shelton 1987 Mol. Phys./PRA, Bishop & Lam 1988, shelton_1993).

  • Table IX (p. 16): calc and expt gamma^e of H2, D2, N2, O2 (static) and CO (ESHG, 694.3 nm = 14399 cm^-1): 9 datasets.

  • Table XI (p. 20): CO2 gamma^v (MP2, bishop_1993) at omega = 0.07 au by process: 5.

  • Table XII(b) (pp. 22-23): CH4, SF6, CO2, calc and expt per column (15 datasets, 20 values).

  • From table notes and text, inline: N2 static theory (7 values), N2 ESHG 694.3 nm calc 1100, the fit value 1058, Ward & Miller rescaled 1042 +- 12; CO static theory (3); CO2 static theory (5), CO2 THG calc 1500, CO2 best estimate 1220 (p. 24).

• Formulas: Table VII (13: He calc; Ne calc x6 and expt; Ar, Kr calc and expt; Xe expt) and Table X (7: H2, D2, N2 calc; H2, D2, N2, O2 expt). Every experimental one reproduces shelton_1990 Table IV (gamma_0 via 6.235377e-65; A, B identical or rounded); Ne expt, MP2, CASSCF, SCF A and B reproduce shelton_1992 Table 2 converted with 1 au = 219469 cm^-1; He’s reproduces Table VI’s THG value (45.34 against 45.338).

• Checks against the paper’s own numbers: N2 ESHG at 694.3 nm from Table X: 1057.7 (printed 1058); Table XII’s ESHG values of CH4, SF6, CO2 (note x) from shelton_1990’s fits: 3257.4, 1564.8, 1368.0 (printed 3257, 1565, 1368).

• Reference slips (not values): Table VII note d (Ne) cites ref 171 and notes k, m (Ar, Kr, Xe) ref 170, the opposite of Table IV, Table V note a and Figs 3-4 (170 = Rice et al. 1992, Ne; 171 = rice_1991). The records follow Table IV. To confirm.

• Inconsistencies in the paper: O2 static gamma^e printed 962 +- 6 (Table IX) and 963 (Table X); shelton_1990 gives 962.7. Ne CASSCF gamma_0 99 (Table VII) against 94.6 (Table V): explained by shelton_1992 (Jensen’s adjusted best static value against the curve’s intercept).

• The curators’ extracted text: references 34, 35, 128 and 131 are missing from it (read from the PDF pages). Table XII note ff: the text drops “1f” of the [6s 4p 3d 1f] basis (read on the page image). Table XII(a) (beta, not extracted) is misaligned in the JSON for SO2, CH3OH, (CH3)2O; the gamma rows used are aligned.

• Choices to review: experimental polyatomic values labelled electronic_vibrational (Shelton & Rice’s gamma^ev), CARS included (alpha^2-type vibrational part subtracted); laser-line wavelengths as standard_air; Table XI’s omega = 0.07 au as 15363 cm^-1. The dc Kerr rows are gamma_K = (3/2)(gamma_par - gamma_perp), noted in each record.

• Duplicate library copy: all 14 tables agree number for number.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open. The factor 2 in n2,rot is resolved in TC-493 (the printed g carries the extra 2).

TC-225 shelton_1990 (existing record: third-order data added)

• Transcribed (script extended; JSON cells, images checked): Table I gamma ratios, 12 curated pairs x 2 wavelengths (check: the raw measurement behind Table III). Table III, 11 gases: present-work 1319/1064 nm values (primary, 22 values), the literature visible values rescaled by the author (reproduced, 99 values; Ne’s 3 excluded, the spurious Shelton & Lu data), H2 and D2 gamma^vR (21 + 11, primary). Text (p. 14): static 1167 +- 6 (Ar), 686 +- 4 (H2), 119 +- 2 (Ne, excluded); ab initio 119 +- 4, 1220 +- 30, 671 +- 6; H2 at 488.0 nm 992 and 969; H2/D2 static ratio 1.026 and 1.029; Hartree-Fock 700 (N2) and 452 (CH4).

• Formulas: Table II (He, au and SI), Table IV (11 gases), Table V (G, H of gamma^vR for H2, D2, N2, O2). Every Table IV fit reproduces the paper’s Table III (reduced chi^2 0.3-1.0; Kr 3.4 with 1064 nm 3.6 sigma off; CH4 0.16 without the 1319 nm point, which is 12.0 sigma off as the paper says). G, H reproduce the tabulated gamma^vR of H2 and D2 in the visible (-0.678 against -0.68 at 632.8 nm).

• Erratum (formula): Table II prints C = 6.043 x 10^-31 cm^6; 6.748 au / 219444.5464^6 = 6.043e-32, and shelton_1992 (p. 3) says “10^-31 in the last line should be 10^-32”. Recorded as corrected = { C = "6.043e-32" } on table2_He_si (formulas have no [[errata]]; format gap, how to carry it is open).

• Format gap: the gamma^vR columns are vibrational plus rotational; there is no combined part, so they are part = "vibrational" with a note (the rotational share for ESHG is ~4 % of it for H2).

• Doubt: the absolute Table III values and the Table I ratios are one measurement; the absolute values are made primary and the ratios check. The rescaled literature values are reproduced although they are the only copies on the new He calibration (the originals, in the older calibration, are in the mizrahi/shelton_198x records).

• Taylor et al.’s Ne calculation is cited as Chem. Phys. Lett. 163, 282 here and 163, 359 by shelton_1994 and shelton_1992: which page is right is not checked.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-226 shelton_1992 (Shelton & Donley, Chem. Phys. Lett. 195, 591 (1992))

• Transcribed (script, CSV cells, images checked): Table 1: gamma_Ne present (2, primary), gamma_Ne/gamma_He present (2, check), rho_He/rho_Ne present (2, primary, phase_match_density_ratio), shelton_1990’s infrared values re-expressed (2, reproduced), Finn & Ward 1971 (1, reproduced), Shelton & Lu 1988 (3, excluded, spurious). Text: half-density ratio 2.554 +- 0.010 and rho ratio 1.879 +- 0.003; static 108 +- 2; dc Kerr 101 +- 8 (Buckingham & Dunmur, as converted) and the predicted 111 +- 2; four ab initio best estimates (p. 4).

• Formulas: Table 2 (expt, MP2, CASSCF, SCF; omega_L^2 in au). The experimental fit reproduces the four fitted points (121.97, 123.69, 110.04, 111.11 against 122.2, 123.5, 111.0, 109.9) and the dc Kerr prediction (110.93). The B of the experimental fit is fixed, not fitted (caption).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-227 donley_1993 (Donley & Shelton, Chem. Phys. Lett. 215, 156 (1993))

• Transcribed (script, JSON/CSV cells, images checked): Table 2, gamma_A/gamma_B for H2/He, Ar/H2, N2/H2 at four densities (3 x 4, check) and the phase-match density ratios (3 x 4, primary, phase_match_density_ratio, filed under B with reference A so the printed rho_B/rho_A is rho_gas/rho_reference); Table 3, the zero-density intercepts (3, primary) and calculated ratios (3, reproduced). Table 3 notes, inline: He 47.946 au (bishop_1989), H2 gamma^e 945.4 (bishop_1991), gamma^v -7.43/-0.13/-7.56, gamma^R -0.38 (the authors’), H2 total 937.3 (check), Ar 1604, N2 1241 (ESHG, 514.5 nm).

• Checks: the calculated ratios are 937.3/47.946 = 19.549 (19.550), 1604/937.3 = 1.7113 (1.711), 1241/937.3 = 1.3240 (1.324). Doubt: 945.4 - 7.56 - 0.38 = 937.46, not the printed 937.3 (0.02 %; unexplained).

• Format gap: the pair (density) coefficients b(AB) (measured +5.6 +- 6.2, -7.0 +- 5.0, -6.9 +- 4.6; DID -2.1, +4.5, +3.4, 1e-6 m^3/mol) and Table 4 (DID b, local-field c) have no quantity; they are in the record’s notes. A “hyperpolarizability density coefficient” quantity would hold them (and shelton_1993’s A = 1.2e-5 m^3/mol).

• The density ratios are linear-optics data (ESHG phase matching) and were taken because the record is new; whether they belong with a later curation of linear data is open.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-228 shelton_1993 (Shelton & Rugar, Chem. Phys. Lett. 201, 364 (1993))

• Transcribed (script, CSV cells, images checked): Table 1, gamma_eff of H2 (dc Kerr, 632.8 nm, 25.2 C) at six densities (check) and the zero-density gamma^evR = 8.827 +- 0.045e-62 C^4 m^4 J^-3 (primary); Table 2, H2 Delta alpha_JJ and Delta alpha_J,J+2 per J = 0-6, static and 632.8 nm (4 x 7, polarizability_anisotropy, reproduced from LeRoy & Schwartz 1987 and Bishop & Pipin 1991 with the authors’ interpolations; two cells marked e) stripped of the mark). Text (p. 4): gamma^R = 697.1 au (Eq. 2, primary) and 685.3 au (Tammer & Huttner’s expression, check); gamma^ev = 718.5 +- 7.2 au (primary) and 730.3 +- 7.2 (check); ab initio gamma^ev = 726.2 (bishop_1991).

• Checks: 8.827e-62 / 6.235377e-65 = 1415.6 au, 4.347e-62 = 697.15 au, 4.48e-62 = 718.5 au, as printed.

• Choices: part total for gamma^evR and gamma_eff, electronic_vibrational for gamma^ev; T recorded as 298.35 K (25.2 C, the common temperature the results were adjusted to). Text slip: minimum electrode separation printed “3.171 nm” (mm meant); not a value used.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-229 shelton_1988 (Shelton & Ulivi, J. Chem. Phys. 89, 149 (1988))

• Transcribed (script, JSON cells, image checked): Table III, SF6 gamma^v (1e-62 C^4 m^4 J^-3) for static, dc Kerr, ESHG, THG at nu = 20000 cm^-1: the totals (4, primary) and the four terms per process (4 x 4, check). Cells with their own power of ten (“-1.9 x 10^-3”) are kept as E notation, not stripped as a column factor (the shared number() would have dropped the exponent: a structural fix in the script).

• Checks: the terms sum to the totals (static 239.3 against 239.4 printed, rounding; dc Kerr 0.3; ESHG -3.21; THG -0.732).

• The calculation assumes all molecules in the vibrational ground state (the room- temperature gamma^v ‘may be substantially larger’); uncertainty ‘a few percent at best to perhaps a factor of 2 at worst’. Tables I-II (Raman cross sections, transition matrix elements) are in the notes only (no quantity).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-230 lu_1987 (Lu & Shelton, J. Chem. Phys. 87, 1967 (1987))

• Short record, no datasets (CF4 only). Noted from the text: the CH4 estimate gamma^v_ESHG = 3e-63 C^4 m^4 J^-3 (~1 % of CH4’s ESHG gamma; no wavelength, p. 1974), and that Elliott & Ward’s gamma includes an extra factor 1/6. shelton_1988 later corrects Eqs (18) and (23) here by factors 2 and 3.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-231 shelton_1982 (existing record: third-order data added; new script)

• Transcribed (new script tools/extract/shelton_1982.py, CSV cells, images checked): Table II gamma at 514.5 nm for Ar, H2, N2, CO2, SF6 (5 one-point datasets, primary); Table III gamma_CH4 at six argon-ion lines (primary), the 694.3 nm Miller & Ward value (reproduced), gamma_He calculated by Sitz & Yaris at seven lines (the calibrant, reproduced); text: the absolute gamma_He = 2.7 +- 0.5e-63 at 514.5 nm. Table II’s CH4 row duplicates Table III’s 514.5 nm row (taken once). CH3F, CHF3, CF4 skipped.

• Old calibration: gamma_He(514.5 nm) = 2.950e-63 (Sitz & Yaris); Bishop & Pipin’s curve gives 2.990e-63 (computed here from shelton_1990 Table II, noted as such). shelton_1985_sf6 (p. 319) states that this paper’s 514.5 nm values ‘are systematically low by 1.5%’: noted, not applied.

• Text slips: p. 2797 prints |Delta k|_opt = 2456.0 +- 0.5 m^-1; the tables print 2465.0 and 0.9965 pi / 1.27 mm = 2465.0 (transposed digits in the text). Eq. (13) as printed shows no square root on S_A/S_B although the text says the square root of the signal is measured. Neither affects a stored value. The existing record’s page numbers for the tables were checked (Table II/III on p. 2793).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-232 shelton_1985_sf6 (existing record: third-order data added)

• Transcribed (script extended; CSV, image checked): gamma_SF6/gamma_N2 (6, check), gamma_SF6 (6, primary, 1e-62 C^4 m^4 J^-3), Ward & Miller’s 694.3 nm value (1, reproduced). Formula: gamma = A(1 + B nu^2), A = 8.21e-62, B = 8.44e-10 cm^2 (nu the fundamental, not nu_L^2); reproduces 9.753 at 670.0 nm and 10.826 at 514.5 nm (table 9.75, 10.84).

• Process ratios in the text (gamma^THG/gamma^ESHG = 1.14 +- 0.07 measured against 1.15 predicted; gamma^ESHG/gamma^Kerr = 0.65 +- 0.06 against 1.11) are in notes only (no quantity for a ratio between processes).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-233 shelton_1986_co2 (existing record: third-order data added)

• Transcribed (script extended; CSV, images checked): Table I gamma_CO2/gamma_N2 (5, check) and gamma_CO2 (5, primary); Table II other processes (dc Kerr 558 +- 120 excluded as the author shows it spurious; FWM/CARS 2 rows, ESHG 2 rows, THG 1 row, reproduced). Text: the reanalysed dc Kerr -61 +- 200e-63 (check), Gentle et al.’s 110 +- 39e-63 (note added in proof; wavelength assumed 632.8 nm, to confirm), gamma^e_Kerr = 72.6e-63 predicted (check), gamma^v_Kerr = 0 +- 2e-63 (primary).

• Formulas: the fit gamma = A[1 + B nu^2] (A = 65.0e-63, B = 14.07e-10 cm^2; reproduces 84.04 and 99.53 against 84.1 and 99.4), and the calibration formulas Eq. 2 (gamma_N2/gamma_He = 20.30 [1 + 6.55e-10 nu^2]) and Eq. 3 (Sitz & Yaris gamma_He = 42.6 au [1 + 2.94e-10 nu^2], 1 au = 6.2360e-65; gives 2.951e-63 at 514.5 nm = shelton_1982’s calibrant).

• Table II note b’s esu factor 7.4279e-25 is 6 x (1 au in SI / 1 au in esu): Ward’s per-molecule esu values are gamma/6 (the trap noted in the survey of nonlinear data), confirmed numerically.

• The FWM rows are CARS-type gamma(-2w1 + w2; w1, w1, -w2) with printed wavelength pairs “694, 975” and “532, 683” (pump, Stokes): the abscissa is the pump and the Stokes is in parameters.stokes_nm as text (two rows share one dataset).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-234 shelton_1986_ch4 (existing record: third-order data added)

• Transcribed (script extended; CSV, images checked): Table I gamma_CH4/gamma_N2 (12, check), gamma_CH4 (12, primary), the other authors’ column (Miller & Ward 694.3 nm, 1; shelton_1982’s six, reproduced); Table II dc Kerr (Buckingham & Orr), FWM x3 (Hauchecorne; Rado as corrected by Lundeen, vibrational correction removed; Lundeen, removed), THG (Ward & Elliott), reproduced.

• Formulas: quadratic fit (A = 149.1e-63, B = 14.70e-10, C = 89.1e-20; 204.17 and 271.33 against 204.1, 271.0) and linear fit (A’ = 136.3e-63, B’ = 22.31e-10; 203.66, 270.16), both against nu^2 of the fundamental.

• Miller & Ward’s 694.3 nm CH4 value is printed 195 +- 2 here and 196 +- 2 in shelton_1982 (conversion differs; both kept as reproductions). The THG reference is printed “J. Chem. Phys. 80, 1002” (the paper starts on 1003).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-235 shelton_1986_krxe (existing record: third-order data added; new script)

• Transcribed (new script, CSV, images checked): Table I ratios gamma_Kr/gamma_Ar, gamma_Xe/gamma_Ar (4 each, check) and gamma_Kr, gamma_Xe (4 each, primary; the parenthesised last-digit uncertainties parsed to sigma, e.g. 2.359(6) = 2.359 +- 0.006); Table II (dc Kerr, FWM (Kr only; Xe “…”), ESHG, THG; reproduced); Lehmeier’s THG Kr 1.74 +- 0.17 and Xe 5.11 +- 0.51e-61 at 1.055 um from the note added in proof.

• Formulas: Kr and Xe fits gamma = A[1 + B nu^2] (reproduce 2.023/2.507 and 5.797/7.964 against 2.024/2.506 and 5.800/7.970); the Ar/He calibration Eq. (7).

• Slips: Buckingham & Dunmur cited as Trans. Faraday Soc. 64, “1176” (it is 1776); the au conversion is 6.2353e-65 here and 6.2360e-65 in the CO2 and CH4 papers (0.01 %).

• The Xe fit’s intercept, 4810 au, is the too-low visible-only static value flagged in the survey of nonlinear data.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-236 shelton_1989 (existing record: third-order data added)

• Transcribed (script extended; JSON cells, image checked): the gamma_Ne/gamma_He column by source: present ESHG (2, check; same as shelton_1990), Buckingham & Dunmur dc Kerr (2 evaluations of one measurement, reproduced), Finn & Ward ESHG (1), Shelton & Lu ESHG (3, excluded: spurious per shelton_1992), Lehmeier THG (1), Ward & New THG (1). Text: static 116 +- 2 au (excluded), MBPT 105 and CCD 114 +- 9 au (reproduced).

• Formulas: the ratio fit and the gamma_Ne fit (A* = 115.8 au, B* = -1.923e-10, C* = 6.924e-20 against nu_L^2): both SUPERSEDED. The ratio fit misses the 1319 nm point by 1.4 sigma (weighted fit over five points); the gamma fit’s minimum (100.3 au at 13.89e8 cm^-2) matches the stated 100.4 at 13.9e8.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-237 mizrahi_1985_arn2o2 (existing record: third-order data added; new script)

• Transcribed (new script, CSV cells, image checked): Table I chi(3)/chi_He(3) for Ar (19), N2 (19), O2 (18), primary, parenthesised last-digit uncertainties as sigma; the four Ar rows and the O2 column measured via N2 (mark “a”) named in the notes.

• Erratum: Ar at 600.0 nm printed 20.99(16), corrected to 30.99 (the image shows 20.99; the fit gives 30.95 there; shelton_1990’s rescaled 90.05e-63 at 600.0 nm equals 30.99 x Sitz-Yaris He x the 1.011 rescaling used at the other lines). The existing record had already flagged it in its notes.

• Formulas: Table II fits A(1 + B omega^2) for Ar, N2, O2 (own) and H2, D2 (reproduced from mizrahi_1985_h2d2), each reproducing the table (e.g. Ar 30.95 at 600 nm, N2 23.62 at 632.8 nm, O2 29.89 at 514.5 nm); He calibration Eq. (2) / Table II caption (42.6 au, B_He = 2.94e-10 = 1/58300^2).

• The record’s old note calls the curators’ library entry UNVERIFIED; it is now VALIDATED_WITH_WARNINGS (stated in the new paragraph, the old text left as it was). Table III’s omega_0 unit misprint (10^13 for 10^3 cm^-1) was already noted.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-238 mizrahi_1985_h2d2 (existing record: third-order data added; new script)

• Transcribed (new script; Table I JSON cells, Table II CSV; images checked): chi_H2/chi_He raw (19) and vibrationally corrected (19), chi_H2/chi_D2 raw (9) and corrected (9), all primary (the raw ones total, the corrected ones electronic: the same measurements in two parts); the static vibrational chi(3)vib(0) = 184 (H2) and 178 (D2) au. Inline: Table III (647 +- 4 au experiment; JR 693, BW 671) and the H2/D2 static ratio (1.025 +- 0.004; 1.029), and four He static calculations (43.10, 42.81, 42.8, 42.6 au).

• Formulas: the four Table I fits (A from the omega = 0 row, B from the caption), all reproducing their columns within the error bars; Eq. (7) vibrational dispersion for H2 and D2. Checks: chi_vib(0) = (6 alpha^2 + 8/15 gamma^2)/omega gives 184.1 and 178.1; the raw-to-corrected shift at 632.8 nm (0.223) is reproduced; 15.13 x 42.8 = 647.6.

• Convention: P_z(2w) = (3/2) chi_zzzz(3) E E E(0), macroscopic chi(3) = (1/6) rho L <Phi^4> gamma, the “microscopic chi(3)” being the isotropic average of gamma, i.e. Shelton & Rice’s gamma_par (T). To confirm: this reading (the paper calls the per-molecule quantity chi(3)).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-239 buckingham_1968 (Buckingham & Dunmur, Trans. Faraday Soc. 64, 1776 (1968))

• Transcribed (script; CSV cells, image checked; the raised decimal points “0·027” written as “.”): Table 1 dc Kerr gamma (esu, x 1e-36) of He, Ne, Ar, Kr, Xe, SF6 at 23 C, 632.8 nm (6 one-point datasets, primary); text: Kuss’s Ar value 0.7e-36 esu at 350 atm (reproduced; its wavelength is not stated: 632.8 nm used as a placeholder abscissa, to confirm).

• Convention: Pi_ab = alpha_ab + (1/2) gamma_ab,cd F_c F_d (Taylor), gamma = (3 gamma_ab,ab - gamma_aa,bb)/10 in general: the dc Kerr gamma_K of Shelton & Rice. Conversions (computed, in the notes as such): He 53.6, Ne 101.3, Ar 1171, Kr 2780, Xe 7743, SF6 2383 au (1 au = 5.0367e-40 esu); Shelton & Rice’s 2338 au for SF6 comes from A_K (81 A_K / 4 pi N), their 53.6 for He from gamma.

• Format gaps: the molar Kerr constant A_K (zero density, per mole) cannot be a kerr_constant (which requires a state); the second Kerr virial coefficients B_K (Table 2) have no quantity. Both are in the notes.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-240 carusotto_1992 (Carusotto, Perrone & Polacco, J. Chem. Phys. 97, 7979 (1992))

• Transcribed (script; CSV cells, images checked): Kerr constants K (Delta n = K rho E^2, rho in amagat; 1e-17 cm^2/statV^2 amagat) of N2, H2, D2 at 295 K, 1 atm, 632.8 nm (primary; sigma statistical, systematic 1 % as systematic_relative) and Ref. 3’s values at 293 K, 514.5 nm (reproduced); Eq. (12) theory 4.145 and 4.263e-17 (check); Table II gamma (dc Kerr, 3.926 and 3.821e-37 esu, reproduced from Bishop & Pipin 1987 and mizrahi_1985_h2d2) and the optical and static polarizability anisotropies of H2 and D2 (reproduced).

• Erratum: kerr_H2 sigma printed 0.041 in Table I (the two uncertainties swapped relative to the text); corrected to 0.042 = 0.39/sqrt(86).

• Noted: Table I’s heading prints 10^17 for 10^-17; Table II’s B_0 are B_e of H2, D2 (60.85, 30.44 cm^-1); the Ref. 5 / Ref. 2 rows (high pressure, T ranges) are in the notes only, their block assignment in the image ambiguous for the H2 245 K row.

• kerr_constant datasets carry state {1 atm, 295 K} although K is per amagat: the state records the conditions (this use to confirm).

Every entry: what was transcribed, the fixes, the formulas and whether they reproduce the paper’s values, and what could not be verified.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-241 bishop_1989 (existing record, third-order data added)

• Transcribed: Table II (8 laser wavelengths) and Table III (omega = 0-0.20 a.u., 23 rows), gamma_zzzz for dc Kerr, DFWM, ESHG, THG and gamma_xxzz for dc Kerr, DFWM, ESHG: 14 files, data/values/third_order/He/bishop_1989__*.csv (7 x 23 + 7 x 8 points). Both images checked cell by cell against the cells files: no differences.

• Process mapping (a trap): Bishop’s “Kerr” column is the dc Kerr effect gamma(-w; w, 0, 0) -> dc_kerr; his “DFWM” is gamma(-w; -w, w, w), the intensity-dependent index -> kerr.

• Convention T: Eq. (1) is the Orr-Ward sum over states without K factors (same static limit for every process); Shelton & Rice adopt these values unchanged.

• Units: infinite-nuclear-mass atomic units. Bishop’s SI factor 6.24136e-65 equals 6.235377e-65 x (1 + m_e/m_alpha)^7; the physical 4He gamma is 0.096 % larger (Shelton & Rice Table VI, dc Kerr 632.8 nm: 44.211 = 44.169 x 1.00096). Check that a He calibration applies the factor consistently.

• Table II’s wavelengths are vacuum wavelengths: a spline of Table III reproduces the THG column at 2 pi c / lambda_vac to rms 0.0015 a.u. (air: 0.021, reduced-mass hartree: 0.009).

• The note added in proof’s gamma^Kerr = (3/2)(zzzz - xxzz) values (44.73 at 5145 A, 44.17 at 6328 A) follow from Table II (44.7285, 44.169).

• Experimental He dc Kerr values quoted in the note added in proof (47.2 +- 3, 54 +- 4, 52 +- 8 a.u.): dataset expt_dc_kerr, reproduced (Carusotto 1985 and Boyle 1966 not in the curators’ library; Buckingham & Dunmur 1968 = buckingham_1968). Shelton & Rice Table VI prints 53.6 +- 4 and 51.6 +- 8 for the last two (their rescaling?): compare with the buckingham_1968 record.

• Formulas: Tables IV and V, eight entries (A, A’, B, B’ per process). All reproduce Table III within 0.001 a.u. in their range, except Table IV dc Kerr A = 2.166 (0.005 a.u. off at omega = 0.05; A = 2.189 would fit to 0.001): a possible misprint, not established, no erratum. Table V’s caption lists “0.05” among the fitted frequencies, a misprint for 0.005 (the text says omega <= 0.02).

• Mapping to Shelton’s A, B (cm^2, cm^4): A / 219474.6307^2, A’ / 219474.6307^4 (A = 2.189 -> 0.4544e-10 cm^2; A’ = 3.494 -> 0.1506e-20 cm^4 (Table V dc Kerr), 3.681 -> 0.1586e-20 (DFWM), 3.507 -> 0.1511e-20 (ESHG)). Bishop’s B, B’ are the perpendicular component’s, not Shelton’s B.

• Duplicate library copy: the six tables’ cells are identical.

• Could not verify: the accuracy (no number in the paper; Shelton & Rice’s “better than 0.1 %”).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-242 bishop_1995 (new, no datasets)

• The erratum corrects only B(omega) (dipole-quadrupole polarizability) of bishop_1989 Table VI; gamma is unaffected. Image checked (the text renders minus signs as “2”). Short record, nothing extracted.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-243 rice_1991 (new)

• Transcribed: the gamma column of Tables I-V (Ar 15, Kr 14, Xe 11, He 6 rows; Ne: 1 own MP2 row + 9 rows reproduced from Taylor et al. 1989) and Table VI’s best estimates (He 43.6, Ne 119 +- 4, Ar 1220 +- 30, Kr 2810 +- 90, Xe 7030 +- 200) and reproduced experimental gammas (Ne 119 +- 2 and 101 +- 8; Ar 1167 +- 6 and 1101 +- 8; Kr 2600; Xe 6888). All six images checked against the cells: no differences.

• Convention: E = E0 - alpha F^2/2 - gamma F^4/24 (p. 4973): static T.

• Neon values excluded: Table IV and the 119 +- 4 are Taylor et al. (CPL 163, 359, 1989) before their erratum (CPL 189, 197, 1992; cited by rice_1992 and Shelton & Rice Ref. 110). The revised values (rice_1992_neon) are 111.0 (same basis, CCSD(T)) and 110 +- 3.

• Xe: Table VI 7030 +- 200 against the text’s 7020 +- 200 (7030 excludes the -10 a.u. relativistic correction). Recorded as printed. Linear alpha: Table VI Ne 2.63 against the text’s 2.69; Xe +- 0.5 against +- 0.8 (not extracted, noted).

• Buckingham & Dunmur is cited as Trans. Faraday Soc. 64, 1987 (1968); the curated buckingham_1968 is 64, 1776, which the neon manuscript cites. Assumed the same paper. The Ne value 101 +- 8 in Table VI’s static column is a dc Kerr value at 632.8 nm (per rice_1992); recorded as dc_kerr at 632.8 nm (wavelength from rice_1992, not Table VI).

• Ratios in Table VI are quotients of the tabulated gammas (checked), not recorded.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-244 rice_1992 (new)

• Transcribed: Tables I-III, SCF and MP2 gamma^K (dc Kerr) and gamma_par (ESHG) of Ar, Kr, Ne at omega = 0-0.10 a.u.: 12 datasets x 11 points. Images checked.

• Structural fix: Table I’s two header rows (omega, angstrom) merged into cells like “0.0145 563”; omega split off and checked against Table II’s header.

• Errata (2): Kr SCF gamma^K at 0.09/0.10 printed 2618/2541, swapped. Evidence: monotonic increments, MP2/SCF ratio 1.206/1.205/1.204 after the swap, and a cubic fit gives A = 7.39 = the text’s “SCF (7.4)” (2.49 as printed).

• Convention: Eq. (1) with E = E0 + E_w cos wt and the factors 1/2, 1/8, 1/4, 1/24 = K/6 of Shelton & Rice: T. Equation image checked (the markdown garbles two arguments).

• Best estimates (text) reproduced from the tables by a cubic fit: Ar 1269/1296/1410/1440 and dc Kerr 1292; Kr 2959/3044 (additive 2954/3036); Ne 112/113/117/124, dc Kerr 113. Kr dc Kerr “2930 +- 130” at 632.8 nm equals the unadjusted MP2 value (2930.3); the static-adjusted value would be 3031 (percentage) or 3023 (additive). Recorded as printed; which to adopt is open.

• Wavelengths of the text values (1319, 1064, 694.3, 650, 632.8, 514.5 nm) recorded as vacuum; air/vacuum not stated (negligible here).

• A coefficients (text only; no B, C): Ar 5.5/5.4 (MP2), 5.6 (SCF), 5.1 (expt); Kr 7.2, 7.4, 6.7; Ne 2.3-2.4, -9.3 (expt, later withdrawn). In the record’s notes, no formula.

• Reproduced experimental values: Shelton 1990 (Ar, Kr, Ne ESHG), Finn & Ward 1971 (Ar, Ne at 694.3 nm; not in the curators’ library), Shelton 1991 revised Ne 122.2 at 514.5 nm, Buckingham & Dunmur dc Kerr (Ar 1070 +- 80, Kr 2780 +- 200, Ne 101 +- 8).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-245 rice_1992_neon (new; library copy unverified, now validated)

• Identified as Rice, Scuseria, Lee, Taylor & Almlof, “Connected triple excitations in coupled-cluster calculations of hyperpolarizabilities: Neon”, Chem. Phys. Lett. 191, 23 (1992) (Shelton & Rice Ref. 170, rice_1992 Ref. 5). During the extraction the curators’ library entry was validated (DOI 10.1016/0009-2614(92)85362-e, version “preprint”): record and script updated. The library copy is the typed manuscript (12 pages).

• Transcribed: Table 1 gamma column (21 rows; image checked). Best estimate 110 +- 3 (text), Shelton’s revised static 108 +- 2 (reproduced), other theory 114 +- 9, 111.0, 108 +- 5 (reproduced).

• Text-table inconsistency: text says CCSDT 110.9 and CCSD(T) 111.2 in basis C + (2s2p1d2f); the table prints the reverse. Table recorded; it is consistent with CCSD(T) 111.0 in the next basis.

• The dynamic values (112, 113, 124 ESHG; 113 dc Kerr) are recorded once, in rice_1992.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-246 host_2005 (new)

• Transcribed: Tables II (Ne), VI (Ar), XI (Kr), t-aug-cc-pV5Z: gamma_par and gamma_perp (ESHG) for CCS, CC2, CCSD, CC3 at omega = 0, 0.042823, 0.088559, 0.093368 a.u. (24 datasets x 4 points) and the experimental gamma_par column (3 datasets, reproduced). Images checked: no differences.

• Best static estimates (text/abstract): Ne 107.4 (108.0 - 0.97 + 0.58 - 0.17, checked), Ar 1159, Kr 2589 (CC3/t-aug-cc-pV5Z directly). No uncertainty stated (Ne: “about 0.5 %” for the CC3/5Z values).

• Convention not written out; T inferred from the direct comparison with Shelton’s values and the static limits (compare rice_1991). To confirm.

• The experimental column’s static Ar is “1167 +- 20” (rice_1991: 1167 +- 6); which reference each row comes from is not stated.

• Not extracted: FCI small-basis benchmarks, basis-set studies, relativistic corrections (summarised in notes; Kr relativistic corrections Table XII image checked).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-247 hattig_1998 (new)

• Transcribed (all images checked): Tables VIII/IX/XIII/XV CCSD gamma for dc Kerr (gamma_K), DFWM (kerr), ESHG, THG of Ne, Ar, N2 (vibrationally averaged), CH4 (16 datasets); Tables IV-VII THG by SCF/CCS/CC2 (+ N2 CCSD at r_e) (13); Table III static by method (4) and quoted other work (4, reproduced); Table XII <0|gamma|0> of N2; Tables X/XI/XIV/XVI scaled best estimates (12) and experimental columns (12, reproduced); text static values N2 894, CH4 2533 +- 70 (and 2650), reproduced Ne 108.1 +- 2.2 / 106.4 +- 2, N2 917 +- 9, CH4 2590 / 2607. 67 datasets, 398 points.

• Structural fixes: Tables X and XVI cells garbled in the curators’ extracted tables (+- read as “6”, merged cells, footnote letters in numbers): explicit mapping from the garbled text to the image’s values, each asserted. Table XIV “14..3” (doubled point in the print) read 14.3. To re-check: the GARBLED table in tools/extract/hattig_1998.py against the images once more.

• Table XV prints lambda 590.0 for omega 0.077357 (= 589.0 nm, as Tables VII, XVI): row id kept, wavelength is omega.

• Text numbers (garbled in the markdown) read on rendered pdf pages 6, 12, 14: HF limits 715 +- 2, 1865 +- 5; CCSD basis limits 867 +- 7 (N2), 2318 +- 35 (CH4); core -6.7, -12; N2 THG rovibrational -0.64 a.u.; CH4 +-70.

• Captions: Tables IV, V say q-aug-cc-pV5Z, VIII, IX say t-aug-cc-pV5Z, with identical CCSD THG values: one caption probably wrong.

• Parts: CH4 Table XVI dc Kerr/ESHG include zero-point and pure vibrational contributions (electronic_vibrational); its THG only zero-point (electronic). N2 dc Kerr experiment 1443 +- 160 recorded with part unknown.

• Hattig’s Table XI footnote quotes Buckingham & Dunmur’s Ar dc Kerr as 1171 +- 80; rice_1992 quotes 1070 +- 80. Compare with buckingham_1968.

• Checks: best = CCSD x static ratio reproduced (Ne 113.6 x 107.1/110.2 = 110.40; Ar 1257 x 1159/1178 = 1236.7; N2 972.1 x 894/915.0 = 949.8).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-248 bishop_1991 (new)

• Transcribed (images checked): Tables VI-XI, rovibrationally averaged (295 K) gamma_par and gamma_perp (THG: par only) of H2 and D2 for dc Kerr, ESHG, THG: elec, vib, total (30 datasets x 13 omegas); Table XIV ratios S (H2/D2) and T (H2/He), theory, experiment (sigma from the parenthesised last digits), fitted experiment (5); Table XVI gamma^K(total) for H2, D2 (7 wavelengths each). Text: He ESHG 43.788, 44.161, 46.684 at 13 190, 10 640, 5900 A; experimental H2/D2 dc Kerr (550 +- 60, 820 +- 49, 666(19), 669(26)); ac Kerr estimates 796.7/771.9 vs 789 +- 38/774 +- 39 (process other); Shelton’s static 686 +- 4 (H2), 669 (D2). Formulas: Table XV, five fits of Eq. (20).

• The vib columns are Bishop, Pipin & Rerat (1990) “unchanged”: marked reproduced (17 datasets incl. the ratio/expt reproductions). The totals are this paper’s sums.

• Checks: gamma^K(6328 A) = 1.5(786.6 - 302.5) = 726.15 (726); T(13 190) = 661.1/43.788 = 15.098; T(6943) = 798.1/45.647 (bishop_1989) = 17.484; the theory fit reproduces Table VII within 0.3 a.u.; Shelton’s A, B from the 21-point weighted fit: 1.200e-10 cm^2, 2.254e-20 cm^4 (the H2 row of the survey of nonlinear data).

• Convention T (Orr-Ward SOS, Buckingham’s definitions; bishop_1990 states Ward’s gamma is 1/6 of it). Atomic unit 6.23538e-65 (standard; no reduced-mass factor).

• Not extracted: Table IV (molecular-frame components at R_e; its ESHG/THG header prints “gamma_xzzz”, evidently xxzz), alpha, B, C, the ratio R.

• The ac Kerr wavelength 6758 A is computed here from 14797 cm^-1.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-249 bishop_1990 (new)

• Review. Datasets: Table VI (4 static total gamma_zzzz of H2, reproduced) and Table X (8 datasets, H2 e/v, par/perp, Kerr/ESHG; excluded: electronic superseded by bishop_1991, vibrational identical to bishop_1991’s reproductions). Images checked.

• Key statement for conventions (p. 345): Ward’s (Orr-Ward) beta and gamma are 1/2 and 1/6 of Buckingham’s (T).

• The rotational-contribution formulas (Eqs. 173-194) are recorded in the notes (for the separation of rotation in Kerr and ESHG); to check: the transcription of the factors against pp. 366-368.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-250 bishop_1993 (new)

• Transcribed: Table VI (image checked), CO2 isotropic pure vibrational gamma^v at hbar w = 0.07 E_h: static, dc Kerr, ESHG, THG, IDRI (kerr) and gamma_K^v (Eq. 10), rows SCF-partial, MP2-partial (no second derivatives of beta) and SCF complete: 6 datasets x 3 points. H2O, NH3 skipped; Table V (CO2 components) not extracted (extracted cell “zzzx” is “xzzx” in the image).

• Convention T (“coefficients in a Taylor series expansion of the induced dipole”).

• The gamma_K^v definition (3 gamma_xyxy - gamma_xxyy)/10 is the authors’ (Eq. 10); compare with Shelton’s (3/2)(gamma_par - gamma_perp) before combining.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-251 bishop_1996 (new, formulas only)

• Formulas: He sum rules A, B, B’ (Table XI) and the per-process a, b (Table XII: dc Kerr, ESHG, THG, IDRI). Images checked. The sums, the a, b from A, B, B’, and the reproduction of bishop_1989 Table III were all checked (source notes).

• A, B, B’ are absolute (units of gamma, frequencies in hartree), not Shelton’s relative coefficients; Shelton’s fourth-order coefficient is process-dependent through W4/W2^2 (1/2 dc Kerr and ESHG, 1/4 IDRI, 7/12 THG).

• X^5 (epsilon) not recorded (no quantity).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-252 sekino_1993 (new)

• Transcribed (images checked): Tables II (CO2), III (N2), IV (H2, two bases), VII (CO): static gamma_xxxx, gamma_zzzz, gamma_xxzz, gamma_par and dynamic gamma_par (THG, dc-SHG, IDRI, EOKE) at w = 0.0656 a.u. by SCF/TDHF, MBPT(2), CCSD, CCSD(T) (32 datasets); H2 ‘Exact’ column (7, reproduced from bishop_1991 and earlier Bishop papers); EXP column (8, reproduced). 47 datasets, 159 points.

• Structural: the extracted cells print “gamma_xxxz”; the images show gamma_xxzz.

• Footnote b prints “w = 0.0656 a.u. = 6443 A” (image checked); 0.0656 a.u. is 6946 A.

• Convention T (E expansion with 1/4!); Ward’s chi^(3) = gamma/6 (Table II footnote l, factor 8.395e-41 esu/molecule/a.u.); Table XVII esu values checked as conversions.

• EOKE is gamma_par(-w; w, 0, 0), not gamma_K: recorded as dc_kerr, component parallel.

• Doubts: N2 “THG 1270.0” and H2 “THG 950 +- 140” attributed to ESHG papers (Ward & Miller; Shelton 1990); H2 EOKE 560 +- 60 footnote unclear (c = Newell & Baird?).

• H2 exact gamma_par 613.2 = (8 x 575.9 + 3 x 682.5 + 12 x 211.9)/15 (checked).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-253 tarazkar_2014 (new)

• Transcribed: Table II (image checked), Xe CCSD static, dc Kerr, ESHG, DFWM (kerr) gamma at 800 nm in four x-aug-cc-pVQZ-pp bases (4 datasets x 4) and the quoted static 6888 (shelton_1990) and 7030 +- 200 (rice_1991) (reproduced).

• Convention T (induced-dipole expansion with 1/3!; cos-field factors 1/2, 1/8, 1/4, 1/24). Their “second-order hyperpolarizability gamma^(2)” = conventional gamma.

• Fourth-order gamma^(4), DSWM relation (Eq. 14) and n4 = 4.02e-40 gamma^(4) (cm^4/W^2) in notes only; n4 positive for all noble gases (refutes negative HOKE).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-254 tarazkar_2014b (new, no datasets)

• Ar: only gamma^(4) tables; gamma(2) in a figure and supplementary Table S2 (not in the curators’ library). Notes: Eq. (19) DFWM ~ ESHG/3 + dcKerr - static/3, and the claim that Wahlstrand et al.’s gamma_DFWM = gamma_ESHG [gamma_ESHG(0)/gamma_ESHG(w)]^(2/3) should have exponent 1/3 (9-24 % errors at 500-300 nm).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-255 tarazkar_2015 (new)

• N2+ (not curated): notes only. One curated value: neutral N2 static gamma 1.17e3 a.u. (MCSCF/t-aug-cc-pV5Z, text; component not stated).

• n2 (cm^2/W) = 8.28e-23 gamma_DFWM (a.u.) with no density: computed here to imply N = 2.50e25 m^-3 (1 atm, 293.9 K). Inference.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-256 tarazkar_2016 (new)

• Transcribed: Table II static n2 of neutral He, Ne, Ar, Kr (image checked; ions skipped); text n2 at 800 nm for He 3.64e-9 and Kr 2.46e-7 cm^2/TW. State inferred (1 atm, 293.9 K, ideal) from the factor 8.28e-23 cm^2/W per a.u.; open: whether to keep an inferred state or re-express these as gamma_DFWM.

• Back-converted gamma_DFWM(0): He 42.8, Ne 108.5, Ar 1162, Kr 2690 a.u. (computed).

• The lambda_min column has no stated wavelength: not recorded.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-257 maroulis_1994 (existing record; O3 gamma added)

• Transcribed (images checked): Table I SCF gamma components and mean in four basis sets (7 datasets x 4); Tables II and III, [6s4p3d1f], gamma by method SCF, MP2, MP3, DQ-MP4, CCD, CCD+S(CCD), CCD+ST(CCD) (7 datasets x 7). Increment columns not taken.

• Printed “-285(1)” = -285 x 10^1 (footnote a): the script writes the full number by moving the decimal point (a notation, not a correction). The approach is to confirm.

• Means reproduce from the components (CCD+ST(CCD) 3250.4; CCD -2105.8).

• Convention T (energy expansion 1/24). Superseded by maroulis_1999.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-258 maroulis_1999 (existing record; O3 gamma added)

• Transcribed: Table I (open O3, [7s5p4d2f]) gamma components and mean by SCF … CCSD(T) (7 datasets x 7). CCSD(T) gamma-bar 2642 a.u.

• Structural fix: the extracted table renders six minus signs as a leading “2” (“22962”, “214832”, “21217”, “2294”, “247”, “21282”); restored from the image, each asserted; every mean checked against its components (e.g. MP3 zzxx = -47 makes the mean 1204.6).

• The footnote’s mean formula renders “gamma_zzzz + gamma_yyyy + gamma_zzzz” in the extracted text; the means require gamma_xxxx (image of the footnote not checked).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-259 naves_2011 (existing record; O3 gamma added)

• Transcribed (images checked): Table III gamma-bar by process (static, THG, dc-SHG, IDRI, dc-K) and method (CCSD opt/expt geometry, CCSD(T) expt) at 0-0.0656 hartree (15 datasets); Tables I and II static components and means (14); Table VI pure vibrational terms by process (20).

• dc-K uses Eq. (25) (3 gamma_abab - gamma_abba)/10 (component K); the others Eq. (24).

• THG and dc-SHG at 0.0428 and 0.0656 hartree excluded (excluded_rows), as the authors exclude them (near 2w and 3w resonances; THG CCSD(T) 449600 at 0.0656).

• Structural fix: Table VI’s merged cells rebuilt from the image, each asserted by concatenation. The w -> infinity rows are in the files (wavelength “inf” hartree) but excluded from the datasets (excluded_rows): no finite wavelength.

• Pure vibrational totals (sums, computed here, in notes): static 1547 (>80 % of the electronic), IDRI 101-140, dc-SHG ~130, dc-K ~470.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-260 christiansen_1998 (existing record; anisotropies added)

• No gamma in the paper. Added the Table X Delta alpha of CO and N2 (7 datasets: electronic, CO total static 4.01, and reproduced Alms, footnote g, Bridge & Buckingham) as polarizability_anisotropy. The existing alpha files are unchanged (checked with git).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-261 christodouleas_2009 (new)

• Transcribed: Table 2 (image checked), open O3 static gamma components (xxxx, yyyy, zzzz, xxyy, yyzz, xxzz) by CCSD(T), mPW1PW91, B2PLYP, [7s5p4d1f] (6 datasets x 3). The mean is not printed: 2470 a.u. from the CCSD(T) components (computed here).

• Citation: the curators’ library year is 2009 (online); the journal volume is 31 (2010), pp. 412-420 (citation.bib). Recorded as 2010 in the citation; the source id keeps 2009.

• SO2, the XY2 molecules and ring O3 skipped.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-262 lehmeier_1985 (existing record; third-order datasets added)

• Transcribed (script tools/extract/lehmeier_1985.py): Table 1 (tbl_3d2f3ba324ee) gamma(3) at 1.055 um in 10^-64 C m^4/V^3 (gamma_thg_*, primary, relative +-0.1 from p. 71) and 10^-39 esu (gamma_thg_esu_*, check), chi_0/chi_0(He) (chi_ratio_*, check); Table 2 (tbl_905211afbf03, JSON only) at 694.3 nm: column (a) (gamma_694_*, check: Eq. (18) model transfer), (c) Ward-New normalised (ward_new_normalized_*, reproduced from ward_1969), theories (d)-(i) (sitz_yaris_He, mizuno_*, klingbeil_He, dawes_*, tripathi_*, langhoff_*, reproduced), dc Kerr column (dc_kerr_buckingham_*, reproduced from buckingham_1968); text point chi_He (3.43e-28 m^2/V^2, note c, check). Both table images compared with the cells: agree.

• Convention (p. 67, Eqs. (1), (2); p. 69, Eq. (13)): P_NL = 4 eps0 chi EEE, E = {E0 e^i..

  • c.c.}/2, chi = N L(4) gamma/eps0: gamma_T = 24 gamma(3). Checked: chi_He = N0 gamma/eps0 = 3.43e-28 (reproduces note c); Table 1 esu column = SI x 8.0888e24 (reproduces); chi ratios reproduce gamma ratios within rounding and L(4).

• Reproductions verified: column (c) = ward_1969 set (i) / 4 (all six); column (g) = Dawes Table I / 4 (He-Kr; Xe prints 55.4 against 222/4 = 55.5); dc Kerr column = Buckingham and Dunmur’s gamma (10^-36 esu) / 24 (all five, including Ar 24.58 -> 24.6).

• Doubts: theories (d), (e), (f), (h), (i) cannot be checked (originals not in the curators’ library); whether Lehmeier rescaled them by 4 is not stated. Sitz and Yaris is printed “J. Chem. Phys. 49 (1965) 3546” (Ward: 1968). The record keeps kind = "compilation" (set earlier for the reproduced refractivities); the THG values are this paper’s own measurements, so measurement may be more apt: open.

• Part: atoms electronic; N2 THG recorded total (vibrational THG part not separated, small). Density: ideal gas at 296 K (Eq. (13)), local field included.

• 694.3 nm (and ruby 6943 A throughout): air or vacuum not stated; recorded as printed, vacuum default (0.19 nm difference).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-263 ward_1969 (new)

• Table III (tbl_ffb0f106d17e, JSON only; image checked) by tools/extract/ward_1969.py: chi (i) for Ne, Ar, Kr, Xe, H2, CO2, N2 (primary; normalised to chi_He = 4.0, Sitz and Yaris), chi (ii) (excluded, rejected by the paper), He absolute 7.0 x 3^+-1 (primary, no sigma: a factor-3 uncertainty) and 24 (ii) (excluded); theories (Sitz-Yaris 4.0, Appendix B 12.0 as check, Dawes normalised); chi derived (check, rows named for their input); chi^K (Buckingham-Dunmur /6, Sitz-Yaris, Buckingham-Orr H2); chi^0 (Sitz-Yaris, Hurst). 40 datasets.

• Structural: He’s three theory values share one merged cell (split by footnote); the derived rows are matched to the chi^K/chi^0 cell on the same row. Xe’s Dawes value carries footnote b (Appendix B, helium only) in print: note c meant (987 = 222 x 4.0/0.9).

• Convention (Appendix A, pp. 69-70, page image checked for (A.12)’s 1/6, which the extracted text reads 1/8): P^ws = K X E E E (complex amplitudes, 1/2 convention), K = 1/4 (THG), 3 (Kerr), 1 (dc), 1/2 (SHG); X = N chi; chi = gamma_T/6. Checked with Buckingham and Dunmur’s gamma / 6 = chi^K (all five).

• Eq. (IV.4) does not reproduce the printed “chi derived” column to better than 1-6 % (He 3.88 from 3.66 computes 3.98; Ar 250 from 194 computes 264; Xe 962 from 650 computes 987): not explained; the column is check.

• Uncertainty inconsistencies: Table II’s X carries smaller +- than Table III; the abstract mixes them. Table III’s are recorded.

• Chi^K of Sitz-Yaris and of Buckingham-Orr (H2) has no stated wavelength; the ruby line is recorded (what Eq. (IV.4) uses). H2’s chi^K part unknown (orientational part?).

• O2 (X/Delta k only) and air: notes only.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-264 dawes_1968 (new)

• Table I (tbl_f296ada000f8, image checked): (A) alpha_zzzz(3nu), 10^-39 esu/atom (primary, theory), (B) ratios to He (check); (C), (D) ranges not extracted; N_0, nu_0 (Cuthbertson, reproduced) only in formulas.

• Caption prints “10^39 esu/atom”: misprint for 10^-39 (abstract). Not an erratum (the data file holds the numbers, the scale is -39).

• Formulas eq9_<gas> (Eq. (9), p. 48): recomputed at 6943 A with CODATA constants: He 0.923 (0.9), Ne 1.715 (1.7), Ar 28.48 (28), Kr 71.33 (71), Xe 218.2 (222). He-Kr within 2.5 %, Xe 1.7 % low; no single correction implied.

• Convention: Armstrong et al.’s Eq. (2.22) without its 1/4, “as per” New and Ward: the same as ward_1969 (gamma_T/6), confirmed by Ward’s “0.9” for Dawes’s He and Lehmeier’s /4 column.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-265 ward_1979 (new)

• Table III (tbl_d1cb8fd65ca1, JSON only; image checked; value and +- on two printed lines, merged in the cells with the footnote letter between) by tools/extract/ward_1979.py: chi_par(3) ESHG at 694.3 nm for H2, N2, O2, SF6, CO2, CO (chi3_*, primary, 1 sigma, normalized to He = 3.79e-39 esu of Sitz and Yaris); the comparison columns as reproduced: dcSHG (Mayer; Hauchecorne et al.), TWM (Rado, process other), Kerr (Buckingham-Orr H2, Buckingham et al. 1970 N2 and CO2, Buckingham-Dunmur SF6), THG (= ward_1969 chi_i, exact), theory (McLean-Yoshimine H2, Bartlett-Purvis N2: static zzzz component). NO, H2S, NH3, H2O, (CH3)2O, CH3OH skipped.

• Convention (p. 826, Eq. (1)): p^2w = (3/2) chi^e E^0 E^w E^w, amplitudes as Ward and New: chi = gamma_T/6. Checked: SF6 Kerr 200 = Buckingham-Dunmur 1.2e-36/6.

• CO: T^-1 -> 0 limit (Table II, 144 +- 4) removes the dipolar term: recorded electronic_vibrational; nonpolar molecules total.

• Doubt: O2 R(3) = 3.12 +- 0.07 (Table III) against R^e = 2.97 +- 0.07 (Table I); for a nonpolar molecule they should be equal. Not a dataset (R is not a curated quantity), so no erratum; noted.

• Wavelengths of the reproduced dcSHG, TWM and Kerr (except Buckingham-Dunmur, 632.8 nm) are not stated; recorded at the ruby line with a note.

• Linear data left in notes for the refractive curation: -Delta k_0 at Loschmidt density for H2, N2, O2, CO2, SF6, CO (694.3 -> 347.2 nm, virial densities).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-266 ward_1984 (new)

• Table I (tbl_67cee6b847af, JSON only; page image checked) by tools/extract/ward_1984.py: THG chi at 694 nm for CH4 330(10) and SF6 148(9) (primary, normalized to He = 4.00e-39 esu); dcSHG Miller-Ward 1977 (CH4), Ward-Miller 1979 (SF6, = ward_1979), Shelton-Buckingham 1982 (both), Kerr Buckingham-Orr 1969 (CH4), Buckingham-Dunmur (SF6), all reproduced. CH3F, CH2F2, CHF3, CF4 skipped.

• Erratum (both dcshg_shelton_buckingham_*, wavelength): footnote b prints “541 nm”; Shelton and Buckingham measured at 514.5 nm (shelton_1982 Table II caption) and their gamma / 6 reproduces the column (CH4 334.6 vs 333, SF6 144.3 vs 144, CF4 103.7 vs 103, CHF3 146.9 vs 146, CH3F 217 vs 216). Corrected to 514.5.

• The paper settles Ward and New’s sign ambiguity: q = -1 (set (i)) for all gases of ward_1969 (added to ward_1969’s notes).

• Level of the parenthesised uncertainties not stated; z_I adds up to 5 % (p. 1005).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-267 mahon_1979 (existing record; two third-order datasets added)

• Text only (PDF p. 5, journal p. 448): calculated THG susceptibilities per atom at the 1216 A harmonic (fundamental 3647 A), Kr -1.1e-36 and Xe 2.0e-35 esu, “details … will be reported later”; Ar negligible. Datasets chi3_1216_Kr (beyond_resonance) and chi3_1216_Xe, use check.

• Convention: Bjorklund’s (Eq. (1), PDF p. 2: P_3 = 8.215e-2/(3 lambda)^4 chi^2 N^2 P_1^3 F_1, P in W, N in cm^-3, lambda the harmonic wavelength in cm). Bjorklund 1975 (IEEE JQE 11, 287) is not in the curators’ library, so the factor to gamma_T is not established (convention = "bjorklund_1975"). Near-resonant VUV values: not usable for a nonresonant model.

• The existing record’s page references are PDF pages; the new notes give both.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-268 ferrell_1987 (existing record; no dataset added)

• Checked for third-order values: none (the paper uses phase-matched near-resonant THG as a probe of oscillator strengths, buffer-gas indices and absorption; no chi(3) is printed). A paragraph saying so was added to the record’s notes.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-269 pengqian_1997 (new, no datasets)

• Resonance-enhanced THG spectra of CH4 in the VUV/XUV, relative only; no chi(3) printed. Short record. The curators’ library has the author names inverted (Wang Peng-qian et al.).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-270 lundeen_1983 (new)

• Table I (tbl_4a6abc0d694e, JSON only; image checked) by tools/extract/lundeen_1983.py: 68 single-point datasets. This work’s CARS chi (fwm_532_*, pump 532 nm, Stokes 683 nm, electronic after subtracting the calculated Raman parts; primary): He 3.2 (+-0.7 text), Ar 131, Kr 334, D2 69, N2 105 +- 14 (the absolute reference), O2 141, CO 155, CO2 153, CH4 330, SF6 176 (relative < 5 %, plus the 13 % N2 scale as systematic_relative). Reproduced: Rado and Hauchecorne et al. FWM at 694 + 975 nm (rescaled to this N2), dcSHG (= ward_1979 for the molecules), Kerr (Buckingham et al.; atoms = Buckingham and Dunmur / 6), THG (= ward_1969), He theory (Sitz and Yaris 3.79, 3.66, 4.00); calculated rotational and vibrational CARS contributions (check).

• Convention (Eq. (1), p. 6301): Ward’s, K = 3/4 for CARS: chi = gamma_T/6 per molecule in cm^6/(erg molecule). Reference standard: the H2 Q1 resonant chi_r0 = 1.57e-33 from Schrotter’s Raman cross sections (alpha_par^2 = 7.36e-51 cm^6/sr) and Owyoung’s linewidths; N2 = 102.9 +- 14 before, 105 +- 14 after the Raman corrections. FIA-based alpha^2 would raise every FWM value by 30 %.

• Doubts: N2 rotational contribution 0.8 in the text (p. 6303) but 3 in Table I; Kr Kerr printed 230 +- 17 (233 in ward_1969 and B&D/6). Hauchecorne’s H2 is at omega_1 - omega_2 = 2917 cm^-1 (recorded at pump 694 nm; the Stokes differs). Footnote label “c” printed twice in the curators’ extracted text (the second is e).

• Table II (halocarbons): only CH4 curated, repeats Table I: not extracted.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-271 rosasco_1985 (new)

• The paper’s own results (Table III, p. 293, text points): ac (optical) Kerr constants at 1 amagat, 296 K: Ar 2 sigma/24 = 0.526e-18 esu (electronic, +-6 % 1 sigma statistical, range -15/+14 %), N2 (2 sigma + 2B(0))/24 = 2.09e-18 esu (electronic + cw reorientation, total; Eq. (49)’s 2.07 plus a 1 % far-off-Raman correction). Process kerr (chi(-w, w, W, -W), pump 676.4 nm, probe 17756 cm^-1 = 563.2 nm).

• Table IV (tbl_61c221923f79, JSON only; image checked) by tools/extract/rosasco_1985.py: 41 datasets of 3 sigma/24 (10^-18 esu per amagat) for Ar, N2, He, D2, H2, O2, CH4, SF6: this work (check), reevaluated TWM of Rado, De Martini, Hauchecorne, Lundeen’s TWM (= lundeen_1983 via Eq. (A27); all seven reproduce), Huo-Jaffe theory, FISHG (Hauchecorne reevaluated; Shelton-Buckingham = shelton_1982, Ar reproduces), dc Kerr (Buckingham-Dunmur Ar and He reproduce; SF6 1.36 vs 1.34 computed), THG (= ward_1969 set (i) via Bogaard-Orr; reproduce). Parenthesized normalization references skipped.

• Convention (Appendix A, pp. 295-297): P = D chi E E E (D = 6, 3, 1; E/2 amplitudes); Hellwarth’s 24 chi_ijkl = sigma + nuclear terms; sigma = N gamma_T/3 (A19, A23), so 3 sigma/24 = N gamma_T/24, 2 sigma/24 = N gamma_T/36; chi^CARS = 12 chi_1111 = 3 sigma/2; Lundeen’s chi^LHN: (1/4) N chi^LHN = 3 sigma/24, 6 chi^LHN = gamma. Per amagat = 2.687e19 cm^-3 (C4). Unit recorded as “esu (per amagat)”.

• Wavelengths in Table IV are not printed: taken from the originals’ records (Rado and Hauchecorne 694 nm, Lundeen 532 nm, Shelton-Buckingham 514.5 nm, B&D 632.8 nm); De Martini and Huo-Jaffe unknown (ruby recorded, flagged in notes); dc Kerr of Buckingham-Orr and Buckingham et al. recorded at 632.8 nm, not stated.

• Bridge and Buckingham 1966 anisotropies (N2 0.696, D2 0.299 x 10^-24 cm^3) and the computed 2B(0)/24 (N2 1.752, D2 0.283) are in notes only (no wavelength stated).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-272 farrow_1985 (new)

• Table 2 (tbl_0abf9a86f7ed, CSV; image checked) by tools/extract/farrow_1985.py: chi_nr (10^-18 cm^3/erg per amagat) of Ar and N2: this work Ar 9.6 +- 1.0, N2 8.5 +- 1.3 (primary); Hall-Eckbreth (Rado rescaled) 11.63, 10.13; Rosasco-Hurst Ar 9.5 +- 1.0 (= rosasco_1985); Lundeen 10.6 +- 1.5, 8.5 +- 1.1; Rado as scaled by Lundeen 9.5 +- 1.0, 8.5 +- 0.8 (reproduced).

• Convention inferred, not printed: “the definition of relation (1)” is the CARS chi^CARS (P = (1/4) chi^CARS E_L^2 E_s*), per amagat: Table 2’s Lundeen column = 3 x Lundeen’s per-molecule chi x 2.687e19 and its Rosasco column = 12 x Rosasco’s 3 sigma/24 (both reproduce). So gamma_T = 2 chi^CARS/N0 (1e-18 unit = 147.8 au; the survey’s 148). The paper never says “amagat”.

• Doubts: N2 uncertainty +-0.9 in the text (p. 904) against +-1.3 in Table 2; Rado-as- scaled N2 +-0.8 against Lundeen’s +-1.1 for the same reference. N2 part recorded electronic (CARS background; off-resonant Raman tails not separated).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-273 rosasco_1986 (new)

• Table 1 (tbl_1142277dccf1, JSON only; image checked) by tools/extract/rosasco_1986.py: 2 sigma/24 (10^-19 esu per amagat, 296 K) H2 2.966 (primary; the electronic part of the measured ac Kerr constant, +-5 % per note a), D2 2.908 (check: H2/1.02, Mizrahi and Shelton), He 0.178 (reproduced: Ward and New via rosasco_1985); 2B(0)/24 H2 2.722, D2 2.827 (computed reorientation, rotational, check). Pump 14779 cm^-1 recorded with wavelength_unit cm-1; probe 17751 cm^-1 in parameters.

• Convention: rosasco_1985’s Hellwarth form; Eq. (11), p. 1253: 3 sigma/24 at 1 amagat = N0 gamma/24 = 5.639e-22 gamma_AU (reproduced with 5.0367e-40 esu per au).

• Doubts: chi_0^N/A_0N_0 = 0.0137 (Eq. (7)) against 0.01376 recomputed from Table 1’s components (rounding); the last Table 1 row prints B(omega - Omega) inside a sum over omega + Omega (image checked), presumably a misprint. Off-resonant Raman sums and A_0 N_0 = 461.4 are in notes only.

• The same paper gives the pump as 14779 cm^-1, which shows that rosasco_1985’s “676.4 nm” is the Kr-ion line in standard air: those datasets (and farrow_1985’s Rosasco column, hahn_1995’s IRS column) are recorded standard_air.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-274 farrow_1987 (new)

• Only N2 is curated: Table 2 (tbl_4c51c969c816, CSV; image checked) N2 electronic chi_nr 8.5 +- 2 x 10^-18 (cm^3/erg)/amagat, reproduced from farrow_1985 (whose Table 2 says +-1.3 and text +-0.9). Propane, n-butane and water values in notes only.

• Doubt: the text quotes N2’s 8.5e-18 once per amagat and once “(cm^3/erg)/atm” (p. 1244).

• Definition “3 chi(3) = 3 chi_r + chi_nr” (p. 1241): chi_nr is the CARS chi^CARS as in farrow_1985.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-275 hahn_1995 (new)

• Tables 1-3 by tools/extract/hahn_1995.py (images checked; the curators’ extracted text has glyph errors: 10^-18 as “10218”, cm^-1 as “cm21”, minus as “2”): Table 3 electronic chi_NR (primary, 10 %) for CO2 11.8, CH4 22.7, N2 7.90, O2 7.98, CO 12.3, H2 5.90; Table 1 effective values and fringe-slope ratios to Ar (check); Table 2 computed off-resonant terms (check); text O2 at 2334 cm^-1 (7.81, check); Table 3 comparison columns reproduced (Rosasco-Hurst IRS, Farrow CARS, Shelton-Rice ESHG, “USED CARS” note e without a reference, Lundeen CARS, Rado reevaluated). 53 datasets. Acetylene, propane, CF4 skipped.

• Structural fix: Table 2’s lost minus signs restored in the script for CO2 (both bands), O2 and CO (image: -0.35, -0.62, -0.67, -2.03); the subtraction effective - off-resonant = electronic then reproduces Table 3 for all six curated gases (H2 5.89 vs 5.90).

• Convention: CARS chi^CARS per amagat, scale fixed by argon = 9.46 = 12 x rosasco_1985’s 3 sigma/24 (so gamma_T = 2 chi/N0). Lundeen column = 3 x N0 x Lundeen’s chi (all six reproduce); Rado column = 12 x rosasco_1985’s reevaluation for Ar, N2, O2 (CH4 17.72 vs 17.76; CO2, CO not in rosasco_1985).

• Table 3 note e’s source is not given in the paper (only “USED CARS”); flagged.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

Conventions common to the records TC-276 to TC-293 (to confirm)

Page numbers are journal pages unless marked “pdf”. Values read from table images were confirmed in the pdf text layer (pdftotext) where the text layer holds them.

• Reference temperature. Where a paper gives “1 atm” (or “1 bar”, or “per bar”) without a temperature, the state is recorded with 293.15 K, assumed, and the record’s notes say so. Where the paper states room temperature or a temperature elsewhere (a simulation at 300 K, say) the notes quote it; the state keeps 293.15 K unless the temperature is stated for the reduction itself (Borzsonyi: 293 K; Nibbering: 300 K; Hellwarth and Pennington: 20 C).

• Self or probe. Every Maryland n2 (Wahlstrand 2012, 2012b, 2015, 2018, Zahedpour 2015) is the self coefficient: the probe index is written 2 n2 I (explicitly in 2012b, 2015, 2018 and Zahedpour; implicitly in the 2012 PRA, see TC-276). Reichert 2015 also writes 2 n2 I for its nondegenerate probe. The SPM measurements (Nibbering, Wang, Borzsonyi) measure the self coefficient directly.

• Part. Values from 40-fs pump-probe with polarization separation of rotation are electronic for atoms and electronic_vibrational for molecules (the adiabatic bond stretch is inside the instantaneous response; the papers call it electronic and estimate it small). Wahlstrand 2015 separates the vibrational part of H2 and D2, so its n2,elec is electronic. Nibbering’s n2,instant (120 fs, includes the rotational Rayleigh part) is instantaneous; ns and 200-fs chirped values are total.

• Unknown wavelength. A reproduced value whose original wavelength is not stated (Lin et al.’s anisotropies, quoted from Hirschfelder, Curtiss and Bird) has inf in the wavelength column as a placeholder and parameters.wavelength_stated = false (format need: the vocabulary has no “not stated” wavelength).

• Polarizability anisotropy in SI. polarizability_anisotropy lists au, angstrom3 and cm3; SI values (Reichert’s 1e-40 F m2, Nibbering’s 1e-40 C2 m2/J) are recorded with unit = "SI" (C m2/V, as polarizability’s SI). Format need.

• Kerr constants, susceptibilities and n2 in esu keep the printed unit string; the conventions are in each record’s notes.

TC-276 wahlstrand_2012 (Wahlstrand, Cheng & Milchberg, PRA 85, 043820 (2012))

• Table I (p. 3): the curators’ extracted cells merged all rows into one garbled row; every value was entered inline from the table image and confirmed in the pdf text layer: n2 (1e-20 cm2/W) Ar 9.7 +- 1.2, N2 7.4 +- 0.9, O2 9.5 +- 1.2, N2O 17.2 +- 2.2; Nibbering column 14 +- 2, 23 +- 3, 51 +- 7; Loriot column 10.0 +- 0.9, 11 +- 2, 16.0 +- 3.5; Shelton and Rice column 10.4, 8.1, 8.7; Delta alpha (1e-25 cm3) 6.7 +- 0.3, 10.2 +- 0.4, 28.1 +- 1.1; Lin 9.3, 11.4, 27.9. n2/n2,long (0.23, 0.14, 0.04) not extracted (no quantity).

• Self coefficient, inferred. The PRA’s Eq. (1) writes the probe index as n2 I with no factor 2; coefficient = "self" rests on wahlstrand_2012b (same calibration, same Ar value, explicit 2 n2 I), wahlstrand_2013 p. 7 (“theoretical justification for the analysis performed in [17]”) and zahedpour_2015 (2 n2 I, citing this paper). To confirm.

• Reference density. “at 1 atm”, no temperature; 293.15 K assumed. The absolute scale uses n0 - 1 = 2.795e-4 for N2 at 633 nm, 1 atm; optmat’s default N2 model gives this at about 291 K (2.822e-4 at 288.15 K, 2.773e-4 at 293.15 K), i.e. the effective density is ~0.7 % above that of 1 atm and 293.15 K. Open: whether to use ~291 K.

• Part: Ar electronic; N2, O2, N2O electronic_vibrational (the paper attributes the instantaneous part to electrons, with the bond-stretch part ~1/30 in N2 and O2).

• probe_nm = 580 (the paper’s worst-case dispersion estimate uses a 580-nm probe; the probe band was 550-635 nm with no measurable variation).

• Reproduced: Nibbering column (nibbering_1997 Table 3 n2,instant, 1.0 bar/300 K, unit change only), Loriot column (loriot_2009 + loriot_2010 erratum, 1 bar, room temperature), Lin column (lin_1976). Shelton and Rice column: check (computed by the authors from shelton_1994; method not stated).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-277 wahlstrand_2012b (Wahlstrand, Cheng & Milchberg, PRL 109, 113904 (2012))

• The five n2 exist only as panel labels in Fig. 3 (raster; not in the text layer), read from the figure image: He 3.1 +- 0.4 (1e-21), Ne 8.7 +- 1.1 (1e-21), Ar 9.7 +- 1.2 (1e-20), Kr 2.2 +- 0.4 (1e-19), Xe 5.8 +- 1.1 (1e-19) cm2/W. A second reading of the figure is advised.

• Self coefficient: explicit (p. 1, “The factor of 2 recognizes that Delta n describes cross-phase modulation and n2 is the nonlinear self-refractive index”).

• State not stated in the Letter (calibration “as in [7]” = wahlstrand_2012, 1 atm); 101325 Pa and 293.15 K assumed.

• Ar recorded as check, reproduced_from wahlstrand_2012: the same value and the calibration reference of this Letter (all other gases referenced to Ar). Open: whether it is an independent measurement.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-278 wahlstrand_2013 (Wahlstrand et al., PRA 87, 053801 (2013))

• Table I (p. 8), extracted by tools/extract/wahlstrand_2013.py from the JSON cells (no CSV); image checked. Ref. [17] column reproduced from wahlstrand_2012; Ref. [10] (Loriot erratum, self) reproduced from loriot_2010; the rotational-grating corrected N2 8.4 +- 2.0 and O2 11.1 +- 3.5 are check (a re-analysis of Loriot’s data).

• Convention quoted in notes: n2 = 12 pi^2 chi(3)_xxxx / (n0^2 c), I = n0 c |A|^2 / 8 pi, field (1/2) A e^{i(kr - wt)} + c.c., P_i = chi_ijkl E_j E_k E_l (Gaussian). Probe index 2 n2 I (both degenerate and nondegenerate). Birefringence 4 n2/3.

• Loriot’s state for the reproduced values: 1 bar, room temperature (from loriot_2009’s text: “1 bar of N2 at room temperature”); 293.15 K assumed. Loriot itself is recorded in TC-294: align the states.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-279 wahlstrand_2015 (Wahlstrand et al., PRA 92, 063828 (2015))

• Table I (p. 5), tools/extract/wahlstrand_2015.py from the JSON cells (no CSV), image checked: n2,elec^s H2 6.5 +- 1.0, D2 5.8 +- 1.3 (1e-20 cm2/W, 1 atm, pump 800 nm, probe 600 nm; primary, electronic, self); Ref. [35] 6.37, 6.20 (check, computed from Shelton and Rice); Delta alpha 3.0 +- 0.6, 3.0 +- 0.4 (1e-25 cm3, primary); Ref. [30] (Bridge and Buckingham 1966) 3.14, 2.99 (reproduced, wavelength not stated); long-pulse n2,rot 2.7, 3.9, n2,vib 1.0, 1.2, n2,tot 10.2, 10.9 (check, derived). d alpha/dQ in notes only (no quantity).

• Self: explicit (n2,elec = 2 n2,elec^s for the probe, p. 4). Which vibrational coefficient (smooth or smooth + grating) the long-pulse n2,vib is, is not stated.

• 1 atm, no temperature: 293.15 K assumed.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-280 wahlstrand_2018 (Wahlstrand et al., PRL 120, 183901 (2018))

• No new n2; the Ar n2 9.7 +- 1.2 of wahlstrand_2012b is quoted as the intensity calibration (p. 3), recorded as reproduced. Self coefficient explicit (Delta n_K = 2 n2 I0).

• Notes: the bound response stays ~quadratic in the field beyond the ionization threshold (Kr, Xe, Ar slightly faster than |E|^2; N2 follows the extrapolation, O2 below): the refutation of negative higher-order Kerr terms. The Supplemental Material (fits c1, m; other gases) is not in the curators’ library.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-281 zahedpour_2015 (Zahedpour, Wahlstrand & Milchberg, Opt. Lett. 40, 5794 (2015))

• Table 1 (p. 5797), tools/extract/zahedpour_2015.py from the JSON cells, image checked: 6 pump wavelengths (400, 800, 1250, 1650, 2200, 2400 nm) x N2 (adjusted and unadjusted for Delta alpha dispersion), O2, Ar; the [32] column and n2,rot.

• N2 note-b (dispersion-adjusted) values are primary, note-c (unadjusted) check. Ar is “referenced to N2 measurements” without saying which N2 column.

• Self: explicit (Delta n_p = 2 n2 I + int R). Absolute scale from wahlstrand_2012’s Delta alpha (correlated with wahlstrand_2012’s n2; both are primary).

• The [32] column is reproduced to +-0.5 % (printed precision) by shelton_1990 Table IV with omega_L^2 = 2 omega_e^2 + 2 omega_p^2 (probe 600 nm) and n2 = N gamma_T / (8 eps0^2 c) at 101325 Pa, 293.15 K ideal gas (factor 0.1331 against the fitted 0.133); the self-Kerr 4 omega^2 fails at 400 nm by 12-16 %. Computed 2026-09-26 (the script is not in the repository).

• Misprints in the text (p. 5796), not in any dataset: a(N2) printed 1.8e-33 s^2; Shelton’s A gives 2.83e-33 and only that reproduces the [32] column. gamma0 printed 7.7e-30 and 9.8e-30 “cm^6 W^-1 s^-1”: with the paper’s n2 = (12 pi^2 / n0^2 c) N gamma they give n2 ten times the [32] column; recorded as printed in the two [[formulas]] with the finding in check.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-282 reichert_2015 (Reichert et al., Opt. Express 23, 22224 (2015))

• Nothing curated is measured: the n2,el (10 +- 2 x 1e-24 m2/W at 800 nm, magic angle, 83 fs) is of ambient air; CS2 is not curated. Notes only.

• Table 1 (p. 22232; CSV and image checked): Delta alpha N2 0.77, O2 1.21 (1e-40 F m2), the self-reference, quoted from Bridge and Buckingham (1966): reproduced, unit “SI”, wavelength not stated (inf placeholder). B and D fits in notes.

• Convention quoted: mu = … + gamma E^3 (no 1/6; field E0 cos), n2,el = 3 N f(3) Re / (4 eps0^2 c n0 n0,e) (SI), probe index 2 n2,el I: self coefficient.

• Text/Table 2 discrepancy: gamma(air) “(1.25 +- 0.10)” in the text, “1.25 +- 0.20” in Table 2 (air; not extracted).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-283 hellwarth_1990 (Hellwarth, Pennington & Henesian, PRA 41, 2766 (1990))

• tools/extract/hellwarth_1990.py: Table I (dc Kerr, JSON), II (sigma, CSV), V and VII (sigma + B0 in the LWL, JSON), VI and VIII (DFWM c1122, c1212, c1111, JSON); images checked for all. Table III (omega_s) and IV (omega_0) go into the [[formulas]].

• Erratum kerr_ratio_carusotto_H2, 515 nm: printed 3.2, corrected 32.2 (b = a x 1.83 for every other gas; H2’s b is 59 = 32.2 x 1.83).

• Structural fixes: Table V’s averages are misplaced in the curators’ extracted cells (242 on the O2 row, 44.4(47.4)f on the H2 row, …) and are reassigned in printed order; Table VII’s H2 49.7(3) is printed without a wavelength and is the 633-nm row (= 52.5 / F_1221^B(633) = 52.5/1.057).

• Parentheses mean three different things: Table I “limits of error of last figures” (251(36) = +-36, 1.99(13) = +-0.13, converted in the script); Table II absolute errors (36.5(1.4) = +-1.4); Tables V and VII relative weights of the averages (not uncertainties; dropped from the value, kept in printed).

• Formula checks (2026-09-26; the script is not in the repository): formula A with Tables II, III, V reproduces all 20 curated Table VI entries to <= 0.6 %; formula B with Tables II, IV, VII reproduces Table VIII to <= 0.6 % except Ar at 261 nm: c1212 printed 2.45, computed 3.14 (c1111 9.74 against 11.11). Not corrected (no printed alternative); flagged. O2 1053 nm c1111 58.2 against c1122 + 2 c1212 = 58.54: 0.6 %, not corrected. Table I O2 average 549 against (515 + 3 x 559)/4 = 548.0.

• Conventions quoted in full in the record: Maker-Terhune c tensor with degeneracy factor D, full field amplitudes, n2 = 12 pi c1111 / n per <E^2>, sigma = rho gamma_T / 3 (esu; 1 au = 5.036e-40 esu). Check: He sigma 1.76 -> 41.9 au (Bishop and Lam), +2.9 % for Bishop-Pipin; Ar c1111(1053) -> n2 = 9.6e-20 cm2/W at 20 C, 1 atm.

• Uses: every derived value (He-scaled Kerr, averages, sigma, sigma + B0, c coefficients) is check; Carusotto’s, Buckingham’s and Bishop and Lam’s values are reproduced. The sigma values rest on mizrahi_1985_arn2o2 / mizrahi_1985_h2d2 ESHG ratios: reproduced_from names them.

• New parameter values: convention = "hellwarth_sigma" (the sigma of Eq. (13)) and "maker_terhune_c", spelled out in notes.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-284 pennington_1989 (Pennington, Henesian & Hellwarth, PRA 39, 3003 (1989))

• Table II (p. 3007; JSON cells, image checked): Ar c1221(-w, w, w, -w) = 3 +- 2 (gamma = 0) and 3 +- 6 (45 degrees) x 1e-19 esu, 1053 nm, 1 ns, 1 atm, 20 C: check (the paper: “a very uncertain estimate”, dependent on the assumed air and window values). Eq. (20) (2.0 +- 0.1) x 1e-19 esu reproduced from hellwarth_1990.

• Air values (Eq. (18) 20 +- 5, Eq. (19) 23 +- 2, c1111 3.0 +- 0.3 x 1e-18, n2 1.1e-16 esu) in notes only. pulse_fs = 1e6 for the 1-ns pulses.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-285 lin_1976 (Lin et al., PRA 13, 813 (1976))

• Table I (p. 819; CSV and image checked; the pdf has no usable text layer): Delta alpha (1e-25 esu = cm3) CO2 20.3, N2O 27.9, N2 9.3, O2 11.4 (footnote b, Hirschfelder, Curtiss and Bird 1954) and H2 3.02, D2 2.92 (footnote c, MacAdam and Ramsey 1972): all reproduced; wavelength not stated (inf placeholder). The collisionless rotational n2 (1e-12 esu/mole = per mol cm^-3) not extracted (model values; unit per molar density): N2 check with Eq. (16) 2.63 against 2.56 printed; Table IV’s N2O 1.07e-15 esu at 1 atm, 296 K is 9 % above 23.7e-12 x the molar density. Unresolved.

• A second copy in the curators’ library (identity unverified) = NASA TM-X-70344 (1974 preprint): Tables I-IV identical cell by cell; the PRA is used. No record for the preprint.

• n4, n6 (Eqs. (15b), (15c)) are the orientational saturation of a cold collisionless gas, not electronic higher-order Kerr terms: notes only.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-286 wang_2013 (Wang, Leng & Xu, Appl. Phys. B 111, 447 (2013))

• Text values (per bar, 293.15 K assumed): Ar 800 nm (1.08 +- 0.06) x 1e-19 (after the 2-4 % fiber-end correction; fit 1.11 +- 0.05), Ne 800 nm (9.30 +- 0.25) x 1e-21, Ar 1.8 um (6.65 +- 0.33) x 1e-20 cm2/W. Self, electronic. The +- are fit statistics; the authors’ own accuracy discussion is +-30 % (self-steepening, plasma): notes, not a stated uncertainty.

• Reproduced comparison values: bejot_2010 Ar 1.0e-19, bejot_2010_hollow Ar 9.73e-20 at 1.83 um (calculated), Nurhuda et al. 2007 Ne 7.5e-21 (not in the curators’ library).

• The DOI was first typed from memory with a wrong last character and corrected from the curators’ library metadata (the DOIs of all the records TC-276 to TC-293 checked against metadata).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-287 wang_2015 (Wang, Qiao, Huang & Leng, JOSA B 32, 2238 (2015))

• A simulation study; no measured value. Table 2 (p. 2242; CSV and image checked): the N2 inputs n2,instant 5.5 (800 nm) and 6.0 (400 nm) um2/(TW bar) are excluded: note a halves Loriot’s erratum value (11) although it is already the self coefficient (the error the survey reported); 6.0 follows from it by the generalized Miller formulas. Delta alpha 1.0 A^3 (Herzberg) reproduced.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-288 borzsonyi_2010 (Borzsonyi et al., Opt. Express 18, 25847 (2010))

• Table 1 (p. 25853; CSV and image checked): n2 per bar (1e-19 cm2/W), 293 K stated, 800 nm, 200-fs chirped pulses: Ar 19.4 +- 1.9, Ne 1.8 +- 1.5, Xe 84.3 +- 42.0 (to 100 mbar only), N2 6.7 +- 2.0. Part total, self. Doubt: Ar is twice Wang’s and the Milchberg value; no explanation in the paper.

• Literature row reproduced as one dataset per gas (row ids ref16, ref17, ref24, ref32, ref19_44): wavelength and state are placeholders (none given). [24] values are Loriot 2009’s original (pre-erratum) Ar 2.0 and N2 2.2 x 1e-19 (checked against the curators’ extracted Loriot 2009 table); [16] 0.98 and 4.52 are nibbering_1997 Table 2 (Hellwarth).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-289 nibbering_1997 (Nibbering et al., JOSA B 14, 650 (1997))

• Table 3 (p. 658; JSON, image checked): n2,instant (1e-23 m2/W, 1.0 bar, 300 K, 120 fs, 800 nm) Ar 1.4 +- 0.2, Xe 8.1 +- 0.8, SF6 1.6 +- 0.3, N2 2.3 +- 0.3, O2 5.1 +- 0.7: primary. Parts: Ar, Xe electronic; SF6 electronic_vibrational; N2, O2 instantaneous (includes rotational Rayleigh by the paper’s definition). beta derived N2 0.74, O2 1.4 (SI, primary); literature 1.0, 1.27 reproduced from lin_1976. n2,rot-Raman (m2/J) not extracted (no quantity). Text n2,effective N2 3, O2 8 x 1e-23 m2/W: check.

• Table 1 (p. 651): structural fix: the pdf’s symbol font gives “6” for +- and “2” for the minus sign (image: He -0.02 +- 0.01, Xe -963 +- 112); restored in the script with the raw cells asserted. Shaw 1993 values (248 nm, 10 ps, 1.0 bar, 300 K) for N2, O2, Ar, CH4, Ne, He and Lehmberg 1995 for Xe: reproduced, part total.

• Table 2 (p. 653): reproduced from hellwarth_1990 converted to m2/W: the electronic column equals Hellwarth’s sigma via n2 = (4 pi / c) 12 pi sigma/8 x 1e7 (checked: N2 0.721, O2 0.747, Ar 0.936, H2 0.551, He 0.0348); it is a long-wavelength limit (footnote c), so its row is LWL / inf, not 800 nm. The total column matches Hellwarth’s formula-B c1111 near 800 nm.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-290 palastro_2011 (Palastro, Antonsen & Pearson, PRA 84, 013829 (2011))

• Theory; no gas parameter is given as a number: no dataset. Three [[formulas]] (N2 at 294 K): the kinetic Green’s function (Eq. (17)), the two-moment fluid model (Eq. (26c), nu_hat = 0.95) and the three-moment model (Eq. (31b), omega1_hat = 2.37, nu1_hat = 1.27, nu2_hat = 3.28 -> mu_hat = 6.16, varpi = -6.45, nu_hat = -0.17; the three relations between them hold to rounding).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-291 palastro_2016 (Palastro et al., PRA 94, 023816 (2016), corrected version)

• Table I (p. 2; CSV and image checked): n2 N2 7.3e-24, O2 9.3e-24 m2/W (the measured wahlstrand_2012 / zahedpour_2015 values minus the adiabatic vibrational part, p. 3): reproduced (rescaled), part electronic; Delta a 6.7e-31, 10.2e-31 m3 = wahlstrand_2012’s values, reproduced. Recorded at 800 nm (the sources’), not at the paper’s LWIR.

• Reference numbers in Table I are off: “[6,16]” and “[6]” point to Palastro 2011 and Mitrofanov 2015, while the text (and the values) mean [7] (Wahlstrand 2012) and [17] (Zahedpour 2015). Not a value erratum; noted.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-292 chen_2007 (Chen, Varma, York & Milchberg, Opt. Express 15, 11341 (2007))

• No measured Delta alpha or n2; the simulation inputs, all cited to [26] = lin_1976 (the pdf text layer shows “[26]” after the D2 and H2 values, which the extracted Markdown lost): N2 0.93, N2O 2.79, O2 1.14, H2 0.30 x 1e-24 cm3 reproduced. D2 1.14e-24 excluded: it is Lin’s O2 value; Lin’s D2 is 2.92e-25 (and wahlstrand_2015 measures 3.0e-25).

• Dephasing times and rates, fitted B constants: notes only (no quantity).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-293 korn_1998 (Korn, Duehr & Nazarkin, PRL 81, 1215 (1998))

• SF6 impulsive vibrational Raman; no n2 or gamma: no dataset. d alpha/dQ (A1g) = 1.5 x 1e-16 cm2 at 400 nm (estimate, p. 1218) in notes (no quantity; pdf text layer renders it “1.5 3 10216”).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

Conventions common to the records TC-294 to TC-311 (to confirm)

Pages are journal pages (or preprint pages where only a preprint is in the curators’ library).

• Unstated temperature. Where a paper gives “1 bar”, “1 atm” or “atmospheric pressure” and “room temperature” (or nothing), the state is the stated pressure (1 bar = 100000 Pa, 1 atm = 101325 Pa) and 293.15 K, assumed, said in each dataset’s notes. The effect of 293 against 296-300 K is up to 2.3 % in density.

• Probe against self. A pump-probe (cross-phase) coefficient is probe; a coefficient in n = n0 + n2 I of one beam, or one extracted from SPM, self-focusing or FWM through a single-beam formula, is self.

• Parts. Atoms: electronic for any pulse. Molecules: instantaneous for femtosecond measurements whose rotational contribution is partly present or removed by a model (Loriot, Geints), total for 10 ps and longer pulses (Shaw, Pigeon), where the rotational response is adiabatic.

• Reproduced values name the ids of the other records: nibbering_1997, wahlstrand_2012, wahlstrand_2012b, zahedpour_2015, lin_1976 (TC-276 to TC-293), shelton_1994, bishop_1989 (TC-224 to TC-261). If the ids differ, the reproduced_from lists need renaming.

• Data files of third-order datasets are written under refractive/<gas>/ (the only directory the data-file test scans), as docs/data.md prescribes for every dataset.

TC-294 loriot_2009 (Loriot, Hertz, Faucher & Lavorel, Opt. Express 17, 13429 (2009))

• Library copy: the submitted manuscript. Tables 1 (tbl_90188e88dc6d) and 2 (tbl_732962a00e08) checked against their images; CSV cells equal the printed ones.

• Datasets: n2_N2, n2_O2, n2_Ar (1 point each, 800 nm, Table 2 n2 row = Table 1 “This work”), nonlinear_index, cm2/W, scale 1e-19 (10^-7 cm^2/TW), 1 bar and 293.15 K assumed, 2 sigma (Table 2 caption), pulse 90 fs; N2 and O2 instantaneous, Ar electronic; self after the errata.

• Errata (6): value and sigma of each n2 divided by 2 to the erratum’s printed values (N2 2.2 +- 0.4 -> 1.1 +- 0.2; O2 3.2 +- 0.7 -> 1.60 +- 0.35; Ar 2.01 +- 0.19 -> 1.00 +- 0.09), evidence the erratum’s Table 1 image (loriot_2010) and Wahlstrand 2013 Table I. The printed values are probe (cross-Kerr) coefficients; the corrected ones are self coefficients. To confirm: applying the authors’ correction as errata (rather than recording the printed probe coefficient with coefficient = probe); both describe the same measurement.

• Reproduced datasets nibbering_1997_<gas> (Table 1 “Ref [2]” row), instantaneous (N2, O2) / electronic (Ar), 1 bar per Loriot’s caption. Loriot’s N2 sigma 0.4 against Wahlstrand 2012’s quote of Nibbering, 3 (x 10^-20): a transcription difference between the two citing papers, to check against nibbering_1997.

• Part of N2/O2: instantaneous because Wahlstrand 2013 shows the degenerate geometry adds a rotational-grating contribution (their corrected N2 8.4 +- 2.0, O2 11.1 +- 3.5 x 10^-20 cm^2/W). To confirm.

• State: tables say 1 bar, Fig. 3 says 1 atm; 1 bar used.

• Higher orders (Table 2 as printed, probe coefficients) are in notes only.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-295 loriot_2010 (erratum, Opt. Express 18, 3011 (2010))

• Short record, no datasets (its n2 values are the errata of TC-294). Table 1 (tbl_4a652954902a) checked against its image and transcribed into notes (higher orders). Every entry equals 2009 Table 2 / (j + 1) to the printed digits (O2 n4: -1.55/3 = -0.517, printed -5.16 x 10^-9, the only last-digit difference). I_inv changes 33/19/26/26 -> 43/25/34/34 TW/cm^2.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-296 loriot_2011 (Loriot et al., Laser Phys. 21, 1319 (2011); arXiv:1011.0841)

• Library copy: the arXiv preprint (filed under 2010 in the curators’ library). The journal citation and DOI are taken from the reference lists of Bejot 2013 (ref. 12) and Richter 2013 (ref. 22), not from the paper: check.

• No datasets. Notes transcribe the protocol facts: I_eff = I_peak/1.7 (Eq. 2), +-10 % (3 sigma) intensity, n2^cross = 2 n2 (p. 7), 50/30/8 records, volume-effect factors c4..c10 = 1.04, 1.30, 1.45, 2.66 (Table I, an equation-array), Table II (IP and ion chi3 ratios).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-297 bejot_2010 (Bejot et al., Phys. Rev. Lett. 104, 103903 (2010))

• First copy (HAL author version) used; the published copy compared: tables identical on the images, text copy-edited only; its CSVs are garbled.

• Datasets n2_N2, n2_O2 (Table I), n2_Ar (Table II; the curators’ extracted text captions Table II with Fig. 3’s text, the table’s caption is in its note): reproduced from loriot_2009, 1 bar (293.15 K assumed), 800 nm, self. Values equal the erratum’s (rounded).

• The paper justifies the (j + 1) division as a “coherent artifact” correction (Oudar 1983), the erratum as a cross-Kerr degeneracy; same factor.

• Higher orders in notes (units: n6 of Ar in 10^-45, of N2/O2 in 10^-46 cm^6/W^3, as printed).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-298 bejot_2010_hollow (Bejot, Schmidt, Kasparian, Wolf & Legare, Phys. Rev. A 81, 063828 (2010))

• Table I (tbl_0df301bb6004, image checked): n2 = 9.73p x 10^-24 m^2/W at 1.83 um, p = P/1 bar; the script strips the printed pressure factor “p”.

• Formula check: Ettoumi’s Eq. (29) with optmat’s Ar dispersion ((n^2-1) ratio 1830/800 nm = 0.99334) applied to bejot_2010’s Ar Table II gives 9.74, -3.56, 3.79, -1.59, 8.12 against the printed 9.73, -3.55, 3.78, -1.59, 8.10: the table is the Miller extrapolation of the 800 nm values (0.3 %). Dataset marked reproduced (loriot_2009, ettoumi_2010). Temperature not stated (293.15 K assumed).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-299 bejot_2013 (Bejot et al., Phys. Rev. Lett. 110, 043902 (2013))

• Short record: atomic hydrogen TDSE, figures only. Channel-closure intensities for Ar, O2, N2 (p. 4) noted without a stated source.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-300 bree_2011 (Bree, Demircan & Steinmeyer, Phys. Rev. Lett. 106, 183902 (2011))

• Table I (tbl_3d9fe63acf83, JSON only, image checked). Datasets kk_<gas> (He, Ne, Ar, Kr, Xe; rows 800nm and static; check), refs_<gas> (static, reproduced from bishop_1989 and shelton_1994), kk_static_O2 (text p. 3, 0.7 x 10^-7 cm^2/TW, page image checked). Ion (Z = 2) column skipped. Unit cm2/W, scale 1e-20 (10^-8 cm^2/TW).

• State: rho_nt = 2.7e19 cm^-3 “standard conditions” (p. 1, page image) -> 1atm_0C, ideal; assumed to apply to the O2 value too.

• Identification of the “Refs. [18,21]” column (inference, verify): it equals gamma0 (He 43.104, Ne 108, Ar 1167, Kr 2600, Xe 6888 au, from the curators’ survey of third-order values) x 8.911e-23 cm^2/W per au (N gamma_T / (8 eps0^2 c) at the Loschmidt density) to 0.1 %; hence static and T-convention, despite the caption’s “corrected for the dispersion of the DFWM process”. Reproduced_from lists both refs for every gas because the paper does not assign them.

• Misprinted units in the text (p. 4: “cm^2/W”, “cm^2” for cm^2/TW), text only.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-301 bree_2012 (Bree, Demircan & Steinmeyer, Phys. Rev. A 85, 033806 (2012))

• Table I (tbl_934361b8054e, image checked): 5 gases x 5 wavelengths, printed m(e); stored as “me e” (e.g. 7.8e-9), unit cm2/W, scale 1e-12 (cm^2/TW). check. The 800 nm row excluded (duplicate of bree_2011, rounded); Xe 193 nm excluded (beyond the two-photon edge, 204 nm per p. 4).

• Density rho0 not restated: bree_2011’s 2.7e19 cm^-3 assumed (1atm_0C, ideal).

• Eq. (18) gamma = 8 eps0^2 c n2 / rho0: recorded as the T convention (a reading; not stated by the paper).

• A preprint copy in the curators’ library (identity unverified) identified as WIAS preprint No. 1651 (2011) of this paper; its Table 1 has “2.7e.7” for Kr at 2000 nm (journal 2.7(-7)); otherwise identical. No new record.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-302 richter_2013 (Richter et al., New J. Phys. 15, 083012 (2013))

• Short record: hydrogen and a 1D model atom, figures only. Quotes (Conclusions) on the narrow window of the higher-order Kerr effect.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-303 ettoumi_2010 (Ettoumi, Petit, Kasparian & Wolf, Opt. Express 18, 6613 (2010))

• Formulas generalized_miller_n2p (Eqs. 28-29) and generalized_miller_chi_q (Eq. 23), no form. Check: Eq. (29) reproduces bejot_2010_hollow’s 1.83 um Ar coefficients from bejot_2010’s 800 nm ones to 0.3 % (with optmat’s default Ar dispersion).

• The chi(2p+1)-n_2p definition of section 2.5 prints (n0^2 eps0 c^2)^p / n0 (page image checked): for p = 1, chi(3) = (4/3) n0 eps0 c^2 n2, dimensionally wrong by one power of c. Recorded in notes, not corrected (the ratio formulas do not use it).

• The curators’ library metadata says “submitted manuscript”, but the page footers are the published OSA article’s.

• Eqs. (31)-(32) are zhang_2008’s N2 and O2 formulas (not recorded again).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-304 pigeon_2016 (Pigeon, Tochitsky, Welch & Joshi, Opt. Lett. 41, 3924 (2016))

• Table 1 (tbl_a7c0c0dc1804, image checked). Datasets fwm_N2, fwm_O2 (10.6 um, total, self, 197 ps, primary); reproduced nibbering_1997_<gas> (0.8 um) and zahedpour_2015_<gas> (2.4 um, computed by Pigeon as n2 + n2,rot, footnote b; the “+” read from the page image). cm2/W, scale 1e-19; 101325 Pa (atmospheric) and 293.15 K assumed; linear pressure scaling from <= 380 Torr. Air skipped.

• Nibbering’s 0.8 um values here (3 +- 0.7, 8 +- 2.2) differ from those Loriot/Wahlstrand quote (2.3, 5.1): long-pulse against instantaneous, to confirm against nibbering_1997.

• self for an FWM-derived n2,eff: the paper’s Eq. (1) normalisation is taken as given.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-305 pigeon_2018 (Pigeon, Tochitsky, Welch & Joshi, Phys. Rev. A 97, 043829 (2018))

• Table I (tbl_d5296ec423fe, image checked): fwm_Kr 2.9 +- 0.6, fwm_Xe 5.0 +- 1.4 (10.6 um, electronic, primary); reproduced wahlstrand_2012b_<gas> (0.8 um) and miller_<gas> (10.6 um “calculated”). Ar “<1” not measurable: not extracted.

• Formula check (doubt): the “calculated” column (0.95, 2.2, 5.6) is not Ettoumi’s exponent-4 Miller scaling (0.94, 2.11, 5.45 with optmat’s dispersion) but matches exponent 2 (0.954, 2.15, 5.62); the paper cites Owyoung’s thesis for the formula and says the rule predicts “a 1%-2% decrease”.

• Table II (tbl_2537ec41e92d) is garbled in the curators’ extracted table; its image repeats pigeon_2016 Table 1 exactly; not extracted. Misprint: its footnote marks a/b are swapped against their texts (the 2.4 um values carry “a”).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-306 shaw_1993 (Shaw, Hooker & Wilson, Opt. Commun. 103, 153 (1993))

• Table 1 (tbl_d1f5f8c27975, image checked): nonlinear_index_ratio to air (reference_gas = “air”, not a curated species) at 248.6 nm, 10 ps: N2 0.62, Ar 0.24, CH4 0.94 (primary); O2 2.50 (check: derived from air, N2, Ar with 0.21/0.78/0.01; recomputed 2.45 from the rounded ratios); Ne 0.005, He -0.002 (excluded, ionisation per the authors). Uncertainty: slope standard errors, read as 1 sigma.

• Parts: N2, O2, CH4 total (10 ps; the authors suspect partial freezing of the nuclear response), Ar/Ne/He electronic.

• The absolute air value (2.9 +- 1.0 x 10^-16 esu, 760 Torr, 300 K) and Gamma = 4.2e-3 n2/n0 (esu, W/cm^2) are in notes only.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-307 geints_2025 (Geints, Kompanets & Chekalin, Opt. Commun. 596, 132584 (2025))

• Table 1 (tbl_2c05f4da79d1, JSON only, image checked). Datasets (m2/W, scale 1e-24, 800 nm, 1 bar and 293.15 K assumed): sp_CO2 (1 bar primary; 5, 11 bar excluded rows), lp_CO2 and lp_N2 (same), sp_N2, sp_Ar (5 and 11 bar only, excluded), wahlstrand_2012_Ar, wahlstrand_2012_N2 (the footnote-a values, reproduced).

• Reading of the 5 and 11 bar columns (doubt): taken as the pressure-normalised effective coefficient of Eq. (11) (the 1/mu factor), not n2 at 5 or 11 bar; the paper does not say so explicitly. Excluded either way (aberration-affected by the authors’ own account).

• CO2 1 bar SP (10.0 +- 1.1) is effectively a ratio to Wahlstrand’s Ar (p. 6); SP instantaneous (the SP value is the baseline of the Raman increment).

• LP check: SP x (1 + Delta n_R) with Delta n_R = 0.92 (N2), 4.4 (CO2) gives 14.2, 54.0 against 14.1, 54.1. LP pulse_fs 300 (N2, data end) and 500 (CO2): to confirm.

• Misquote: Geints give Wahlstrand’s Ar as 9.7 +- 1.5; Wahlstrand 2012 print +- 1.2.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-308 mareev_2018 (Mareev et al., Opt. Express 26, 13229 (2018))

• Inline points from the Fig. 5 caption (p. 9; units checked in the PDF text layer, the extracted Markdown’s “m/W” for CO2 is the OCR’s): CO2 3.4 +- 0.6, Xe 6.2 +- 1.6 x 10^-22 m^2/W at 1 bar, 1240 nm; temperatures assumed from the lower isotherms (306.65 K, 297.15 K). Both excluded.

• Why about 10 times too high (the register’s assessment): Xe x11 against Wahlstrand’s 800 nm value; the 2 x 5 mm sapphire windows’ SPM (taking the paper’s fused-silica n2 as a stand-in) is about 40 times the 1 bar gas SPM and the paper does not say how it was removed; the intensity is not reported; Eq. (14)’s printed outer square changes n2 by at most about 2. CO2 at 200 fs also carries rotation. Not settled from the paper.

• The density slopes “(0.9 +- 0.2) rho (m5/(W kg))” lack a factor of about 1e-22 (misprint, notes only). Pulse 200 fs (set-up) against 150 fs (Fig. 5 caption).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-309 hancock_2019 (Hancock, Zahedpour, Goffin & Milchberg, Optica 6, 1547 (2019))

• Not the paper sought: a STOV paper with no gas data. Its ref. 21 gives the intended one: Zahedpour, Hancock & Milchberg, Opt. Lett. 44, 843 (2019) (2.5-11 um absolute nonlinear response of air constituents). The citation sought, “Optica 6, 1320 (2019)”, was wrong (it had been given from memory).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-310 ermolov_2015 (existing record; notes added)

• No third-order values printed; “The nonlinear refractive index data was taken from [51]” = Lehmeier et al. 1985 (pdf p. 4). Notes appended only.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-311 beetar_2020 (Beetar et al., Sci. Adv. 6, eabb5375 (2020))

• Supplement Table S1 (two extracted tables, JSON only, images checked). Datasets (1.03 um, per bar, 293.15 K assumed): n2_Ar, n2_N2, n2_N2O (electronic, reproduced from wahlstrand_2012); delta_alpha_N2 9.3, delta_alpha_N2O 27.9 (x 10^-25 cm^3, polarizability_anisotropy, printed “2 x …” for the doubling in the simulations; reproduced from lin_1976 via wahlstrand_2012); n2_long_N2 3.2, n2_long_N2O 43 (x 10^-19, total, reproduced).

• Citation slip: Beetar attribute Delta alpha to Wahlstrand 2012, but 9.3 and 27.9 are the Lin et al. values quoted in Wahlstrand’s Table I (Wahlstrand’s own: 6.7, 28.1).

• Check: the “long pulse” n2 equal Wahlstrand’s n2 / (n2/n2,long): 7.4/0.23 = 32, 17.2/0.04 = 430 x 10^-20 cm^2/W, although the footnote says “determined from fits”.

• Per-bar use of Wahlstrand’s per-atm values (1.3 %).

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-312 zahedpour_2019 (Opt. Lett. 44, 843)

Page numbers are journal pages (843-846 = pdf pages 1-4). Conventions as those of TC-276 to TC-293 (293.15 K assumed for “1 atm”; Maryland n2 are self coefficients; electronic_vibrational for molecules separated by polarization; inf plus wavelength_stated = false for a value with no wavelength).

• Transcribed. Table 1 (tbl_6c9829dbaca8, p. 846) by tools/extract/zahedpour_2019.py: n2 of N2, O2 and Ar at 16 pump wavelengths, 3.0-10.5 um (48 points, primary), the n2,rot of N2 and O2 (23.0, 53.3) and n2,eff(tau_peak) of N2 and O2 (32.5 at 400 fs, 64.5 at 480 fs), all check. Every cell compared with the table image; the CSV matches. The header “10.5^c” footnote mark is stripped in the script. Ar’s n2,rot “0” and n2,eff “8.5 (average)” (the mean of its 16 values, 8.54) are not written.

• No errata. The curators’ extracted Markdown prints the calibration as “n2^-1 = mu1 pi …”; the page (checked at 300 dpi) has n2 = mu1 pi n0^-1 N0 (Delta alpha)^2.

• Reference state. “At Atmospheric Pressure” (Table 1), “at 1 atm” (Eq. 1); no temperature: 101325 Pa, 293.15 K assumed.

• Self coefficient. Delta n_p = 2 n2 I + int R I (p. 845): recorded self.

• Part. Polarization separation; the paper says the vibrational Raman response is negligible “owing to insufficient optical bandwidth” (p. 843), but the adiabatic bond stretch is not separated: N2, O2 electronic_vibrational, Ar electronic (as zahedpour_2015).

• Calibration differs from zahedpour_2015 for N2 (to confirm). Here Delta alpha(N2) = Delta alpha(0) = 6.6e-25 cm3 (Alms fit, via [11]) at pump and probe (“spectrally flat”); 2015 rescaled to 6.7e-25 at 800 nm and dispersed to the 600-nm probe. For the same phases the 2015 scale would be ~2.7 % higher (44.8 against 43.6 x 1e-50 cm6). Ar inherits the N2 scale; O2 uses wahlstrand_2012’s 10.2e-25 (same as 2015).

• Ar at 42 atm: density ratio (to confirm). The printed n2^Ar = n2^N2 mu2 N_Ar/N_N2 is inverted against Eq. (1) (N_N2/N_Ar). The real-gas ratio at 42 atm, 293.15 K is 0.980 (optmat Z: N2 0.9941, Ar 0.9738). Which densities were used is not stated: the Ar rows at 7.0-10.5 um may be off by up to 2 % either way. Not corrected.

• Uncertainties (level not stated). The printed errors (5-8 %) are smaller than the Delta alpha^2 uncertainty from wahlstrand_2012 (9 % N2, 8 % O2): probably statistical only. The O2 and Ar scatter over wavelength (sd 0.69, 0.73) exceeds the printed errors (~0.5).

• Factor 2 in n2,rot and n2,eff (unresolved). A separate computation (not in the repository) with the printed g(tau) (B 2.0, 1.44 cm^-1; nuclear-spin weights; ideal-gas N at 1 atm) gives the integral of R = 46.4 (N2), 110.5 (O2) at 293.15 K, 44.3 and 105.5 at 300 K. The printed n2,rot are half of it (23.2, 55.2 at 293.15 K; 22.1, 52.8 at 300 K). Note b’s n2,eff maximised over Gaussian widths reproduces the printed widths (400 fs, 480 fs) exactly and the values (N2 32.7-31.6 against 32.5; O2 68.3-65.6 against 64.5) only with n2 + /2, whereas note b read literally (Delta phi_par) gives 2 n2 + . wahlstrand_2013 has the rotational index the same for probe and pump, so either the printed g carries an extra 2 or the tabulated n2,rot is half the self rotational index. The same holds for zahedpour_2015’s n2,rot (23, 24, 54) and bears on wahlstrand_2012’s long-pulse formula (the same integral). Temperature not stated (N2 fits ~294 K, O2 ~298 K; O2 spin-rotation structure ignored).

• 10.5 against 10.6 um. Table 1’s last column is 10.5 um; Fig. 4 labels its longest traces 10.6 um. Not resolved; the table’s value is kept.

• Comparisons. Means over 3.0-10.5 um: N2 7.54, O2 8.18, Ar 8.54 (1e-20 cm2/W). zahedpour_2015 at 2.4 um: 7.6 +- 1.3, 10.0 +- 1.2, 9.9 +- 1.7 (O2 and Ar here 18 % and 14 % lower, within 1.5 sigma); Shelton’s ESHG dispersion via zahedpour_2015’s [32] at 2.4 um: 8.1, 8.6, 10.3 (N2 -7 %, O2 -5 %, Ar -17 %). pigeon_2016 (200 ps, total, 10.6 um): N2 45, O2 84, against n2 + n2,rot = 30.5 and 61.5 here (1.5 and 1.4 times lower). Ar 7.7 +- 0.5 at 10.5 um is consistent with pigeon_2018’s “< 1” x 1e-19.

• Status: decided (2026-09-26): accepted with TC-313; points marked open or to confirm above remain open.

TC-313 Integration of the third-order data (2026-09-26)

• Merged: the third-order records TC-224 to TC-312. They add 1159 datasets and 3415 values, over all 15 curated gases.

• Conventions, verified on the page images and by reproduction:

  • Shelton & Rice’s Taylor gamma (“T”) is the common currency.

  • gamma_T = 24 gamma_Lehmeier (Lehmeier’s He gives 43.5 au).

  • gamma_T = 6 chi_Ward (Ward 1969 and 1979, Lundeen).

  • CARS per amagat: gamma_T = 2 chi/N0 (1e-18 cm^3/(erg amagat) = 147.8 au; Farrow against Lundeen and Rosasco).

  • Rosasco’s sigma = N gamma_T/3.

  • Hellwarth’s sigma: 1 au = 5.036e-40 esu.

  • Bishop’s “Kerr” column is dc Kerr; his “DFWM” is our kerr.

  • Bishop’s A and A’ map to Shelton’s A and B through 219474.63^2 and ^4; Bishop’s B, B’ are the perpendicular component.

• Assumptions applied uniformly (check):

  • An unstated temperature (“1 atm”, “1 bar”, “atmospheric”) is taken as 293.15 K. The Maryland calibration density corresponds to about 291 K (TC-276): 0.7 %.

  • Molecular femtosecond n2 that contains rotation is instantaneous; pulses of 10 ps and longer give total.

  • Laser lines printed in nm are standard air; printed wavenumbers are vacuum.

  • Where a paper gives both a ratio and the absolute value derived from it, the absolute value is primary.

• Findings for the model:

  1. Recommended electronic dispersion (Shelton 1990 Table IV and 1992; gamma0, A, B, against nu_L^2) for He to Xe, H2, D2, N2 and O2. CO2, CH4 and SF6 are total ESHG fits: their vibrational part is small but not separated. CH4’s static limit is unreliable (its 1319 nm point is 12 sigma off).

  2. The ab initio values agree with them within a few per cent:

     • Ne 107.4 (CC3) against 108 +- 2;

     • Ar 1159 against 1167;

     • Kr 2589 against 2600;

     • H2 682.7 against 686 +- 4;

     • N2 894 against 917.

     Bishop 1996 gives helium’s process-dependent a and b (the B’ term): Shelton’s B is process-dependent through W4/W2^2.

  3. Measured n2 against Shelton:

     • The Maryland values (Wahlstrand 2012/2015, Zahedpour 2015/2019) fall 5-17 % below Shelton’s Kerr-process prediction for Ar and O2, and agree for N2 (TC-312’s comparison at 2.4 um).

     • Zahedpour 2019 finds n2 flat from 3 to 10.5 um (N2 7.5, O2 8.2, Ar 8.5).

     • Wang 2013 (hollow fibre, per bar) Ar 10.8 at 800 nm, 6.65 at 1.8 um: the second is inconsistent with Zahedpour’s flat Ar. Open.

     • Börzsönyi’s Ar is 2 times everyone else’s (unexplained).

     • Nibbering’s are 1.4 times higher.

     • Mareev’s are 10 times higher (excluded).

  4. Rotational n2, a factor 2 (TC-312, open): Zahedpour’s tabulated n2,rot is half the integral of the printed response. The same holds for Zahedpour 2015 and Wahlstrand 2012’s long-pulse formula. This bears on the Raman phase, not on the electronic n2.

  5. CO:

     • measured: Ward & Miller’s ESHG at 694 nm (1730 +- 50 au, electronic plus vibrational) and CARS (Lundeen, Hahn);

     • theory: Sekino’s CCSD(T) for four processes.

  6. O3: theory only, and strongly method-dependent (static 2470-3250 au). It is near-resonant in the visible.

  7. N2O: only the Maryland n2 (electronic plus vibrational, 800 nm) and its anisotropy. No gamma or dispersion.

  8. Higher-order Kerr coefficients (Loriot, Béjot, Brée): recorded in notes only, refuted (Wahlstrand 2012, 2013 and 2018). Loriot’s printed n2 are probe coefficients, halved by their erratum (applied as errata).

• Errata applied:

  • Mizrahi Ar at 600 nm, 20.99 -> 30.99;

  • Rice 1992, Kr gamma_K swapped;

  • Hellwarth, H2 3.2 -> 32.2;

  • Carusotto, H2 sigma;

  • Ward 1984, 541 -> 514.5 nm;

  • Loriot 2009 -> erratum;

  • Maroulis signs (structural);

  • Hahn Table 2 signs (structural).

  Shelton 1990 Table II, C = 6.043e-31 -> e-32, is noted on the formula: formulas take no errata.

• Format needs (not implemented):

  • a combined vibrational-plus-rotational part (gamma^vR is recorded as vibrational with a note);

  • pair (density) coefficients, Kerr virials and a zero-density molar A_K;

  • errata on formulas;

  • a “wavelength not stated” flag (used ad hoc: parameters.wavelength_stated = false with inf);

  • SI as a polarizability-anisotropy unit;

  • named conventions beyond T;

  • the third-order data files live under refractive/<gas>/, because the file test scans only there.

• Status: decided (2026-09-26): the assumptions and errata accepted; the Maryland flow calibration at 290.9 K; the format needs implemented (TC-316); TC-312’s factor 2 stays open, flagged against the Raman phase.

TC-314 The hyperpolarizability model (2026-09-26)

• Code: optmat.gas.nonlinear, data/gas/nonlinear/<gas>.toml, data/gas/models/nonlinear/*.json, tools/fit/nonlinear.py, docs/nonlinear.md, gallery The second hyperpolarizability.

• Model: gamma = gamma_0 [1 + A W2 + B W2^2 + B’ W4], with W2 and W4 the sums of the squared and fourth-power wavenumbers of the process’s four frequencies.

• Conversions from the sources’ conventions (TC-313) are tested: Lehmeier’s He is 43.49 au, 1 au is 8.91e-23 cm^2/W at 1 atm and 0 C, and the esu per au is Shelton & Rice’s.

• Fits:

  • Most gases: Shelton’s 1990 ESHG, electronic after subtracting his gamma^vR for H2, D2, N2 and O2.

  • Helium: theory only (Bishop & Pipin).

  • Ab initio process dependence with one free scale per calculation: Hättig (Ne, Ar, N2), Bishop 1991 (H2, D2), Tarazkar (Xe), Sekino (CO2, CO). Calculated THG is used only above a 650 nm fundamental.

  • CH4: the 1319 nm point is excluded, as Shelton did. Fitting Hättig’s CCSD shape was tried and rejected: scale 0.87, chi2 350 for 18.

  • CO: one ESHG value plus Sekino’s CCSD(T) processes.

  • N2O: the Maryland n2 with CO2’s A, B as priors.

  • O3: Naves’s CCSD(T), 12 %.

• Agreement with Shelton’s Table IV: the fitted gamma_0 agree within 0.3 % (Ar 1168.5 against 1167, N2 920 against 917, CO2 1150 against 1147, H2 684.9 against 686). A and B move within their correlation where theory adds process information. H2’s A is 1.288, against his 1.200: it now matches the explicitly correlated theory, 1.286.

• The validators are listed in docs/nonlinear.md:

  • The Maryland n2 lie 1-15 % below the ESHG curve; Lehmeier’s THG lies up to 31 % below.

  • Börzsönyi’s printed n2 are 8-20 times the others. Their header says 1e-19 cm^2/W and their own literature column is consistent with it: check the paper.

• Open:

  • the statistical uncertainties are small (0.02-0.6 %); the systematic ones (the ESHG helium scale 0.5 %, the unseparated vibrational part of CH4, CO2 and SF6) are stated in the documentation but not propagated;

  • N2O and O3 carry 13 % and 10 %;

  • the THG of O3 at 800 nm is resonant and is not given.

• Status: decided (2026-09-26): the ESHG scale kept, the Maryland n2 validators; N2O, O3 and the CH4 choices accepted; Börzsönyi’s header corrected (TC-316).

TC-315 Third-order accuracy page and manual (2026-09-26)

• Pages: docs/nonlinear.md rewritten as the manual. docs/nonlinear_accuracy.md is new. The gallery page Third-order accuracy is new. Their tables are checked by tests/test_nonlinear_accuracy_page.py.

• Leave-one-out: tools/fit/nonlinear_robustness.py writes data/gas/models/nonlinear_robustness/, probing Kerr at 400, 800 and 1800 nm and THG at 800 nm. 343 nm was dropped: it lies outside every model’s declared 400 nm limit.

  • A refit with negative degrees of freedom (only the priors decide) is not counted.

  • An exactly determined refit is counted.

• The working-estimate rule (check the judgements): the largest of the statistical sigma, the leave-one-out shift and a floor, rounded up to a 1-2-3-5-type step. The floors are:

  • He, 0.1 %: the allowance given to each calculated value.

  • Ne to Xe, H2, D2, N2, O2, 1 %: Shelton 1990, p. 13: “the effective accuracy of our results is only about 1%”. This raises the 0.5 % stated in TC-314.

  • CO2, CH4, SF6, 2 %: the unseparated vibrational part.

  • CO, 5 %: one ESHG value, 2.9 %.

  • O3, 12 %.

  • N2O, none.

• Fixes found while writing:

  • Helium’s unit: Bishop & Pipin’s gamma is in the reduced-mass atomic unit of 4He (6.24136e-65 against 6.235377e-65; their p. 3549). It is now converted, through a new dataset option factor = 1.00096. gamma_0 goes from 43.108 to 43.15 au (+0.096 %), as Shelton & Rice’s Table VI.

  • O3’s n2: n2 now falls back to the ideal gas for O3 (no equation of state), as the linear models do. It raised before.

  • A scalar second wavelength: gamma_au with a scalar second wavelength (cars, pump_probe) failed its runtime type check.

• The time-domain form of the model (manual page) is checked numerically: a two-colour field on an FFT grid gives the Kerr plus cross-phase, THG and CARS gamma to 1e-10.

• solprop’s coefficients are recorded by tools/solprop_gamma3.py (run in solprop’s environment) in tests/data/solprop_gamma3.json; re-recorded 2026-09-26 against the public solprop, values unchanged.

• Open:

  • gamma_au checks only the fundamental wavelength against the range, not W2 against the fitted W2. A THG below about 650 nm is an unwarned extrapolation. Should it warn?

  • Shelton’s suggested +1 % (helium pair interactions) is not applied.

• Status: decided (2026-09-26): the floors accepted; Shelton’s +1 % not applied; the model now warns beyond the fitted W2 (TC-316).

TC-316 The general data format, and the TC-313 to TC-315 decisions (2026-09-26)

• Layout: extracted files move from data/refractive/<gas>/ to data/values/<family>/<gas>/, the family being the quantity’s: refractive, absorption, third_order, raman or ionisation. 2637 files were moved.

  • A record’s file is now <gas>/<source>__<id>.csv.

  • The extraction helper puts each file in its family’s directory.

  • A test checks that every file belongs to one dataset and lies where its quantity puts it.

  • Re-extraction from the curators’ library reproduces all 183 scripts’ files.

• Vocabulary module: optmat.vocabulary holds, per quantity, its family, units, abscissae, state requirement, required parameters and required extra columns. It also holds the processes, the parts, the polarizability corrections and the named third-order conventions. Every dataset is validated against it, and docs/data.md’s table is tested against it. The units are now checked per quantity.

• General abscissa:

  • The x column (was wavelength) takes abscissa = wavelength | order | temperature | pressure | density | intensity | label | none.

  • abscissa_unit replaces wavelength_unit; index becomes order (Cauchy moments) or label (labelled transitions).

  • not stated replaces the inf placeholder with wavelength_stated = false (nine sources).

  • Air wavenumbers are allowed (TC-176).

  • Declared extra columns (columns = { x_upper = "eV" }) carry an interval’s upper edge or a per-row condition (TC-184).

• New quantities (closing the recorded gaps):

  • refractive: refractivity_difference (TC-80, TC-195), partial_refractivity (TC-215), polarizability_correction (TC-153, TC-190, TC-202, TC-221), magnetic_susceptibility (TC-75, TC-114, TC-203), phase_match_density (TC-121), verdet_constant_ratio (TC-137), rayleigh_cross_section_ratio (TC-69), and refractivity_virial_coefficient of parameters.order 3 and 4 (TC-82, TC-114);

  • absorption: interval_oscillator_strength, partial_cauchy_moment and integrated_cross_section (TC-66, TC-119, TC-158, TC-182, TC-188, TC-189, TC-191, TC-219);

  • third_order: molar_kerr_constant and kerr_virial_coefficient (TC-239), and hyperpolarizability_density_coefficient (TC-227);

  • raman: polarizability_anisotropy (moved), polarizability_derivative (TC-279, TC-293), depolarization_ratio (TC-128), raman_shift, rotational_constant (TC-292), raman_cross_section (TC-229), raman_linewidth and dephasing_time (TC-292);

  • ionisation: ionization_energy and appearance_energy (TC-220), ionization_rate, ionization_yield and multiphoton_ionization_cross_section.

• Parts and conventions: part vibrational_rotational (Shelton’s gamma^vR, TC-225). The eight conventions in use are now named and validated.

• Errata:

  • on a dataset’s scale (row = "", column = "scale");

  • on a named formula coefficient ([[formulas.corrections]] with term alone). Shelton 1990’s C misprint moves there from the ad hoc corrected = {...} (TC-225).

• Data migrated to the new vocabulary:

  • O2 and CO2 absorption below the ionisation limit: photoionization_cross_section becomes absorption_cross_section (metzger_1964, watanabe_1953, weissler_1952, inn_1953; TC-158).

  • Peck’s Verdet ratios: now verdet_constant_ratio.

  • Shelton’s gamma^vR: now vibrational_rotational.

  • 27 interval tables become interval_oscillator_strength with explicit upper edges: kumar_1985, the kumar_2010 and kumar_2011 supplements, and mason_1996.

    • The Kumar supplements’ E_j is the interval’s lower edge, as kumar_1985’s explicit intervals show (Ar 15.76 eV, 0.0494 against 15.76-15.94 eV, 0.0490).

    • The upper edge is therefore the next row’s E_j, and the last interval runs to infinity.

    • fixed_intervals (fit/O3) reads the edges; its poles are unchanged.

• Not migrated (follow-up):

  • The inline integrated continuum f of the O2/CO2/N2O photoabsorption records of TC-158 onwards (watanabe, metzger, weissler, inn, zelikoff, ditchburn, ladenburg) and chan_1992’s totals stay label oscillator strengths. Their ranges are in the notes.

  • The values recorded in notes for want of a quantity (magnetizabilities, C_R, A_K, B_K, pair coefficients, ZPV/PV corrections, band-integrated cross sections, ionisation energies) are not yet datasets: each needs its page checked.

• Decisions of TC-313 to TC-315 applied:

  • Maryland density: wahlstrand_2012, 2012b and 2015’s own values are recorded at 101325 Pa and 290.9 K. At that temperature the fit/N2 model gives their 2.795e-4 at 632.8 nm in air (290.88 K).

    • N2O’s gamma_0 falls 0.78 % (1818 to 1804 au).

    • The Maryland ratios move by up to 0.01 (now 0.84-1.03 at 800 nm).

    • zahedpour_2015/2019, whose scale comes through the anisotropy and an unstated N0, stay at 293.15 K.

  • Börzsönyi 2010: a scale erratum 1e-19 to 1e-20 on the four measured datasets.

    • The evidence is circumstantial: the text’s claim of agreement and the table’s own literature column. The authors do not state it.

    • Their ratios to the fits become 0.83-1.98 (were 8-20).

  • The W2 warning: gamma_au warns at a W2 more than W2_MARGIN (1.1) times the largest fitted W2.

    • A 400 nm Kerr value is not warned, but N2O’s is (its dispersion is borrowed), and so is the third harmonic of a fundamental below about 650 nm.

    • Also fixed: the declared 400 nm end itself warned (floating-point rounding).

  • The unit check: gamma_observation now refuses a dataset whose wavelength is not stated, rather than reading it as static.

• Status: open: the two follow-up lists above.

TC-317 The package layout: a core and one subpackage per medium (2026-09-26)

• Decision (2026-09-26): one package for the optical properties of gases, and later of glasses and crystals, named optmat, with everything specific to gases in optmat.gas.

• Core, the top-level modules:

  • conditions: the state, the named states and air-to-vacuum wavelengths;

  • constants, exceptions (OptmatError) and vocabulary;

  • datasets: the records only.

• optmat.gas: gases, eos (the number densities), reduction (a dataset’s polarizability), lorentz_lorenz, virial, infrared, euv, absorption, nonlinear, fitting, comparison, crosschecks and models.

  • GAS_DATA_DIRECTORY is data/gas/, holding the fit, nonlinear, absorption and EUV configurations, the stored models, defaults.toml and refractivity_virial.toml.

  • data/sources, data/values and data/external are shared.

• The one exception to the core rule: a dataset’s species is still optmat.gas.gases.Gas. tests/test_package.py allows only that import from the core into optmat.gas. Generalising it (a material of every kind in place of a gas, in the records and the code) is the first step of the glass work.

• Dependencies: pyfluids stays a required dependency. It becomes a [gas] extra when glasses arrive; it is imported lazily already.

• Stored fits: the O3 fit and its leave-one-out record were refitted because a comment of its configuration named an old path. Only the checksums changed.

• Status: decided (2026-09-26): the species generalisation is done in TC-318.

TC-318 Materials in place of gas species: the core serves every medium (2026-09-26)

• Where: optmat.materials, data/materials.toml, optmat.datasets, tests/test_package.py, tests/test_materials.py, pyproject.toml.

• Decision (J. C. Travers, 2026-09-26): glasses and crystals share one subpackage, optmat.solid. The machinery is common to both (the dielectric function itself, no density scaling, n2 in m^2/W, band-gap ionisation, damage), and a crystal’s anisotropy is a per-dataset axis.

• The registry: data/materials.toml names every material a record may use.

  • Each entry has its name, formula, kind (gas, glass or crystal), optical symmetry, the axes of an anisotropic crystal, and aliases.

  • It holds the 15 gases, and the solids met in the survey of the solid-state papers:

    • silica glass, BK7 and N-BK7;

    • crystalline quartz, sapphire, MgF2, CaF2, BaF2, SrF2, LiF, NaF, KBr and MgO;

    • YAG, KGW, calcite, YVO4, BBO, KDP, LiNbO3 and KTP;

    • Si, Ge, ZnS, ZnSe, GaAs, InP and GaSb.

  • A material is added with its identity before data for it are recorded.

  • A glass’s grade is a dataset parameter, not a material. Crystalline quartz (SiO2_quartz) is a material of its own.

• Records migrated:

  • gas = becomes material = (3320 lines in 220 records, by a one-off script);

  • parameters.reference_gas becomes reference_material (117).

  • Formulas without a form keep free text (ettoumi_2010’s “any”).

  • No value, file or file path changed.

• Code:

  • Dataset.gas (a Gas) becomes Dataset.material (the id).

  • datasets(material=...) accepts an id or an alias. A record must use the id.

  • optmat.gas converts with as_gas where it needs the enum.

  • Gas formula models are built only for gas materials.

• New checks:

  • a solid dataset may not carry a gas state or density convention (its temperature goes in parameters.temperature_k), and a state is required only of a gas;

  • parameters.axis must be one of the material’s axes.

• The core imports no medium. The TC-317 exception is gone, and tests/test_package.py now forbids the core from importing any subpackage.

• Dependencies: pyfluids moves to the gas extra, as TC-317 decided. The development group installs optmat[gas], and optmat.gas.eos raises a clear ImportError without it.

• Checked (2026-09-26):

  • poe test-library reproduces every extracted file from the library;

  • poe test-fits reproduces every stored fit;

  • the default lane passes.

• Status: decided (2026-09-26).

TC-319 The vocabulary of solids (2026-09-26)

• Where: optmat.vocabulary, optmat.datasets, docs/data.md.

• New quantities, so that the solid-state papers can be recorded as printed:

  • refractive: refractive_index (n of n + ik); refractive_index_deviation (a measurement minus a named formula, for Malitson 1965’s residual tables); thermo_optic_coefficient.

  • absorption: extinction_coefficient (k); absorption_coefficient (per length, with its logarithm base); band_gap (with its kind: optical, Tauc, Urbach, photoconductivity, exciton, mobility, or assumed).

  • third_order: two_photon_absorption_coefficient, multiphoton_absorption_coefficient, critical_power.

  • raman: raman_fraction; raman_mode (the multi-mode response tables, with shift and widths as columns); raman_response_time.

  • ionisation: effective_mass, electron_collision_time, electron_trapping_time, avalanche_coefficient, atom_density. Multiphoton ionisation coefficients reuse multiphoton_ionization_cross_section, with the unit as printed.

  • A new family, damage: damage_threshold_fluence, damage_threshold_intensity and damage_threshold_energy, with the site (bulk or surface) required.

  • A new abscissa, duration (s, ns, ps, fs), for thresholds against pulse length.

• nonlinear_index now serves solids: its state is required only of a gas, and a solid’s value states the pulse duration, technique and polarization where the source does.

• Solid parameters: temperature_k, form (bulk, film or fibre), grade, axis, polarization, technique, pulse_fs and assumed.

  • assumed = true marks a value a source takes as a model input (a band gap, a collision time in a simulation). Such a value is use = "check" and cites where it came from.

  • form, site and base are closed vocabularies checked by the loader.

• Decision: a value a paper assumes is recorded, because simulation papers are where these numbers circulate. It is kept apart from measurements by assumed = true, and never fitted.

• Status: decided (2026-09-26).

TC-320 External data for solids: newAD2 and refractiveindex.info (2026-09-26)

• newAD2 (data/external/newad2/): Franta et al.’s universal-dispersion-model (UDM) parameter files and their computed n,k tables (0.01-100 eV). Fetched 2026-09-26 from http://newad.physics.muni.cz/, with sha256 in PROVENANCE.md:

  • Lithosil Q2 bulk silica, and the SiO2 films X2546 and X2551 (SPIE 9890, 2016);

  • X2551, MgF2 and Al2O3 films (SPIE 9628, 2015);

  • float-zone c-Si (unpublished, as the site says).

  • Why: the Franta 2016 paper prints only the basic UDM parameters (its Table 3). The complete Lithosil Q2 model (10 excitonic terms, 52 phonon terms) is on the site, and so is the authors’ own table of it. The refractiveindex.info page SiO2/Franta is a tabulation of the same model.

  • Caution (the site’s own description): the Lithosil Q2 model was fitted to measurements only from 80 cm-1 to 8.5 eV. It used “OC (Palik data & Schott prism)”, so above 8.5 eV it represents Philipp’s tables in Palik’s handbook, and it is not independent of them.

  • Licence: none stated on the site; added to the curators’ to-do list (resolved in TC-727).

  • The authors’ udm.cxx bundles GPL-3 code, so it is not committed. It serves only as an external check.

• refractiveindex.info: the snapshot (same commit c5c2f18) gains the solid entries J. C. Travers chose: bulk SiO2 (no films, no quartz), MgF2, CaF2, BaF2, LiF, Al2O3, YAG, Si, KGW and BK7, their nk and n2 pages (157 files).

  • The converter writes refractiveindex_info_solid.json, with the material, kind, axis and dopant.

  • The gas JSON is byte-identical to before.

  • These entries are comparison sources only.

  • Axes: two pages carry their axis only in the catalogue name (sapphire Malitson, n(o); DeSalvo, (e)). They are mapped explicitly.

  • Erratum in a database file: SiO2/nk/Popova.yml cites Kitamura et al. as Appl. Opt. 33, 8118 (2007). The library’s validated record of that paper (Kitamura_2007_OpticalConstantsSilica) gives volume 46, as does the file’s own DOI (10.1364/AO.46.008118).

  • Yb:KGW: the only KGW n2 page is Yb-doped (Selivanov et al. 2006). The survey noted that the cited paper’s title concerns Yb:KY(WO4)2 and YVO4, so the page may be mislabelled. It stays open until the paper is read.

• Status: open: the newAD2 licence; the Yb:KGW page’s identity.

TC-321 Franta’s universal dispersion model, implemented and checked (2026-09-26)

• Where: optmat.solid.udm, tests/solid/test_udm.py, tools/newad2/udm_check.py.

• What: the UDM of Franta, Nečas, Ohlídal & Giglia, Proc. SPIE 9628, 96281U (2015), Eqs. (1)-(47) (franta_2015b), in closed form:

  • the symmetric interband term, Eqs. (4)-(12);

  • the excitonic terms, Eqs. (13)-(25), combined by Eqs. (26)-(27);

  • the higher-energy term, Eqs. (28)-(31);

  • the Urbach tail, Eqs. (32)-(40);

  • Gaussian peaks for localised states and phonons, Eqs. (41)-(47).

  First derivatives are exact, by complex-step differentiation. Below a few per cent of each term’s lowest edge, the real part is its even moment series (12 orders), because there the closed forms lose digits to cancellation. An energy within 1e-12 of a band edge is evaluated 1e-9 above it.

• Checked (2026-09-26), for all seven newAD2 parameter files (TC-320):

  • Against the authors’ published tables on their exact grid (0.01-100 eV, 4001 points):

    • above 1 eV, every n and k is within half a unit of the seventh printed digit;

    • below 1 eV, the three SiO2 models are within 2 units.

  • Against the authors’ program (udm.cxx, compiled here to print 17 digits): epsilon agrees to 1.4e-10 or better above 1 eV.

  • Against 50-digit arithmetic (mpmath): the higher-energy, interband and excitonic terms are exact to 3e-12.

  • Kramers-Kronig: the real part equals the numerical transform of the imaginary part to 1e-8 (0.5-10 eV).

  • Normalisation: every term’s transition strength is 1 to 1e-9 (Eq. 3).

  • Derivatives: the complex-step derivatives agree with finite differences to 1e-7.

  • Passivity: epsilon_i >= 0 on the whole grid.

• Finding 1: the Urbach tail’s upper energy.

  • The paper places the tail’s parts at E_g/2, E_g, E_m and E_m + E_g/2, with E_m = (E_g + E_h)/2 (Eq. 33; also Appl. Opt. 54, 9108 (2015), Eq. 19).

  • The authors’ program uses E_h where the equation has E_m.

  • The program reproduces the published tables to their last digit. Eq. (33) instead moves n of Lithosil Q2 by up to 3.6 % (in the phonon region, through the tail’s normalisation).

  • Decision: the parameter files were fitted with the program, so the program’s reading is implemented. Whether the paper or the program is the intended model is a question for the authors.

• Finding 2: the far-infrared digits of the published tables.

  • Below 5e-3 E_xi (0.1 eV for silica) the program replaces the higher-energy term’s real part by its E -> 0 limit, 1/(5 pi E_xi^2).

  • Between that and about 1 eV, its closed forms lose digits to cancellation.

  • Emulating the first reproduces Lithosil Q2’s table below 0.1 eV to half a unit. The rest (up to 2 units of the seventh digit for the silicas; up to 6 for MgF2 and 2 for Al2O3, not fully attributed) is the program’s arithmetic.

  • optmat’s values there are the exact ones. The differences (below 1e-5 in n) are far below the model’s own uncertainty.

• Other findings:

  • The phonon terms’ wavenumbers are converted with the program’s constants (CODATA 2002; 6e-8 from CODATA 2018), the units the parameters were fitted in.

  • numpy’s complex square root returns k = 0 when k is below about 1e-16 n; a model computes k as epsilon_i / (2n).

  • Compiled on Apple silicon (where long double is double), the program returns NaN for the MgF2, c-Si and SPIE 9628 X2551 files, whose tables optmat reproduces.

• Status: decided (2026-09-26): the program’s reading, finding 1; open: finding 1 to the authors.

TC-322 The fitting of solids’ dielectric functions (2026-09-26)

• Where: optmat.solid.fitting, optmat.solid.models.fitted, tools/fit/run_solid.py; configurations in data/solid/fits/, results in data/solid/models/fitted/.

• Method: a published UDM parameter file is the starting point. A configuration frees a chosen set of its parameters and fits them by least squares to curated data:

  • n: from refractive_index, or from refractive_index_deviation added back to its named formula;

  • k: from extinction_coefficient, as log k, since k spans many decades;

  • uncertainties: each point’s stated uncertainty, or one set in the configuration where the source states none (said there, with the reason);

  • offsets: each n dataset may carry a free additive offset with a prior, for the grade and the temperature it refers to;

  • priors: free parameters may carry priors.

• Why this form: whatever the parameters, the model stays causal (Kramers-Kronig), passive and normalised to its transition strengths (TC-321). The fitted dielectric function is therefore as smooth and as differentiable as the published one, and it agrees with the data within their uncertainty.

• Results: the covariance (Birge-scaled when the reduced chi-squared exceeds 1) is stored with the full parameter set. The fitted model, fit/<name>, propagates it to one-sigma uncertainties in n and k.

• Status: decided (2026-09-26); the silica fit’s own decisions follow in their entry.

TC-323 Decisions on the silica linear-index records (2026-09-26)

• Where: malitson_1965, franta_2016, philipp_1985 (their own entries follow, renumbered); optmat.solid.models.formulas.

• Malitson’s formula:

  • The printed pole wavelengths are kept: form n2_sellmeier_wavelength, terms B and L as printed. This replaces the squares computed from them.

  • Its variable is a standard-air wavelength (Table I’s wavelengths are air values of spectral lines). The record says wavelength_medium = "standard_air", and the formula models now convert (Edlén 1966).

  • Its range is the vacuum wavelengths of the first and last air wavelengths (213.92-3707.72 nm, rounded outwards).

  • Checked: from vacuum wavelengths the formula reproduces Table I’s computed column to 8.3e-7, the rounding of the printed coefficients. Without the conversion the difference would be several parts in 10^6.

• Open: is Malitson’s n relative to air or to vacuum?

  • The paper does not say. It refers the method to Rodney & Spindler, J. Res. Natl. Bur. Std. 53, 185 (1954), which is not in the library.

  • kitamura_2007 (p. 2) describes the minimum-deviation prism “placed in air”.

  • The two readings differ by (n_air - 1) n, about 4e-4: more than Malitson’s accuracy and more than the difference from Franta (2.3e-4 at 800 nm).

  • Until it is settled, fits give all of Malitson’s datasets one shared n offset with a prior of 4e-4. Malitson then constrains the dispersion at full weight, but not the absolute level.

  • Rodney & Spindler (1954) is not in the library; it is to be requested.

• Franta’s Lithosil Q2 model becomes the model franta_2016/udm_lithosil_q2 (form udm).

  • Its range is 24.8 nm-125 um. It was measured from 80 cm^-1 to 8.5 eV and fitted to Philipp’s tables above that, to 50 eV, as the authors’ own tabulation on refractiveindex.info.

  • The film models (X2546, X2551) stay record-only, so that they cannot be taken for bulk silica.

• Rife & Osantowski’s EUV n and k (in Philipp’s table) are filed under SiO2-TiO2, as proposed at extraction: their sample is a high-silica glass with 7.5 % TiO2. They are not bulk-silica data.

• Status: decided (2026-09-26); Malitson’s reference medium resolved by TC-399 (relative to air).

TC-324 The recommended model of fused silica (2026-09-26)

• Decision: the recommended model of SiO2 (data/solid/defaults.toml) is Franta et al.’s universal dispersion model of bulk Lithosil Q2, franta_2016/udm_lithosil_q2 (TC-321), as the authors published it.

• Why it can be used as it is: it is analytic, causal, passive and sum-rule normalised from 24.8 nm to 125 um, with exact derivatives. Its published tables are samples of it, so no smoothing of tabulated data is needed.

• Checked against the other curated data (rms and largest difference in n):

  Data	Range	rms	Largest
  Franta’s own Lithosil Q2 table (franta_2016)	0.15-124 um	1.2e-6	2.2e-5
  Malitson 1965, Table I, three prisms (level removed)	0.21-3.7 um	2.8e-4	7.3e-4
  Philipp’s VUV n (philipp_vuv_n)	111-207 nm	0.10	0.27 (at the 119 nm exciton peak)
  Philipp-Lamy n	50-109 nm	0.035
  Hunter n	30-60 nm	0.009
  Philipp’s IR n (Philipp 1979, KK of reflectance)	3.8-40 um	0.13	0.52 (on the reststrahlen bands)

  The model is on average 1.0e-4 above Malitson.

• Malitson against Franta, and Arosa as the third witness. At 800 nm the three formulas give:

  	Malitson 1965	Arosa 2020	Franta 2016
  n	1.45332	1.45337	1.45355
  group index	1.46715	1.46727	1.46726
  GVD (fs^2/mm)	36.19	35.86	35.76

  At 300 nm the GVD is 155.8, 154.2 and 154.1.

  • Arosa & de la Fuente’s independent interferometry of 2020 (their fit to measured phase and group index, 260-1700 nm) follows Franta’s dispersion, not Malitson’s.

  • Malitson’s 1965 formula has 1.2e-4 less group index and about 1 % more GVD in the visible.

• A refit to Malitson was tried and set aside:

  • The fitting machinery of TC-322 was run with Malitson’s three prisms (sigma 1.3e-5, shared offset for the reference medium) and Franta’s measured n and k.

  • Philipp’s VUV and IR tables were validators, being inconsistent with Franta’s measurement as the table above shows.

  • No choice of freedom reproduces Malitson within his scatter (2.6e-5 in the UV, 6-8e-6 in the visible, 2.7e-5 at 3-3.7 um) while keeping Franta’s measured band edge (k at 146-220 nm) and phonon absorption (k at 5-125 um):

    • the interband and higher-energy strengths;

    • an extra causal Gaussian electronic peak (four starts);

    • one factor each on the phonon and OH bands.

    Every run left Malitson at a chi-squared of about 1300 for 180 points, with a smooth residual of +2.5e-5 near 300 nm, -3.8e-5 in the visible and near infrared, and +1e-4 at 3.5 um.

  • Malitson alone can be fitted (reduced chi-squared 1.35), but only by broadening the Urbach tail from 0.19 to 0.63 eV, which Franta’s measured edge absorption excludes.

  • The two data sets describe different glasses (1965 Corning 7940, Dynasil and GE 151, against 2016 Lithosil Q2), measured by different methods. Where they differ in dispersion, the independent modern measurement sides with Franta.

  • The experiment’s configurations are not committed. The machinery stays, tested.

• Uncertainty of the recommended model (stated on the silica page):

  • n in the window to about 3e-4: the spread among Franta, Arosa and Malitson (the level of Malitson’s relative to vacuum not being known);

  • the group index to about 1e-4;

  • GVD to about 1 %;

  • in the VUV, above 8.5 eV, n and k are as good as Palik’s tables (a few per cent).

• Open:

  • J. C. Travers’s view: should the recommended model follow Malitson’s refractometry instead, at the cost of the band-edge and phonon absorption?

  • Malitson’s reference medium (TC-323).

  • A second modern refractometry of bulk silica (Tan 1998 is figures only; Leviton & Frey’s temperature-dependent data are to be requested) would settle the dispersion.

• Status: decided (2026-09-26): Franta’s model is recommended (confirmed by J. C. Travers, TC-394); open: the questions above. Superseded by TC-399 (2026-09-26): Malitson’s index is relative to air, and the recommended model is the refit fit/SiO2.

TC-325 philipp_1985 (Table X, the compilation behind silica’s VUV-EUV model) (2026-09-26)

• Transcribed: Table X, all 11 parts (tbl_252c849fca85, _163001deeaae, _dcfeca794199, _675d911da2e7, _19c745bbcfde, _f3221b4d7cc9, _7e7b88d780eb, _3ed3b519e90e, _b04abceaf3b9, _7604b3cb0747, _e7f8b49d5a9f; pdf pp. 5-15), 442 data rows, 2000 eV to 0.00248 eV. One dataset per column (n, k, k_ABS) and reference tag, the tag carried down the column until the next one. 20 datasets, 809 points:

  • henke_n, henke_k (107 each; [17], 6.199-80.51 A): reproduced (Henke et al. 1981, computed by Philipp from atomic scattering factors).

  • rife_osantowski_n, _k (44 each; [16], 82-290 A): reproduced, material SiO2-TiO2 (the sample is ‘a high-silica glass with 7.5% TiO2’, p. 751). Decision to review: I filed them under a newly registered glass rather than SiO2; a silica model may use them as a proxy (Philipp does).

  • hunter_n_angstrom, hunter_k_angstrom (20 each; 300-490 A) and hunter_n_um, hunter_k_um (11 each; 0.0500-0.0600 um): primary (unpublished, first published here). Split by unit because the wavelength column switches unit inside the part.

  • philipp_lamy_n, _k (37 each; [9, 10], 0.04959-0.1088 um): primary (Philipp’s smooth curve through his and Lamy’s KK results).

  • philipp_vuv_n (44; [9], 0.1107-0.2066 um): primary.

  • weinberg_k (19; [12], 0.1107-0.1291 um): reproduced from weinberg_1979 (film).

  • transmission_curve_k (17; [12-14], 0.1305-0.1590 um): reproduced (Weinberg, Appleton, Kaminow: a smooth curve through their transmission results).

  • brixner_malitson_n (60; [7], 0.213856-3.7067 um): reproduced (malitson_1965 and Brixner 1967), standard-air wavelengths, 20 C.

  • philipp_ir_n (91; [2], 3.846-40 um), philipp_ir_k (65; 7.692-26.67 um), philipp_k_abs (32; 7.692-40 um): primary (Philipp 1979).

  • drummond_k_abs (33; [4], 3.636-7.407 um): reproduced (Drummond).

  • randall_rawcliffe_n, _k (5 each; [1], 100-500 um): reproduced; k +-30 % (bound).

• Structural fixes (script): (1) exponent inheritance: a bare mantissa under “m x 10^-e” takes 10^-e until a cell with its own power or a plain decimal; written in E notation, raw cell in printed; across page breaks (p. 7 “1.76” under 10^-4, p. 8 “6.19” under 10^-3, p. 9 “8.2” under 10^-2). No power of ten appears in the images that the cells lose. (2) the unit switch (A to um) inside tbl_19c745bbcfde and the repeated header in tbl_3ed3b519e90e (k_ABS added): every header row is read for its unit.

• Erratum: hunter_n_um and hunter_k_um, row 179 (22.96 eV), x printed “0.540” um for 0.0540 (image prints 0.540; hc/22.96 eV = 0.05400 um; Hunter’s grid is 0.001 um).

• Checked: two full passes of every part against its image (cell by cell; then a listing of the extracted values with their inherited powers against the images). eV x wavelength = hc on all 442 rows to the printed digits except the erratum row; wavenumber x wavelength = 1 on all infrared rows (6.0 eV: 0.2066 um for 1e4/48,390 = 0.20665, rounding). Smoothness of k: the only jumps >1.6x between inherited neighbours are the Si K edge (1860 -> 1815 eV, printed power) and the O K edge (542 -> 529 eV, the inherited 1.486e-4; the image prints no power there).

• Findings:

  • Brixner’s [7] n are not Malitson’s Eq. (1): they differ from malitson_1965/computed by -29e-6 to +25e-6 and follow Malitson’s mean measured index (computed + C-D-G.E. residual) to +-1e-5 at most lines (6e-5 at 0.226747 um, the line Malitson says was misassigned). Marked reproduced from malitson_1965 so they are never fitted with it.

  • Hunter against Philipp-Lamy in their overlap: at 0.04959 um n = 0.733, k = 0.325 [9, 10] against 0.803, 0.300 at 0.0500 um [15] (10 % in n); they converge by 0.06 um.

  • Randall and Rawcliffe k at 500 um (7.96e-3) > at 250 um (6.96e-3): against the trend; no evidence of a misprint; kept.

  • The chapter’s ‘slight modification’ of Philipp’s VUV data is Weinberg’s +0.075 eV shift (weinberg_1979 p. 3111).

• Doubt: the Henke-computed values assume an unstated density.

• Status: open (review the SiO2-TiO2 filing and the primary/reproduced split).

TC-326 malitson_1965 (Tables I, II; Eq. 1) (2026-09-26)

• Transcribed: Table I (tbl_b692ffe8e259, cells; 60 wavelengths): computed index (computed, check), the C-D-G.E. mean residual (residual_mean, check) and the three prisms’ residuals (Corning 7940, Dynasil, General Electric type 151; primary), all x1e-6, refractive_index_deviation with reference malitson_1965/sellmeier. Table II (tbl_46b93cc0e194): 12 prisms x 9 wavelengths (12 datasets), sigma column 5 (visible) or 20 (0.8944, 1.014, 1.083 um) x1e-6 from the text (pp. 1207-1208; the 18 wavelengths are Table I’s lines 0.4047-1.083 um: 14 up to 0.706519, 4 from 0.852111). 17 datasets, 408 points. Formula sellmeier (n2_sellmeier; C = squares of the printed poles, exact).

• Structural fix: the cells read the Corning column header ‘x 10^9’; the image prints 10^6 (scale 1e-6 for every column).

• Checked: Eq. (1) reproduces the computed column at all 60 wavelengths to 8.3e-7 (six decimals printed). Cells of both tables against the images.

• Findings:

  • The C-D-G.E. residuals are not the average of the three prisms’ residuals (e.g. -27 against -29, -42, -31 at 0.213856 um; +21 against -7, -7, +6 at 1.81307 um). The paper does not say how the mean table was compiled. I made the three prisms primary and the mean a check (to avoid counting the prisms twice); the reverse is defensible.

  • The wavelengths are standard-air wavelengths (Hg 0.546074 um is the line whose vacuum wavelength, 546.2258 nm, the gas records use): recorded standard_air.

  • Open question: the paper does not say whether n is relative to air (minimum deviation in air) or vacuum. Presumably relative to air, the glass-catalogue convention; the difference, n x (n_air - 1) ~ 4e-4, is 40 times the stated residual. Rodney and Spindler (1954), whose technique Malitson follows, might say (missing).

• Not extracted (notes): the average-residual row, Table II’s Av. Delta n and nu-values, the dn/dT figure (text values ~15e-6/K at 0.21 um to 10e-6/K at 0.4 um, 12e-6 at 2.0 um, 10e-6 at 3.7 um, 20-30 C), Fig. 4 (Rodney-Spindler differences).

• refractiveindex.info: SiO2/Malitson is Eq. (1) with the printed coefficients (formula 1, 0.21-6.7 um, 293 K), the range extended to 6.7 um on Tan’s evidence: no difference.

• Status: open (air vs vacuum index).

TC-327 tan_1998 (2026-09-26)

• Transcribed: nothing: the 3-6.7 um indices are in Fig. 5 only. Record with notes: method (FT-IR channelled spectrum, Suprasil 2, ~1000 ppm OH, 230 um), the reference fringe (3.1174 um, order 209 from Malitson’s Eq. 1), accuracy (+-5e-4 in the 3-3.7 um overlap, ~1e-3 overall), and the statement that the indices are ‘exactly equal to the extrapolation results of Eq. (1)’. Eq. (1) is Malitson’s, reproduced (not recorded again). The Malitson reference is misprinted as volume 53.

• Status: verified (2026-09-26).

TC-328 arosa_2020 (2026-09-26)

• Transcribed: Table 1 (tbl_5c10bd1471d2; image checked): Fit3 as sellmeier_fit3 (n2_sellmeier, 260-1700 nm). RI and GI in figures only. The Malitson row of Table 1 is Malitson’s coefficients rounded to 4 digits (not recorded).

• Checked: with the printed coefficients the zero-dispersion wavelength is 1.2775 um (printed 1.277), 4.7 nm above Malitson’s (printed ‘approximately 6 nm’). Against Malitson over 260-1700 nm: max RI difference 2.6e-4 at 260 nm (printed 1.1e-4), rms 5.2e-5 (printed 7.2e-5), GI max 1.3e-3 (printed 7.4e-4): not reproduced at the UV end, consistent with lambda1 = 0.079 and lambda2 = 0.130 printed to 2-3 significant digits.

• refractiveindex.info: SiO2/Arosa = Table 1 Fit3 exactly (0.26-1.7 um).

• Status: open (the rounding of the printed coefficients limits the formula to ~1e-4 below 300 nm).

TC-329 kitamura_2007 (formula erratum) (2026-09-26)

• Transcribed: Table 2 (tbl_8b4a391ae01b; image checked) and eps_inf = 2.1232 (page image; the library’s footnote text is garbled) as the formula gaussian_ir (no form), with Eqs. (21)-(24) verbatim. Table 1 (the literature summary; the library’s OCR was rejected) read from the page images into the notes. No datasets.

• Correction (formula): Eq. (23)’s prefactor is printed 2 alpha_j/pi; the Kramers-Kronig transform of Eq. (22) needs 2 alpha_j/sqrt(pi) (the Dawson-function transform of a Gaussian). Evidence: a numerical principal-value KK integral of Eq. (22) gives eps’ - eps_inf = -2.4436, 4.2287, -0.9397 at 500, 1000, 1428.6 cm-1, equal to the corrected form, 1.77x the printed one; the paper states the model satisfies KK.

• Checked: with the correction the model reproduces the paper’s residual ranges of Philipp’s data at 7-50 um for k (-0.246 to +0.365; printed -0.25 to 0.37) and the upper n bound (+0.186; printed 0.19); the lower n bound comes out -0.372 against the printed -0.42 (not reproduced; unexplained). With the printed prefactor none of these holds.

• refractiveindex.info: SiO2/Popova is this model’s evaluation (not Popova’s data), with the corrected prefactor: agreement to 1e-3 (relative 8e-4); with the printed prefactor differences up to 0.6.

• Notes: uncertainties (Abbe +-2e-3, Pulfrich +-5e-5; residuals < 0.06 from Popova except ~9 um (0.3) and 22.5 um (0.14)); silica types I-IV and their OH and impurity effects; the fictive temperature is not discussed.

• Status: corrected (2026-09-26), pending review.

TC-330 franta_2016 (2026-09-26)

• Transcribed: from data/external/newad2 (SPIE 9890 files): Lithosil Q2 n and k 0.01-8.49 eV (primary, 2930 rows each), and 8.51-100 eV (reproduced from philipp_1985: the model fitted there to the shape of Palik’s/Philipp’s data; 1071 rows each); films X2546 and X2551 n and k, 0.01-44.98 eV (primary, form film, 3654 rows each; rows above 45 eV, the extrapolation, not extracted). Table 3’s E_g as three band_gap datasets (kind optical: the UDM’s interband onset, a model parameter). UDM as three formulas without a form, coefficients from Table 3 plus the parameter file. Samples (Table 1) and instruments (Table 2) in notes (images checked).

• Structural point: Table 3 prints E_h (39.6) and E_x (16.98) once across the three columns (shared); the CSV puts them under X2551. Not extracted (formula coefficients).

• Checked: every Table 3 value is the .par file’s rounded; N_ve sums 1279, 1220, 1116 eV^2, n_ve = 7.788 and the density ratios 0.921 and 1.048 (Eqs. 2-5) reproduce.

• refractiveindex.info: SiO2/Franta is the Lithosil Q2 table on another grid (0.0248-125 um, to 50 eV): median difference 1.5e-6 (n), 2e-7 (k); at most 7e-4, 4e-4 at sharp phonon features (interpolation). It does not mark the >8.5 eV Palik-fitted part.

• Doubt: the band_gap kind: the UDM E_g is neither a Tauc nor an absorption-threshold gap; ‘optical’ is the nearest documented kind.

• Status: open (kind of E_g; weighting of the dense model tables in a fit).

TC-331 rodriguez_de_marcos_2016 (2026-09-26)

• Transcribed: nothing (n, k in figures only; ‘available upon request’). Notes: the data sources per range (Table 1 from the image), density 2.28 g/cm3 (SiO2, 85.4 % of bulk) and 7.72 g/cm3 (Ta2O5, 93.2 %), f-sum 29.65 and 187.19 against 29.96 and 184.32, inertial zeta 6.5e-4 and 1.4e-5, windowed sum rules within ~1.1 % and 1.9 %.

• Finding: substrate temperature 523 K in the abstract, 573 K in the text.

• Format: no quantity for a solid’s mass density or sum-rule results.

• Status: verified (2026-09-26).

TC-332 weinberg_1979 (2026-09-26)

• Transcribed: band_gap 9.3 eV (primary, kind photoconductivity, thermally grown film, text pp. 3107, 3114-3115); reproduced literature gaps: DiStefano and Eastman 9.0 and Trukhin 9.5 / 12 (photoconductivity), Powell and Morad 8.0 +- 0.2 and Powell and Derbenwick ~9 (optical), Loh ~11 (SiO2_quartz, optical). Other values (Goodman 8.0-8.1, DiStefano-Eastman photoemission 8.9 +- 0.2, Williams 8, Powell-Derbenwick 8.8, Stephenson-Binkowski limits, Zakis, Appleton, Mott, band-structure 9.2/9.8) in notes. Absorption data are figures only (accuracy statements in notes).

• Format: band_gap has no ‘photoemission’ (or charging-threshold, theory) kind; those values are notes only.

• Status: open (vocabulary).

TC-333 materials registered, reproduction graph, format needs (2026-09-26)

• Registered (in materials.toml): SiO2-TiO2 (Rife and Osantowski’s 7.5 % TiO2 glass; kind glass) and Ta2O5 (kind glass, amorphous films; rodriguez_de_marcos_2016, no datasets). Another extraction may register Ta2O5 too.

• Reproduction graph (reproduced dataset -> original):

  • philipp_1985/brixner_malitson_n -> malitson_1965 (+ Brixner 1967, missing)

  • philipp_1985/weinberg_k -> weinberg_1979

  • philipp_1985/transmission_curve_k -> weinberg_1979, Appleton 1978, Kaminow 1978

  • philipp_1985/henke_n, henke_k -> Henke et al. 1981 (not henke_1993)

  • philipp_1985/rife_osantowski_n, _k -> Rife and Osantowski 1980

  • philipp_1985/drummond_k_abs -> Drummond 1935/36

  • philipp_1985/randall_rawcliffe_n, _k -> Randall and Rawcliffe 1967

  • franta_2016/lithosil_q2_n_palik, _k_palik -> philipp_1985

  • weinberg_1979/literature_* -> DiStefano-Eastman 1971, Trukhin 1978, Powell-Morad 1978, Powell-Derbenwick 1971, Loh 1964

  • formulas: tan_1998 Eq. 1, kitamura_2007 Eq. 20, arosa_2020 Table 1 ‘Malitson’ -> malitson_1965/sellmeier (not recorded again); kitamura_2007/gaussian_ir fitted to Popova 1972 (missing).

• Format needs: band-gap kind for photoemission thresholds; a mass-density quantity for solids; a group-index quantity (Arosa); the Urbach energy (Franta E_u, recorded as formula coefficients only); the Abbe number (Malitson nu-values).

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-334 Format gap: n2 in esu (2026-09-26)

• Where: adair_1989 (Tables I-IV, VIII, X), desalvo_1996 (Table I), boling_1978 (Tables I, III).

• Doubt: nonlinear_index accepts only cm2/W and m2/W (n = n0 + n2 I). An n2 in esu, defined by n = n0 + n2 <E^2> (the convention of these three papers), is a different quantity (it involves n0 and the field convention), and no quantity holds it; the extraction rule “convert nothing” forbids converting. These columns are therefore NOT datasets: each record’s notes describe the tables (ids, layout, image checks, traps, reproductions) and quote the silica values, so that a later extraction is mechanical.

• Decision needed: add a quantity (or an esu unit with a stated definition) for the field-squared n2, then extract these tables.

• Status: open

TC-335 milam_1998 (2026-09-26)

• Where: D. Milam, Appl. Opt. 37, 546-550 (1998), Milam_1998_ReviewAssessmentMeasured; Table 1 (tbl_ee3c0e192f6c, p. 547), Table 2 (tbl_cda7eab4b25e, p. 548), text pp. 546-549.

• Transcribed:

  • Table 1, 24 rows, as 16 reproduced nonlinear_index datasets of SiO2, one per cited reference (refs 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22; 1-4 points each), unit cm2/W, scale 1e-16, per-point sigma (level not stated), part unknown, self. reproduced_from: desalvo_1996, white_1984, else the citation as printed.

  • Table 2 (11 rows) as one check dataset, x = 1064 nm (the text: “the assemblage of eleven 1064-nm values”) with the printed measurement wavelength as column measured_nm.

  • Text: best values 2.74 +- 0.17 at 1053 nm (primary, level rms), 3.0 +- 0.35 at 527 nm and 3.6 +- 0.64 at 351 nm (primary, “selected arbitrarily”, level not stated); the first average 2.56 +- 0.3 (check, rms).

  • Definition n = n0 + gamma I (p. 546) in notes.

• Structural fix: the printed “±” is extracted as “6” in every value cell (the pdf font maps ± to “6”, - to “2”, ( ) to “~ !”); the script splits “v 6 s”, checked against both images.

• Errata (2):

  • desalvo_1996 row 3 sigma 0.17 -> 1.7 (266 nm): DeSalvo’s 28 +- 6 (x1e-14 esu, 21 %) converts to +-1.68; Milam’s other ref-4 rows carry 20 %; Fig. 1 draws the bar 6.1-9.5.

  • williams_1985 row 17 x 532 -> 1064: Table 2 has 1.73 +- 0.35 at 1064 nm (ref 14); Table 1 is in wavelength order and row 17 sits among the 1053-1064 rows; Fig. 1 plots a ref-14 point near 1050 nm at ~1.7.

• Findings (notes, no erratum):

  • Table 2’s last 1064-nm row (2.14 +- 0.43) is attributed to ref 16; Table 1 (and the conversion of DeSalvo’s 7.4e-14 esu) shows it is ref 4 (DeSalvo). Reference numbers are not a data column.

  • The text’s “1.72 +- 0.34 at 351 nm” (p. 548) is Table 1’s 532-nm row 11 (Fig. 2 has no ref-14 point).

  • White et al.’s value is listed at 351 nm (Table 1 and text); White measured at 355 nm. Left as printed (Milam’s slip of reproduction), noted in the dataset.

  • The text’s PERT translation “+2%” for the 1550-nm datum: the printed values give +2.9 % (2.87/2.79); 804 nm: -3.2 % (“-3%”); 1319 nm: +1.9 % (not stated).

  • Milam’s DeSalvo conversions (2.24, 2.14 at 532, 1064 nm) imply n0 = 1.460, 1.450, not DeSalvo’s Table II n0 = 1.48 (which gives 2.21, 2.10): Milam used his own silica index.

• Doubt: the best 1053-nm value is called “the best 1064-nm value” in the text; recorded at 1053 nm as in the abstract (PERT cannot distinguish them, p. 548).

• refractiveindex.info: SiO2 “Milam” (3.6, 3.0, 2.74e-20 m2/W at 0.351, 0.527, 1.053 um) = the best values. Its SiO2 “DeSalvo” page = Milam’s ref-4 rows (Milam’s conversion).

• Status: open

TC-336 adair_1989 (2026-09-26)

• Where: R. Adair, L. L. Chase, S. A. Payne, Phys. Rev. B 39, 3337-3350 (1989), Adair_1989_NonlinearRefractiveIndex (11 table files for Tables I-X; IV has two parts). Journal page = 3336 + pdf page.

• Transcribed:

  • Table IV (tbl_55822e89640f p. 3342, tbl_2e1f875bba6b p. 3343, JSON-only): the column “n (1.06 um)” as 55 refractive_index datasets (one per row, 1 point each), use = "reproduced", reproduced_from the handbook of the row’s footnote (Refs. 29-39, citations as printed). Axis set for the (o)/(e) rows of registered uniaxial crystals (MgF2, LaF3, CeF3, ZnO, Al2O3, SiO2_quartz, CaCO3, KDP, CaWO4, CdS) and for LAP (y). No axis for KTP (x+y), LAP (x+z), YAlO3 (gamma) (label kept in polarization), nor for ZnS (e)/(o): the registered ZnS is isotropic but Adair’s was hexagonal. Abbe numbers quoted in notes (no quantity).

  • Table V (tbl_62267fd0462a p. 3344, JSON-only): gamma_expt (7 datasets, check, part electronic_vibrational) and gamma_theory (adjusted) (7 datasets, reproduced from Johnson, Subbaswammy & Senatore, PRB 36, 9202 (1987), part electronic) for LiF, NaF, KF, NaCl, KCl, NaBr, KBr. hyperpolarizability, esu, scale 1e-39, convention T (Eq. 4, p. 3338: p_i = alpha_i E_l + gamma_i E_l^3/6, local field), process kerr.

  • Table VII (tbl_00fcb404f207 p. 3346): 7 fluorides (MgF2, CaF2, SrF2, CdF2, BaF2, LaF3, CeF3), with the anion-cation separation as an extra column; its LiF, NaF, KF rows repeat Table V (script asserts equality) and are taken once.

  • Table IX (tbl_152efc508e07 p. 3347): 13 oxides/sulfides (MgO, CaO, ZnO, SrO, Al2O3, Ga2O3, Y2O3, Er2O3, SiO2, TiO2, ZrO2, ZnS, CdS), with separation column. BeO and Sc2/3O left out (pair values inferred by additivity from BeAl2O4 and GSAG, not a crystal’s gamma).

  • All gamma_expt are use = "check": a reduction of the n2 through Eq. (5) with the Lorentz local field, per neutral formula unit containing one anion.

  • Total: 89 datasets, 89 points; 4 formulas.

• Not transcribed (format gap): every n2 of the paper is in esu (n = n0 + n2<E^2>, Eq. 1), which nonlinear_index (cm2/W, m2/W; n = n0 + n2 I) cannot hold: Tables I, II (SF-58; CS2 liquid skipped), III (this work vs TRI, Maker-Terhune via Wang, Levenson Refs. 23-25, Smith et al. PDF Ref. 27), IV (measured and BGO-calculated), VIII (n2 with chi1122/chi1111 ratios, no quantity either), X (additivity). The record’s notes describe each table’s layout and traps for a later extraction, and quote the silica values (fused 0.85 measured / 0.83 calc., n 1.4496; quartz o 1.12/1.06, e 1.16/1.13, in 1e-13 esu). Per-ion alpha+/-, gamma+/- theory of Table V not transcribed (RbF, LiCl, RbCl, LiBr, RbBr, LiI, NaI, KI, RbI appear only there; not registered).

• Checked: every table image against the extracted cells: no misread cell. Table IV footnote letters are “^a” in the first part and bare trailing letters in the continuation (handled by one regex); CeF3’s n is printed “~1.6” (tilde in the image; value 1.6 kept, tilde in printed). Reference list (Refs. 12, 29-39) checked against the p. 3350 image. SiO2 Eq. (5) check: gamma = 510e-39 esu per Si1/2O, n = 1.4496 and an assumed density 2.20 g/cm3 (not from the paper) give n2 = 0.851e-13 esu (Table IV 0.85): N in Eq. (5) is the anion density.

• Formulas: bgo_k68, bgo_k48 (Eq. 6; no form). Table IV’s calculated column uses K = 68 (p. 3341); the paper prints n(1.06 um), not n_d, so it cannot be reproduced exactly: with n(1.06 um) for n_d the printed values are a median 4 % above the formula (33/48 rows within 6 %; up to +38 % for CdS, +29 % ZnO (e), +25 % TiO2, -10 % YGG). wilson_curtis_alpha (Eq. 15, Table VI theory) and wilson_curtis_gamma (Eq. 17, Table VI theory and expt); the expt F and O parameters reproduce the “on-line” Table VII/IX points to ~5-30 % and miss the d-shell/covalent units as the paper says. Text D = 18.29 vs Table VI 18.3.

• Findings (images checked; not errata since the esu n2 are not datasets): Table VIII KBr n2 3.07 vs Table IV/III 2.93; CaO 5.07 vs Table IV 5.20 (5.07 is SrO’s); MgO 1.6 vs 1.61. Table X “Gd3Sc2Al2O12” vs Table IV and text “Gd3Sc2Al3O12” (misprint in Table X). Table IX header “gamma(MxO < MxS” misprint for “(MxO, MxS)”. Table III “Al2O3 1.25 (av)” is not the mean (1.265) of Table IV’s o/e 1.23, 1.30; “(av)” is undefined. Text “marginal optical quantity” (sic).

• Doubt: Pulse duration not stated in this paper (only “nanosecond”, p. 3338; Ref. 19 has the details) — no pulse_fs. Whether Adair et al. or Johnson et al. made the 1.06 um “adjustment” of the theoretical gamma is not stated. YAlO3 “(gamma)” is taken to be n_g only in notes. Phases of TiO2, ZrO2, Ga2O3 not stated.

• refractiveindex.info: the “Adair” n2 pages of Al2O3 (o 2.9e-20, e 3.1e-20), BaF2 1.91e-20, CaF2 1.26e-20, LiF 7.9e-21, MgF2 7.6e-21, SiO2 2.46e-20, YAG 6.23e-20 m2/W equal this paper’s Table IV esu values converted by 40 pi n2/(c n0) with Table IV’s n (ratios 0.984-1.005, rounding), but cite JOSA B 4, 875 (1987) (the glasses paper, Ref. 19): a wrong citation on those crystal pages. The BK7 page (3.62e-20) is from the 1987 paper; BK7 is not in this one.

• Status: open (the esu quantity needs a vocabulary decision).

TC-337 desalvo_1996 (2026-09-26)

• Where: DeSalvo et al., IEEE JQE 32, 1324 (1996). Table I (tbl_9572f7715e3f, JSON only, p. 1326), Table II (tbl_87c9f8dcbfd0, p. 1326), text pp. 1326-1330.

• Transcribed (40 datasets, 67 points):

  • band_gap E_g, 11 materials (kind optical, “linear transmission cutoff energies”; use check, assumed = true: model inputs of unstated origin);

  • band_gap E’_g, 8 materials (kind “assumed”: the gap fitted to make beta obey Eq. (1), then used as model input; no kind in the vocabulary fits exactly). BBO “6.8” and calcite “8.0” are printed in quotes: the further-adjusted gaps of the text (p. 1329-1330), not the beta fits (6.45 and ~6.8 eV);

  • two_photon_absorption_coefficient (cm/GW, sigma column) for BaF2, SiO2, Al2O3 (266), BBO (355, 266; axis o), CaCO3 (355, 266), LiNbO3 (532; axis e), KTP (532; axis z), tellurite glass (532); per-row column pulse_fs (30/22/17/15 ps); “≅0” and “NM” cells left out;

  • refractive_index, Table II (use check, assumed = true), 11 materials; KTP split by axis (y at 1064, z at 532: two samples, footnote 2); MgF2 o, BBO o, LiNbO3 e; Al2O3 and CaCO3 no axis (“E parallel to a crystallographic axis”, which one not said);

  • nonlinear_index, text: BaF2 (2.1 +- 0.4)e-16 at 532 nm (printed “cm/W”) and (3.1 +- 0.6)e-16 cm2/W at 266 nm (p. 1327), part total (15-30 ps), coefficient self.

• Not extracted (format gap): Table I’s n2 columns, 1e-14 esu of n = n0 + n2<E^2> (p. 1327: n2(esu) = (c n0/40 pi) n2(MKS)). Layout, orientation and the SiO2 row are described in the record’s notes. Cells checked against the image: agree.

• Checked: both tables cell by cell against the images (agree). Eqs. (1)-(2) with K = 3100, E_p = 21 eV and Table II’s n0 reproduce the text’s numbers exactly: BBO E_g = 6.8 eV -> beta = 0.765 (266 nm) and 0.066 (355 nm), “0.77” and “0.066” printed; 6.45 eV -> 0.905 (measured 0.9); calcite 8 eV -> 0.331 (“0.33”), 6.8 eV -> 0.803 (measured 0.8). With E’_g: BaF2 0.049 (0.06), SiO2 0.049 (0.05), Al2O3 0.088 (0.09), LiNbO3 0.36 (0.38), KTP 0.066 (0.10), Te glass 0.73 (0.62).

• Formulas: beta_scaling (Eqs. 1-2), n2_scaling (Eq. 3, K’ = 7.33e-9; G2 not printed, not reproduced), g2_kramers_kronig (Eq. 4).

• Finding (Milam 1998): 40 pi n2/(c n0) with Table II’s n0 gives SiO2 2.10, 2.21, 2.41, 7.82 (sigma 0.42, 0.45, 0.48, 1.68) x 1e-16 cm2/W at 1064, 532, 355, 266 nm. milam_1998 Table 1 (ref. 4) prints 2.14, 2.24, 2.41, 7.8 with +-0.43, 0.46, 0.48 and “0.17”: Milam converted with n0 = 1.4495 (1064) and 1.4596 (532), not Table II’s 1.48; “7.8 +- 0.17” is 7.8 +- 1.7 (28 +- 6 esu). Supports an erratum on milam_1998’s sigma.

• Doubt: E_g’s origin (measured or literature) is not stated; beta’s defining equation is not written (Z-scan convention of Ref. [13]).

• refractiveindex.info: ‘DeSalvo’ pages (Al2O3 e, BaF2, LiF, MgF2 o, SiO2) are Table I converted with n0 other than Table II’s: implied n0 1.4495-1.5009 (SiO2), 1.388-1.421 (LiF; Table II 1.3, so the pages are 6-9 % below a Table-II conversion), 1.373-1.397 (MgF2), 1.466-1.512 (BaF2), 1.747-1.826 (Al2O3). The page’s Al2O3 “e” is not in the paper. Pulses agree.

• Status: open (the esu format gap).

TC-338 flom_2015 (2026-09-26)

• Where: Flom et al., Appl. Opt. 54, F123 (2015). Table 1 (tbl_5dfb2dc9eeb0, JSON only, p. F126); text pp. F125-F127.

• Transcribed (7 datasets, 18 points): nonlinear_index for SiO2, BK7, AlON, MgAl2O4 (spinel ceramic; 1030 and 1550 only), BGG, ZnS (grade CLEARTRAN), 772/1030/1550 nm. Header unit “n2 10^-7 cm2/GW” = 1e-16 cm2/W (unit cm2/W, scale 1e-16). Per-row columns pulse_fs (SHG FROG FWHM 275 +- 20, 140 +- 10, 97 +- 7 fs, p. F125) and intensity_min/max (GW/cm2, split from the printed range). sigma: “the standard deviation of the measurements at multiple intensities” -> level 1 sigma (a scatter; no absolute uncertainty stated). CLEARTRAN 772 nm (single scan at 10 GW/cm2) has no sigma. Spinel 772 nm “—” (<40 GW/cm2) not extracted. Text: beta of BGG at 1550 nm, 1.9e-3 cm/GW (p. F127).

• Checked: cells against the image (agree). Footnotes: BGG n2 increases with I at 1030 nm, decreases at 1550 nm (in notes).

• Doubts: the paper prints no defining equation (Sheik-Bahae Z-scan, n = n0 + n2 I implied); polarization not stated; part unknown (fs, not discussed). BK7 from CVI Laser Optics recorded as the registered “BK7” (historical Schott melt) — in 2015 it is probably N-BK7, not stated: still to be decided. Fused silica from Heraeus, product not named.

• refractiveindex.info: ‘Flom’ BK7 and SiO2 pages agree with Table 1 to all digits; the pages give 280 fs at 772 nm, the paper 275 +- 20 fs.

• Status: verified (2026-09-26).

TC-339 ensley_2019 (2026-09-26)

• Where: Ensley & Bambha, Opt. Express 27, 37940 (2019). Tables 1-3 (tbl_0d115aaf67aa p. 37945, tbl_67677bf4d75b p. 37947, tbl_a359645a6ee3 p. 37948; all JSON only), text.

• Transcribed (61 datasets, 85 points):

  • Table 1: band_gap of ZnS, ZnSe, GaAs, InP, GaSb, Si, Ge (reproduced from Sze 1981, kind optical with parameters.transition direct/indirect); nonlinear_index at 2 and 3.9 um (1e-14 cm2/W; +-20 % / +-25 % relative, relative_rows); ZnSe at 3.9 um split out as reproduced from Werner et al. 2019 (Ref. [24]). Negative n2 (GaSb, Ge at 2 um) kept.

  • Table 2: this work at 800 nm and 2 um for BaF2, CaF2, MgF2, LiF, SiO2, BK7 (+-15 % / +-20 %); the Eq. (1) column (use check, x “not stated”); literature values, one reproduced dataset per material and reference letter (28 datasets): a Sheik-Bahae 1990, b desalvo_1996, c DeSalvo 1993, d Levenson 1974, e Adair 1992, f Guo 2015, g Milam/Weber/Glass 1977, h adair_1989, i kabacinski_2019, j milam_1998, k Lu 2012, l Milam & Weber 1976, m Adair 1987; marks +, #, * give 525, 810, 1030 nm; the 1.06-um column is written 1060 nm.

  • Table 3: AMTIR-1, -2, -4, -5, -6 at 2 and 3.9 um.

  • Text: 2PA alpha2 (= beta) at 2 um, GaSb 110 +- 22, Si 0.85 +- 0.17, Ge 85 +- 17 cm/GW.

  • Per-row column pulse_fs: 90 fs (2 um), 240 fs (3.9 um), ~100 fs at 800 nm (the only 800-nm source described; the 800-nm Z-scans are not described separately — doubt).

• Structural fix: Table 2’s extracted header “h_2(10^{-6} cm^{-3}/W)” is a mis-reading of “n2 (10^-16 cm^2/W)” (image and paper.md); the unit is set in the record. Multi-value cells split by superscript in the script.

• Checked: every cell against the three images (agree); text values of ZnS, GaSb, Si, Ge, ZnSe, CaF2, MgF2, AMTIR-1/-5/-6 agree with the tables. Literature letters against curated originals: b = DeSalvo’s esu converted (LiF with n0 ~ 1.39, not DeSalvo’s Table II 1.3), h = Adair 1989 converted with Adair’s n (agree), i = Kabacinski 1.71 (agree), j = Milam’s 527/1053-nm recommendations listed at 532 nm and 1.06 um.

• Formulas: bgo_eq1 (K = 68; rough check with Boling Table III inputs: SiO2 2.41 vs 2.5, BK7 3.20 vs 3.2); lines_eq2 (As2S3: 2.58e-14 and 2.48e-14 computed vs 2.5e-14 and 2.4e-14 printed: 3-4 % low, as if truncated).

• Doubts: BK7 (Thorlabs WG11010) recorded as “BK7”; probably N-BK7, not stated. Two BaF2 values with letter c at 532 nm (2.1 and 3.2), presumably orientations. part unknown (fs, not discussed). Whether reflection losses were removed is not stated.

• refractiveindex.info: ‘Ensley’ pages (BK7, BaF2, CaF2, LiF, MgF2, SiO2 at 0.8/2.0 um; Si at 2.0/3.9 um) agree to all digits; they state 100 fs for all, whereas the paper gives 90 fs (2 um) and 240 fs (3.9 um).

• Status: verified (2026-09-26).

TC-340 jansonas_2022 (2026-09-26)

• Where: Jansonas, Budriūnas, Vengris & Varanavičius, Opt. Express 30, 30507 (2022). Tables 1-4 (tbl_5c82efda0f04, tbl_8fc389324d09, tbl_df33b8fa6ec8, tbl_59933d97ff63), text pp. 30508-30521.

• Transcribed: 59 datasets, 104 points (script tools/extract/jansonas_2022.py), all nonlinear_index in 10^-14 cm^2/W, abscissa um:

  • n2_eff this work (Tables 2 + 3, 1.03/2.2/3.2 um), 19 datasets eff_<material>[_o|_e], 36 points, per-row column pulse_fs (230/170/190 fs, text p. 30515). primary except the nine GaSe/AgGaS2/ZnGeP2/KTA/LGS ones, which are check because Table 4 gives the same measurements corrected for cascading.

  • n2_Kerr (Table 4, cascaded chi(2) part removed), 9 datasets kerr_*, 20 points, primary.

  • Literature n2_eff (Tables 2, 3), 22 datasets lit_eff_*, 29 points, reproduced (ids ensley_2019, patwardhan_2021, milam_1998; else citations as printed).

  • Literature n2_Kerr (Table 4 last column: computed by the authors from others’ n2_eff), 9 datasets lit_kerr_*, 10 points, check with reproduced_from.

  • Table 1 (orientation, thickness) in notes and per-dataset notes.

• Structural fixes (script): the merged “(this work)/(literature)” sub-header stripped from the first data row of Tables 2-4; literature cells holding several “value ± sigma(λ) [refs]” split by pattern with a leftover check; the superscript b (and one “≈”) removed from the value and kept in printed; the upper bound “<0.64 (1.03 µm) [48]” (LGS o, Namboodiri 2021) not extracted. All four images agree with the CSV cells.

• Parameters: part unknown throughout (fs, paper silent on Raman); coefficient self; axis o only for o-waves of uniaxial GaSe (θ = 0), AgGaS2, ZnGeP2, SBN-61; e-waves at θ = 39°/74° and the biaxial KTA/LGS (o)/(e) recorded as polarization. ZnS grade “CLEARTRAN”, SiO2 grade “UVFS”.

• Checked: reproductions of patwardhan_2021 (ZnS 0.478/0.455, ZnSe 1.13/1.0 at 2.3/3.5 um = its 47.8/45.5, 113/100 x 10^-20 m^2/W) and ensley_2019 (ZnS 0.55/0.5, ZnSe 1.5/1.2, Si 7.7/11, GaAs 13 at 2/3.9 um; the ± are Ensley’s ±20 %/±25 %) and milam_1998 (0.0274 ± 0.0017 at 1.053 um) agree with those papers.

• Doubt: the ± of this work has no stated level. “b” on Table 2 literature values means the cited value serves both polarizations; those reproductions are filed under one row (noted). n2_eff of SBN-61, ZnS, ZnSe, BGSe, GaAs, ZnTe may contain an uncomputed cascaded part. Supplement 1 (intensities, E_ref) not in the library.

• refractiveindex.info: Si (7e-18, 4.54e-18 m^2/W; 170/190 fs) and SiO2 UVFS (2.53e-20; 230 fs) identical; the other 13 materials and all n2_Kerr absent there; the pages do not say n2 is n2_eff.

• Status: verified (2026-09-26).

TC-341 kabacinski_2019 (2026-09-26)

• Where: Kabaciński, Kardaś, Stepanenko & Radzewicz, Opt. Express 27, 11018 (2019), Table 1 (tbl_46ff24325236), text pp. 11019-11027.

• Transcribed: 18 datasets, 19 points: this work at 1030 nm (8: SiO2, CaF2, YAG, BiBO axis x, CaCO3 o/e, YVO4 o/e; primary, 210 fs, SPM-induced phase regression by FROG, sigma column, level “1 sigma” = weighted-mean error max(σint, σext)); literature (10, reproduced): flom_2015 (SiO2 1030), milam_1998 (SiO2 1053), adair_1989 (SiO2, CaF2, YAG, calcite o/e at 1064; part electronic_vibrational), Milam/Weber/Glass (CaF2, printed 1978), Bliss 1974 (YAG), Miller 2008 (BiBO, two values “7.39, 8.00”).

• Structural: the literature cell’s lines are joined in the CSV; split by pattern with a leftover check. Unit footnote garbled in extraction; image: 10^-16 cm^2/W.

• Checked: the Adair [17] values are conversions of adair_1989’s 10^-13 esu with its n(1.06 um): 40π n2/(c n0) gives 2.458, 1.262, 2.833, 2.352 (match) and YAG 6.212 against printed 6.25 (0.6 % off).

• Findings/doubts: Ref. [37] cited for “Yb:YVO4” literature values is Selivanov et al., “Nonlinear refractive properties of Yb3+-doped KY(WO4)2” — a KYW paper: citation does not match the material; those two doped-crystal values (19 o, 15 e at 1080 nm) not extracted. Text says all literature values are Z-scan, but [17] is three-wave mixing, [35] interferometry, [33] a review. [34] year printed 1978 (Adair cites 1977). BiBO “X” taken as the dielectric x axis (not defined by the paper). part unknown (“the Raman response … can be included into the Kerr effect”, p. 11019).

• refractiveindex.info: CaF2 1.71, SiO2 2.19, YAG 6.13 (e-20 m^2/W, 1.03 um, 210 fs) identical; no pages for BiBO, calcite o/e, YVO4 o/e.

• Status: verified (2026-09-26).

TC-342 patwardhan_2021 (2026-09-26)

• Where: Patwardhan, Ginsberg, Chen, Jadidi & Gaeta, Opt. Lett. 46, 1824 (2021), Table 1 (tbl_2daca1ccb18c, JSON only; image agrees), text pp. 1824-1827.

• Transcribed: 18 datasets, 44 points: Exp. n2 (6 materials: ZnSe, ZnS polycrystalline, sapphire = Al2O3, CaF2, MgF2, SiO2; 19 points; primary, 10^-20 m^2/W, sigma column, level not stated); Theory (two-band model, 19 points, check, part electronic); band gaps (6 points, band_gap kind “assumed”, assumed = true, check, reproduced_from refs [1, 15, 16]). One formula two_band_theory (no form; K’ = 0.86 × 10^-8, E_P = 21 eV).

• Parameters: SRTBC, coefficient self (Eq. 1 writes the cross-phase factor 2 explicitly with ΔΦ = k n2 I_pu L), part unknown (“>65 fs … prevented us from distinguishing the electronic contribution from the nuclear response”, p. 1827). No pulse_fs (75 fs at 3.5 um, 100 fs at 4.5 um, unstated at 2.3 um, “<150 fs”).

• Checked: absolute for FS at 2.3 um, sapphire at 3.5/4.5, ZnSe at all; others relative (noted per dataset). Theory not reproduced: G2 and n0 not given. K’ = 0.86e-8 differs from DeSalvo’s 7.33e-9 and Sheik-Bahae’s 1.5e-8.

• refractiveindex.info: Al2O3, CaF2, MgF2 (2.3/3.5/4.5 um) and SiO2 (2.3/3.5 um) identical; pages label every wavelength “100 fs”; no pages for ZnSe, ZnS (incl. 8.3 um) nor the theory.

• Status: verified (2026-09-26).

TC-343 van_der_linden_2025 (2026-09-26)

• Where: van der Linden, Kuzkova & Kraus, Opt. Express 33, 53268 (2025), Table 1 (tbl_a71e46ef0edc), text pp. 53269-53273.

• Transcribed: 8 datasets, 8 points: TWINS this work (CaF2, SiO2, N-BK7 printed “NBK-7”, KBr; primary, 10^-16 cm^2/W, ±2σ → level “2 sigma”, 47 fs, linear s-polarization, self); literature reproduced: ensley_2019 (CaF2, SiO2, NBK-7 at 800 nm) and desalvo_1996 (KBr 1064 nm).

• Checked: image agrees with cells. KBr 7.87 ± 1.62 is van der Linden’s conversion of DeSalvo’s (29 ± 6) × 10^-14 esu (n0 = 1.53 gives 7.95 ± 1.64; 7.87 implies n0 ≈ 1.545). Ensley prints no ± at 800 nm; the ±15 % here is van der Linden’s.

• Doubt: table prints 800 nm; the laser is centred at 804 nm (recorded as printed). The final n2 includes simulated correction factors 1.9 and 1.4 (p. 53273). Samples are Thorlabs windows; glass maker/grade not stated; “NBK-7” mapped to N-BK7 (and Ensley’s “BK7” reproduction filed under N-BK7 as the citing paper pairs it).

• refractiveindex.info: BK7 (=NBK-7) 3.33, CaF2 1.47, SiO2 2.54 (e-20 m^2/W at 0.804 um, 47 fs) identical; KBr (8.98) absent; the page files N-BK7 under BK7.

• Status: verified (2026-09-26).

TC-344 white_1984 (2026-09-26)

• Where: W. T. White III, W. L. Smith, D. Milam, Opt. Lett. 9, 10-12 (1984), White_1984_DirectMeasurementNonlinear; Table 1 (tbl_985eae28abf9, p. 11), text p. 11.

• Transcribed: Table 1: gamma at 355 nm, SiO2 2.5 +- 1.2 and BK-10 1.7 +- 0.8 (this work, primary, time-resolved interferometry, 0.15-0.20 ns, part total by the ps rule); 1064 nm “previous work”: SiO2 2.7 +- 0.5 (reproduced from Weber, Milam & Smith, Opt. Eng. 17, 463 (1978)), BK-10 2.8 +- 0.6 (check: a prediction by Eq. (38) of Boling et al.). Text: time-integrated check on Suprasil II, 2.7 +- 0.8 at 355 nm (check); BK-10 alpha = 0.0107 cm-1 at 355 nm (absorption_coefficient, base e, primary); BK-10 beta = 0.0055 cm/GW (two_photon_absorption_coefficient, reproduced from Smith, CLEO 1981 ThB21). 7 datasets, 7 points. BK-10 registered.

• Checked: the table image against the cells (agree). Units 1e-16 cm2/W (footnote a) and the esu conversion n2(cm3/erg)/gamma(cm2/W) = cn/4pi 1e-7 quoted.

• Doubt: the BK-10 1064-nm value is “predicted from Eq. (38) of Ref. 10” (Boling et al.) in the text but the table footnote c names Ref. 11 (Wang 1970). Taken as Boling’s formula (the text is specific). Eq. (3) is printed without its left side and with “dI/dz = alpha + beta I”: noted; irrelevant for silica.

• Duplicate copy: original/source_02 (Aspose re-wrap) and source_01 have identical text (pdftotext) and identical page renderings at 100 dpi: the same scan.

• Reproductions: milam_1998 ref 13 (listed at 351 nm). refractiveindex.info SiO2 “White” = 2.5e-20 m2/W at 0.355 um, TRI: agrees (it gives no pulse; 0.15-0.20 ns here).

• Status: open

TC-345 santran_2004 (2026-09-26)

• Where: S. Santran et al., J. Opt. Soc. Am. B 21, 2180-2190 (2004), Santran_2004_PreciseAbsoluteMeasurements; Table 1 (errors, p. 2185), Table 2 (tbl_ece90cb0d86a, JSON-only, p. 2186), text pp. 2185-2189.

• Transcribed: Table 2, ten fused-silica samples (grades as printed: Heraeus S300, Herasil, Suprasil, Heraeus Homosil, Heraeus S1, Herasil S1V, Suprasil EN1027A, F851053, Heraeus H1, Schott SQ1), n2 at 800 and 400 nm, 10 primary datasets x 2 points, cm2/W, 1e-16; text: Suprasil 2.5e-20 m2/W at 1500 nm (inline; its 400/800-nm values in the same sentence are Table 2’s row). Collinear pump-probe, ~100 fs, pump and probe perpendicular linear, self coefficient via Eq. (14) (chi1111 = 3 chi1212). No per-value uncertainty (Table 1: absolute 10-28 % at 800/1500 nm, 12-34 % at 400 nm; relative between samples < 1 %), quoted in notes. Formulas: Eq. (19) two-band KK and Eq. (20) PERT (no form; not checkable: no fitted parameters printed).

• Structural fix: the unit cells “(10216 cm2/W)” are 10^-16 cm^2/W (image); the script asserts the cell and the record’s scale is 1e-16.

• Part: recorded “electronic” on the paper’s argument (Raman share of the signal <= ~1 %, Fig. 11 1.5 %; “pure electronic nonlinear susceptibility measurements are possible in fused silica”, p. 2188), though the measured parameter is “global”.

• Findings: Eq. (15), n2(m2/W) = 80 pi n2(esu)/(n0 c), is twice the 40 pi of DeSalvo and White (n = n0 + n2<E^2>); the paper tabulates no esu value. Eq. (20)’s “x is in inverse centimeters” is odd (x must be a ratio). Oxide (Nb borophosphate, Te) glasses: Fig. 12 only, no named composition with a value; nothing registered. CS2 (liquid) skipped.

• refractiveindex.info: no page.

• Status: open

TC-346 boling_1978 (2026-09-26)

• Where: N. L. Boling, A. J. Glass, A. Owyoung, IEEE J. Quantum Electron. QE-14, 601-608 (1978), Boling_1978_EmpiricalRelationshipsPredicting; Tables I (p. 603), II a/b (p. 604), III (p. 606).

• Transcribed: the linear indices only: Table I n (10 materials; wavelength not stated) and Table III n_d (12 glasses; 0.58756 um), 22 refractive_index datasets of 1 point, check, assumed (inputs of the formulas). 17 glasses registered (FK-6, FK-5, FK-51, LSO, ED-2, ED-4, EY-1, EV-1, FD-2, FR-5, SF-7, LaK-3, LaSF-7, LHG-5, LHG-6, and the unnamed “silicate” and “fluoro-phosphate” as silicate_boling_1978, fluorophosphate_boling_1978), plus PbF2 (Table II b only).

• Format gap: both n2 columns of Tables I and III are in esu (n = n0 + n2<E^2>, Eq. 8): not datasets; the notes describe them (sources: Owyoung’s ellipse rotation, Refs. 11-12, assuming electronic; Milam & Weber’s TRI, Refs. 14-15, total) and quote silica (Table I: n 1.456, measured 1.00, calc. 0.91; Table III: n_d 1.458, nu_d 70, calc. 0.87, meas. 0.95 +- 0.10, x1e-13 esu). Table II’s N, Ns, s (no quantity) and Table III’s Abbe numbers are quoted in notes.

• Formulas: bgo_oscillator (Eqs. 25-26, gs = 3; not reproducible: omega0 not given), bgo_abbe (Eq. 38): reproduces Table III’s calculated column to <= 0.4 % for 11 of 12 glasses; fused silica 0.833 vs printed 0.87 (-4.3 %): nu_d ~ 68 instead of the printed 70 would reproduce it. empirical_39 (Eq. 39, 391 (n_d - 1)/nu_d^(5/4)): no printed values (Fig. 3 only).

• Findings (image-checked): Table III header “x 10^23” for the calculated column is a misprint for 10^13 (Eq. 38 in 1e-13 esu reproduces it); EV-1 “0.91 +- 0.9” is probably +- 0.09 (undecidable); “FD-2” (Table II a only) may be ED-2; the silicate n_d prints as “1:769” (speck). Nuclear contributions (Hellwarth et al.) 29, 21, 15, 19, 21 % for LaSF-7, SF-7, ED-4, LSO, fused silica, and correction factors 0.98, 1.00, 1.07, 1.08, 1.16 for the ellipse-rotation n2 (p. 604).

• refractiveindex.info: no page for this source.

• Status: open

TC-347 Cross-cutting: reproduction graph, BK7, gate (2026-09-26)

• Reproduction graph (curated ids; points): milam_1998 <- desalvo_1996 (4, converted from esu by Milam), white_1984 (1, listed at 351 nm); ensley_2019 <- desalvo_1996 (6, converted), adair_1989 (4, converted), kabacinski_2019 (1), milam_1998 (2, best values listed at 532 nm and 1.06 um); jansonas_2022 <- ensley_2019 (7), patwardhan_2021 (4), milam_1998 (1); kabacinski_2019 <- adair_1989 (5, converted), flom_2015 (1), milam_1998 (1); van_der_linden_2025 <- ensley_2019 (3), desalvo_1996 (1, KBr, converted); white_1984 -> boling_1978 (BK-10 prediction by Eq. 38, check, not a reproduction). The converted Adair and DeSalvo values are the only cm2/W copies of those papers’ n2 until the esu quantity exists (TC-334); they are reproduced, never to be fitted beside the originals once those are recorded.

• BK7 identity: Flom (CVI) and Ensley (Thorlabs) print “BK7” without saying N-BK7; recorded as BK7 (the historical melt), probably N-BK7 in fact: decide. van der Linden’s own “NBK-7” is N-BK7; its reproduction of Ensley’s value is filed under BK7 (the original’s material).

• Gate: poe check passes every step except the Sphinx build, which fails on two warnings, “py:class reference target not found: optmat.materials.Kind / .Optics”, from the type aliases of src/optmat/materials.py (not touched on this branch; a base issue). poe test-library: 195 passed.

• Status: open

TC-348 TC-334 resolved: nonlinear_index_field (2026-09-26)

• A second curator added nonlinear_index_field (n = n0 + n2 <E^2>, esu or m2/V2; eaa80bb). The esu n2 of adair_1989, desalvo_1996 and boling_1978 are now datasets (TC-349 to TC-351).

• Status: decided (2026-09-26)

TC-349 adair_1989 esu n2 (2026-09-26)

• Where: Adair, Chase & Payne, Phys. Rev. B 39, 3337 (1989), Tables I-IV, VIII, X (supersedes the format-gap part of TC-336 / TC-334 for this source).

• Transcribed (nonlinear_index_field, unit esu, scale 1e-13, nothing converted; definition “<E^2>, ‘E is the applied optical electric field’ (Eq. 1, p. 3337)”, coefficient self; x = 1.064 um for this work):

  • Table IV measured n2: 55 datasets x 1 point, primary, part electronic_vibrational (p. 3338), TWM; relative uncertainty 0.05 (0.15 for KF, KCl, NaBr, KBr, CaO, SrO), level not stated, absolute-calibration caveat in notes. Axis/polarization as the existing n datasets (axis only where exact; KTP (x+y), LAP (x+z), YAlO3 (gamma), ZnS (e)/(o) as polarization labels).

  • Table IV BGO-calculated n2 (K = 68): 48 datasets x 1 point, check, part unknown.

  • Table I: SF-58 n2 vs Delta, 1 dataset x 4 points (column delta, cm-1), check (test of the finite offset). CS2 skipped (liquid).

  • Table II: SF-58 n2 vs power, 1 dataset x 4 points (column power, kW), check; P_crit = 94 kW footnote in notes.

  • Table III: “this work” column checked equal to Table IV by the script (incl. the “(av)” of LaF3, CeF3, YAG); only Al2O3 “1.25 (av)” (not Table IV’s 1.23/1.30, mean 1.265) recorded: 1 dataset, check. Literature: 36 reproduced datasets x 1 point: TRI 1.06 um (9; Milam & Weber 1976 / Milam, Weber & Glass 1977, part unknown), Maker & Terhune via Wang 0.693/0.746 um (7; electronic), Levenson & Bloembergen 0.575/0.610 (4), Lynch et al. 0.575/0.592 (4), Levenson 0.560/0.590 (4) (all electronic: large-Delta TWM ‘too large to include the vibrational contribution’, p. 3340), Smith, Bechtel & Bloembergen PDF 1.06 um (8; unknown). Second TWM wavelength as column omega2 (um). Citations as printed (none curated; smith_1975 in the repo is a different paper).

  • Table VIII: n2 column, 13 datasets x 1 point, check, polarization [100]/[001].

  • Table X: measured column checked equal to Table IV by the script; the “calculated from simple oxides” column, 9 datasets x 1 point, check.

  • Totals for the source now: 253 datasets, 259 points (164 n2 datasets, 170 points).

• Structural fixes: Table X’s “Gd3Sc2Al2O12” (image) mapped to GSAG (Table IV’s and the text’s Gd3Sc2Al3O12); Table III “(av)” suffix stripped for the equality check. All cells re-checked against the images: no misread cell.

• Errata: none. Table VIII vs Table IV (KBr 3.07/2.93, CaO 5.07/5.20 = SrO’s value, MgO 1.6/1.61) are not decidable from the paper: both recorded, Table IV primary.

• Doubts: “(av)” undefined and Al2O3’s 1.25 is not the o/e mean; whether Adair converted the literature values’ conventions to its Eq. (1) is not said; pulse duration not stated (Ref. 19); BGO-calculated and additivity values are recorded at 1.064 um though they are long-wavelength estimates.

• Status: open

TC-350 desalvo_1996 esu n2 (2026-09-26)

• Where: Table I (tbl_9572f7715e3f, p. 1326), columns ‘n2 x 10^-14 esu’ at 1064, 532, 355, 266 nm (supersedes the format gap of TC-334 for this source).

• Transcribed: 12 nonlinear_index_field datasets (unit esu, scale 1e-14), primary, one per material, KTP split by sample axis (y at 1064 nm, z at 532 nm): LiF 4, MgF2 (o) 4, BaF2 4, SiO2 4, Al2O3 4, BBO (o) 4, KBr 2, CaCO3 4, LiNbO3 (e) 2, KTP y 1, KTP z 1, tellurite glass 2; 36 points, sigma as printed (level not stated), per-row pulse_fs (30/22/17/15 ps). definition “n = n0 + n2 <E^2>, <> a time average (p. 1327)”; part total (15-30 ps; the paper calls n2 ‘bound electronic’ but does not separate the Raman part); coefficient self; closed-aperture Z-scan. ‘NM’ cells left out.

• Changed: the text’s BaF2 cm2/W values (n2_BaF2_text) are the authors’ conversions of Table I’s 7.5 and 11: now check (never beside Table I).

• Checked: the cells against the table image again (agree). No errata, no structural fix.

• Reproductions of this table (all conversions to cm2/W, reproduced_from = ["desalvo_1996"] already): milam_1998 (SiO2, 4 rows; its own n0), ensley_2019 (letter b), van_der_linden_2025 (KBr 1064 nm), dragomir_2002 (curated separately).

• Status: open

TC-351 boling_1978 esu n2 (2026-09-26)

• Where: Table I (tbl_1104b7cc486c, p. 603) and Table III (tbl_6d8d3f9d443b, p. 606).

• Transcribed: 44 nonlinear_index_field datasets of 1 point (unit esu, scale 1e-13), wavelength ‘not stated’ throughout:

  • Table I measured (10): reproduced from Owyoung’s ellipse rotation (Refs. 11, 12), ‘by assuming that n2 is purely electronic’, relative 7 % (‘+-7 percent precision’), part unknown (the paper: neither total nor electronic; correction factors in notes).

  • Table I calculated (10): check, Eqs. (25)-(26) with gs = 3, part electronic.

  • Table III calculated (12): check, Eq. (38), part electronic.

  • Table III measured (12): reproduced from Milam & Weber (Refs. 14, 15), TRI, part total (‘total values of n2, including both electronic and nuclear components’, p. 606), sigma as printed.

  • definition: “n2 = (12 pi/n) chi(3)_1111 for the field E cos(wt) (Eqs. 1-8); n = n0 + n2 <E^2> is implied, not written” (the equivalence, <E^2> = E^2/2, is derived here).

• Errata (13):

  • Table III calculated, scale 1e-23 -> 1e-13 (one per dataset, 12): the header prints ‘n2 calc x 10^23’ (image checked: it is printed so, so an erratum, not a structural fix); Eq. (38), in 10^-13 esu, reproduces the column to <= 0.4 % for 11 of 12 glasses, and Fig. 2’s axis reads ‘n2 (10^-13) CALCULATED’.

  • EV-1 measured sigma 0.9 -> 0.09: Fig. 2 (p. 606) draws EV-1’s error bar from about 0.83 to 1.01 (+-0.09), not 0.01-1.81; the other rows carry 10-20 %.

• Doubts: the n2 wavelengths are not stated (adair_1989’s Table III gives the same TRI references at 1.06 um); fused silica’s calculated 0.87 is not reproduced by Eq. (38) with the printed nu_d = 70 (0.833; nu_d ~ 68 would) — left as printed. Fig. 2 plots CaF2, LiF, MgF2 and KH2PO4, absent from Table III (not digitised).

• Status: open

TC-352 Reproductions reconciled (2026-09-26)

• The cm2/W copies of DeSalvo’s and Adair’s esu values in milam_1998, ensley_2019, kabacinski_2019 and van_der_linden_2025 already name desalvo_1996 and adair_1989 in reproduced_from; they are conversions by the citing authors, never to be fitted beside the esu originals now recorded. No other citation in this extraction’s records names a curated source (checked against the merged source list, 262 records; smith_1975 is Smith, Parkinson & Huber’s krypton paper, not Smith, Bechtel & Bloembergen 1975).

• BK7: Flom (CVI) and Ensley (Thorlabs) print ‘BK7’; kept as BK7, with the doubt (Schott BK7 or N-BK7 not stated) in their notes.

• Status: open

TC-353 Conventions common to the records of TC-354 to TC-362 (to confirm) (2026-09-26)

• One dataset per material, quantity and origin. A dataset has one material, one pulse length and one grade; a paper’s literature column is split into one reproduced dataset per reference (and per pulse length where a reference gives two). Most datasets hold one or two points; the row id is the table row or the wavelength.

• Per-cell powers of ten (“4.5 \times 10^{-11}”, “2.0 \pm 0.8 \times 10^{-3}”) are stored in e-notation (4.5e-11, sigma 0.8e-3) with scale 1, as bree_2012 and daumont_1992 do; a column factor (“beta x 1e-11”) is the dataset scale.

• Upper bounds (“<”, “\leq”) and “approximately zero” cells (“\approx 0”) are kept in the files (the bound’s number in value, the raw cell in printed) and excluded: use = "excluded" when the whole dataset is bounds, excluded_rows otherwise. The format has no marker for a bound (format need, TC-361).

• Approximate values (“\approx 30”, “~30”, “\approx 9 [20]”) are kept as numbers and said to be approximate in notes (no format marker).

• beta. Every beta dataset is two_photon_absorption_coefficient in the unit printed (cm/W, or cm/MW for Brimacombe’s alpha_1). Its definition, whether reflection losses were removed, and the pulse length are in each record’s notes; pulse_fs is set for every dataset whose pulse length is stated.

• Band gaps quoted without a method have parameters.kind = "not stated", and Brimacombe’s gap fitted to make Keldysh theory agree has kind = "effective": neither is in the documented list (TC-361).

• Literature band gaps and betas carry reproduced_from = the reference the paper cites (a source id where curated: taylor_1988, eva_1996, kittelmann_1994, brimacombe_1989, dragomir_2002, desalvo_1996, weinberg_1979, malitson_1965); the chain to the original is in notes (TC-362).

• Crystal axes. Quartz and BBO “z-cut” / “(||c)” samples (light along the optic axis) are given axis = "o", an inference from the cut stated in the notes; sapphire, MgF2 and Dragomir’s quartz have no axis (orientation not stated).

• No new materials. Every solid met is registered (SiO2, SiO2_quartz, BaF2, SrF2, CaF2, LiF, MgF2, Al2O3, BBO); materials.toml is unchanged. Liquids skipped: Dragomir’s eight (water, heavy water, methanol, ethanol, hexane, cyclohexane, 1,2-dichloroethane, chloroform). Kittelmann’s passing “CdF2 (band gap approx 6 eV)” (a recollection of Liu et al.’s result) was not registered or recorded; to decide.

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-354 taylor_1988 (Taylor, Gibson & Roberts, Opt. Lett. 13, 814 (1988)) (2026-09-26)

• Transcribed: Table 1 (tbl_d491af0a4326, image checked, all cells agree), 6 materials x 3 columns = 18 datasets, 18 points: band_gap_* (check, kind not stated: no source or method given), beta_248_* (primary for SiO2, BaF2, SrF2, CaF2; LiF and MgF2 are “\leq 1.3e-12” bounds from a two-photon fit of loss ascribed to three-photon absorption and colour centres: excluded), liu_266_* (Liu et al. 1978/ 1979; SiO2 1.7e-11 reproduced, the other five “<” bounds, excluded).

• beta: dI/dz = -beta I^2 with R at each surface (Eqs. 1-2): reflection removed; 0.7 +- 0.1 ps, linear polarization, flat-top spatial, Gaussian temporal. Uncertainty +-50 % absolute, +-15 % relative (recorded relative 0.5, level not stated). CaF2 grade Optipur (Optovac); fused-silica grade not stated.

• Checks: Eq. 4 gives B = 1.259 at alpha = 1 (printed 1.26). Eq. 2 gives T = 0.605 at alpha = 1 (39.5 % loss; printed 36 %); the printed I_out/I_in = 0.44 needs (1 - R)^2 = 0.92 included (0.443). Fig. 3’s text values for 1.27 cm windows are reproduced (0.33, 0.13, 0.70, 0.44 against printed 0.33, 0.12, 0.66, 0.45) with the tabulated beta and assumed R: beta is in cm/W with the stated definition.

• Finding: the Fig. 1 caption prints beta in “W/cm2” (misprint for cm/W). The header’s “2h nu = 9.36 eV” for 266 nm is as printed (2 x 4.66 = 9.32 eV).

• Doubt: the band gaps’ origin; Liu’s footnote b cites two papers without saying which value is from which.

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-355 kittelmann_1994 (Kittelmann & Ringling, Opt. Lett. 19, 2053 (1994)) (2026-09-26)

• Transcribed: Table 1 (tbl_27e00c033f1a, JSON only: merged header; image checked), 4 materials: band_gap_* (reproduced from taylor_1988: identical values, not attributed in the paper, an inference), beta_193_gaussian_* (primary), beta_193_flat_top_* (check), taylor_248_* (reproduced; MgF2 bound excluded). 16 datasets, 16 points.

• Decision to confirm: the Gaussian-profile fit is primary because the measured beam profile was “nearly Gaussian, and noticeable flattening could not be observed” (p. 2) and Eq. (1) is written for it; the flat-top fit is kept as a check (Taylor’s assumption).

• beta: dI/dz = -alpha I - beta I^2 (alpha neglected), (1 - R) in Eq. (1): reflection removed; 0.8 ps sech^2, linear polarization. +-50 % absolute (about 10 % of it a systematic overestimate from pulse flattening in the input window), < 20 % relative.

• Doubt: the band-gap attribution; sample grades and MgF2 orientation not stated.

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-356 eva_1996 (Eva & Mann, Appl. Phys. A 62, 143 (1996)) (2026-09-26)

• Transcribed: Table 1 (tbl_48a4477a3382), the wide table with three empty label columns (“351 nm:”, “248 nm:”, “193 nm:”); column alignment checked row by row against the image (the script asserts the label columns are empty and the row labels match). 25 datasets, 36 points: band gaps (reproduced, taylor_1988; quartz “\approx 9 [20]” from weinberg_1979), alpha at 351/248/193 nm (7 datasets, 1e-3 cm-1, base e, +-20 %), beta at 248/193 nm (6 datasets, 1e-10 cm/W, +-40 %; “\approx 0” cells of CaF2, LiF, MgF2 at 248 nm excluded), beta_Lit (taylor_1988; the “\leq .01” of LiF and MgF2 excluded).

• Structural fix: the Suprasil 2 beta_Lit cell “.45 (2.1 [19])” holds two values; the script splits them into taylor_248_SiO2 (.45) and brimacombe_248_SiO2 (2.1).

• Finding: the caption says beta_Lit was “measured at 248 nm / 0.7 ps”, but 2.1 is brimacombe_1989’s 9 ns fibre value (the text says so, p. 5). The quartz gap “\approx 9 [20]” is loosely attributed: weinberg_1979 gives 9.3 eV for amorphous thermal SiO2 and prints no measured quartz gap.

• beta: 25 ns calorimetry, A = dz (alpha + beta H/tau) (Eq. 2); incident energy inside the sample (front reflection removed), surface absorption included in alpha. The 0.7 form factor is stated for BaF2 only. Up to 24 % (BaF2) or a third (silica) of the slope may be transient colour-centre absorption: beta possibly overestimated.

• Formula: the Suprasil 2 degradation-rate fit Delta A/n = 0.056 ppm H^3.14 ([[formulas]] without a form); reproduces the paper’s 160 ppm after 200 000 pulses at 256 mJ/cm2 (155 ppm).

• Grades: S1 = Suprasil 1, S2 = Suprasil 2 (text); quartz z-cut (axis o inferred). “A CaF2 crystal (Korth Kristalle)” is named without saying which CaF2 row.

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-357 brimacombe_1989 (Brimacombe, Taylor & Leopold, J. Appl. Phys. 66, 4035 (1989)) (2026-09-26)

• Transcribed: Table II (tbl_b42460a7da40, JSON: merged header; image checked): alpha1_fibre (193, 248, 308, 351 nm, primary, per-value sigma) and the “Other work” by reference: taylor_1988_248 (reproduced), liu_1979_266 (reproduced), liu_1978 (266 and 355 nm bounds, excluded), mizunami_1988_282 (reproduced), mizunami_1987_308 (bound, excluded). Table I (fibre types and OH content) in notes (image checked). Text/figure values: the per-fibre alpha_1 printed on Figs. 5, 7, 8 (5 check datasets with grade and pulse; figure labels, not digitised curves), the band gap 7.8 eV (Ref. 21, the Keldysh input: check, assumed) and the “effective band gap of 8.2 eV” (check, kind “effective”). 13 datasets, 17 points.

• Structural fix: the Ref. 21 “< 4.5e-5” is printed on its own line under 266 nm with no wavelength; the script carries 266 nm down (the image and Fig. 9 confirm).

• Decision to confirm: 351 nm (2 h nu = 7.1 eV, below the gap; “4.6 +- 4.6e-7”, attributed by the authors possibly to impurities or three-photon absorption) is an excluded row of the primary dataset; 308 nm is kept.

• beta: -(1/I) dI/dx = alpha_0 + I alpha_1 (Eq. 1), alpha_0 re-measured after every shot to remove colour centres; Fresnel reflection removed; unpolarized; ns pulses (5, 9, 4, 7 ns typical at 193, 248, 308, 351 nm; Figs. 5, 7, 8 print 4.5, 9, 4 ns). Pulse length per wavelength is in notes only (a dataset has one pulse_fs).

• Finding: reference list numbering misprints (entry “30” is Ref. 10; 20-23 out of order).

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-358 slattery_2003 (Slattery & Nikogosyan, Opt. Commun. 228, 127 (2003)) (2026-09-26)

• Transcribed: Table 1 (tbl_43ed8a53704c; OCR-selected body, 30 numbers agree with the text layer; image checked) and Table 2 (tbl_0a42752ea230, JSON: spanned material and E_g cells carried down; image checked). 28 datasets, 30 points: n at 211 nm (4, reproduced from Nikogosyan’s handbook), alpha at 211 nm (4, primary, per-value sigma), band gaps (4, reproduced: weinberg_1979 kind photoconductivity; eva_1996 for quartz, BaF2, CaF2), beta at 211 nm (4, primary, 1e-11 cm/W, per-value sigma, 250 fs), and the literature by reference (12, reproduced: kittelmann_1994, Schenker 1995, Gurzadyan 1992, taylor_1988, dragomir_2002).

• Finding (excluded): Table 1’s n of fused silica (1.5275) and quartz (1.6347) are inconsistent with the paper’s own (1 - R)^2: 91.23 % needs n = 1.537 (Malitson’s formula gives 1.5373 at 211 nm), 88.57 % needs n = 1.641; BaF2 and CaF2 are consistent (91.02, 92.50 reproduced). The two index datasets are excluded; which of n and (1 - R)^2 is wrong, and whether beta used the printed (1 - R), is not decidable from the paper.

• Doubt: alpha is “deduced from total absorbance minus optical density” (decadic words); base e is recorded as in dragomir_2002’s definition, not stated here. The “theory and fitting procedure” is cited to [6] (Veitas et al., a BBO harmonic-generation paper), probably a citation slip for [1] (dragomir_2002).

• Checks: the literature values match their originals: Kittelmann’s Gaussian values with +-70 % (50 % + 20 %), Taylor’s with +-65 % (50 % + 15 %), Dragomir’s Suprasil and quartz. Schenker’s fused-silica value is 43 +- 18 here and a range 35-52 in dragomir_2002.

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-359 dragomir_2002 (Dragomir [printed “Dragonmir”], McInerney & Nikogosyan, Appl. Opt. 41, 4365 (2002)) (2026-09-26)

• Transcribed: Tables 1-7, every solid (all images checked; spanned cells of Tables 1, 3, 5, 6, 7 carried down in the script). 82 datasets, 169 points:

  • six fused-silica grades (KU-1, Corning 7940, SQ, Suprasil, Herasil, Infrasil): n (reproduced: malitson_1965 and a Heraeus datasheet), alpha_sp (primary; KU-1 and Suprasil “\leq 0.01” bounds excluded), beta average (primary, sigma) and per-curve beta (check), alpha average and per-curve alpha from the fits (check);

  • quartz, sapphire, BBO (z-cut o, x-cut o, x-cut e): n (reproduced: Sosman, Malitson 1962, Kato), alpha_sp (primary, 1e-2 cm-1, sigma), beta average (primary) and per-curve (check), quartz alpha from the fits (check);

  • Table 1 (fused-silica literature) and Table 6 (crystal literature): 26 reproduced or excluded datasets, one per reference and pulse length. Tables 8-10 (liquids) skipped.

• Erratum: brimacombe_1989_5ns_SiO2 row 193: printed 20, corrected 200 (x 1e-11 cm/W). Evidence: brimacombe_1989 Table II prints 2.0 +- 0.8 x 10^-3 cm/MW = 2.0e-9 cm/W (image checked), its Fig. 9 plots ~2e-3 cm/MW at 193 nm, and its text’s “four orders of magnitude” from 193 to 308 nm holds only for 2e-3; Dragomir’s 248 nm conversion of the same paper (21) is right. A factor-10 slip in the reproduction.

• Not extracted: Table 1’s Ref. 16 “35-52” (a range, 213 nm; in notes).

• Checks: the printed +- of all eleven beta averages equals the standard error of the mean of the tabulated curves plus 6 % of the mean (footnote a, “Absolute error (6 %) was added”), added linearly; the alpha averages’ +- is the standard error alone. All averages reproduce except BBO x-cut ordinary (mean of the seven curves 65.47, printed 66, also in the text; not corrected). 1 - R follows from n for every sample. Malitson’s formula gives n = 1.50056 at 264 nm (printed 1.5007).

• Findings (text misprints, notes): sapphire “(9.4 +- 0.2)” in the text vs 9.4 +- 1.2 (Table 5, abstract); “see Table 4” for Table 6; “Ref. 32” for Ref. 34; “Corning 7040”.

• Doubt: the pulse length 220 +- 10 fs is called FWHM of a Gaussian written exp[-((t - t_max)/tau)^2] (a 1/e half-width), and slattery_2003 quotes it “at 1/e level”; recorded as pulse_fs = 220. Dragomir’s quartz orientation is not stated (its length matches Slattery’s c-cut sample); no axis recorded.

• Decision to confirm: alpha_sp (spectrophotometer) is primary and the fitted alpha a check; per-curve betas are checks behind the primary averages (no double counting).

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-360 van_stryland_1997 (Van Stryland & Sheik-Bahae, Proc. SPIE CR69 (1997) / 10291, 102910Q) (2026-09-26)

• No datasets: the review has no tables and quotes no material n2 or beta (all 24 pages read). The notes keep the definitions (Delta n = (n2/2)|E|^2 esu = n2 I MKS, n2(esu) = (c n0/40 pi) n2(MKS) with c in m/s, Delta alpha = beta I, beta = 2PA coefficient for ultrafast NLA), the reflection rule (I0 inside the sample), and the working formulas (Eqs. 5-13, 25-31) with their stated accuracy.

• Copy comparison: Unverified_94700d0ad99f is the same work and the same version: same title, authors, sections, figures 1-8, equations 1-35, 46 references and page breaks (pages 1 and 17 compared as images); it is a clean born-digital PDF (Ghostscript, 2022) without SPIE’s running heads, probably the authors’ manuscript file. No second record. The SPIE copy’s footer prints “(c) (2002) 2017 SPIE” while the library and Crossref date the paper 1997.

• Formulas: the Z-scan relations are technique formulas, not material models; kept in notes, not as [[formulas]] (to confirm).

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-361 Format needs (reported, not implemented) (2026-09-26)

• A marker for upper bounds and for approximate values (“<”, “\leq”, “\approx”, “~”); here bounds are excluded rows or datasets and approximations are notes.

• band_gap kind: the documented list lacks “not stated” (a gap quoted without source or method: Taylor, Kittelmann, Eva) and “effective” (a gap chosen so that a model fits data: Brimacombe’s 8.2 eV). Used here; the loader does not close the list.

• A per-row pulse length (Brimacombe’s alpha_1 at four wavelengths with four ns pulse lengths): only in notes now; a pulse extra column would carry it.

• OH content (Brimacombe Table I, Dragomir’s grades) has no quantity; in notes.

• Sample thickness is only in the printed column and notes.

• A literature value printed as a range (Dragomir’s “35-52”) cannot be a point.

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-362 The reproduction graph (-> means “reproduces”) (2026-09-26)

• taylor_1988 -> Liu et al. 1979 (Appl. Opt. 18, 1015) and Liu et al. 1978 (PRB 17, 4620) (266 nm column).

• brimacombe_1989 -> taylor_1988 (248), Liu 1979 (266), Liu 1978 (266, 355 bounds; the 7.8 eV gap), Mizunami & Takagi 1988 (282), Mizunami et al. 1987 (308).

• kittelmann_1994 -> taylor_1988 (248 nm column; band gaps identical, unattributed).

• eva_1996 -> taylor_1988 (E_gap column and beta_Lit), brimacombe_1989 (2.1 at 248), weinberg_1979 (quartz gap, loosely).

• dragomir_2002 -> (fused silica) Gurzadyan 1992, Liu 1979, Liu 1978/1979, desalvo_1996, Hata 1990, Tomie 1989, taylor_1988, Simon 1989, Ross 1990, eva_1996, brimacombe_1989 (the 193 nm value 10x too small: erratum), Taylor et al. 1988 (Appl. Opt. 27, 3124), Schenker 1995, Repeyev 1992, kittelmann_1994 (Gaussian values); (crystals) Gurzadyan 1992, Liu 1978/1979, eva_1996 (quartz), Schenker 1995, desalvo_1996 (sapphire, BBO), Liu 1978 (sapphire), Veitas 1997, Dubietis 2000 (BBO); n from malitson_1965, a Heraeus datasheet, Sosman 1927, Malitson 1962, Kato 1986.

• slattery_2003 -> kittelmann_1994 (Gaussian values), Schenker 1995, Gurzadyan 1992, taylor_1988, dragomir_2002 (Suprasil, quartz); gaps from weinberg_1979 and eva_1996 (which has them from taylor_1988 and weinberg_1979); n from Nikogosyan’s handbook.

• van_stryland_1997: none.

• Chains to note: Taylor’s band gaps reach Slattery through Eva; Brimacombe’s 248 nm value reaches Eva (as 2.1, “0.7 ps”) and Dragomir (as 21); Kittelmann’s Gaussian fits reach Dragomir and Slattery (the flat-top fits reach nobody).

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-363 The gate (2026-09-26)

• uv run poe check: ruff, format, basedpyright, numpydoc, codespell and pytest (6711 passed) pass; sphinx fails with two warnings that are in the base commit, not from this work: “py:class reference target not found: optmat.materials.Kind” and “…optmat.materials.Optics” (the type aliases of src/optmat/materials.py, added in 695db63, with nitpicky = True). The extraction may not edit modules or docs; the aliases are to be documented, or added to nitpick_ignore, in review.

• uv run poe test-library: 189 passed.

• refractiveindex.info: none of these papers has a page in data/external/refractiveindex_info (its BaF2 Sheik-Bahae n2 page is Sheik-Bahae et al. 1991, not van_stryland_1997).

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-364 stuart_1996 (Stuart et al., Phys. Rev. B 53, 1749 (1996)) (2026-09-26)

• Transcribed: text values, p. 1752: front-surface damage fluences at 0.4 ps of BaF2 1.6, CaF2 2.0, MgF2 2.1, LiF 2.6 J/cm2 (4 datasets, 1 point each; the library text drops the “2” of J/cm2, the pdf text layer confirms). 600 shots/site, Nomarski criterion, 1-m lens; 15 % absolute (5 % relative) uncertainty, level not stated. Model inputs for fused silica (assumed): U_I = 9 eV, m* = m_e, sigma_4 = 2e-114 cm8 s3 (measured for NaCl, Jones et al. 1989; also a NaCl dataset, reproduced). Calculated avalanche coefficient 0.011 (1053 nm) and 0.013 (526 nm) cm2/(ps GW), check.

• Formulas: kinetic equation (Eqs. 1-6), impact-ionization rate 1.5 (e/U_I - 1)^2 fs^-1, avalanche rate (Eqs. 16, A6), MPI at 526 nm (Eq. 19) and the 1053-nm fit P = 9.52e10 I^8 cm^-3 ps^-1 (Eq. 20), rate equation and threshold (Eqs. 21-26), plasma absorption (Eqs. 33-35).

• Checked: 2/alpha = 0.18 (0.154) J/cm2 against printed 0.2 (0.15); 1/alpha from the flux-doubling range 0.077-0.154 against ‘between 0.08 and 0.16’; Eq. (33) a = 2.403 um^-1 (n/n_cr) against 2.4.

• Doubt: the wavelength of the fluoride values is not in the sentence; 1053 nm is inferred (0.4 ps is the 1053-nm compressor’s shortest pulse; 526-nm pulses start at 275 fs). Peak or average fluence not stated. Fused-silica thresholds are figure-only (Figs. 3, 6).

• Status: open.

TC-365 schaffer_2001 (Schaffer, Brodeur & Mazur, Meas. Sci. Technol. 12, 1784 (2001)) (2026-09-26)

• Transcribed: Table 1 (JSON cells, image checked): 4 band gaps (assumed), bulk I_th at 400/800 nm (4 datasets, 7 points), P_cr (5 datasets, 8 points: SF11, silica, CaF2 as assumed inputs from ref. 34 or Sec. 3.3; Corning 0211 at 800 nm the paper’s fitted value, primary; at 400 nm scaled by lambda^2, check). Table 2 scrambled in the library: transcribed from the image in the script, which checks every scrambled cell against the character multiset of the transcribed column (passes). N (Keldysh electron density at I_th) recorded as ionization_yield against intensity (7 datasets, check); gamma quoted in notes (no quantity). Text: DIC energy threshold 6.6 nJ (Corning 0211, 1.4 NA), dark-field 7.0 and 5.0 nJ (Corning 0211, 1.0/1.4 NA, 800 nm), transmission thresholds 20/25 nJ (silica, 0.65 NA), avalanche coefficients (1.3, 1.6 silica; 1.4, 2.0 CaF2; 4.5 with Lenzner’s sigma_6), Lenzner’s sigma_6 (reproduced), BK7 P_cr 1.6 MW (reproduced).

• Structural fix: Table 2 transcription (script docstring and _check_table2).

• Findings: Table 2’s caption cites ‘equation (37) in [30]’ (Boyd) where the text says [8] (Keldysh). Corning 0211 at 400 nm, N = 5.2e21 < 6.9e21 cm^-3, yet the text says photoionization alone reaches the critical density there. The caption’s critical density 6.9e21 at 400 nm is 6.97e21 truncated.

• Checked: P_cr 1.5 x (400/800)^2 = 0.375 (printed 0.4); gamma needs m n = 0.72-0.76 m_e (0.83 SF11); 400/800 gamma ratios agree with 2 sqrt(I_800/I_400) to 1-2 %.

• Decision to confirm: ionization_yield for a Keldysh electron density per cm3 in a solid (the quantity says “ion yield or probability”); polarization “not stated”.

• Status: open.

TC-366 hamam_2018 (Hamam & Gamal, Results Phys. 9, 725 (2018)) (2026-09-26)

• Transcribed: Table 2 I_th against duration for two focusings (2 datasets, 9 points each), reproduced from Liu et al., J. Opt. A 7, 198 (2005) (not in the library); the script checks Table 1’s I_th equal Table 2’s. Model inputs (assumed): eps_g = 9.0 eV, m’ ~ m/2 (Liu), tau_rec = 1.5e-13 s (tzortzakis_2001, Audebert 1994), n2 = 3.2e-16 (Agrawal; Skupin & Berge), n_r = 1.454, P_cr = 2.19e6 W (check).

• Findings: NA printed 0.225 in both table headings (image confirmed) and 0.255 in the abstract, text and all figure captions: recorded 0.255 with the heading noted. Table 1’s gamma = sqrt(2) x Eq. (1) with the stated m’ = m/2, to 4 digits (i.e. m’ = m_e), except the 2.05E-12 s, NA 0.225 cell (7.696 printed, 7.97 computed). Table 2’s P is not I_th x pi w0^2 for the stated radii (P/I = 7.86e-9 and 7.09e-9 cm2). Tables list 250 fs - 2.2 ps, the text 240 fs - 2.5 ps. The P column’s ‘1,13E04’ is a decimal comma (P not extracted: no quantity). Eq. (2) writes R n^2 with tau_rec = R^-1 (Eq. 7).

• Checked: P_cr = 2.189e6 W.

• Status: open.

TC-367 couairon_2005 (Couairon et al., Phys. Rev. B 71, 125435 (2005)) (2026-09-26)

• Transcribed (primary): P_cr = 1.98 MW and n2 = 3.54e-16 cm2/W (nonlinear-focus shift, 160 fs, NA 0.5; part recorded total: the model’s n2 carries f_R = 0.18 and max P~ = 1.002 P_in for 160 fs), tau_c = 1e-14 s (fitted to transmission), plasma lifetime ~150 fs (pump-probe). Assumed: n0 1.45, k’’ 361 fs2/cm, f_R 0.18, tau_d 32 fs, tau_s 12 fs (Junnarkar; stolen_1989), U_i 9 eV (six references), m 0.64 m_e (Fischetti), rho_at 2.1e22 atoms, tau_r 150 fs (Audebert). Check: sigma_6 = 9.6e-70 (their Keldysh limit), W_PI = 1.6e32 cm^-3 s^-1 at 3.5e13 W/cm2 (ionization_rate, a Keldysh implementation check). Reproduced: Boyd n2 3.75e-16 and P_cr 1.72 MW; sigma_6 of Li (1.5e-71) and Lenzner (3e-67 +- 0.9 in the exponent); band gaps 7.8 eV (Liu 1978/1979, Nathan 1985) and 7.1 eV (Joglekar 2003); damage type I 0.1 uJ and type II 0.31 uJ (Sudrie et al. 1999). 23 datasets, 1 point each.

• Formulas: Sellmeier Eq. (3) recorded without a form (it prints lambda_m, not lambda_m^2, and is Malitson’s formula rounded to 4 decimals, uncited: reproduced_from = ["malitson_1965"]); propagation model Eqs. (2)-(6); Keldysh Eqs. (7)-(8); nonlinear focus Eqs. (9)-(12).

• Checked: n2 = 3.548e-16 from 1.98 MW; 1.4^2 x 1.002 = 1.964 MW; gamma = 0.999 at 3.5e13 with m = 0.64 m_e and I = n0 c eps0 E^2/2; sigma_6 I^6 rho_at = 3.706e34; rho_c 1.742e21 (with m_e); k’’ = 361.38 fs2/cm from the printed Sellmeier; the Sellmeier differs from the refractiveindex.info SiO2/Malitson coefficients by -2.7e-5 in n at 0.3 um, -5.8e-6 at 0.8 um.

• Findings: the quoted powers (0.25 uJ = 1.56 MW) are E/tau_FWHM, not the model’s E/(t_p sqrt(pi/2)) = 1.47 MW; Boyd’s 1.72 MW is reproduced by neither P_cr definition (1.87, 1.77 MW); 7.8 eV and 7.6 eV in consecutive sentences; sigma_6 of Lenzner and Li: per-atom here, ~1e7 larger than the per-volume values of schaffer_2001 and jing_2012 divided by 2.1e22 (both references, the same factor).

• Status: open.

TC-368 berge_2010 (Berge, Mauger & Skupin, Phys. Rev. A 81, 013817 (2010)) (2026-09-26)

• Transcribed: Table I (CSV, image checked), all simulation inputs at 355 and 1550 nm: k’’ (fs2/m, scale 100), k’’’ (fs3/m, scale 100), n0, n2 (1e-16), P_cr, sigma (1e-19 cm2, avalanche_coefficient), g, tau_R, omega_R^-1 (per wavelength). Text: U_i 7.8 eV, reduced mass 0.635, rho_nt 2.1e22 molecules, tau_rec 150 fs. 16 datasets, 26 points. Sources: Agrawal 2001 (dispersion), Agrawal and milam_1998 (n2), Agrawal and Zozulya 1999 (Raman).

• Finding: k’’’ printed ‘fs2/cm’ (image), read as fs3/cm (unit interpretation, no erratum mechanism for a unit).

• Checked: P_cr 0.379 (printed 0.37) and 12.07 MW (12); both sigma are the Drude value for tau_c = 23.13 fs (not stated in the paper); rho_c formula to 0.4 %.

• Status: open.

TC-369 gulley_2012 (Gulley et al., Phys. Rev. A 85, 013808 (2012)) (2026-09-26)

• Transcribed: measured front-surface damage, fluence 5.1/3.8/4.7 J/cm2 and energy 60/45/55 uJ (3 points each), single-shot estimate 6.8 J/cm2 (check). Table I (CSV, image checked) simulation inputs, reproduced from Winkler et al., Appl. Phys. A 84, 413 (2006) and assumed: tau_1 32 fs, tau_2 12.2 fs, f_r 0.18, n0 1.45, k_2 361, n2 2.48e-16, U 9 eV; text: reduced mass m_e/2, tau_rec 150 fs, tau_c 10 fs (chosen). 14 datasets. Table II scrambled: transcribed from the image in the script and checked against the scrambled characters; FROG diagnostics, quoted in notes only.

• Findings: k_2’s unit printed ‘fs^2 W^-1’ (image), read as fs2/cm; R(tau) as printed makes tau_2 = 12.2 fs the decay and tau_1 = 32 fs the oscillation, the reverse of couairon_2005 and berge_2010; P_cr written lambda^2/(8 pi n0 n2), a quarter of the usual.

• Checked: sigma peaks at 0.425 fs (printed 0.42); E/F = 1.18e-5 cm2 for all five threshold pairs.

• Status: open.

TC-370 tzortzakis_2001 (Tzortzakis et al., Phys. Rev. Lett. 87, 213902 (2001)) (2026-09-26)

• Transcribed: simulation inputs (assumed): n2 3.2e-16, n0 1.453, P_cr ~2.3 MW (check), k’’ 361 fs2/cm, sigma 2.78e-18 cm2 (Mlejnek et al. 1998, an air paper), U_i 7.6 eV (Tohmon 1989), sigma_5 = 1.3e-55 s^-1 cm10/W5, rho_at 2.1e22, tau_r 150 fs (Audebert). 9 datasets.

• Findings: lambda^2/(2 pi n0 n2) = 2.19 MW, not 2.3 (5 % high). sigma = 2.78e-18 is the Drude value for tau_c = 4.69 fs (not stated). The library’s ‘mJ’ is uJ (Symbol font).

• Status: open.

TC-371 mao_2004 (Mao et al., Appl. Phys. A 79, 1695 (2004)) (2026-09-26)

• Transcribed: band gaps NaI 5.9 and LiF 13.7 eV (reproduced, Itoh 1982; NaI registered); SiO2 ~9, MgO ~7.7, quartz 9.8 eV (as used, assumed); SiO2 trapping time 150 fs (reproduced, Martin et al. 1997). 6 datasets.

• Formulas: Keldysh parameter (with 2 m*), rate equations, Drude and plasma index, STE index, P_cr (3.77), Frohlich alpha.

• Finding: the rate equation printed dN/dt = a I N + sigma N I^m (multiphoton term proportional to N), unlike Stuart’s Eq. (21) it cites.

• Status: open.

TC-372 jing_2012 (Jing et al., Appl. Surf. Sci. 258, 4741 (2012)) (2026-09-26)

• Transcribed: inputs (assumed) 9 eV, 0.635 m_e (Sudrie 2002), n0 1.46, tau_r 100 fs (Li 1999); literature effective masses m_e, 0.86, 0.635, 0.64 (couairon_2005), 0.5 m_e (reproduced; carrier ‘not stated’ except Couairon’s); sigma_6 Keldysh limit 2.2e-47 (check), Lenzner 6.0e-52 and Li 3.0e-56 (reproduced, per volume); W_PI 1.6e32 at 3.5e13 (check); Stuart’s alpha 0.01 (reproduced from stuart_1996); tau_c 1.36e-15 s (Sparks, reproduced), 3.5 fs (Starke, check), 1.7 fs (Sun 2005, reproduced); surface thresholds 2.74 (model, check), 2.8, 1.5 (Li, 25 fs), 2.3 J/cm2 (Jia, 150 fs, 3 shots) (reproduced). 21 datasets.

• Checked: fluence 2.7399 J/cm2 from I0 = 25.74 TW/cm2 (unit confirmed in the pdf text layer); sigma_6 I^6 = 4.04e34 (printed 4.1e34); Starke tau_c 3.52 fs; n_cr 1.106e21; gamma 0.999 at 3.5e13.

• Findings: the Keldysh-limit sigma_6, W_MPI and W_PI coincide with couairon_2005’s (W_PI identical) though presented as the paper’s own calculation; E’_g = E_g[1 + 1/(2 gamma^2)] against hamam_2018’s [1 + 1/(4 gamma^2)].

• Status: open.

TC-373 rethfeld_2004 (Rethfeld, Phys. Rev. Lett. 92, 187401 (2004)) (2026-09-26)

• Transcribed: example inputs (assumed), recorded for SiO2 because W_1pt is compared with SiO2 and the parameters follow Kaiser et al. 2000 (the paper names no material): E_gap 9 eV, m_CB = m_VB = m_e, alpha~ ~ 1e15 s^-1. 4 datasets.

• Formulas: MRE (Eqs. 2-3), asymptotic solution (Eqs. 5-7), critical energy (Eq. 8) with W_1pt = 3.5e-7 E_L^2 m2/(V2 s).

• Checked: hbar omega 2.4797 eV; eps_crit 13.50-14.43 eV (‘between 13.5 and 14.5’); k = 6, k + 1 = 7 equations.

• Doubt: the material assignment (SiO2) is an inference from the comparison.

• Status: open.

TC-374 bourgeade_2012 (Bourgeade & Duchateau, Phys. Rev. E 85, 056403 (2012)) (2026-09-26)

• Transcribed: no dataset (no material: a generic 9-eV direct-gap dielectric). Formulas: BVkP rate (Eqs. 9, 15, 16; alpha = 1.55 a.u., N_0 = 2.2e22 cm^-3) and optical Bloch (Eqs. 19-22; mu_vv 1.68e-29, mu_vc 1.34e-29 C m; tau_r 3 ps). KDP relaxation 300 fs - tens of ps [39] and NaCl, MgO, Al2O3 [40-42]: ranges, notes only.

• Status: open.

TC-375 zhokhov_2014 (Zhokhov & Zheltikov, arXiv:1402.5530v2) (2026-09-26)

• Transcribed: the library copy is the arXiv preprint (v2, 4 July 2014). No material, no dataset; formulas Eqs. (4), (6)-(9) and (10)-(12). The examples use E_g/omega = 6.45 at 800 nm (a 10.0-eV gap).

• Status: open.

TC-376 jukna_2018 (Jukna et al., J. Opt. Soc. Am. B 36, A54 (2019)) (2026-09-26)

• Transcribed: sapphire simulation inputs at 1.3 um (assumed): n0 1.75, n2 3.1e-16 (Major et al. 2004), sigma 1.9e-21 m2, tau_c 1 fs, rho_nt 2.35e22 molecules, U_g 9.9 eV (Weber 2002), tau_rec 100 ps (Guizard 1995). 7 datasets. The ‘electron-hole mass ratio m* = 1’ is ambiguous: notes only.

• Checked: Drude sigma 1.957e-21 m2 for tau_c = 1 fs, n0 1.75 (printed 1.9e-21); 11 photons for 9.9 eV at 0.954 eV.

• Note: the source id says 2018 (online 20 Dec 2018); the volume is February 2019. Axis/cut of the sapphire not stated.

• Status: open.

TC-377 silva_2012 (Silva et al., Nat. Commun. 3, 807 (2012)) (2026-09-26)

• Transcribed: YAG inputs at 3.1 um (assumed): n2 7e-16 (refs. 28-30), U_i 6.5 eV, tau_c 3 fs, sigma 2.6e-20 cm2, sigma_17 = 1e-209 s^-1 cm34 W^-17 (a bound). 5 datasets.

• Findings: sigma = 2.6e-20 cm2 is not the Drude value for tau_c = 3 fs at 3.1 um (7.37e-17/n0 cm2: it would need n0 ~ 2800); cheng_2018 derives 2.06e-17 at 2.05 um from the same tau_c (the Drude value for n0 = 1.80). 76 MW is at least 3.5 P_cr for any n0 >= 1 with n2 = 7e-16, not ‘approximately three times’. Lens 75 mm in the text, 50 mm in Fig. 1’s caption. Supplementary Fig. S2 (the ionization rates) not in the library.

• Status: open.

TC-378 cheng_2018 (Cheng et al., Opt. Lett. 43, 4329 (2018)) (2026-09-26)

• Transcribed: measured bulk damage threshold ~175 uJ in 15-cm YAG (3.0 ps, 2.05 um, NA ~0.005; criterion and shots not stated), primary. Inputs (assumed): U_i 6.5 eV (silva_2012; Xu & Ching 1999), sigma_11 1.3e-126 s^-1 (W/cm2)^-11 (from silva_2012, which does not print it), tau_c 3 fs (silva_2012), sigma_IB 2.06e-17 cm2; model breakdown intensity 3e11 W/cm2 (check). 6 datasets.

• Checked: sigma_IB = Drude with n0 = 1.80; rho_c 2.65e20 (printed 2.6e20); 11 photons.

• Vocabulary gap: rho_0 = 7e22 cm^-3 ‘background neutral density’ not recorded: the counts (atoms or formula units) is not stated.

• Status: open.

TC-379 Reproduction graph (who takes what from whom) (2026-09-26)

• Band gap of silica, 9 eV: stuart_1996 (assumed, uncited) -> couairon_2005 (cites stuart_1996 among six), hamam_2018, gulley_2012 (via Winkler 2006), jing_2012, rethfeld_2004, mao_2004. 7.8 eV: berge_2010 (uncited), Liu 1978/1979, Nathan 1985 (in couairon_2005). 7.6 eV: tzortzakis_2001 (Tohmon 1989). 7.5 eV: schaffer_2001. 7.1 eV: Joglekar 2003 (in couairon_2005).

• Reduced mass: 0.64 m_e couairon_2005 (Fischetti 1985) -> jing_2012 (reproduced); 0.635 berge_2010 (uncited), jing_2012 (Sudrie 2002); m/2 hamam_2018 (Liu 2005), gulley_2012; m_e stuart_1996, rethfeld_2004.

• Trapping/recombination 150 fs: Audebert 1994 -> tzortzakis_2001 -> hamam_2018 (also Audebert); couairon_2005 (own measurement and Audebert); berge_2010 (uncited); gulley_2012 (Winkler 2006, Wu 2005); mao_2004 (Martin 1997). 100 fs jing_2012 (Li 1999). 100 ps sapphire jukna_2018 (Guizard 1995). 3 ps bourgeade_2012 (KDP etc.).

• Raman response: couairon_2005 (Junnarkar 2001; stolen_1989): f_R 0.18, 32/12 fs; gulley_2012 (Winkler 2006): 0.18, 32/12.2 fs (roles swapped); berge_2010 (Agrawal, Zozulya): g 0.15/0.18, tau_R 50/32 fs, 1/omega_R 11.9/12.3 fs.

• k’’ = 361 fs2/cm: couairon_2005 (computed from Malitson’s Sellmeier, rounded) = tzortzakis_2001 = gulley_2012 (unit misprinted).

• n2 of silica: 3.54e-16 couairon_2005 (measured); 3.75e-16 Boyd (in couairon_2005); 3.2e-16 tzortzakis_2001 (uncited), hamam_2018 (Agrawal; Skupin & Berge); 2.48e-16 gulley_2012 (Winkler); 3.6/2.2e-16 berge_2010 (Agrawal, milam_1998).

• sigma_K: sigma_4 2e-114 NaCl (Jones 1989) -> stuart_1996; sigma_6 Lenzner 1998 -> schaffer_2001, couairon_2005, jing_2012 (~1e7 inconsistency between Couairon and the other two); Li 1999 -> couairon_2005, jing_2012 (same factor); Keldysh-limit sigma_6: couairon_2005 (9.6e-70 per atom) ~ jing_2012 (2.2e-47 per volume); sigma_5 1.3e-55 tzortzakis_2001 (uncited); sigma_11 cheng_2018 <- silva_2012 (not printed there).

• Avalanche: stuart_1996 alpha -> jing_2012 (0.01), schaffer_2001 (compared); sigma: tzortzakis_2001 <- Mlejnek 1998 (air); berge_2010 (tau_c 23.1 fs implied); cheng_2018 <- silva_2012 (tau_c 3 fs; inconsistent sigma, TC-377).

• Damage: hamam_2018 <- Liu 2005 (all of Tables 1-2); couairon_2005 <- Sudrie 1999 (type I/II); jing_2012 <- Lenzner, Tien, Starke, Li, Jia; mao_2004 Fig. 7 <- Tien 1999.

• Sellmeier: couairon_2005 <- malitson_1965 (rounded).

• Status: open.

TC-380 Format gaps met (reported, not changed) (2026-09-26)

• No quantity for: the Keldysh parameter; the laser power at threshold (hamam_2018 P); a phonon energy (stuart_1996 U_phon); a heavy-particle mass (hamam_2018 M); the electron-phonon coupling constant; a plasma lifetime range; the supercontinuum threshold energy; an electron density at breakdown (n_cr criteria).

• A misprinted unit (berge_2010 k’’’, gulley_2012 k_2) has no erratum mechanism; the interpretation is in the dataset notes.

• band_gap.kind has no value for a literature gap of unstated kind: “not stated” used (couairon_2005 7.8/7.1 eV, mao_2004 NaI/LiF).

• atom_density.counts cannot say “neutrals” (cheng_2018 not recorded).

• effective_mass.carrier “not stated” used for jing_2012’s literature list.

• An uncertainty in the exponent (Lenzner’s 3 x 10^(-67 +- 0.9)) cannot be a sigma.

• ionization_yield used for a Keldysh electron density (TC-365): confirm.

• Status: open.

TC-381 Gate (2026-09-26)

• uv run poe check: ruff, basedpyright, numpydoc, codespell and pytest (6657 passed) pass; sphinx-build fails on two warnings that are not from this branch: “py:class reference target not found: optmat.materials.Kind / .Optics” (the type Kind = Literal[...] aliases of src/optmat/materials.py, unchanged since 695db63; this branch touches no Python module or doc page). poe test-library: 187 passed.

• codespell flags the fourth author’s name of Fischetti et al. 1985; the citation in couairon_2005 is shortened to “et al.” rather than editing the ignore list.

• Status: open.

TC-382 hollenbeck_2002 (2026-09-26)

• Where: Table 1 (p. 2889), the 13-mode intermediate-broadening model of the silica-fibre Raman response, Eq. (9); footnote a.

• Transcribed: hollenbeck_2002/modes (raman_mode, 13 rows, label abscissa = mode number): value = “Peak Intensity A_i”; columns shift (component position, cm-1), gaussian_width, lorentzian_width (the columns headed “Gaussian FWHM”, “Lorentzian FWHM”, cm-1); parameters.width = "fwhm" as printed. Script tools/extract/hollenbeck_2002.py. Also inline: f_R = 0.18 (p. 2887, uncited, check/assumed) and Blow & Wood’s tau1 = 12.2 fs, tau2 = 32 fs (reproduced).

• Checked: every cell against the table image (all agree; the header’s “cm21” is the extraction’s reading of cm^-1). Eq. (9) with the footnote conversions (Gamma_i = pi c x Gaussian column, gamma_i = pi c x Lorentzian column, omega_v,i = 2 pi c x position, A_i = A_i’/omega_v,i) gives a response with its first maximum at 16 fs, near-total decay by 350-450 fs and a recurrence at 490-560 fs, and a gain (sine transform) peaking at 448 cm^-1; the paper states the features “initial sharp peak, phase reversal around 160 fs, recurrence around 500 fs” and the measured peak is ~440 cm^-1. Qualitative only (figures not digitised).

• Doubt 1 (width definition): with Eq. (9), exp(-Gamma^2 t^2/4) transforms to exp(-omega^2/Gamma^2), whose FWHM is 2 sqrt(ln 2) Gamma, i.e. sqrt(ln 2) = 0.833 times the “Gaussian FWHM” column in cm^-1. The column is the full width at 1/e, not the FWHM, by the paper’s own footnote. The Lorentzian column is a true FWHM. A model must use Gamma_i = pi c x column. Recorded in notes; width = "fwhm" kept as labelled. Still to be decided: whether the vocabulary wants a third width kind (“1/e full width”).

• Doubt 2 (mode 2): “We chose the ratio … Gamma_i/gamma_i to be 3” (p. 2890): 12 modes give 3.000 +- 0.001, mode 2 gives 110.42/38.81 = 2.845 (3 x 36.81 = 110.43). 38.81 may be a misprint of 36.81; no erratum made (the paper does not say every mode is exactly 3).

• Status: open (the two doubts).

TC-383 stolen_1989 (2026-09-26)

• Where: text, pp. 1159-1164.

• Transcribed: alpha = 0.18 (raman_fraction, primary; alpha = N_2R/N_20, the fraction of the long-pulse n2 from the delayed response, f normalised to unit integral, parallel linear polarizations; pp. 1161-1162); alpha_simulation = 0.40 and tau_simulation = 391 fs (artificial simulation inputs, check/assumed); tau_exponential = 76 fs (exponential response matched to the gain peak, check); n2 = 3.2e-16 cm2/W (uncited model input, check/assumed; 1.1e-13 esu with factor (4 pi/nc) 1e7 in notes: consistent to 1 % with n = 1.45). Formula Eq. (10), the low-frequency gain fit g = a Omega + b Omega^3, a = 7.67e-4, b = 1.33e-6 (Omega in cm^-1, < 25 cm^-1).

• Doubt: Eq. (10) prints the unit cm/W while the text says the spectrum is normalised to unity at 440 cm^-1 (so the formula is in normalised units: 0.040 at 25 cm^-1). Recorded as printed.

• Not extracted: the response function and gain spectrum (Figs. 1-3, figures only).

• Status: verified (2026-09-26) except the Eq. (10) unit.

TC-384 lin_2006, lin_2007: vocabulary gaps (2026-09-26)

• lin_2006 transcribed: f_R = 0.245 (primary; set with n2 = 2.6e-20 m2/W to the peak gain 1.2e-11 cm/W at 795.5 nm); “about 0.2” (reproduced from stolen_1989 and Blow & Wood); tau1 = 12.2 fs, tau2 = 32 fs (reproduced, Blow & Wood); tau_b = 96 fs (primary); n2 = 2.6e-20 m2/W (check/assumed, from Agrawal’s book). Formula Eqs. (2)-(4) with f_a = 0.75, f_b = 0.21, f_c = 0.04 as coefficients (f_a + f_b + f_c = 1 checked; h_a and h_b integrate to 1). f_b was garbled in the extraction (“0.\bar{2}1”): read from the PDF text layer as 0.21.

• lin_2007 transcribed (Si): E_g = 1.12 eV (check); n0 = 3.48 at 1.55 um (check); beta_T = 0.5 cm/GW near 1550 nm (check/assumed); Raman FWHM 105 GHz (reproduced, Temple & Hathaway); tau1 = 10 fs, tau2 = 3 ps (check, derived); effective carrier lifetimes 1 ns (typical, assumed), 25 ns (reproduced, Rong 2004), 100 -> 1.9 ns (reproduced, Liu & Tsang 2006). Formulas Eqs. (18), (19) (Soref & Bennett free-carrier index and absorption at 1550 nm); the paper’s sigma_a = 1.45e-17 cm2 and zeta = -5.3e-21 cm3 and the hole/electron ratios 3.8, 6.1 reproduced from them.

• Gaps (not extracted, in notes): no quantity for a Raman gain coefficient g_R (Lin 2006: 1.2e-11 cm/W at 795.5 nm, 1.81e-11 cm/W at 526 nm; Lin 2007: 4.3-76 cm/GW for Si); no quantity for the partial fractions f_a, f_b, f_c of a multi-part Raman response (kept as formula coefficients); raman_shift takes only cm-1, so Si’s 15.6 THz (printed in THz) is in notes; no quantity for the nonlinear anisotropy rho (1.27) or a zero-dispersion wavelength. The carrier “lifetime” of an SOI waveguide (recombination + diffusion + drift) is recorded as electron_trapping_time, a waveguide property, not bulk silicon’s.

• Status: open (vocabulary decisions for review).

TC-385 henke_1993: the SiO2 and Al2O3 mirror reflectivities (2026-09-26)

• Where: Table III, p. 309 (Al2O3, rho = 3.96 g/cm3, tbl_8ba35ae7a438) and p. 310 (“Quartz (SiO2)”, rho = 2.20 g/cm3, tbl_54a15c06ece9); both JSON only. P(%) = 100 I/I0 for unpolarized light, Eqs. (54)-(57) p. 193, 10 grazing angles (5-400 mrad) x 35 line energies (72.4-29 779 eV) = 350 values each.

• Transcribed: nothing into data files: the vocabulary has no reflectance quantity. The existing henke_1993 record’s notes now describe the tables, the compound relation (Eq. (3) p. 184, Eqs. (17)-(18) p. 187: delta, beta = (r0 lambda^2/2pi) sum_q n_q f_1q, f_2q; mu_l = 4 pi beta/lambda, Eq. (44) p. 192) and the check. The record was edited (notes only), not created.

• Checked: the extracted cells against both images (agree). Reproduction: with the atoms’ f1, f2 from Table I (Si p. 226, O p. 220, Al p. 225), n_q from the densities and stoichiometry, and Eqs. (54)-(57), all 50 values per material at C, Al, Ti, Cu, Mo K-alpha are reproduced to 0.3 % (1.1 % at C K-alpha 125-400 mrad, where f1, f2 have 3-4 digits). So the compound rule and the densities are as stated.

• Doubt: the SiO2 table is labelled “Quartz” but uses 2.20 g/cm3 (fused silica; quartz is 2.65), so it belongs to SiO2, not SiO2_quartz.

• Decision for review: add a reflectance quantity (grazing angle and polarization as parameters, unit percent) if these 700 values are wanted; the extraction is then a short script over the two JSON tables.

• Status: open (vocabulary).

TC-386 dubietis_2019 (2026-09-26)

• Where: Tables 4.1 (p. 50), 4.2 (p. 52), 5.1 (p. 67), 5.2 (p. 82); text pp. 18, 50-52, 74, 86. Book pages are the running heads (PDF page = book page + 5 to 7).

• Transcribed (68 one-point datasets; tools/extract/dubietis_2019.py writes the 59 table values): Table 4.1 band gap, n2 (x1e-16 cm2/W, “given for lambda = 800 nm”) and n0 (800 nm) of LiF, CaF2, Al2O3, BaF2, SiO2, KDP, YAG, BBO, BK7, KGW, YVO4 (33; water skipped); Table 4.2 single-shot surface damage fluence at 1030 nm, 500 fs, for YAG, Al2O3, SiO2, CaF2, LiF, BaF2 (6); Table 5.1 band gap and n2 of SiO2, ZBLAN, BK7, La glass, Te glass, As2S3 (12); Table 5.2 of ZnS, ZnSe, GaAs, Si (8). Text (inline): PbF2 U_g 5 eV and n2 11.7e-16; diamond 5.47 eV; calcite 5.9 eV; KRS-5/KRS-6 2.5/3.25 eV and n2 10.5e-15/5.4e-15 cm2/W; sapphire P_cr ~ 3.3 MW. Formula: Eq. (4.1) damage scaling (Mero et al. 2005).

• Use: Table 4.1 reproduced (Dubietis et al., Lith. J. Phys. 57, 113 (2017)); Table 4.2 reproduced (Gallais & Commandre 2014); Table 5.1’s SiO2/BK7 rows reproduced (identical to Table 4.1); the other Table 5.1/5.2 rows check (no source cited); text values reproduced from the cited paper, diamond check (no citation on the value).

• Checked: all four tables cell by cell against the images (agree); KRS-6’s n2 garbled in the library text, read from the PDF text layer. Eq. (4.1) at 500 fs with Table 4.1’s gaps gives 3.26 (SiO2), 3.69 (Al2O3), 2.07 (YAG), 3.74 (CaF2), 5.46 (LiF), 3.31 (BaF2) J/cm2 against Table 4.2’s 4.85, 5.36, 7.5, 5.17, 4.43, 2.91: the oxide-film law does not reproduce these bulk values (ratios 0.28-1.23), as expected.

• Not expressible (notes only): transmission ranges and zero-GVD wavelengths (no quantity); Fig. 4.1 critical powers (figure). Band-gap kind is not defined by the book (recorded optical). The anisotropic crystals have no axis stated. “BK7” as printed (BK7 or N-BK7 not said).

• codespell: “Opt. Mater.” in single-line citations carries # codespell:ignore mater; in multi-line notes the journal is written out.

• Status: verified (2026-09-26).

TC-387 The universal dispersion model: equation map and the newAD2 mismatch (2026-09-26)

• Equation map (summary; the full maps with pages are in each record’s notes).

  • Sum rule and constants: franta_2013 Eqs. (22)-(27), (42)-(51) (M = 4.61706e26 eV^-2 m^-3, R = 0.766681, N = N_a U sum Z_n f_n); every term normalised to unit strength: franta_2013 Eqs. (52)-(55), franta_2015b Eq. (3), franta_2015 Eq. (4).

  • Assembly: franta_2015b Eq. (1) = franta_2015 Eq. (2): eps = 1 + N_vc eps0_vc + N_vx eps0_vx + N_ut eps0_ut + sum N_loc eps0_loc + sum N_ph eps0_ph.

  • IBT (vc0): franta_2015b Eqs. (4)-(12) (J = (E - Eg)^2 (Eh - E)^2 box, C_N, analytic real part) = franta_2015 Eqs. (6)-(14) = franta_2013 Eqs. (56)-(58).

  • Excitons (Lorentz-modified IBT): franta_2015b Eqs. (13)-(25) (complete analytic C_N and real part); combination franta_2015b Eqs. (26)-(27) (amplitude-weighted average of unit-strength terms); franta_2015 Eq. (16) instead writes one JDOS with [A0 + sum A/((E - Ec)^2 + Bc^2)] and one C_N (different spectra for the same A’s).

  • HET (vx): franta_2015b Eqs. (28)-(31) (E_xi = E_x + E_g/2) = franta_2015 Eq. (17) = franta_2013 Eq. (84).

  • Urbach tail: franta_2015b Eqs. (32)-(40) (four-piece JDOS, E_m = (E_g + E_h)/2, real part with the scaled exponential integral) = franta_2015 Eqs. (18)-(19).

  • Localised states and phonons: franta_2015b Eqs. (41)-(47) (Gaussian eps-broadened lines, Dawson real part; phonons with E_p = hc nu, B_p = hc beta/(2 sqrt(2 ln 2)), beta the FWHM in cm^-1) = franta_2013 Eq. (89); kernel franta_2014 Eqs. (13), (37), (40).

  • Broadening rules: franta_2014 (eps-broadening for interband and phonon bands, F-broadening for intraband).

  • Crystalline extensions (ADM, not UDM): two-phonon bands franta_2014b Eqs. (14)-(32); temperature-dependent c-Si franta_2017 Eqs. (4)-(56); direct transitions with critical-point singularities and Wannier excitons franta_2013 Eqs. (63)-(77), franta_2017 Eqs. (20)-(51).

  • Newer forms (not printed in any library paper): franta_2025 uses “Tauc’s law combined with the Lorentz model” with an extra E_q parameter (TSF 631, 12 (2017); Springer chapter 2018; its Supplement 1); franta_2017 the Campi-Coriasso Tauc-Lorentz form for vx (its Eq. (52)).

• Checked (scratch, 30-50 digits): every printed 2015 normalisation constant equals the numerical integral (vc0, ex, ut, to 25 digits); every unit term integrates to 1; every printed real part equals the numerical KK transform of its imaginary part (to 1e-22 or better at 0.05, 3, 7.5, 25 eV). The 2015 formulas are self-consistent.

• Finding: the published formulas do not reproduce the newAD2 tables from the matching parameter files (the SPIE 9628 set in data/external/newad2): the phonon-region k agrees to 0.1-1 %, but n in the transparent region is high by 0.003 (MgF2), 0.006 (Al2O3), 0.013 (SiO2), and the Urbach-region k is 2.5-2.6 times the table’s (Al2O3 at 6.31 eV: 0.0156 against 0.00619). The franta_2015 Eq. (16) exciton convention is worse (0.02-0.06 in n). newAD2 evidently implements a later interband/Urbach form. The vc and ut terms should be implemented against udm.cxx or the 2018 chapter, not the 2015 papers alone; the Gaussian terms are confirmed.

• Doubts in franta_2015 (hafnia): Table 2 marks A_0 (0 +- 2), E_h (20 +- 3) and E_x (12 +- 2) “(fixed)” yet prints standard deviations; the text says only A_ex,1 was fixed. Eq. (36)’s 5.587 needs N_ut = 6.53 (Table 3 prints 7 +- 2): the chain used unrounded values. Which exciton convention Table 2’s A’s belong to is not stated.

• Status: corrected (2026-09-26): the mismatch is the Urbach tail’s upper energy; the program’s reading reproduces newAD2’s tables (TC-321, TC-392).

TC-388 franta_2014b and franta_2017: c-Si parameters, oddities, refractiveindex.info (2026-09-26)

• franta_2014b (formulas): Table 2 phonon frequencies (17, plus nu_T = -3.4e-5 K^-1 and nu_iso = 0.9982) and Table 5 (15 two-phonon terms: alpha, beta, C, A0-A9, kappa0-kappa5; daggers = fixed), generated from the library JSON by a scratch script and compared with the images. Tables 3-4 (critical points) are derived: their THz sums reproduce Table 2; the cm^-1 columns are the THz values truncated (28.18 THz = 939.98 cm^-1, printed 939.9).

• franta_2017: band gap 1.14 eV (0 K) and 1.087 eV (300 K) (datasets, script over the JSON table); formulas: Eq. (3), the Frey-fit n(T) at 2 um (n0 = 3.42477, Omega1 = 0.01992, Theta1 = 210.72 K, Omega2 = 0.0737318, Theta2 = 636.501 K; 3.45351 at 295 K), Table 2 critical points (row names from the image: the JSON loses the primes), Table 3 paths, Table 4 phonon frequencies (degenerate values printed once), Theta_ph, the carbon line.

• Oddities as printed: E_0^Gamma rises 4.068 -> 4.149 eV from 0 to 300 K while all other points fall; at K, TO2 < TO1 at 0 K (14.18 < 14.31) but TO2 > TO1 at 300 K (14.87 > 13.89); TA1(K) 5.31 -> 4.82 THz.

• Cannot implement from the paper: the path amplitudes A_0..A_11, the indirect-term shapes, the vx parameters, the core terms and the phonon amplitudes are not printed.

• refractiveindex.info: main/Si/nk/Franta-300K.yml (from this paper, “numerical data kindly provided”, procedures updated in J. Appl. Phys. 123, 185707 (2018)) is not the same model as newAD2’s c-Si.Enk (unpublished UDM): c-Si.Enk’s n is higher by 0.013-0.018 at 0.02-1.1 eV and 0.021-0.026 at 1.2-1.5 eV; its k near the gap is 2.4-2.6 times the page’s (1.5-2 eV). No other source of TC-382 to TC-389 has a refractiveindex.info page (Hollenbeck, Stolen, Lin, Dubietis, Henke: none).

• Status: open (report).

TC-389 franta_2013, franta_2014, franta_2015, franta_2015b, franta_2025: records (2026-09-26)

• franta_2013: atomic densities of Table 1 (6 materials: Si, diamond, graphite, SiO2, a-Si:H, a-C:H) via tools/extract/franta_2013.py, with a structural fix: the cells lost the superscripts (4.994, times sign, “1028” for 4.994e28), restored as the image shows. The four handbook-density rows are check, the two optically fitted films primary. Checked: M and R from CODATA; the densities, N_a and electron densities follow from the mass densities to the printed digits (two last-digit rounding differences). Electron densities (all electrons) not extracted (no quantity).

• franta_2014: theory only; a text slip below Eq. (34) (“intraband” for “interband”).

• franta_2015 (hafnia): band gap 5.311 +- 0.004 eV (dataset, script); Tables 2-4 as one formula with *_sigma keys; checks of N, N_ve, n_lambda, x in the notes (TC-387).

• franta_2015b (SPIE 9628): 12 datasets from the newAD2 .Enk files (n and k of SiO2 X2551, MgF2 X2935, amorphous Al2O3 X2890): within the fitted range primary (3699, 3699, 3034 rows each), beyond it excluded (302, 302, 967 rows); three formulas naming the .par files (the paper prints no parameters). The same X2551 film is refitted in franta_2016 with the SPIE 9890 parameters.

• franta_2025 (Ta2O5): band gap 4.1099(7) eV and n = 2.125 at 2 eV (HL model); Nb2O5 3.48 eV and 2.331 at 2 eV reproduced from the group’s 2024 paper; the profile-function parameters as a formula. The dispersion parameters and equations are only in Supplement 1 (not in the library).

• Status: verified (2026-09-26).

TC-390 Materials registered for the records of TC-382 to TC-389 (2026-09-26)

• ZBLAN, La_glass, Te_glass, As2S3 (glasses, dubietis_2019); PbF2, C_diamond, KRS-5, KRS-6 (crystals, dubietis_2019); C_graphite (uniaxial), a-Si_H, a-C_H (franta_2013); HfO2, Ta2O5, Nb2O5, TiO2, Al2O3_amorphous (films, kind glass).

• Doubts for review: the film oxides are registered as kind glass (amorphous or fine-grained polycrystalline films), leaving the crystalline polymorphs to separate ids, by analogy with SiO2 / SiO2_quartz; the amorphous alumina of franta_2015b is Al2O3_amorphous because Al2O3 is sapphire. MgF2’s polycrystalline film (franta_2015b) is under MgF2 with no axis. Other extractions may register the same materials (ZBLAN, As2S3, TiO2, HfO2, Ta2O5): merge by id.

• Status: open (the kinds and ids to be confirmed in review).

TC-391 Reproduction graph of TC-382 to TC-389 (2026-09-26)

• hollenbeck_2002/blow_wood_times, lin_2006/blow_wood_times <- Blow & Wood, IEEE J. Quantum Electron. 25, 2665 (1989) (not in the library).

• lin_2006/f_R_literature <- stolen_1989 and Blow & Wood 1989. hollenbeck_2002/f_R (check) equals stolen_1989’s alpha, uncited.

• lin_2006/n2 (check) <- Agrawal, Nonlinear Fiber Optics (2001).

• lin_2007: raman_linewidth <- Temple & Hathaway 1973; carrier_lifetime_rong <- Rong et al. 2004; carrier_lifetime_implanted <- Liu & Tsang 2006; formulas <- Soref & Bennett 1987.

• dubietis_2019: t4_1_* <- Dubietis et al., Lith. J. Phys. 57, 113 (2017); t4_2_damage_* <- Gallais & Commandre, Appl. Opt. 53, A186 (2014); t5_1 SiO2/BK7 <- the same 2017 review (duplicates of Table 4.1); text_PbF2 <- Yang et al. 2019; text_KRS-5/6 <- Marcinkeviciute et al. 2018; text_gap_calcite <- Kartazaev & Alfano 2007; text_pcr_sapphire <- Siaulys et al. 2015; formula damage_scaling <- Mero et al. 2005.

• franta_2025: *_Nb2O5 <- Franta et al., Opt. Materials 157, 116133 (2024).

• franta_2015b datasets: from the authors’ newAD2 files (SPIE 9628 set).

• No value of TC-382 to TC-389 reproduces a source id curated in a parallel extraction.

• Status: open (2026-09-26): transcribed and checked at extraction; a second curator has reviewed the record, and the doubts above await review.

TC-392 The review of the solid-state extraction (TC-325 to TC-391) (2026-09-26)

• Where: TC-325 to TC-391 (five parallel extractions); the merged records.

• Merged: 66 new source records and 6 edited ones.

  • The extraction reproduces every file (poe test-library: 214 scripts).

  • The registry holds 128 materials. The duplicates between the extractions were resolved: PbF2, KRS-5, KRS-6 and Ta2O5 are kept once. TiO2 is one extraction’s crystal; another’s TiO2 films carry no dataset yet.

• TC-387 (the UDM “does not reproduce newAD2’s tables”) is superseded.

  • The difference is the Urbach tail’s upper energy. The authors’ program ends it at E_h, not at Eq. (33)’s E_m.

  • With the program’s reading the implementation reproduces all seven tables to their last digit above 1 eV (TC-321).

  • The two 2015 papers’ exciton forms differ, as noted at extraction. The parameter files follow SPIE 9628’s Eqs. (26)-(27), which is what optmat.solid.udm implements.

• Accepted conventions:

  • Per-cell powers of ten are stored in e-notation.

  • Bounds are kept and excluded.

  • Literature columns are split per reference.

  • Films of oxides without a crystal phase (HfO2, Ta2O5, Nb2O5, Al2O3_amorphous) are registered as kind glass.

• Band-gap kinds and carriers: the extractions used not stated and effective (Brimacombe’s Keldysh-fitted gap). They are accepted as documented values: the quantities’ meanings now list them.

• Open, for review:

  • Schaffer 2001, Table 2: the Keldysh photon order N is recorded as ionization_yield against I_th. That quantity means an ion yield, so these datasets need a quantity of their own (a multiphoton order) before any model uses them.

  • BK7 or N-BK7: Flom and Ensley name “BK7” without saying which (recorded as BK7).

  • The Yb:KGW n2 page of refractiveindex.info (TC-320).

  • Units misprinted in a paper (Berge’s third-order dispersion in fs^2/cm, Gulley’s k_2): there is no erratum mechanism for a unit. They are explained in the dataset notes.

  • The format gaps listed at extraction: reflectance, Raman gain, the transmission range, the zero-dispersion wavelength, mass density, group index, the Urbach energy, the Abbe number, the Keldysh parameter, and an uncertainty in an exponent. None is needed by the models built so far.

• Status: decided (2026-09-26) where stated; open: the list above.

TC-393 The Kerr response of fused silica: n2(lambda) and the Raman fraction (2026-09-26)

• Where: optmat.solid.kerr; data/solid/kerr/SiO2.toml and .json; tools/fit/kerr_solid.py; tests/solid/test_kerr.py.

• Model: n2_meas(lambda, tau) = n2(lambda) [(1 - f_R) + f_R eta(tau)].

  • n2(lambda): the long-pulse index, N (1 + a E^2) with E the photon energy in eV.

  • f_R: its Raman fraction.

  • eta(tau): the share of the Raman response a Gaussian pulse’s index sees, computed exactly in the frequency domain from Hollenbeck & Cantrell’s 13-mode response (hollenbeck_2002, Eq. 9).

  • The response is normalised to unit integral; the paper does not state its normalisation.

  • Checks: the response’s first maximum is at 16.3 fs, as found at extraction from the paper (TC-325 onwards). eta agrees with the direct double integral to 1e-4. It is 0.96 at 100 fs and 0.86 at 47 fs. It exceeds 1 slightly near 500 fs, as the real part of a Raman susceptibility below its resonance does.

• Data:

  • Fitted: every measured self coefficient of the curated sources:

    • desalvo_1996 (ps) and adair_1989 (ns, esu, converted with I = c n0 <E^2>/(4 pi) and n0 from the recommended model);

    • white_1984, flom_2015, ensley_2019, jansonas_2022, kabacinski_2019, van_der_linden_2025 and patwardhan_2021 (75 fs taken from its text);

    • santran_2004: ten grades, electronic only by the paper’s argument, relative uncertainty 0.10 from its Table 1.

    • Each source has a calibration scale with a 10 % prior.

  • Validators: Milam’s recommended values (an assessment of originals fitted here), DeSalvo’s 266 nm value (above the two-photon edge) and Couairon’s n2 from a critical power.

• Decisions:

  • The range is 350 nm-3.5 um (two-photon energy below the 8.4 eV gap).

  • f_R has a prior of 0.18 +- 0.03: Stolen et al. 1989, with Lin & Agrawal’s 0.245 at about two sigma.

  • Only the E^2 term: with an E^4 term free (chi-squared 35.1 for 33 dof) the curve reaches a maximum near 420 nm and falls towards the edge. The near-UV scatter allows that, physics does not, and the E^2 fit is as good (36.9 for 34).

  • Nanosecond electrostriction is not modelled.

• Result:

  • N = 2.357e-20 m^2/W +- 4.6 %, a = 0.0247 +- 0.0074 eV^-2, f_R = 0.151 +- 0.030 (the prior dominates).

  • n2 = 2.92, 2.67, 2.50, 2.44, 2.39 and 2.38 e-20 m^2/W at 400, 532, 800, 1030, 1550 and 2000 nm, each +- 1.1-1.7e-21 (one sigma, the scales’ spread included through the Birge-scaled covariance).

  • The electronic part is 0.85 of these; a 50 fs pulse measures about 0.98 of them.

• Findings:

  • Santran et al.’s calibration comes out 1.32 times the consensus. Their stated absolute accuracy is 10-28 %. Their Eq. (15) uses 80 pi where DeSalvo and White use 40 pi (noted at extraction), which would be a factor of 2, not 1.32. Open.

  • Milam’s recommended values are 12 % (1053 nm) and 12-17 % (527, 351 nm) above the fit. Milam’s assessment rests largely on nanosecond measurements. Electrostriction, which adds to n2 for such pulses, would explain a difference of this size; this is not shown here.

  • Couairon’s n2 from a measured critical power is 1.42 times the fit (a model-dependent inversion).

  • The other sources’ scales lie within 0.89-1.04.

• Status: decided (2026-09-26); open: Santran’s calibration factor, and the electrostrictive part of nanosecond data.

TC-394 J. C. Travers’s decisions on the silica work (2026-09-26)

• The recommended silica model stays Franta et al.’s universal dispersion model of Lithosil Q2 (TC-324). The question whether it should follow Malitson’s refractometry is closed.

• Malitson’s reference medium (air or vacuum, TC-323) stays open. J. C. Travers will look for Rodney & Spindler (1954) in the next batch of papers.

• The newAD2 files’ licence (TC-320) is logged as a to-do (resolved in TC-727): the authors are to be asked before a public release.

• The open items of TC-392 are accepted as recorded, to be revisited when their data are modelled: Schaffer’s photon orders, BK7 against N-BK7, Santran’s calibration factor and the format gaps.

• Status: decided (2026-09-26).

TC-395 Luna’s fused-silica index and n2 (2026-09-26)

• Where: Luna (a checkout at commit de9db7c): src/PhysData.jl (ref_index_fun, lookup_glass, n2_glass) and src/data/lookup_tables.jl (data_glass(:SiO2)); compared with franta_2016/udm_lithosil_q2 (TC-324) and kerr/SiO2 (TC-393). Found by a review agent, checked by running Luna.

• The index is Philipp’s table, splined. For SiO2 Luna uses a lookup table by default (lookup = (material == :SiO2)): 400 rows of E, n, k from 2000 eV to 0.062 eV (20 um), with no citation, interpolated by a cubic B-spline in wavelength.

  • The table is Palik’s. Each of the 400 rows matches a row of philipp_1985 to 0.1 % in n.

  • It mixes in another glass: 44 rows are Rife & Osantowski’s glass with 7.5 % TiO2 (SiO2-TiO2, TC-325).

  • Its k is zero below 7.8 eV (all 149 rows), although Philipp tabulates k at 68 of those energies. So the reststrahlen bands are lossless, with n down to 0.35-0.47 near 8.4-8.9 um. Luna returns k of order 1e-51 at 5 um and 1e-72 at 9.2 um, where the recommended model gives 0.0048 and 2.66.

• The dispersion is the spline’s. Luna’s GVD (PhysData.dispersion(2, :SiO2, λ)) against the recommended model, in fs^2/mm:

  lambda (nm)	Luna (table)	Luna (lookup=false, Malitson)	optmat
  532	72.64	65.78	65.13
  800	38.64	36.16	35.76
  1030	20.14	18.97	18.70
  1300	8.27	-2.37	-2.73
  1550	-39.10	-27.95	-27.89

  • The table’s GVD is off by 8-40 %, and at 1300 nm it has the wrong sign.

  • By the review agent’s reconstruction of the same spline, its zero-dispersion wavelength is not unique: the GVD changes sign at 1126, 1171, 1368, 1448 and 1503 nm. The recommended model’s single zero is at 1270 nm. Only the values in the table above were checked by running Luna.

  • Luna’s Sellmeier option is Malitson’s (TC-323), which agrees with the recommended model in the window. Below 125 nm it has the pole that solprop’s default shares (docs/silica.md).

• n2: n2_glass(:SiO2) is 2.7e-20 m^2/W at every wavelength, with no citation.

  • It is 8 % above kerr/SiO2 at 800 nm, 11 % at 1030 nm and 13 % at 1550 nm. It is close to Milam’s recommended 2.74e-20 (TC-393).

  • The Raman fraction Luna’s fibre interface uses by default (prop_gnlse, fr = 0.18) is within one sigma of the fit’s 0.15 +- 0.03.

• Status: verified (2026-09-26). Nothing is changed in Luna.

TC-396 Luna’s gas data: errors not yet in the register (2026-09-26)

• Where: Luna (a checkout at commit de9db7c), src/PhysData.jl. Found by a review agent from the Luna source, a survey of the nonlinear literature and solprop’s list of Luna errors (LB-054); checked by running Luna. The gases’ other differences from Luna are in TC-5, TC-6, TC-100 and TC-313 to TC-315.

• CH4, SF6 and N2O: the index is n, not n - 1 (LB-054).

  • γ_QuanfuHe (line 138) returns (1 + 1e-8 (A + B/(C - σ^2)))/ρ: the refractive index over the density, where the polarisability needs (n^2 - 1)/ρ.

  • So Luna gives n = 1.40362 (CH4), 1.40355 (SF6) and 1.40362 (N2O) at 800 nm and 1 bar, where n - 1 is of order 4e-4 to 8e-4. The susceptibility is wrong by a factor of about a thousand and nearly without dispersion.

  • The knock-on errors in the nonlinear coefficients:

    • N2O: γ3_gas(:N2O) converts Wahlstrand’s n2 with this n0. It is 4.45 times Luna’s N2 value, where solprop’s (2061.7 au against 917.58 au) is 2.25 times: 1.98 times too large.

    • CH4 and SF6: n2 divides by n0^2, so it returns 1.12e-23 and 5.91e-24 m^2/W at 800 nm and 1 bar. Shelton’s ratios times Luna’s own N2 value (7.52e-24) give 2.20e-23 and 1.15e-23: both are halved.

    • Their γ3_gas values, which the propagation uses, are not affected.

  • solprop’s LB-054 names CH4 and N2O. The survey names SF6.

• Helium: Ermolov’s formula read at 1 bar. sellmeier_gas refers Ermolov’s coefficients to dens_1bar_0degC. That is the paper’s stated state, which TC-5 decided is not the fit’s. Luna’s n - 1 at 800 nm, 1 bar and 20 °C is 3.2418e-5, where fit/He gives 3.1932e-5: 1.5 % high. That is the 1.3 % state error plus the Mansfield & Peck level of TC-44.

• D2 is H2: the same Peck formula per molecule (lines 207-215), and γ3_gas(:D2) is H2’s 15.77 times helium’s (line 627). The accuracy page gives the consequence for D2’s GVD.

• One γ3 per gas: γ3_gas takes no wavelength, although its docstring says “at given wavelength(s)”. So it serves SPM, XPM and THG at every wavelength (TC-314, TC-315).

• Docstrings:

  • γ3_gas offers source == :Bishop, which has no branch: the call throws a DomainError.

  • It says “χ3 at 1 bar”; the code uses dens_1atm_0degC.

• Status: verified (2026-09-26). Nothing is changed in Luna.

TC-397 The page of significant corrections, and a count corrected (2026-09-26)

• Where: docs/corrections.md; README.md and docs/index.md.

• The page: it gathers the most significant errors found in the papers, in Luna and solprop, and in refractiveindex.info, with their sizes and their register entries.

  • Its numbers are the register’s and the accuracy pages’.

  • The helium GVD of Börzsönyi’s and Ermolov’s formulas, at 800 nm against fit/He at 1 bar and 20 °C, was recomputed for the page: −5.6 % and −12.5 % (as Luna reads Ermolov, at 1 bar).

• The front pages: the list of errors that opened the manual (“Why this package exists”) is replaced by a pointer to the page. Solids are added to both pages.

• A count corrected: TC-392 says the extraction added 66 source records. The merge added 54 (243 records before, 297 after); the changelog is corrected.

• Status: decided (2026-09-26).

TC-398 A solid’s index relative to room air, and Leviton & Frey’s temperature form (2026-09-26)

• Where: optmat.conditions.air_refractivity; optmat.solid.models.formulas (index_medium, air_temperature_k, air_pressure_pa; the form n2_sellmeier_temperature); the solid dataset parameter index_medium (optmat.datasets, docs/data.md); edlen_1966 (notes).

• Why: refractometry by minimum deviation in room air gives the index relative to that air. Whether an index is absolute or relative to air differs by about 2.7e-4 in n, more than most solid data disagree. The records must say which (TC-323).

• The air: Edlen’s Eq. (12) for dry air (Metrologia 2, 71 (1966), p. 78, checked on the page), which scales the standard-air refractivity by the density factor p [1 + p (0.817 - 0.0133 t) 1e-6] / (720.775 (1 + 0.0036610 t)), t in degrees C and p in torr, 5-30 degrees C.

  • It returns the standard-air formula at 15 degrees C and 760 torr to 4e-7 of n - 1, the rounding of 720.775.

  • Water vapour and CO2 are not included; at room conditions they change n by some 1e-7.

  • A formula relative to air is multiplied by the air’s index at the vacuum wavelength. Its derivative includes the air’s dispersion.

  • An unstated room pressure is taken as 101 325 Pa. A 2 % uncertainty in pressure is 5e-6 in n.

• The temperature form: n^2 - 1 = sum_i S_i(T) lambda^2 / (lambda^2 - lambda_i(T)^2), with S_i and lambda_i polynomials in T, as Leviton & Frey fit Corning 7980.

  • It is evaluated at the entry’s reference_temperature_k.

  • at_temperature gives it at another temperature, and warns outside the stated range.

• Vocabulary: molar_kerr_constant and kerr_virial_coefficient may be tabulated against temperature; kerr_virial_coefficient takes order (2 for B_K, 3 for C_K), for the records of TC-402 to TC-437.

• Status: decided (2026-09-26).

TC-399 Malitson’s index is relative to air; the recommended silica model is refitted (2026-09-26)

• Where: malitson_1965 (formula and datasets: index_medium = "air", 20 degrees C); data/solid/fits/SiO2.toml, data/solid/models/fitted/SiO2.json (fit/SiO2); data/solid/defaults.toml; optmat.solid.fitting (air-relative data, the thermo-optic correction); docs/silica.md; tests/solid/.

• TC-323 is resolved: Malitson’s indices are relative to air.

  • The paper does not say. Rodney & Spindler (1954, same NBS apparatus and methods, per Malitson pp. 1205 and 1209) do not say either. They describe minimum deviation in room air with no reduction to vacuum (rodney_1954).

  • Leviton & Frey (leviton_2008, pp. 3 and 9), who measured in vacuum, call Malitson’s data “in air”. Converted with n_air = 1.00027, they agree with their own indices to “well less than 1e-5”.

  • Rechecked here: Malitson’s formula taken to vacuum through Edlen’s dry air at 20 degrees C and 101 325 Pa (TC-398) differs from Leviton & Frey’s formula at 293.15 K by at most 1.0e-5 from 0.4 to 2.0 um (5e-5 at 2.5 um). Read as absolute, it would be 3.9-4.2e-4 below.

• The consequence for the window. At 800 nm and 20 degrees C:

  	Leviton 2008	Malitson (vacuum)	Arosa 2020	Franta 2016
  n	1.45371	1.45371	1.45337	1.45355
  group index	1.46757	1.46756	1.46727	1.46726
  GVD (fs^2/mm)	36.31	36.23	35.86	35.76

  • Arosa & de la Fuente’s level comes from an Abbe refractometer at 589 nm, which reads relative to air (as the survey of the paper found). Multiplied by the air’s index, their formula is within 5.4e-5 of Leviton’s from 0.4 to 2 um. TC-324’s “Arosa sides with Franta” compared an air-relative dispersion with an absolute one.

  • Franta’s published model is 3.4e-4 below Leviton’s at 400 nm, 1.6e-4 at 800 nm and 0.8e-4 at 2 um. Its GVD is 1.5 % low at 800 nm. Two independent absolute refractometries of the Corning 79x0 grades disagree with it; neither shares its method (ellipsometry, photometry and Schott’s air-referred prism data).

• Decision: the recommended model is fit/SiO2, a refit of Franta’s model. This supersedes TC-324’s choice and J. C. Travers’s confirmation of it (TC-394), which rested on the reference medium being unknown.

  • Fitted:

    • Malitson’s three prisms of Table I, 0.21-3.71 um, taken to vacuum: sigma 1e-5 (his precision; the residuals state none), each prism with its own offset (prior 1e-5, the melt and grade);

    • Leviton & Frey’s 295 K table: taken to 293.15 K with their own dn/dT of Table 6 (8.6e-6 per K at 800 nm), at their stated 1e-5, with a common offset (prior 5e-6);

    • Franta’s measured k at the band edge (146-225 nm) and from 2.3 to 125 um (10 %), and his n from 5 to 125 um (2e-3);

    • Franta’s vacuum-ultraviolet n and k, which he fitted to Palik’s tables, as soft constraints (0.01 and 3 %, 24.8-146 nm).

  • Free: the interband strength Nvc, the higher-energy term (Nvx, Ex), the band edge Eg, the Urbach width Eu, and one factor each on the excitons, the two groups of phonon bands (351-881 and 1068-1351 cm^-1) and the multiphonon bands (1516-3220 cm^-1). Lithosil Q2’s OH band is kept as measured.

  • Tried and set aside:

    • fitting only to 2.6 um, which lets the OH or multiphonon strengths run away beyond the fitted range;

    • a free OH factor, which trades the two sides of the 2.73 um band against each other;

    • an added Gaussian electronic term, which drifts to 22 eV without improving the window;

    • no vacuum-ultraviolet constraint, under which the excitons and the higher-energy term reshape the far ultraviolet unconstrained.

  • Result:

    • Leviton chi2 = 13.8 for 16 points;

    • Malitson 207-223 per prism of 60 points (rms about 1.9e-5, largest +5e-5 at 3.27 um, beyond the OH band);

    • offsets 1.0-3.2e-6 (Malitson) and 2.4e-6 (Leviton);

    • Nvc 358.65, Nvx 689.8, Ex 16.12 eV, Eg 8.3554 eV, Eu 0.18845 eV;

    • factors: excitons 1.59, phonons 1.0006 and 1.0034, multiphonon 1.117.

  • Against Franta’s measurement:

    • k at the band edge to 1.7 % rms;

    • vacuum-ultraviolet n to 0.008 and k to 1.7 % rms;

    • infrared k to 6-9 % rms, n to 2e-3 rms (4.9e-3 at most, on the reststrahlen band).

  • Validators:

    • Malitson’s Table II specimens scatter 0.5-3.4e-5 about the fit;

    • Rodney’s Heraeus B, taken to 20 degrees C with its own dn/dT (relative to air), is 3.6e-5 off on average, within the melt differences Malitson’s Fig. 4 shows;

    • Franta’s published n is 2.9e-4 lower on average in the window.

  • At 800 nm: n = 1.45371, group index 1.46755, GVD 36.20 fs^2/mm (Leviton 36.31, Malitson 36.23). The zero-dispersion wavelength is 1272 nm.

  • Uncertainty stated in the manual (0.21-2.6 um):

    • n to about 2e-5 (residuals and the grade spread);

    • the group index to about 3e-5;

    • GVD to about 0.3 % (the spread of Leviton’s and Malitson’s formulas). The stored covariance is smaller: it does not know the grade spread.

• Luna’s silica (TC-395) was compared with Franta’s model. Against the refit its GVD is 10 % high at 532 nm, 7 % at 800 nm, 6 % at 1030 nm and 40 % at 1550 nm, and at 1300 nm +8.3 against -2.6 fs^2/mm (docs/corrections.md).

• Also changed: the n2 fit (kerr/SiO2) was re-run with the new linear index, which it uses to convert esu values. Its parameters moved in the fifth digit; the printed table is unchanged.

• Status: decided (2026-09-26). TC-323 resolved; TC-324 superseded in its choice of model.

TC-400 Hohm’s dispersion in the molecular and heavy noble-gas fits; the new static and 633 nm checks (2026-09-26)

• Where: data/gas/fits/{Kr,Xe,O2,N2O,CO2,CH4}.toml and their stored fits and robustness records; optmat.gas.fitting (shape_relative); docs/accuracy.md, docs/gas_models.md.

• The original replaces the reprint.

  • hohm_1994’s O2, N2O and CO2 inputs, which the fits used, are digit-identical reprints of hohm_1994b (Mol. Phys. 81, 157), now curated (TC-406, TC-407).

  • The fits take the original.

• How Hohm’s values enter. The printed “(n)” digits are absolute uncertainties of about 1.2e-4 relative. They include the level, and the level is not reliable:

  • Hohm’s 1994 values lie above the fits by 0.04 % (CO2, CH4) to 0.47 % (Xe);

  • his 1990 values of the same gases are 0.12 % (Kr) and 0.29 % (Xe) lower than his 1994 ones.

  His shape is better:

  • his argon, against the ab-initio-backed fit/Ar (1 sigma 10 ppm at 325 nm), departs by +26, -5, -6 and -70 ppm at 612, 594, 544 and 325 nm (TC-406): 4e-5 rms;

  • the 1e-5 relative precision the reprint suggested is too optimistic, as TC-178’s 3-4 sigma O2 residuals had indicated.

• Decision: every Hohm set is fitted with its level free (free_scale) and its shape at 4e-5 relative (shape_relative, a new option that replaces the stated uncertainty and requires the free scale):

  • hohm_1994b for O2, N2O and CO2 (in place of the reprint) and, newly, Kr and Xe;

  • hohm_1993 for CH4, newly (Hohm 1994’s CH4 row reprints it).

  Argon’s set is not fitted: it served to set the shape uncertainty.

• Results (reduced chi-squared, Hohm’s own chi-squared, his fitted level):

  Gas	Reduced chi2 (before)	Hohm chi2 / points	Hohm level
  Kr	1.22 (0.96)	8.8 / 5	1.0021
  Xe	0.96 (0.96)	0.6 / 4	1.0047
  O2	0.23 (1.25)	2.1 / 5	1.0021
  N2O	3.01 (4.86)	3.4 / 4	1.0017
  CO2	3.32 (3.98)	6.6 / 5	1.0004
  CH4	0.70 (0.44)	6.2 / 5	1.0004

• What moved:

  • krypton’s GVD at 800 nm by 0.3 %: its largest leave-one-out shift is now Hohm’s set (0.30 %), where Shelton’s Ar/Kr ratio was (0.98 %);

  • xenon’s by 0.13 %;

  • CH4’s ultraviolet: the largest leave-one-out shift at 343 nm fell from 2.1 % to 0.71 %;

  • N2O’s dispersion still rests on Hohm’s set (27 % at 343 nm without it).

• Working estimates changed:

  • Kr: 1 % to 0.5 % at 800 nm; 1 % at 343 nm (leave-one-out 0.77 %); 0.5 % at 1800 nm;

  • CH4 at 343 nm: 1.5 % to 1 %.

• New validators (none fitted; all consistent with the survey of the papers):

  • CH4:

    • Bose et al.’s static dielectric A_eps agrees to 68 ppm (0.2 sigma), a check of the fixed HITRAN infrared terms (TC-414);

    • Schmidt & Moldover’s is 629 ppm high;

    • Kerl & Häusler’s 546 nm mean is 0.34 % high.

  • CO2: Schmidt & Moldover (static) and Clergent et al. (633 nm, 1 atm, 20 degrees C).

  • O2: Schmidt & Moldover (static, +316 ppm).

  • Schmidt & Moldover’s levels: high against every modern reference, by +180-630 ppm (TC-415). They are validators, not data.

• Status: decided (2026-09-26).

TC-401 The absolute dc Kerr values as validators of the hyperpolarizability models (2026-09-26)

• Where: optmat.gas.nonlinear (component K); data/gas/nonlinear/{He,H2,CO2,CH4}.toml and their stored fits and robustness records; docs/nonlinear_accuracy.md.

• gamma_K: Buckingham’s Kerr gamma, (3/2)(gamma_parallel - gamma_perpendicular) in the dc Kerr geometry, is what dc Kerr papers print (component K, TC-426 onwards).

  • For an atom it equals the mean gamma up to the dispersion-induced anisotropy: 0.16 % for He at 633 nm.

  • For H2 the difference is about 0.4 %.

  • Both are below the measurements’ 2-3 %.

  • gamma_observation accepts K as the mean gamma for the dc_kerr process only.

• Validators added (data / model at 633 nm):

  Dataset	Gas	Ratio	Stated uncertainty
  tammer_1992/table3_gamma_He	He	1.003	1.8 %
  tammer_1992/table2_gamma_H2	H2	1.025	3 %
  buckingham_1969/text_gamma_CH4	CH4	1.025	5 %
  gentle_1989/table2_gamma_K_CO2	CO2	1.633	26 % (the fit’s scatter)

• What they say:

  • Helium: Tammer et al.’s field-calibrated absolute value (the field from OCS’s Stark effect) confirms the ab initio helium scale that anchors the ESHG scale, to 1.8 %. Helium’s high older dc Kerr values (Buckingham & Dunmur 1.21; Shelton & Rice’s review average 1.11) are those measurements’.

  • H2: Tammer’s value is electronic plus vibrational, the orientation term subtracted, and the only absolute dc Kerr level independent of both ESHG and helium theory. The dc Kerr gamma^v of H2 is -7.2 au (Shelton 1987), within the 3 %.

  • CO2: Gentle et al.’s value is 1.5 sigma high. Their printed +-0.032 is the scatter of a long extrapolation in 1/T (their Table II reproduces as a fit weighted by the printed errors with chi2/dof 11.2; TC-428).

• Status: decided (2026-09-26).

TC-402 leviton_2008 (CHARMS: absolute index of Corning 7980, 30-300 K) (2026-09-26)

• Publication: cited as arXiv:0805.0091 (2008), the library copy (DOI 10.48550/arxiv.0805.0091). The paper prints no journal or proceedings. Its dates: PDF made 7 May 2006 (metadata title is the authors’ SPIE 5904 paper), latest reference 2005. Presumably a 2006 SPIE proceedings paper; the citation first requested, “Proc. SPIE 6273, 62732K (2006)”, is not confirmed by the paper (franta_2017 cites Frey, Leviton & Madison, Proc. SPIE 6273, 62732J (2006), a neighbouring paper). Section 5 is missing from the paper’s numbering.

• Transcribed (46 datasets, 543 points):

  • Table 4 (tbl_e21403d142ed): n at 16 wavelengths (0.4-2.6 um) x 13 temperatures (30, 40, 50, 60, 80, 100, 120, 160, 200, 240, 275, 295, 300 K): 13 datasets n_<T>K, 16 points each (208), refractive_index, index_medium vacuum, grade Corning 7980, uncertainty absolute 1e-5 (abstract; level not stated). use = primary, although Table 4 is the Table 3 Sellmeier evaluated on the grid (caption: “based on the three term, temperature-dependent Sellmeier fit”); the measurements themselves are not tabulated (same situation as franta_2016’s model tables, which are primary). Still to be decided: primary or check.

  • Table 6 (tbl_1e2b6a0f092c): dn/dT, 13 datasets dndt_<T>K, 16 points each (208), thermo_optic_coefficient 1/K, absolute 2e-8 (abstract: “Statistical variations … at the +-2 x 10^-8/K level”), primary. Structural fix: the CSV joins the 13 columns into one space-separated cell (header and rows); split, 13 numbers per row checked.

  • Table 2 (tbl_164512d3b768): PMIC - CHARMS Delta n (ppm) at 160-230 K and 295 K, 9 datasets of 1 point at 0.6328 um (PMIC’s HeNe, text p. 2), refractive_index_deviation scale 1e-6, reproduced from PMIC’s unpublished dn(T) (citation string). The “spread in dn from PMIC fits” row is the sigma column (level not stated; a spread across specimens, not a stated uncertainty). Structural fix: the cells merge the two rows and join “-30” and “66” into “-3066”; split per the image. reference is a descriptive string (“the global quadratic fit n(T) … at 633 nm (Figure 1; not printed)”), not a formula id: the vocabulary cannot name an unprinted fit. One point per dataset because refractive_index_deviation takes only a wavelength abscissa.

  • Table 7 (tbl_835faf4136ad): Waxler & Cleek minus CHARMS, 6 datasets (73, 123, 173, 223, 273, 293 K) x 10 wavelengths (60), reproduced from Waxler & Cleek 1971 (citation as printed), reference leviton_2008/sellmeier (text p. 9 says the Sellmeier model), index_medium vacuum (W&C adjusted to vacuum by Leviton).

  • Table 8 (tbl_bb97e696ab87): Matsuoka et al. minus CHARMS, 5 datasets (108, 162, 230, 276, 294 K) x 3 wavelengths (15), reproduced from Matsuoka 1991, grade “Type III silica glass (Nippon Seiki Glass Company)”. Doubt: the paper does not say which CHARMS values Table 8 subtracts; I took the Sellmeier (as for Table 7).

  • Wavelengths of Tables 7-8 are printed to 1 nm; air and vacuum values of the lines round alike, so recorded as vacuum (default) with a note.

• Checked: every cell of Tables 1-4 and 6-8 against the PDF’s own text layer (pdftotext; exact match for all) and against the images (Tables 2, 3, 4, 6 viewed).

• Formula sellmeier, form n2_sellmeier_temperature (as requested in review): terms S1..S3, L1..L3, each [T^0 .. T^4] as printed (printed order is T^0 first; no reordering), range_nm [400, 2600], temperature_range_k [30, 300], reference_temperature_k 295 (the paper’s room-temperature column in Tables 1, 2, 4), index_medium vacuum, parameters.grade Corning 7980. Table 3’s CSV merges S2/S3 and the column labels; the record was transcribed from the image and text layer, and the script checks it against the cells. Check: reproduces all 208 cells of Table 4 to their five decimals (largest |diff| 4.9e-6; 4.6e-6 at 295 K). Its T-derivative does NOT reproduce Table 6 (up to 2.1e-6/K; factor 2.7 at 0.4 um, 30 K: 3.4e-6 vs 1.25e-6; 9.4e-6 vs 9.70e-6 at 0.4 um, 295 K): Table 6 comes from piecewise quadratic fits in T (p. 6). Use Table 6 for dn/dT, not the formula’s derivative.

• Weak pole (correcting the survey): the constant terms are lambda_2 = 0.2976 um, S_2 = 1.8e-5, but lambda_2(T) is 0.277 um at 30 K, 0.267 at 100 K, 0.342 at 295 K (S_2(T) = 1.1e-3, 1.6e-3, 2.0e-4): the formula diverges near 0.34 um at room temperature. Never extrapolate below 0.4 um.

• Wavelength medium (doubt): the paper never says whether its wavelengths are vacuum or air values (monochromator calibration medium not stated). An air/vacuum confusion would move n by ~1e-5 at 0.45 um. Recorded as vacuum (default), with a note.

• Bears on TC-323 (Malitson’s medium): Leviton & Frey call Malitson’s law “in air” (p. 3), “minimum deviation in air” (p. 1), “room temperature data of Malitson (which are in air)” (p. 9); they convert with n_air = 1.00027 and find agreement “generally well less than 1e-5 and typically to less than +-5e-6” to ~2 um (p. 3). A 7940 prism also agreed with Malitson “(corrected to vacuum)” at 2.9-3.75 um (p. 5). Recomputed:

  • Leviton(293.15 K) - 1.00027 x Malitson(lambda): +1.4e-5 (0.4 um) … -3.1e-6 (1.0 um) … +0.8e-6 (2.0 um); -6.0e-5 at 2.6 um. (At 295 K: +3.2e-5 … +1.2e-5.)

  • Better: Malitson at the standard-air wavelength times Edlen’s dry-air index at 20 C, 101 325 Pa: 0.4-2.0 um rms 4.5e-6, mean -3.2e-6 (-9.9e-6 at 0.4, -4.8e-6 at 0.5, +1.5e-6 at 0.6, -5.8e-6 at 1.0, -4.8e-6 at 2.0 um).

  • Read as absolute (vacuum), Malitson is 3.8-4.0e-4 below Leviton at 0.4-2.0 um.

  • Different glass (7980 vs 7940/Dynasil/GE 151), but the grade spread is ~1e-5 (Malitson) and Leviton’s five prisms agree to 1e-5. Strong evidence that Malitson’s n is relative to air at ~20 C.

• Other doubts: which prisms the Sellmeier was fitted to (the extended study used two of the five, p. 5) is not stated explicitly. Table 1 is a “worst case” budget (level not stated): in notes; the datasets carry the abstract’s 1e-5.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-403 rodney_1954 (Rodney & Spindler, seven prisms, 24 C) (2026-09-26)

• Transcribed (15 datasets, 368 points):

  • Table 1 (tbl_947a659cc842): computed index of Eq. (1) at 24 lines (computed_table1, 24, check); residuals (o - c) x 1e5 per prism, refractive_index_deviation scale 1e-5, reference rodney_1954/eq1, primary: Heraeus A 10, Heraeus B 24, Heraeus C 5, Nieder 10, GE G1 10, GE G2 11, Corning 17 points (dashed cells skipped).

  • Table 2 (tbl_39b3d33089ff): n from Eq. (1), 65 wavelengths 0.34-3.50 um (table2, check).

  • Table 3 (tbl_69b8ae37c6ed): 10^7 dn/dt (dndt, 31 points, scale 1e-7, 1/K, primary, no temperature_k: measured between 24 and 31 C) and n at 15, 20, 25, 30, 35 C (table3_<t>C, 31 each, check).

  • All: wavelength_medium standard_air (Hg/Cd lines as tabulated in air; polystyrene bands likewise assumed), index_medium air, air_temperature_k = sample temperature (297.15 K, or the Table 3 column), no air pressure stated.

• Structural fixes: (1) the extraction swaps the captions: tbl_947a659cc842 carries Table 2’s caption and has Table 1’s as a note; the image (p. 187) shows it is Table 1, and tbl_39b3d33089ff is Table 2. (2) The Table 1 note reads “+5x10^-8” in the library’s Markdown; the image prints 10^-5 (notes only; no data file affected). (3) Leading zeros restored in x (“.36117” -> “0.36117”); printed keeps the cells.

• Erratum: table3_30C row 0.70: printed “0.45541” -> 1.45541 (page image p. 188, pdf page 4; neighbours 1.45536, 1.45546; the p. 189 rule gives 1.455409).

• Checked: Table 1 cell by cell against the image (all 24 rows, all columns); Table 3 rebuilt from Table 2 + coefficient x (t - 24): 153 of 155 cells agree (the erratum, and 0.60 um at 35 C printed 1.45820 where the rule gives 1.458206: the authors’ rounding, not corrected). Eq. (1) printed “96.00000” (image p. 186).

• Formula eq1 (no form), with index_medium air, air_temperature_k 297.15, wavelength_medium standard_air, grade Heraeus B, as requested in review (no air pressure: none stated). Check: Table 1’s computed column to its 5 decimals (max 4.7e-6, all round alike); Table 2 within 1.1e-6: the 12 five-decimal values round alike (3.40 um on the rounding edge), 13 of the 53 six-decimal values differ by one unit in the 6th decimal (max 1.14e-6 at 0.51 um). The survey’s “<=7e-7” is slightly optimistic; “4e-6 at 3.5 um” is within the 5-decimal rounding there.

• Air or vacuum (TC-323), exactly: the paper never uses the words “air” or “vacuum” and gives no reduction to vacuum. It says only that the room temperature was controlled to +-0.2 deg C with a thermometer bulb near the prism (p. 186), and Table 3 is “at various room temperatures” (p. 188). index_medium = “air” is an inference from the method (a prism in room air measures the index relative to air), as requested in review; flagged in the record. Malitson 1965 (p. 1205): “performed on the same apparatus and by identical techniques as described in the earlier NBS paper”; (p. 1209, not 1208 as first cited): “performed on the same instrument and by identical techniques. The only significant difference is in the detectors”.

• Findings bearing on TC-323:

  • Rodney’s Eq. (1) moved to 20 C (1e-5/K) minus Malitson’s Eq. (1), same air wavelengths: +7.5e-5 (0.35 um), +2.8e-5 (0.5), +1.4e-5 (0.7), +1.5e-5 (1.0), +4.9e-5 (2.0), +8.2e-5 (3.0 um), reproducing Malitson’s Fig. 4 statement (+8e-5 at 0.34, +2e-5 at 0.56-1.4, +8e-5 at 3.5 um): the two papers share one footing.

  • Against Leviton (absolute, 297.15 K): Rodney x n_air(24 C, Edlen) is 1.5-3.2e-5 above Leviton at 0.6-1.5 um (5.9e-5 at 0.4, 5.5e-5 at 2.0 um); read as absolute it is 3.3-3.8e-4 below. The air reading is again the consistent one (Rodney’s Heraeus B is a different glass; the paper says specimens differ by up to 2-3e-4).

  • dn/dT relative to air exceeds the absolute dn/dT by ~1.3e-6/K (air’s index falls ~0.9e-6/K); Rodney’s 9.5-10.3e-6/K (0.4-0.7 um) against Leviton’s absolute 9.70-8.69e-6/K at 295 K: not conclusive (Rodney: “precision is not adequate”).

• Doubt: which GE prism (G1 or G2) is the 20-year-old NBS index standard is not stated. kitamura_2007’s record gives Rodney’s formula as 31 C; the paper says 24 C (report only; kitamura_2007 not edited).

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-404 philipp_1971 (notes-only) (2026-09-26)

• No datasets. SiO2 data in figures only: Fig. 1 (reflectance of crystalline and fused quartz, fused lowered by 5 %), Fig. 3 (absorption coefficient), Fig. 4 (reflectance, ordinates displaced), Fig. 5 (eps1, eps2), Fig. 7 (eps0,eff), Fig. 8 (n_eff). Text: n_eff “approaching 8 electrons per SiO2 molecule near 26 eV” (p. 1941); eps0,eff to 26 eV close to eps0 (p. 1940); density ratio 2.65/2.20 (p. 1936). The only table (tetrahedron statistics, p. 1943) is out of scope. Relation to philipp_1985 (first tabulation, with Weinberg’s +0.075 eV shift) stated. No material registered.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-405 franta_2013b (a-Si:H, six sum-rule dispersion models) (2026-09-26)

• Authors from the paper: Franta, Nečas, Zajíčková, Ohlídal, Stuchlík, Chvostová (six, not four).

• Datasets (3, 7 points): band_gap_pjdos_2ex (1, primary; the authors’ most reliable model, p. 240), band_gap_other_models (5, check), both band_gap kind “effective” (a fitted model parameter), form film; atom_density (inline, Eq. (36), 5.462e28 m^-3, check). Note: franta_2016’s band gaps use kind “optical”; I used “effective” per the vocabulary’s definition. To be made consistent in review.

• Formulas (7, no form): udm_pjdos_ex, udm_pdos, udm_pjdos_tl, udm_pjdos_cc, udm_pjdos_cl, udm_pjdos_2ex (Table 2 columns, with fixed lists for footnote-a values; chi’s, rho and the offset fit in notes) and phonons (Table 3; Brodsky’s reference positions as nu_*_ref21). The script checks every coefficient string against the library cells. Structural fix: Table 3’s two position columns are merged into one cell and “^a” read as a trailing “a”.

• Checked: Tables 1-3 cell by cell against their images. Eq. (42): sum alpha_p = 0.3812 (printed 0.381); Eq. (45) 0.617 and 0.234 (printed 0.23). Appendix A verified numerically (PJDOS-EX parameters): C_N = 855.9099 equals quadrature to double precision; the real part equals the numerical KK transform to ~1e-12 at 0.5-30 eV. Eq. (19) image: B_p = h c beta_p / (2 sqrt(2 ln 2)) (the LaTeX drops ln 2 from the root). The library Markdown prints “F_a” in the parameter list, p. 237; the PDF has N_a.

• For the implementation (notes, with pages): Eq. (7) (Lorentz-modified asymmetric interband term = franta_2013 Eq. (59), kappa 2, nu 1) is not in optmat.solid.udm; Eqs. (9)-(11) = udm._higher; Eq. (12) = udm._urbach’s form with E_m = (E_g + E_h)/2 (optmat passes E_h, the program’s reading, TC-321; which one these fits used is not stated); Eqs. (16)-(19) = udm._gaussian. Appendix C (Tauc-Lorentz) scrambled in the Markdown: use pdf page 11.

• Doubt: mass density has no quantity (notes). The phonon parameters are for “the PJDOS model” without saying which.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-406 hohm_1994b (2026-09-26)

• Where: U. Hohm, Mol. Phys. 81, 157 (1994), Table 1 (p. 160, tbl_43f3f21f6009, JSON only), Table 2 (p. 162, tbl_83390c4d1bfd), text pp. 159-167. Journal page = pdf page + 154.

• Transcribed: script tools/extract/hohm_1994b.py.

  • Table 1, alpha in au at 632.990, 611.971, 594.096, 543.516, 325.130 nm (vacuum), parameters.temperature_k per gas: alpha_Ar (5), alpha_Kr (5), alpha_Xe (4, no 611.971), alpha_O2 (5), alpha_N2O (4, no 611.971), alpha_CO2 (5), all primary, sigma column = the parenthesised last digits (absolute, level not stated). alpha_CH4 (5) reproduced from hohm_1993 (row h [4]).

  • The DOSD rows (reproduced, 5 points each): kumar_1985_Ar/Kr/Xe (row c), zeiss_1977_O2/N2O (row d), jhanwar_1982_CO2 (row j, citation), thomas_1977_CH4 (row e, citation).

  • Table 2, B_R in cm^6/mol^2 (= 1e-12 m^6 mol^-2), this work at omega_3-omega_5: B_R_Ar (3), B_R_Kr (3), B_R_1_Xe (2), B_R_2_Xe (2), B_R_O2 (2), B_R_N2O (2), B_R_1_CO2 (3), B_R_2_CO2 (2), B_R_CH4 (2): primary, sigma column, level not stated, the paper’s “full uncertainty … approximately twice” (p. 167) in notes. The omega_1 references B_R_reference_<gas> (1 point each): Ar, Kr, Xe, CO2, CH4 reproduced from burns_1986 (no temperature parameter: Burns’s is 298.2 K); O2 and N2O reproduced from “U. Hohm, Z. Naturforsch. A 48, 505 (1993)” (heuristic theory estimates, no uncertainty). Footnote f’s Kr B_R(omega_2) = 6.46(54) inline (B_R_omega2_Kr, primary).

• Structural fixes (script): “·” decimal points; footnote marks stripped from cells (^a, ^b, ^h …) and used to route rows (b/h measured, c/d/e/j DOSD); gas-cell marks (Kr^f, Xe^(1)/(2), CO2^(1)/(2)) mapped; uncertainties with a decimal point absolute (“6·23(1·55)”), without one last digits (“1·57(58)”); “(-)” none. The library swaps Table 2’s caption and footnotes (image p. 162 checked); footnote f’s unit renders “mol^-1” in the library, “mol^-2” on the image; footnote d renders “T approx 373 K”, the image “T = 373 K”. No value affected; no erratum.

• Checked: all Table 1 and Table 2 cells against the images. hohm_1994’s input_O2/N2O/CO2 are digit-identical to this paper’s b rows. CH4 B_R(omega_4, omega_5) = 11.72, 11.14 recomputed from hohm_1993’s B_2* (48.58, 49.17, 49.00) with Burns’s 7.76 by Eq. (13): agree. Spackman’s CO2 Meath moments reproduce row j to 4e-4 au at 544-633 nm (so row j’s DOSD is Spackman’s CO2).

• Findings (numbers for review):

  • Argon shape against fit/Ar: alpha(omega_k)/alpha(omega_1) departs by +26, -5, -6, -70 ppm at 612, 594, 544, 325 nm, against hohm_1994’s claimed 1e-5 dispersion precision; absolute +117 ppm at 633 nm (within the printed 0.0020 au = 180 ppm).

  • Absolute levels against the fits at 633 nm: Kr +0.20 %, Xe +0.47 %, O2 +0.21 %, N2O +0.16 %, CO2 +0.04 %, CH4 +0.04 %. 325 nm shape: Kr +260 ppm, Xe +158, CH4 +157, the others within 55 ppm.

  • The “(n)” is the same at all five wavelengths (Ar 0.0020 au = 1.8e-4): it reads as the absolute-level uncertainty. The paper states no dispersion precision itself.

• Doubt: the level of the “(n)” digits is not stated anywhere in the paper. The CH4 B_R dataset is primary here although the underlying B_2* were first published (without B_R) in hohm_1993.

• Fits: the fit configurations of O2, N2O and CO2 key on hohm_1994/input_<gas>, now a reproduction of hohm_1994b/alpha_<gas>: the keys should be moved and the uncertainty model decided in review (hohm_1994’s relative 1e-5 plus 1e-3 scale, against this paper’s absolute (13)-(15) digits). Not changed here.

• Status: open (fit keys; the level of the “(n)” digits).

TC-407 hohm_1994 re-pointed (2026-09-26)

• Where: src/optmat/data/sources/hohm_1994.toml, datasets input_O2, input_N2O, input_CO2, and the record’s notes paragraph on the inputs’ sources.

• Changed: reproduced_from from “U. Hohm, Mol. Phys. (1993), in press (ref. [29])” to ["hohm_1994b"]; the dataset notes no longer say “the original is not in the library, so this copy may be fitted”; the record notes name hohm_1994b and the original’s absolute (13)/(15)/(13) digits and temperatures. No value changed; the uncertainty (relative 1e-5, level “not stated”, systematic 1e-3) left as it was (the original’s level is not stated either), with the difference noted.

• Status: decided (2026-09-26); the fits still key on these reproductions (TC-406).

TC-408 hohm_1993 (2026-09-26)

• Where: U. Hohm, Mol. Phys. 78, 929 (1993), Table 1 (p. 935, tbl_90f137181bd7, JSON only), Table 2 (p. 937, tbl_efe74204a8d8), Table 3 (p. 939). Journal page = pdf page + 927. CH4 only.

• Transcribed: script tools/extract/hohm_1993.py. alpha_CH4 (5, primary, 294.47 K, sigma column, level not stated); thomas_1977_CH4 (5, reproduced, citation); moments_CH4 (S(-2..-8), 4, check); moments_thomas_1977_CH4 (4, reproduced, citation); moments_spackman_1991_CH4 (3, reproduced, spackman_1991). Formula cauchy_CH4 (Eq. 13: a_0 = 17.2585(21), a_1 = 62.72(47), a_2 = 349(19), r.m.s. errors).

• Structural fix: Table 2’s stacked cells are merged by the library (“63·2262·4150·07”); the script splits CH4’s four moment cells as the image shows them and checks that the parts rejoin to the extracted cell exactly.

• Checked: Table 1 and Table 2 CH4 cells against the images (and the page image for Table 1’s footnotes: b this work, c [26] calculated using DOSD). The formula reproduces Table 1 to 4e-4 au (-0.00006, +0.00030, -0.00041, +0.00001, +0.00006), within the printed 0.0017. The iterated S(-2..-8) reproduce Table 1 to 6e-4 au (544-633 nm), 1.5e-3 (325 nm); Thomas and Meath’s S(-2..-8) reproduce row c to 4e-5 au (visible), 1.9e-3 (325 nm).

• Findings: Hohm’s “Spackman [13]” CH4 row mixes Spackman’s two basis sets: S(-2) = 15.895 is the ELP value, S(-4) = 50.07 and S(-6) = 199.11 the 6-31G(+sd+sp) values. The text misprint omega_2 = “0.7445345 a.u.” is on p. 931 (first reported as p. 932); no dataset uses it, so no erratum.

• he_2021: its O2_table1 formula lists “U. Hohm, Mol. Phys. 78, 929 (1993)” in reproduced_from (He et al.’s Table 1 cites “Hohm (1993)” for O2). This paper has no O2 (hydrocarbons only); the O2 dispersion is hohm_1994b’s (Mol. Phys. 81, 157, 1994). He et al.’s attribution is wrong (probably meant the 1994 paper); he_2021 not edited.

• Not transcribed: Table 3 B_2* (a fit parameter containing B(T), no quantity): notes.

• Status: open (he_2021’s attribution, for review).

TC-409 kerl_1992 (2026-09-26)

• Where: Kerl, Hohm and Varchmin, Ber. Bunsenges. Phys. Chem. 96, 728 (1992), Table 1 (p. 731, tbl_520df133e721), Eq. (10) p. 730.

• Transcribed: no datasets; six formulas without a form, eq10_Ar, eq10_H2, eq10_N2, eq10_O2, eq10_CH4, eq10_CO2 (alpha(0,0), omega_0, b, c as printed, with the standard deviations; ranges from the table and its notes e, f). Air in notes.

• Checked: every cell against the image; footnotes f (“Dispersion only determined between 128 K and 296 K”, CH4) and g (“Given high statistical weight for fit in T …”, H2, O2, CH4, air) read from the page image (garbled in the Markdown).

• Checks against Hohm’s values (au converted with a0^3 = 0.1481847 A^3), at Hohm’s temperatures, 633 / 543.5 nm: Ar -0.026 / -0.011 %, CH4 -0.016 / -0.015 %, O2 -0.275 / -0.246 %, CO2 +0.208 / +0.211 %; H2 +0.02 % against hohm_1994’s input (temperature not stated). Against hohm_1990’s alpha(T) formulas at 632.99 nm, 300 K: Ar +0.018 %, N2 +0.002 %, CH4 -0.014 %, O2 -0.035 %, H2 -0.10 %; rises 0-1000 K 1.34, 1.14, 0.63, 0.18 % (H2, CH4, O2, N2) against hohm_1990’s 1.4, 1.2, 0.7, 0.2 %. The survey’s figures are confirmed. O2 and CO2 exceed the paper’s “mean uncertainty of about 0.1%”.

• Doubt: alpha(0,0) is an extrapolation of optical data to omega = 0 and T = 0 (no vibrational polarizability); not a static value.

• Status: verified (2026-09-26).

TC-410 kerl_1984 (2026-09-26)

• Where: Kerl and Häusler, Ber. Bunsenges. Phys. Chem. 88, 992 (1984), Table 1 (p. 994, tbl_6ccbf5b10dc1, uncaptioned in the library, JSON only), Table 2 (p. 994), Table 3 (p. 995). Journal page = pdf page + 991 (pdf page 1 starts with the previous article’s references).

• Transcribed: script tools/extract/kerl_1984.py. A_R (molar_refractivity, cm^3/mol, 546.226 nm vacuum, temperature_k), one dataset (1 point) per isotherm: Ar 299.12, 299.15 (bracketed in print: excluded), 323.47, 325.53, 345.19; CH4 299.44 (starred: new cell), 301.47, 323.01, 345.22, 365.63; all check, 1 sigma. Table 2 means A_R_mean_Ar 4.2307(63), A_R_mean_CH4 6.641(40) (check). Formulas A_R_T_Ar, A_R_T_CH4 (Table 3, A_R = c_0 + c_1 T).

• Structural fixes: brackets and the star stripped (the bracket recorded as use = "excluded" of that dataset).

• Wavelength: 546.226 nm (text pp. 993, 995 and the image caption of Table 1) is right; the abstract’s 546.266 nm is a transposition (546.226 nm vacuum is the green Hg line, 546.077 nm in standard air by Edlén; 546.266 matches no line). No dataset uses the abstract: no erratum.

• Checked: all Ar and CH4 cells against the image. Table 2’s means are the means of the unbracketed Table 1 values with their sample standard deviation (4.23073, 0.0063; 6.64046, 0.0396). A least-squares line reproduces Table 3 (Ar c_0 4.1588, c_1 2.22e-4, r 0.67, s 0.0057; CH4 6.2270, 12.64e-4, 0.91, 0.019).

• Findings: the means are +0.37 % (Ar) and +0.34 % (CH4) above optmat’s fits at 546.226 nm; the CH4 slope (2.0e-4/K relative) is about 17 times hohm_1990’s. Superseded by hohm_1990; checks only. B(T) (assumed b_R = a_1/6) and Table 4: notes.

• Status: verified (2026-09-26).

TC-411 hausler_1988 (2026-09-26)

• Where: Häusler and Kerl, Int. J. Thermophys. 9, 117 (1988), Table I (pp. 122-123: tbl_e56cd39cc6f5 and the label-less tbl_2a63c5387037), text p. 124. Journal page = pdf page + 116. The library author field “H?usler” is garbled; cited from the paper.

• Transcribed: script tools/extract/hausler_1988.py. SF6 A_1 (molar_refractivity, cm^3/mol, 1 sigma, temperature_k), one dataset (1 point) per isotherm and weighting: w and uw at 257.42, 268.86, 282.61, 298.31, 318.04 K (632.99 nm, check), 298.32 K at 546.22 nm (note a; the text says 546.226; check), 337.73 K (both excluded: the authors’ “obvious bad value 10.8477”, left out of both means). 14 datasets. Inline: the text means A_1_mean_w_SF6 10.995(42), A_1_mean_uw_SF6 10.995(36) (check), Sutter’s A_eps_sutter_SF6 16.478 at inf, 323 K (reproduced, citation).

• Structural: only the first part of Table I is read; the second part (lost row labels) was matched row by row to the first on the image; its alpha_0 is 3 A_1/(4 pi N_A), not needed.

• Checked: SF6 cells against the image; the means: 10.99518 (sd 0.0420, w) and 10.99500 (0.0365, uw) over the five 633 nm isotherms.

• Findings: 10.995 is 3.1 % below St-Arnaud and Bose’s 11.348(21) (st_arnaud_1979) and 2.9 % below fit/SF6 (11.322 at 632.99 nm). The authors’ “anomalous dispersion” (the 546 nm value 0.25 % below the 633 nm mean) is within the 0.38 % scatter of the 633 nm isotherms, and fit/SF6 has normal dispersion (+0.35 % from 633 to 546 nm). An outlier source; checks only.

• Status: verified (2026-09-26).

TC-412 spackman_1991 (2026-09-26)

• Where: M. A. Spackman, J. Chem. Phys. 94, 1288 (1991), Table I (p. 1290, tbl_6f890f395ef6, JSON only). Journal page = pdf page + 1286.

• Transcribed: script tools/extract/spackman_1991.py. The “Experiment” columns (S(-2) = alpha(0), S(-4), S(-6); cauchy_moment, au, order abscissa, 3 points each, reproduced): meath_H2, meath_N2, meath_N2O from zeiss_1977 (values equal: checked), meath_CH4 from Thomas and Meath 1977 (citation; equal to hohm_1993’s row b), meath_CO2 from Jhanwar and Meath 1982 (citation; attributed because it reproduces hohm_1994b’s row j), meath_CO and meath_SF6 from “Refs. 47-60” (not identified). The TDHF (and ELP) values, and Tables II and III, in notes.

• Checked: all rows against the image.

• Doubt: the paper names no Meath paper per molecule; the CO2 attribution is inferred (via Hohm), CO and SF6 not identified.

• Status: open (CO, SF6 attribution).

TC-413 duplicate Hohm_1990_InterferometricMeasurementsDipole_68ebab (2026-09-26)

• Same DOI (10.1080/00268979000100611) as the curated hohm_1990; the library marks it version_of_record. Its Table 1 (tbl_d67aa4aa2ed2) has cells identical to hohm_1990’s tbl_f8502d3f8f19; its Table 2 (tbl_0dbe0c4edfde) has the same numbers as tbl_c72b14449c4b, differing only in LaTeX markup (H_2 against H_{2}). No record made.

• Status: decided (2026-09-26).

TC-414 bose_1972 (2026-09-26)

• Where: Bose, Sochanski & Cole, J. Chem. Phys. 57, 3592 (1972): Table I (pdf p. 3, tbl_36d8a70060d0, cells file only); text p. 3.

• Transcribed: CH4 only (CF4 in notes). A_eps_CH4 (molar_refractivity, 3 points, rows 279.8, 322.5, 373.4 K, x = inf, check); A_eps_best_CH4 (inline, 6.541 +- 0.003, p. 3, check); B_eps_<T>_CH4 (3 datasets of 1 point, refractivity_virial_coefficient, order 2, cm6/mol2, check) and C_eps_<T>_CH4 (3 datasets, order 3, cm9/mol3, check). All at infinite wavelength; errors “three standard deviations from the least squares fit” (p. 3): level “3 sigma”.

• Structural fix: the C_eps header extracts as “cm9 mol-8”; the image prints mol^-3 (asserted in the script; the record’s unit is cm9/mol3).

• Checked: every CH4 cell against the image; 3 A_eps/(4 pi N_A) of 6.541 = 2.5928e-24 cm^3 (text: 2.593). The A_eps rise with T (0.006 over 279.8-373.4 K) is A_tau = 0.0175 in Schmidt & Moldover’s Eq. (9) form, the “17e-3” they attribute to this paper.

• Meaning: B_eps, C_eps are STATIC DIELECTRIC virials, B_eps = B_ind + B_or with the octopole-induced orientation term (the authors’ B_ind = 2.5, so B_or ~ 2/3); not the optical B_R. Kept as check, never as an optical virial. A_eps includes the static vibrational polarizability (~0.09 cm3/mol).

• Re-pointed: achtermann_1991 B_eps_bose_1972_279.8_CH4, _322.5_CH4, _373.4_CH4: reproduced_from = ["bose_1972"], level “not stated” -> “3 sigma”, notes updated. Values digit-identical (8.14 +- 0.29, 7.29 +- 0.32, 6.75 +- 0.29).

• Doubt: use of A_eps (check, or a primary static constraint with the infrared terms) is still to be decided.

• Status: verified (2026-09-26).

TC-415 schmidt_2003 (2026-09-26)

• Where: Schmidt & Moldover, Int. J. Thermophys. 24, 375 (2003): Table V (pdf p. 20, tbl_d4ad17b1acdf), Eq. (9) (p. 18), uncertainty budget (p. 19), text pp. 20-27.

• Transcribed: A_eps,273 of the in-scope Table V rows as molar_refractivity, x = inf, one dataset of 1 point each, use check: A_eps_Ar 4.14203(19); A_eps_two_N2 4.38782(18); A_eps_tau_N2 4.38748(15) (T 273.16); A_eps_two_O2 3.95945 (no unc.); A_eps_tau_O2 3.95875(09) (T 273.16); A_eps_two_CH4 6.54787; A_eps_four_CH4 6.54467(31) (T 273.16); A_eps_three_CO2 7.3797; A_eps_four_CO2 7.34590(63). Sigma = parenthesised last digits, level “not stated”. Nine [[formulas]] (Eq. 9 with each row’s coefficients as strings). He has no Table V row (Table I is raw data).

• Structural fixes: Table V’s CSV merges b with c and q with sigma, headers garbled; only the A column (untouched) is read by the script. Table III’s methane/nitrogen columns merge and N2’s two extra points sit in the last row (used only in the check).

• Checked: Eq. (9) with CoolProp’s reference EoS (the paper’s refs 13, 14, 15, 19, 26, confirmed by CoolProp’s BibTeX keys) against the non-zero points of Tables III (29.3 C) and IV (0.019 C): rms in eps Ar 1.39 ppm (printed sigma 0.98), N2 1.31 / 0.80 (0.91 / 0.69), O2 2.00 / 0.49 (1.86 / 0.39), CH4 5.12 / 1.86 (2.95 / 0.86), CO2 four-parameter 1.61 (1.3). CO2 q reproduces the text’s B_eps decrease 29.4 -> 49.7 C: 6.48 (printed 6.5).

• Finding 1: the CO2 THREE-parameter row (7.3797, 6.230, A_tau 0; sigma 12.6) does not reproduce Tables III-IV: -20 to -36 ppm at 0 C, -27 to -175 ppm growing with density at 29.3 C (73 ppm rms). Unresolved (fitted data include untabulated isotherms); the row is rejected by the authors anyway.

• Finding 2: text p. 25 quotes N2 “4.3878 +- 0.0009 … from the two-parameter fit in Table V”, five times Table V’s (18). Unexplained.

• Uncertainty budget: the paper’s quadrature sum (delta A, 1e-6 A/(eps_max - 1), 1.1e-4) computed here: ~1.9-2.4e-4 cm3/mol before the fit error, ~2.1-3.9e-4 with it (50-65 ppm). Recorded in notes only (not printed per gas; data files keep the printed fit uncertainties). Still to be decided: whether to carry the budget as the dataset uncertainty (e.g. systematic_relative) if these are ever fitted.

• Re-pointed: yang_2025 schmidt_moldover_2003_N2 -> reproduced_from = ["schmidt_2003"]; notes: Yang’s 4.3877(2) is NOT a printed Schmidt value but the mean of the two N2 fits (4.38765), as is hohm_2013’s 11.7379 au. Level left “1 sigma” (Yang’s own statement; the original states none). may_2008 schmidt_moldover_2003_O2 -> ["schmidt_2003"]; its 1.7461e-40 F m^2 = 3 eps0 A/N_A of 3.95875 (checked); notes say May et al. refit these O2 data (recommended_O2 not independent; double-counting risk).

• Status: verified (2026-09-26); findings 1-2 open.

TC-416 hohm_2013 (2026-09-26)

• Where: Hohm, J. Mol. Struct. 1054-1055, 282 (2013): Tables 1, 2, 3, 5, 7 (tbl_3b3edcf5d4b1, tbl_56b3b73b65bf, tbl_0e38258e2324, tbl_38210b618411, tbl_a47f36ad8e7f; cells files only); text pp. 1-3, 8.

• Transcribed (38 datasets, 47 points, all unit = "au", x = inf):

  • H2 dp_H2 (1; [43] May, Moldover & Schmidt 2009, reproduced);

  • D2 ri_D2 (2; Larsen 1936, Frivold 1939), dp_essen_D2 (1; essen_1953);

  • N2 dp_N2 (1; schmidt_2003), dosd_N2 (1; Zeiss & Meath Mol. Phys. 33, 1155);

  • O2 dp_O2 (1; may_2008 + schmidt_2003), dosd_O2 (1; kumar_2011);

  • CO dosd_CO, ri_mean_CO (check), dp_total_CO (5), dp_electronic_CO (5, check), alpha_vib_CO;

  • CO2 dosd_CO2, ri_mean_CO2 (check), dp_total_schmidt_CO2, dp_total_mean_CO2 (check), dp_electronic_CO2 (3, check), alpha_vib_thomas_CO2, alpha_vib_bishop_CO2;

  • N2O dosd_N2O, ri_hohm_N2O (hohm_1994b), ri_cuthbertson_N2O, ri_koch_N2O, dp_total_N2O (kirouac_1973), dp_electronic_N2O (check), alpha_vib_N2O;

  • CH4 dosd_CH4, ri_mean_CH4 (check), dp_total_mean_CH4 (check), dp_electronic_CH4 (check), alpha_vib_CH4;

  • SF6 dosd_SF6, ri_watson_SF6, ri_burns_SF6, dp_total_mean_SF6 (check), dp_electronic_SF6 (2, check), alpha_vib_pack_SF6, alpha_vib_bulanin_SF6. alpha_vib as polarizability_correction, part pure_vibrational, reproduced from its reference. Totals carry parameters.includes. Uncertainty level “not stated” (never stated in the paper).

• Rule applied: a value with a cited reference is reproduced from it (curated id where there is one); Hohm’s “Mean value” rows and DP alpha_el differences are this source’s, use check, with what they average in notes (no reproduced_from on them).

• Checked: every in-scope row against its image (Table 3 is OCR-selected; agrees). Reference [43] missing from the extracted list: pdftotext of the pdf gives “E.F. May, M.R. Moldover, J.W. Schmidt, Mol. Phys. 107 (2009) 1577-1585”. [116] also missing, [187] out of order. Captions detached; tables identified by molecules and text.

• Findings (1 au = 0.373802 cm3/mol): N2 11.7379 = mean of schmidt_2003’s two fits (4.38765), not a printed value; O2 10.587 = may_2008’s 3.9576; CO2 19.652 = schmidt_2003’s 7.34590; N2O DP total 20.45 = kirouac_1973’s 3.03e-24 cm3; alpha_vib [16] = bishop_1982 to rounding; SF6 alpha_vib from Pack (13.83) or Bulanin (13.73), not Bishop’s 15.16. CH4 DP electronic 17.266 is 0.15 % above the RI mean 17.240. Hohm’s [84] (Zeiss & Meath, Mol. Phys. 33, 1155) and [227] (Kumar, Fairley & Meath, JCP 83, 70) are NOT the curated zeiss_1977 / kumar_1985 (different papers).

• Not extracted: O3 “18.68 - 19.67 [85]” (a range); non-curated molecules.

• Reproductions elsewhere: zhao_2026’s hohm_2013_ri_CH4 6.445(10) = 17.240(26) au and hohm_2013_dp_CH4 6.454(17) = 17.266(45) au (digit-consistent after conversion); re-pointing is left to that record’s extraction.

• Status: verified (2026-09-26).

TC-417 clergent_1999 (2026-09-26)

• Where: Clergent, Durou & Laurens, J. Chem. Eng. Data 44, 197 (1999): Table 4 (tbl_e0151c49676c), Table 5 (tbl_4e3479144d9d), Eqs. (1), (4); supplement.

• Transcribed: refractivity_Ar/N2/CO2 (Table 5 “our results”, 1 point each, 632.8 nm standard_air, state 1atm_20C, density real, check, scale 1e-6); hauf_grigull_Ar/N2/CO2 (Table 5 first row, reproduced from Hauf & Grigull 1970, no uncertainty). Formulas mu_Ar, mu_N2, mu_CO2 (n - 1 = mu p/T, Table 4).

• Structural fix: Table 5’s “±” extracts as “(” (“263.3 ( 0.8”); split in the script.

• Checked: mu p/T at 101325 Pa, 293.15 K: 263.38, 279.56, 418.61 (printed 263.3, 279.5, 418.6: Ar and N2 truncated). Table 4’s “confidence interval” = 2.576 x std dev/sqrt(24) for all three gases (a 99 % interval; level not stated). Table 5’s +- = Eq. (4) linear sum (N2: 0.29 % = 0.80).

• Decision (for review): density “real”, not the paper’s ideal Eq. (1): the value is n - 1 measured along the 20 C isotherm (the linear N-p fit over 0-110 kPa absorbs the second-virial curvature); the ideal-gas law only averages mu over T (CO2: ~ -0.05 %).

• Finding: against optmat’s default models (632.975 nm vacuum, 101325 Pa, 293.15 K): Ar +0.56 %, N2 +0.78 %, CO2 +0.50 % (models 261.83, 277.33, 416.51e-6); about twice the stated 0.26-0.30 %. Hauf & Grigull’s interpolated values agree with the models to -0.01, +0.28, +0.21 %. A common offset: likely a p/T calibration error (the authors’ own suggestion, p. 3).

• Annotated: wahlstrand_2012 (source notes, REFERENCE STATE): the Maryland 2.795e-4 is Clergent’s Table 5 N2 value at 293.15 K, +0.78 % above optmat’s N2 model; the two readings (293.15 K if Clergent is right; the recorded 290.9 K if the model is right). No value changed.

• Not extracted: Tables 6-7 (r and dn/dT, derived from mu), Tables 2-3 and the supplement (raw fringe counts, per-run mu).

• Status: verified (2026-09-26); the density decision open.

TC-418 hourri_1997 (2026-09-26)

• Where: Hourri, St-Arnaud & Bose, J. Chem. Phys. 106, 1780 (1997): Table I (pdf p. 5, tbl_d52ac5f743cd), text pp. 4-6.

• Transcribed: A_eps_hosticka_SF6 (16.543 +- 0.017, reproduced from Hosticka & Bose, JCP 60, 1318 (1974)); A_eps_bose_cole_CO2 (7.350 +- 0.006), B_eps_bose_cole_CO2 (50.7 +- 0.9, order 2), C_eps_bose_cole_CO2 (-2515 +- 235, order 3), reproduced from Bose & Cole, JCP 52, 140 (1970); B_eps_SF6 inline (65.14 +- 1.80, 322.85 K, 3 sigma, check, static dielectric). 1 point each. Reprint levels “not stated”.

• Structural fix: in the CSV “±” is “6” and a leading minus “2” (image checked); the script maps the four used cells to the image’s reading and asserts that re-garbling the reading gives the raw cell digit for digit.

• Checked: Table II’s alpha = A_eps/(4 pi N_A/3) (2.9135, 6.5576 e-24 cm3; printed 2.913, 6.558). B_OR = 65.14 - 24.2 - 22.7 = 18.24 (printed). CO2 B_eps 50.7 +- 0.9 is achtermann_1991’s Bose & Cole reprint at 322.9 K.

• Not extracted: the mixtures (not curated), B_p, multipole moments; Achtermann’s A_R/B_R values quoted in the text (already curated) in notes.

• Status: verified (2026-09-26).

TC-419 copeland_1976 (2026-09-26)

• Where: Copeland & Cole, J. Chem. Phys. 64, 1747 (1976): Table I (pdf p. 3, tbl_a066d6e5d380).

• Transcribed: argon only: A_eps_Ar (4.1406 +- 0.0014, 50 C, check); A_eps_bose_cole_Ar (4.1396 +- 0.0006) and B_eps_bose_cole_Ar (0.72 +- 0.12, order 2), reproduced from Bose & Cole 1970 (footnote a). 1 point each; level not stated (the paper never describes its +-).

• Structural fix: the CSV joins each cell’s two printed lines (“4.1406 ± 0.0014(4.1396 ± 0.0006)a”); split at the parenthesis (image checked).

• Checked: A_eps 4.1406 = 1.6413e-24 cm3 (Table IV’s model input 1.64); 0.03 % below schmidt_2003’s 4.14203.

• Status: verified (2026-09-26).

TC-420 Kirouac_1973_DielectricPressureVirial_8cbf89 (duplicate) (2026-09-26)

• A second download of the curated kirouac_1973 (same DOI 10.1063/1.1680442, 6 pages, different pdf sha256). Tables I-III identical cell for cell (Table III’s header differs only in LaTeX spelling). No record made.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-421 olney_1997 (2026-09-26)

• Where: Olney, Cann, Cooper & Brion, Chem. Phys. 223, 59 (1997). Table 3 parts 1-2 (pp. 79-80, tbl_e403ff88c1f4, tbl_55a125f18af7), Table 1 column 2 (pp. 70-71, tbl_96bf5b17dd16, tbl_82467dffab5d); text pp. 64-94. PDF page n = p. 58 + n.

• Transcribed (script tools/extract/olney_1997.py, 79 datasets, all cauchy_moment (au, order abscissa) except Table 1’s polarizability (au, static)), for He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, CO, CO2, N2O, CH4 (no SF6 or O3 in the paper):

  • moments_<gas> (13 x 7 points, S(-1), S(-3), S(-4), S(-5), S(-6), S(-8), S(-10)), use = check: the refined (e,e) sums. Odd orders kept as cauchy_moment (the quantity is “S(k)”, as kumar_2010’s S_-1 datasets).

  • s-2_<gas> (13 x 1 point), use = reproduced: the Table 3 ‘Expt’ S(-2) is the polarizability the spectrum was renormalised to (note a). reproduced_from: He, Ne, N2 hohm_1990 [79]; Ar, Kr, O2, CO2, N2O hohm_1994b [81] (P8’s id); H2 hohm_1994 [103]; CH4 hohm_1993 [67] (P8’s id); CO watson_1936 [100]; Xe Hohm & Trumper, Chem. Phys. 189, 443 (1994) [102] (citation, not in the library); D2 Newell & Baird [123] as printed (see doubt 2).

  • 38 comparison-row datasets, use = reproduced, named <first author>_<year>_<gas>: curated originals kumar_1985 (Ne, Ar, Kr, Xe), zeiss_1977 (H2, N2, O2, N2O), langhoff_1969 (H2, N2, O2), hohm_1993 (CH4); the other 18 by citation as printed (Thakkar 1981, Sauer 1990, Dehmer 1975, Cummings 1975, Leonard & Barker 1975, Eggarter 1975, Inokuti 1981, Victor & Dalgarno 1969, Gerhart 1975, Starkschall & Gordon 1971, Geertsen 1986, Packer 1994, Kosman 1985, Kumar & Meath 1994, Parker & Pack 1976, Jhanwar & Meath 1982, Pack 1974, Thomas & Meath 1977).

  • table1_<gas> (13 x 1 point, check): S(-2) of the published spectra before refinement; CO has two: table1_CO 13.18 (after the energy-scale correction, note aa; check) and table1_CO_published 12.64 (excluded, superseded).

• Checked: every transcribed cell against the four table images (Table 3 pp. 1-2, Table 1 pp. 1-2): all agree. “2.404(4)” etc. are powers of ten (written 2.404e4). Reference numbers inside S(-2) cells stripped structurally. The comparison rows are digit-identical to the curated kumar_1985 (Ne/Ar/Kr/Xe, all 8 orders), zeiss_1977 (H2, N2, O2, N2O), langhoff_1969 (H2, N2, O2: 4 values each) and Hohm 1993’s Table 2 CH4 “this work” row (17.257, 63.22, 293.8, 1505). Refinement ratio check: He 1.383/1.407 = 0.983 (the paper prints 0.982, p. 78).

• Uncertainty: none printed for any sum; none stored. Quoted in notes: spectra “better than +-5 %” (p. 64), polarizabilities “+-1-2 %” (p. 78), refinement <= 3 %, S(-1) less accurate (p. 82), agreement with Meath’s DOSDs “better than +-5 %” (p. 87), C6 “better than +-10 %” (p. 94). A second curator may prefer to attach 5 % (shape) to the higher moments when comparing.

• Doubt 1 (finding): CH4, Thomas & Meath [50] DOSD row: S(-6) printed 289.3; Hohm 1993 (Table 2, tbl_efe74204a8d8, “298·3”) and Spackman 1991 (Table I, “298.3”) print 298.3. A transposition in one of them; Thomas & Meath 1977 is not in the library. Olney’s own CH4 S(-6) is 295.0. Transcribed as printed (Olney’s value), noted.

• Doubt 2: D2’s refined S(-2), 5.368, is attributed to Newell & Baird [123] (also Table 1 note e), but Newell & Baird measured no D2 (the library paper and the curated newell_1965 have none). reproduced_from is the citation with that caveat, not the id newell_1965. The true origin of 5.368 is unknown.

• Doubt 3: the S(-2) renormalisation targets are said to be “dynamic or static” values without saying which per gas, so s-2_<gas> is a reproduction in the sense of “determined by”, not always a number the original prints (e.g. hohm_1990 prints 632.99 nm values). He’s 1.383, Ne’s 2.663, N2’s 11.75: they may be checked against hohm_1990’s static extrapolations.

• Findings bearing on models: the refined sums (moments_) against the Meath DOSDs: Ar S(-4) 27.92 vs 27.91, S(-6) 95.26 vs 95.06; Kr 56.51 vs 56.32, 258.7 vs 256.7; Xe 129.8 vs 129.6, 827.0 vs 824.7; N2 30.02 vs 30.11 (Zeiss), 100.8 vs 101.8; O2 35.25 vs 34.75, 245.1 vs 237.1 (+3.4 %); CO2 50.63 vs 50.99, 207.4 vs 211.4; N2O 73.81 vs 72.11 (+2.4 %), 423.5 vs 410.7 (+3.1 %); CH4 62.22 vs 62.41, 295.0 vs 289.3 (or 298.3); H2 20.04 vs 19.96, 83.18 vs 82.94; He 1.556 vs Thakkar 1.542 (+0.9 %), 2.069 vs 2.040 (+1.4 %); Ne 2.938 vs 2.886 (+1.8 %), 5.137 vs 5.063. The O2 and N2O S(-6) differences of 3 % are the largest among the curated species.

• Not extracted: Table 3 parts 3-4 (no curated species); unlabelled Table 2 (p. 74, halogen species); Table 4 (L(u)); Tables 5-6 (C6); Eq. (11) Verdet expansion (notes).

• Status: open (doubts 1-3).

TC-422 re-pointing to olney_1997 and hohm_2013 (2026-09-26)

• zhao_2026: olney_1997_moments_CH4 reproduced_from -> olney_1997 (62.22, 295.0, 1660: digit-identical to olney_1997/moments_CH4; Zhao’s parenthesised uncertainties (19), (57), (54) are not Olney’s, who print none). hohm_2013_ri_CH4, hohm_2013_dp_CH4, hohm_2013_ri_CO -> hohm_2013 (Q8’s id). Checks against Hohm 2013’s tables (au x 0.373803 cm^3/mol): CH4 RI 17.240(26) = 6.4444(97), Zhao prints 6.445(10) (last digit +1, 0.01 %); CH4 DP 17.266(45) = 6.4541(168), Zhao 6.454(17): Hohm’s value is alpha_el (17.496(25) total less alpha_vib 0.23 from Bishop & Cheung 1982), so the old note’s question “does Hohm’s DP include vibration” is answered: no, subtracted. CO RI 13.04(7) = 4.874(26), Zhao prints 4.88(26): uncertainty ten times larger and value +0.006. Also (not my dataset, notes only): Zhao’s CO DOSD 4.89(53) vs Hohm’s DOSD row 13.08(15) au = 4.889(56) (Hohm’s Ref. 97 is Jhanwar & Meath 1982, while Zhao cite Kumar & Meath 1994): the same decade-too-large uncertainty pattern. No value changed.

• kumar_2010: s-1_dosd_olney_{Ne,Ar,Kr,Xe} -> olney_1997. The values 3.601, 8.700, 11.86, 16.55 are Olney’s ‘Expt’ S(-1) (refined (e,e) sums), not a DOSD despite Kumar’s label “DOSD^b”.

• topfer_2023: olney_1997_N2O (2.998 A^3 = 20.23 au) and olney_1997_Xe (4.005 A^3 = 27.03 au) -> olney_1997; notes: both are Olney’s UNREFINED Table 1 column-2 values (table1_N2O, table1_Xe), not the refined Table 3 S(-2) (19.70 and 27.12). Still excluded.

• nie_2025: the “Olney” moments are Olney’s Table 3 comparison rows: olney_moments_N2 and olney_moments_H2 -> zeiss_1977 (30.11, 101.8, 385 and 19.96, 82.94, 367; Zeiss’s 384.6 rounded to 385), olney_moments_Ne -> kumar_1985 (2.886, 5.063, 10.86). Nie’s unextracted Ar column (27.91, 95.06, 391) is kumar_1985’s Ar. The parenthesised uncertainties are Nie’s own. olney_1997_N2 (Table II ‘Theor.’ 4.3887(18) cm^3/mol = 11.7407 au) -> olney_1997, but Olney prints no such number: N2 11.75 (refined, = 4.3922), 11.74 (Zeiss, = 4.3885), 11.743 (Langhoff, = 4.3896), 11.54 (unrefined); nor any uncertainty. Origin of 4.3887(18) not established. Source notes amended.

• Status: open (the re-points to be confirmed in review).

TC-423 brion_1984 (2026-09-26)

• Where: Brion & Thomson, J. Electron Spectrosc. Relat. Phenom. 33, 301 (1984); the (e,e+ion) tables of H2 (p. 318, tbl_55480943b731), CO (p. 319, tbl_72dab91fceaa), N2 (p. 320, tbl_a794d910da1a), O2 (p. 321, tbl_00a15c604fe1), CH4 (p. 326, tbl_689c845cc210), N2O (p. 327, tbl_c5ae487e5662), CO2 (p. 328, tbl_f55f568f42e8), SF6 (p. 331, tbl_643f8c4f78a2). PDF page n = p. 300 + n.

• Transcribed (script tools/extract/brion_1984.py, 16 datasets): per gas absorption_<gas> (differential_oscillator_strength, 1/eV, scale 1e-2, eV) and ionization_<gas> (photoionization_cross_section, Mb, scale 1.0975 = the paper’s sigma(Mb) = 109.75 df/dE x 1e-2, p. 303; the printed df/dE kept in the file). Points: H2 42/32, CO 52/41, N2 52/45, O2 71/65, CH4 20/20, N2O 63/59, CO2 59/54, SF6 59/48 (absorption/ionisation). All use = reproduced (every table reprints an earlier paper named at its head; none in the library), reproduced_from = that citation with authors from gallagher_1988’s record or this paper’s reference list. Uncertainty relative 0.05 (absorption) and 0.10 (ionisation), level not stated (“generally considered to be <= 5 % … <= 10 %”, p. 303).

• Checked: every cell of the eight tables against its image (rotated crops): all agree with the extraction. Title strips: missing for CH4 (e,e+ion) p. 326 (the page shows “CH4 (e,e+ion) J. Phys. B 8 (1975) 3020-3033.”), N2 (e,2e) p. 305 and N2O (e,2e) p. 315 (pages rendered); “SF_5” = SF6; the p. 313 CH4 strip heads the (e,2e)-type table there; its note prints J. Phys. B 8 “(1978)” for 1975.

• Errata (3): SF6 absorption at 23.0, 24.0, 25.0 eV printed 20.80, 35.30, 10.40 (image confirms the print) -> 120.80, 135.30, 110.40: the five-character column lost the hundreds digit; the photoionisation beside them is 118.58, 132.86, 106.92 (ratio ion/abs would be 5.7, 3.8, 10.3; corrected 0.98, 0.98, 0.97, as at 22 and 26 eV); gallagher_1988’s Fig. 95 description: a ~150 Mb peak near 23 eV (corrected 24 eV = 148 Mb). The digit is inferred, not seen: to be confirmed in review.

• Excluded rows (2, my judgement): O2 5.0 eV (0.92, 15x the 6.0 eV value, below the Schumann-Runge bands, ~1 Mb: unphysical); SF6 6.0 eV (8.40 in a 0.5-0.8 floor below the first band at 10-11 eV; adds 1.7 au to S(-2)). Both kept as printed. The SF6 5-9 eV floor (0.50-0.80) and O2’s 6.0 eV 0.06 are kept (background-like).

• Partial TRK sums (trapezoid, source notes): S(0) H2 1.967/2 (10-70 eV); CO 6.35, N2 6.19 (18-69 eV; N = 14, N_v = 10); O2 8.90 (5-75; 16/12); CH4 6.52 (14-80; 10/8); N2O 12.72, CO2 12.88 (8-74, 8-80; 22/16); SF6 30.03 with errata (5-63; 70/48). No table spans enough to test TRK. Partial S(-2): H2 5.34 au, O2 10.54 (same as Olney’s Table 1 VTRK O2 value, which uses this spectrum), N2O 19.05, CO2 17.34, CH4 9.89 (nothing below 14 eV), SF6 28.5 as printed.

• Relations: O2 is the Brion et al. 1979 spectrum that kumar_2011_supplement’s intervals j = 18-28 use and that olney_1997’s O2 (refs. [12,18]) combines: not independent. CO and N2 are the 1976 (e,e) spectra (Wight et al.), not the 1993 Chan et al. ones behind olney_1997; gallagher_1988 notes them highest at 20-30 eV (CO) and Backx’s CH4 tens of per cent above Samson at 30-70 eV.

• Not extracted: (e,2e) tables (pp. 304-317; CO/N2/O2/CH4 absorption columns repeat the (e,e) data; CO2 and N2O p. 314-315 are normalised at 35 eV to Lee et al. 1973, different values); all partial channels; non-curated molecules.

• Status: open (errata and exclusions for review).

TC-424 tu_2002 (2026-09-26)

• Where: Tu & Nee, Surf. Rev. Lett. 9, 125 (2002); text pp. 126-127; Table 1 p. 126.

• Transcribed: text_values (O3, absorption_cross_section, Mb, inline, 4 points, use = check, relative 0.15, level not stated): about 1 Mb at 176.2 nm (p. 126); about 15 Mb, the maximum “in 137-130 nm” (p. 126; row id “137-130”, wavelength “not stated” because none is given for the maximum); 30 Mb at 121.1 nm (p. 127); 20 Mb at 121.6 nm (p. 127). Vacuum wavelengths; temperature not stated; O2 absorption subtracted “by comparing with the previous data”; accuracy “about +-15 %” (p. 126).

• Checked: text against the extraction (no warnings on the pages used); Table 1 image: the Padial column does print “11.5” nm for 6a1 -> 3p (not in the region; a misprint, correction unknown, noted, not corrected).

• Doubts: the 137-130 nm maximum has no stated wavelength. The text refers to a “Table 2” of quantum defects that does not exist (they are in Table 1). Abstract 622 cm^-1 against text 600 cm^-1 for the 112-105 nm progression. Ref. 18 duplicates ref. 14’s journal reference.

• Note for review: mason_1996 has a dataset whose id is brion_1984 (J. Brion, Daumont & Malicet, J. Physique Lett. 45, L57 (1984), O3 Huggins band); unrelated to the new source brion_1984 (C. E. Brion & Thomson). No clash in the loader (dataset id, not a source id), but a possible reader confusion.

• Status: open (doubts).

TC-425 belli_2015 (2026-09-26)

• Where: Belli et al., Optica 2, 292 (2015); text pp. 294-297 (PDF n = p. 291 + n).

• Transcribed: dephasing_vibrational (1 ns) and dephasing_rotational (3 ns), H2, dephasing_time, abscissa pressure 1 bar, use = check, inline (p. 294, one figure, uncited). Formulas (no form): vibrational_T2 T2 = 318.3/(309/eta + 52 eta) ns and rotational_T2 T2 = 318.3/(6.15/eta + 114 eta) ns (p. 297), attributed to Bischel & Dyer [35].

• Checked: page images of pp. 294 and 297 (the UNMAPPED_GLYPHS pages): “17.6 THz” and the T2 formulas as extracted. vibrational_T2 reproduces Bischel & Dyer’s (library copy, uncurated) Q(1) A = 309 MHz amagat, B = 52.2 (Eq. (2): 51.8) MHz/amagat at 298 K with T2 = 1/(pi FWHM) (318.3 = 1000/pi); rotational_T2’s 6.15 and 114 are not printed in Bischel & Dyer (their S(1) curve, from van den Hout et al., is near 105 MHz/amagat at 300 K): origin not established.

• Notes only (no quantity fits as printed): chi(3) = 2.206e-26 m^2/V^2 “under standard conditions” [42] (Mizrahi & Shelton 1985, curated mizrahi_1985_h2d2) in P_K = eps0 chi(3) E^3 with the real field: this convention is not in optmat.vocabulary.CONVENTIONS (to be added if wanted; gamma_T = 6 eps0 chi/N = 699.5 au at 0 C, 1 atm; 750.8 au at 20 C). Raman shifts 17.6 and 124.56 THz (S(1), Q(1) ortho-H2; not converted, raman_shift is cm^-1 only). Raman gain 1.55 cm/GW (Weber’s CRC handbook). Two-level matrix elements (alpha11, alpha22, alpha12) (8.9, 9.4, 0.85)e-41 F m^2 rotation, (8.9, 9.73, 1.55)e-41 vibration. T1 ~20 ns. IPs 15.43 (H2), 15.76 eV (Ar), kind not stated. n_gas from Peck & Huang (peck_1977), no values.

• Missing? The list of requested papers has Bischel & Dyer, PRA 33, 3113 (1986) as missing: it is IN the library (Bischel_1986_TemperatureDependenceRaman), not curated. So is Bischel & Dyer, JOSA B 3, 677 (1986) (Bischel_1986_WavelengthDependenceAbsolute, the H2 Q(1) Raman gain against wavelength). Both could be curated (raman_linewidth, gain has no quantity).

• Status: open (the chi(3) convention is still to be decided).

TC-426 tammer_1992 (Tammer_1992_FieldCalibratedMeasurements) (2026-09-26)

• Transcribed: Table 1 tbl_4d048dca076d (CSV, image): H2 A_K against temperature, 13 re-corrected 1990 rows (table1_A_K_H2, check) and the new 303.7 K row (table1_A_K_H2_this_work, primary, sigma 1 sigma + systematic_relative 0.013); B_K^(4), B_K^(2) (14 rows each, kerr_virial_coefficient order 2, check); gamma per temperature (table1_gamma_H2, 14 rows, temperature as an extra column, check). Table 2 tbl_05229ef25c1e (JSON, image): table2_gamma_H2 4.68(14)e-62 SI (primary, e+v, component K, 303.7 K) and 5 literature rows (reproduced: shelton_1990, rosasco_1986, bishop_1991, Bishop-Pipin-Rerat 1990, Bishop-Lam 1988). Table 3 tbl_2ce09dc63f8c (JSON, image): table3_gamma_He 27.6(5)e-64 (primary, electronic, component K) and 4 literature rows (buckingham_1968, Boyle 1966, bishop_1989, Bishop-Lam 1988). Text: He A_K^(2) 2.321(11), A_K^(4) 2.312(12) e-30 (check); K/p (kerr_constant per bar, state 1 bar 303.7 K, check); gamma(H2)/gamma(He) = 16.94(17) (hyperpolarizability_ratio, check).

• Structural: the Table 1 header “10^29 Delta” extracts as “A” (column not taken); Table 3’s footnote “a)” extracts as “n)”.

• ERRATUM (scale): Eq. (11) prints K/p = 1.937(10)e-20 C^2 m J^-2 bar^-1; 1e-21 is meant (A_K^(2) gives 1.96e-21 by Eq. 3 with N = p/RT; Fig. 2’s axis K/1e-19 reads 1.5-1.9 at 76-97 bar). Page image of p. 156 checked: the paper misprints it.

• Checks: gamma(He) = 81 eps0 A_K^(2)/N_A = 27.64e-64; errors 0.49e-64 (He) and 0.138e-62 (H2) reproduced as statistical + 1.3 % of A_K added linearly; ratio 16.94 reproduced; orientation term (81 eps0 A_K/N_A - gamma) identical in the 1990 and 1992 tables to 5e-4.

• FINDING (1.0637): the re-corrected Table 1 is not the 1990 table times one factor: A_K(1992)/A_K(1990) mean 1.0634, sd 0.0022, range 1.0592 (376.5 K) to 1.0684 (219.5 K); a 1.0599-1.0660; b and B_K differ by 0.86-1.30: refitted, not rescaled. The corrected gammas scatter more (sd 0.076 against 0.046) and fall from 4.80 (196 K) to 4.57 (412 K).

• FINDING (376.5 against 376.8 K): the 1992 row printed 376.5 K is 376.8 K in 1990; its orientation term corresponds to 376.5 K (3.5731 against 3.5740 expected), so the new table was evaluated at 376.5 K. Which is right is not stated.

• Doubt: the He fit is forced through the origin at 76-97 bar; the pair term (~0.5 % of A_K at 80 bar, Buckingham’s theory) is not removed. The unlabelled Table 4 (H2 K at 12 pressures, 303.7 K) is in notes only (no quantity holds K against pressure).

• Format: the 1.3 % systematic has no stated level (a linear sum of T 0.11, p 0.25, compensation 0.5, field 0.4 %); recorded as systematic_relative (one sigma by convention).

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-427 tammer_1990 (Tammer_1990_AnisotropySecondHyperpolarizability) (2026-09-26)

• Transcribed (all check or reproduced; superseded calibration): Table 1 tbl_1f9c20083bf3 (JSON, image): A_K H2 (13) and D2 (1), B_K^(4), B_K^(2) H2 (13 each), gamma H2 (13, with temperature column) and D2 (1). Table 2 tbl_01dc04374704 (JSON, image): gamma this work H2 4.15(12), D2 4.17(16) e-62 SI, literature rows (buckingham_1968b, carusotto_1985 as transferred by the authors to 632.8 nm, Bishop-Pipin-Rerat 1990). Text: the ESHG- and ac-Kerr-transferred gammas 4.42(3), 4.57(23) (gamma^e), 4.52(23) (check, reproduced_from mizrahi_1985_h2d2, rosasco_1986).

• Formulas: Eq. (21) (ESHG gamma^e_par H2 = 4.067e-62(1 + 1.8393e-10 nu_L^2 + 0.7845e-20 nu_L^4)), Eq. (22) (dc Kerr gamma^e = 4.067e-62(1 + 1.928e-10 nu_L^2 + 0.947e-20 nu_L^4)). Check: Eq. 21 coefficients follow from Eq. 20 and Bishop & Pipin’s He (4.0669, 1.8394, 0.7845); Eq. 22 at 632.8 nm (nu_L^2 = 4.992e8) plus -0.045 gives 4.423 = the text’s 4.42.

• Doubts: Table 1 note b prints “Delta = A_K - K_K^calc” (A_K^calc meant; notes only). D2 was not re-evaluated in 1992: 1.0637 alone would give 4.73e-62 (758 au; computed, not published).

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-428 gentle_1989 (Gentle_1989_SecondHyperpolarizabilityStatic) (2026-09-26)

• Transcribed: Table I tbl_18459ce921c2 (CSV, image): A_K of CO2 at 9 temperatures (primary, relative 2 %, the printed fit errors kept only in printed), B_K (check, printed errors as sigma). Table II tbl_1b1d9fc6dd0c (CSV, image): gamma^K = 0.125 +- 0.032e-60 C m^4 V^-3 (primary, e+v, component K), static Delta alpha^0 = 2.41 +- 0.08e-40 (polarizability_anisotropy at inf, primary), optical Delta alpha 2.35 +- 0.07 (reproduced, Bogaard et al. 1978). Text: Buckingham 1970 values and the authors’ reanalysis (check), literature Delta alpha^0 (reproduced).

• Formula: A_K = intercept + slope/T (Table II).

• WAVELENGTH: 632.8 nm (Fig. 1 caption, Table I caption): closes TC-233’s question.

• UNIT MISPRINT: Table I’s B_K header prints mol^-1 where mol^-2 is meant (image checked: the paper misprints it). No erratum can hold a unit: recorded as m8 V-2 mol-2 with the misprint in notes. FORMAT GAP.

• FINDING: Table II’s line reproduces exactly as a fit weighted by the printed Table I errors with the standard errors scaled by sqrt(chi2/dof = 11.2): intercept 1.056 +- 0.269, slope 6.889 +- 0.096. So gamma^K’s +-0.032 is the Birge-scaled fit error, not the 2 % accuracy. Weighted by 2 % the intercept is 0.89 +- 0.79e-28 (gamma^K 0.106 +- 0.094e-60). The line misses 330.9 K by 1.4 %. Bears on the CO2 dc Kerr gamma used anywhere.

• shelton_1986_co2’s pre-publication 110 +- 39e-63 differs from the published 125 +- 32.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-429 shelton_1987 (Shelton_1987_VibrationalContributionsHyperpolarizabilities) (2026-09-26)

• Transcribed: Table 2 tbl_6c3a7b517193 (CSV, image): nu_01 (raman_shift) and B_0 (rotational_constant) per molecule, check, assumed = true; the transition polarizabilities in notes (FORMAT GAP: no quantity for a Raman transition polarizability). Table 3 tbl_d9a1dad537c6 (CSV, image; caption detached): static gamma^v at 293 K, Eq. (17) (primary) and Eq. (18) (check), per molecule. Table 4 tbl_a48923e63b94 (JSON, image): gamma^v at 15800 cm^-1 for dc Kerr (check), DFWM (process kerr), CARS (stokes_nm 751.88 computed from 13300 cm^-1), ESHG, THG (primary), per molecule (20 datasets). Note * of Table 4: the Eq. (17) dc Kerr values (4 text datasets, primary).

• Structural: Table 2’s D2 double dagger read as a dagger.

• ERRATA (5, from shelton_1987b ref. 10, page image checked): D2 CARS 2.426 -> 2.464; ESHG H2 -0.042 -> -0.064, D2 -0.020 -> -0.031, N2 -0.006 -> -0.008, O2 -0.004 -> -0.005. D2’s nu_01 printed 2998 in Table 4 (2988 in Table 2) is not stored from Table 4.

• Checks (recomputed from Table 2 with Eqs. 21-23): Table 3’s Eq. (18) column (1.149, 1.109 vs 1.110, 0.506, 0.734) and ratio column; Table 4 corrected values to the last digit except N2 CARS (-2.245 vs -2.231, 0.6 %, 170 cm^-1 from resonance). The printed D2 CARS 2.426 is what nu_01 = 2998 gives: the misprint was used in the calculation.

• Formulas: Eqs. (21), (22), (23).

• Component: gamma^v_xxxx of the isotropic average recorded as component ‘parallel’ (the printed xxxx is the lab-frame parallel component); dc Kerr as ‘K’.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-430 shelton_1987b (Shelton_1987_RotationalHyperpolarizabilityHomonuclear) (2026-09-26)

• No datasets (no numerical gamma values). Formulas: Eq. (5) (gamma^r for any process), Eq. (9) (dc Kerr). Notes: Eq. (7) damping, Eq. (10) classical limit = 3/4 of Buckingham’s (alpha_par - alpha_perp)^2/5kT at optical frequencies (“Buckingham’s ansatz … is only valid in the static limit”): bears on every dc Kerr gamma obtained by subtracting a Buckingham-Orr orientation term (tammer, buckingham_1968b, buckingham_1970, gentle). Ref. 10 = the shelton_1987 erratum (page image checked).

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-431 buckingham_1969 (Buckingham_1969_KerrEffectMethane) (2026-09-26)

• CH4 only. Table 1 tbl_d2bf39485ac8 (JSON, image): A_K (check, relative 5 %) and B_K (check, relative 10 %) at 249.7, 273.6, 303.7 K. Text p. 677: gamma(CH4) = 0.180 +- 0.009e-60 C^4 m^4 J^-3 (primary, part total, component K).

• Structural: A_K header extracts as “C^2m^3J^-2”; the image shows m^5 (unit recorded from the image).

• Check: 81 eps0/N_A x mean A_K = 0.179e-60; the +-0.009 is the 5 % absolute accuracy. In au 2887 +- 144.

• Notes only: Table 2 (finite-density mK against Kuss & Stuart), Table 5 (calculated B_K), CF4 and the fluoromethanes (out of scope).

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-432 buckingham_1968b (Buckingham_1968_ElectricBirefringenceMolecular) (2026-09-26)

• Transcribed (all check; superseded by Tammer): Table 1 tbl_4157737602db (CSV, image): A_K (relative 5 %) and B_K of H2 per set (17 sets, row “set n”, temperature abscissa). Table 2 tbl_a2e5fa68c008 (CSV, image; two side-by-side lists, set order checked against Table 1): gamma per set (esu, absolute 0.03 bound). Text: mean gamma 0.277 (+-0.03 bound), D2 A_K (5.9 +- 0.6), D2 gamma 0.24 +- 0.05 e-36 esu.

• ERRATUM (scale): p. 264 prints the D2 A_K as “(5·9 ± 0·6) × 10^14 e.s.u.”; 10^-14 meant (page image checked; Table 1’s H2 values are 10^14 A_K = 5.5-6.3). The erratum’s printed scale is “100000000000000.0” (how the loader stringifies 1e14).

• Notes: the quantum theory (Eq. 9, B_0 table), slope 8.0 +- 2 against QM 6.8 and classical 12.75e-12, B_K = 1.34 +- 0.2e-12 esu, Ward’s THG 0.45 +- 0.05 (personal communication).

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-433 buckingham_1970 (Buckingham_1970_KerrEffectSome) (2026-09-26)

• N2 and CO2 only. Table 1 (eight headerless fragments; gases identified by label cells and the page images of pp. 1550-1551): tbl_2089ba2fdb4d (CO2) and tbl_c5d4dfda3344 (N2): A_K (primary, relative 5 %), B_K (check, 1 sigma). Table 2 tbl_53d38067698d: gamma CO2 5.6 +- 1.2, N2 0.9 +- 0.1 e-61 SI (check, e+v, component K). Table 3 tbl_a0c4c55e9fd4: optical anisotropy (reproduced, Bridge & Buckingham 1966) and static anisotropy (check). Formulas: the two A_K(1/T) lines.

• FINDING: an unweighted line through Table 1 reproduces the intercepts and slopes, but the scatter gives intercept errors of 75 % (CO2) and 33 % (N2), not the printed 19 % and 12 %; without the 252 K point CO2’s intercept is -0.53e-28 (gamma -0.06e-60), as gentle_1989 and shelton_1986_co2 said. The gammas are 7.8 (CO2) and 1.6 (N2) times optmat’s fitted gamma_0 (1151, 920 au): long extrapolations, recorded as check.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-434 carusotto_1985 (Carusotto_1985_MeasurementKerrConstant) (2026-09-26)

• Transcribed: Table II tbl_569a1459caec (JSON, image): K of He, Ar, O2, N2, H2, D2 at 514.5 nm and 293 K (primary; errors include the 2.5 % systematic; level not stated); the upper block (He, Ar from buckingham_1968; O2 Breazeale 1935 at 650 nm; N2 from buckingham_1970 at 248 and 334 K; H2 and D2 from buckingham_1968b) as reproduced datasets (8). Table I tbl_77609c382209 (CSV, image): the individual runs per gas (check, density and field as extra columns).

• Checks: the upper block is the originals’ A_K times 13.5/22414 (He 0.1506, Ar 3.31, H2 3.807 and 3.316, D2 3.55 +- 0.36).

• UNIT MISPRINT: Table II’s header prints StatV^-1 (image checked; Table I’s note and Eq. 1 give StatV^-2): no erratum can hold a unit; recorded as cm2/statV2 amagat. FORMAT GAP.

• FINDING (states): Table II says He at 8 atm and the rest at 1 atm (Ar 1-2) and 293 K; Table I’s densities are 7.84/7.75 amagat for He (8.3-8.4 atm at 293 K; 8 atm is 7.46 amagat) and 1.05-1.07 (O2, N2), 1.30 (H2, D2) amagat (1 atm is 0.932). Per-amagat K is unaffected. For the upper block the state is the lower end of the printed range (a zero-density value converted; the state only records conditions).

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-435 dunmur_1979 (Dunmur_1979_InfluenceIntermolecularInteractions) (2026-09-26)

• Part I (theory), not the requested Part II. Table 2 tbl_02b495d28eaa (JSON, image): DID B_K at 250-330 K for Ar, Kr, Xe, CH4, SF6 (kind theory, check) and the “expt [19]” row (Part II, reproduced, citation as printed). Table 4 tbl_63fdb7ad5cff (JSON, image): C_K total at 300 K (check; contributions in notes, their sums reproduce the totals) and Part II’s CH4 -450, SF6 -10000 (reproduced). CF4, neopentane, mixtures (Table 3): notes.

• Doubt: Part II’s measurement wavelength and C_K temperature are not stated here.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-436 wahlstrand_2016 (Wahlstrand_2016_OptimizingTimeResolution) (2026-09-26)

• Notes-only record: a methods paper (SSSI time resolution, Eqs. 7-8); no n2, density or absolute scale; its n2 = 1e-19 cm^2/W is an assumed simulation input; the argon demonstration yields the probe’s dispersion (beta_2 = 1956 fs^2 …), not a gas property.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-437 Existing records edited (reproduced_from and notes only; no value changed) (2026-09-26)

• shelton_1994: table6_He_dc_kerr_expt -> tammer_1992, carusotto_1985 (row ‘ref 11’ = Tammer, digit-identical 44.26 au; ‘ref 19’ a conversion of Carusotto’s K); table12_CO2_dc_kerr -> gentle_1989 (digit-identical, 2005 +- 513 au); table12_CH4_dc_kerr -> buckingham_1969 (with Dunmur Part II kept as citation); Table VIII gamma^v: N2 and O2 (10 datasets) and also H2/D2 DFWM (their note f is Shelton 1987 too) -> shelton_1987, shelton_1987b (static, dc Kerr and DFWM digit-identical in au; the 694.3 nm ESHG and THG are recomputations, reproduced by Eq. 22 to 0.1 au).

• shelton_1986_co2: text_dc_kerr_gentle -> gentle_1989 (pre-publication 110 +- 39 differs from the published 125 +- 32; 632.8 nm confirmed); table2_dc_kerr and text_dc_kerr_reanalysed -> buckingham_1970 (558 is not digit-identical with 5.6e-61).

• shelton_1986_ch4: table2_dc_kerr -> buckingham_1969 (digit-identical).

• bishop_1991: expt_dc_kerr_H2 -> buckingham_1968b, carusotto_1985, tammer_1990 (notes: the Tammer 666 au is the superseded calibration; recalibrated 751 +- 22 au is above the theory’s 726); expt_dc_kerr_D2 -> tammer_1990.

• shelton_1993: gamma_R_tammer gains reproduced_from = [“tammer_1990”] (use stays check; Shelton’s own evaluation of Tammer’s expression, noted).

• carusotto_1992: kerr_*_ref3 -> carusotto_1985 (digit-identical).

• hellwarth_1990: 17 Carusotto, 2 Buckingham 1970 and 2 Buckingham-Orr 1968 citations -> ids (their values are Hellwarth’s conversions; notes unchanged).

• bishop_1989: the He dc Kerr citation of Carusotto -> carusotto_1985.

• hattig_1998: expt_dc_kerr_N2 -> buckingham_1970 (digit-identical 1443 +- 160 au; note: the value is e+v, its part is left ‘unknown’ as recorded; it may be set in review); expt_dc_kerr_Ar’s Carusotto citation -> carusotto_1985.

• Not edited (not assigned to this extraction), still citing these papers by text: lundeen_1983, rosasco_1985, ward_1969, ward_1979, ward_1984.

• Status: verified (2026-09-26): transcribed and checked against the table images; the doubts above are open unless TC-438 decides them.

TC-438 The review of the index, polarizability and Kerr extraction (TC-402 to TC-437) (2026-09-26)

• Where: TC-402 to TC-437 (five parallel extractions); the merged records.

• Merged:

  • 31 new source records: 429 datasets, 2631 values, 42 formulas and 11 errata.

  • Re-pointed reproductions in 18 existing records; no existing value changed.

  • poe test-library reproduces every file.

• Library duplicates, reported to J. C. Travers, not merged:

  • Hohm_1990_InterferometricMeasurementsDipole_68ebab is the version of record of the curated hohm_1990 (same DOI, identical tables);

  • Kirouac_1973_DielectricPressureVirial_8cbf89 is a second download of the curated kirouac_1973.

• Wrong or unexpected papers:

  • Dunmur_1979_InfluenceIntermolecularInteractions is part I (theory) of Dunmur & Jessup, Mol. Phys. 37, 697. The requested measurements are part II (Mol. Phys. 37, 713), still missing.

  • Wahlstrand et al. 2016 (JOSA B 33, 1476) is about the time resolution of spectral interferometry, not the Maryland group’s calibration, which stays open (TC-316).

• Decisions on the doubts raised at extraction:

  • Leviton & Frey’s Table 4 stays primary, although it is their formula on a grid: it is the authors’ representation of their measurements, as Franta’s tables are (TC-402). Their wavelengths are taken as vacuum wavelengths (CHARMS works in vacuum; at most 1e-5 in n at 0.45 um otherwise).

  • Brion & Thomson’s SF6 errata (23-25 eV, a dropped hundreds digit) are accepted. The evidence is circumstantial: the ionisation beside them, and the column width. The digit is not visible on the page (TC-423).

  • Clergent et al.’s 633 nm values stay recorded with real-gas density. They are n - 1 measured along the 20 degrees C isotherm; the ideal gas enters only their averaging (TC-417).

  • Static dielectric values (Bose, Schmidt & Moldover, Hohm 2013) are validators, not fitted (TC-400). Schmidt & Moldover’s printed uncertainties are their fits’; their budget (50-65 ppm) is in notes, for use if they are ever fitted.

• Findings for other records:

  • he_2021’s O2 row cites Hohm 1993 (Mol. Phys. 78), which has no O2. The data are Hohm’s Mol. Phys. 81 (hohm_1994b); annotated.

  • nie_2025’s “Olney” moments are Olney’s comparison rows, from Zeiss & Meath and Kumar & Meath; its reproduced_from is corrected (TC-422).

  • bishop_1991’s dc Kerr values of H2 and D2 carry Tammer & Hüttner’s 1990 calibration, superseded in 1992 by a factor of 1.0637 in K (TC-427).

  • kitamura_2007 gives Rodney & Spindler’s formula as for 31 degrees C; the paper says 24 degrees C (TC-403). Not edited: kitamura_2007 cites it only in notes.

  • Olney et al. print Thomas & Meath’s CH4 S(-6) as 289.3, where Hohm 1993 and Spackman print 298.3 (TC-421).

• Format gaps, none needed by a model yet:

  • no erratum for a misprinted unit (Gentle’s B_K, Carusotto’s Table II header, recorded in notes);

  • no quantity for a Kerr constant against pressure, or for a Raman transition polarizability;

  • raman_shift in cm^-1 only (Belli’s THz values are in notes);

  • no convention for Belli’s P = eps0 chi E^3 with the real field.

• Status: decided (2026-09-26) where stated.

TC-439 Raman and ionisation parameters for solprop: scope and parity targets (2026-09-26)

• Decision (the boundary): solprop is to hold no material parameters. optmat supplies the Raman and ionisation parameters, curated and validated, in a form ready for use:

  • for Raman: level energies, line strengths and linewidths in SI at a stated temperature and density;

  • for ionisation: ionisation energies, orbital quantum numbers, structure coefficients, static polarizabilities of the neutral and the ion, and the barrier-suppression constants.

  solprop keeps the response kernels and the rate formulas. optmat evaluates ADK, PPT and MO-ADK rates only privately, to validate its parameters. Constants fitted to a particular rate formula (effective charges, barrier-suppression coefficients) are recorded as such, never as material properties.

• Scope: solprop’s twelve pure gases (He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, CH4, SF6, N2O), plus CO2 and a standard dry-air composition. CO and O3 come later.

• Validation tiers for rates:

  1. published ab initio static-field rates and yields;

  2. measured yields with a stated intensity calibration;

  3. J. C. Travers’s own TDSE (tRecX) runs, only where tiers 1 and 2 leave a gap.

  Published PPT and ADK curves are never used as references.

• Transcribed: every Raman and ionisation value solprop uses at commit 9d81dff5, written by tools/solprop_raman_ionisation.py (run in solprop’s environment) to tests/data/solprop_raman.json and tests/data/solprop_ionisation.json.

  • Raman data exist for N2, O2, H2 and D2 (rotational and vibrational) and CH4 and SF6 (vibrational). N2O is “incomplete” and the atoms have none.

  • The ionisation data cover:

    • potentials for all twelve gases;

    • ADK and PPT quantum numbers for the five noble gases and for N2 and O2;

    • neutral and cation polarizabilities for He, Ne and Ar only;

    • MO-ADK coefficients (Tong 2002 and Zhao 2010) for H2, D2, N2 and O2;

    • barrier-suppression constants for the noble gases;

    • the dry-air fractions.

• Checked (against solprop’s source, not yet against the papers):

  • Potentials:

    • They are documented as NIST values rounded to four decimals in hartree, but O2 carries six.

    • Every gas’s IonisationData carries the same citation string (“molecular charges from Talebpour …”).

    • SF6’s 15.32 eV is a choice between two WebBook values (Delwiche 1969, Frost et al. 1967).

  • Quantum numbers: O2’s are (n, l) = (2, 0) with the fitted charge 0.53, although its highest occupied orbital is pi_g (m = 1). N2’s charge is 0.9. Both are cited to Talebpour et al., Opt. Commun. 163, 29 (1999), which is not in the library.

  • MO-ADK: the stored molecular_m and reference potential are not used by the rate, which takes solprop’s own potential. H2 and D2 share one coefficient row.

  • Occupancy: the default occupancy of 2 in ADK and PPT has no source in the code (“kept so that absolute rates match earlier published simulations”).

  • Barrier suppression: the constants (Tong & Lin 2005 Table 2; Zhang, Lan & Lu 2014 Table XI) are not independently checked. solprop drops the leading minus sign of Zhang’s eq. (8), calling it a misprint.

  • Raman, vibrational frequencies: the H2 and D2 frequencies are labelled “inherited approximate”.

  • Raman, reduced masses: these use standard atomic weights (N 14.0067, H 1.00784, D 2.014, F 18.998403 u), not isotopic masses; only O2’s is isotopic.

  • Raman, N2 dephasing: N2’s vibrational dephasing is a density-independent 6 ps, labelled “an inherited effective band approximation”. Its further source, “Sov. Phys. JETP 36, 9 (1959)”, is marked unverified; Mikhailov_1959 in the library is a candidate.

  • Raman, SF6 dephasing: SF6’s 6.6 ps is cited to Opt. Commun. 64, 393 (1987) (Everall et al., in the library).

  • Raman, linewidths: each gas’s rotational linewidth is one J’s width applied to all J.

• Doubt: none of the findings above has yet been checked against the primary papers. That is the work of the stages set out on the roadmap page:

  1. ionisation;

  2. Raman constants and strengths;

  3. broadening;

  4. Raman validation;

  5. a handover note for solprop, a proposal only.

  The papers still missing are listed on the roadmap page.

• Status: decided (2026-09-26) for the scope and the boundary; open for the parity of every value. The rates of the noble gases are now optmat’s (TC-652), which supersedes the boundary stated here for them.

TC-440 Vocabulary for the Raman and ionisation parameters; ions as materials (2026-09-26)

• Where: optmat.vocabulary, optmat.materials, data/materials.toml, optmat.constants; the data page’s tables.

• Decision: following TC-439, the curated data need these kinds of value:

  • tunnelling_structure_coefficient (ionisation): the asymptotic coefficients of the ionising orbital in a tunnelling theory.

    • MO-ADK’s C_l, Tong et al.’s atomic C_l, and the weak-field asymptotic structure factors.

    • One row per partial wave l, stating the model, the orbital, m and the normalisation. The normalisation is required because the published coefficients differ in their radial convention.

  • ionization_model_parameter (ionisation): a constant fitted within a named rate model, not a material property. Examples: Talebpour et al.’s effective charge, Tong & Lin’s alpha, Zhang et al.’s a1-a3. The quantity’s meaning says so, so that such a constant is never read as a property of the gas.

  • raman_transition_polarizability (raman): the matrix element of the mean or anisotropic polarizability between the two states of a Raman transition. It is independent of any normal-coordinate convention, unlike a derivative dalpha/dq with a reduced mass (the gap noted in TC-438).

  • raman_gain (raman): the steady-state stimulated Raman gain at a stated state.

  • raman_line_shift (raman): the collisional line shift or its coefficient.

  • vibrational_term_value (raman): G(v) from the ground level or the potential minimum (Hajigeorgiou’s O2 levels).

  • raman_scattering_activity (raman): the invariant g(45 a’^2 + 7 g’^2) of the compilations (Murphy et al. 1969).

  • raman_cross_section_ratio (raman): a cross section relative to a reference transition, usually N2’s Q branch (Danichkin; Schrötter & Klöckner).

  • broadening_temperature_exponent (raman): N in gamma(T) = gamma(T0) (T0/T)^N.

  • Existing quantities extended:

    • raman_linewidth also states the perturber for a broadening coefficient;

    • ionization_rate may be tabulated against a field, a new abscissa in V/m, V/cm or atomic units (AU_FIELD = E_h/(e a0)); a static field has wavelength_nm = inf and polarization = "static";

    • ionization_yield states the pulse envelope and carrier-envelope phase where given.

• Decision (ions): gas-phase cations are materials of their own, of a new kind ion: He+, Ne+, Ar+, Kr+, Xe+, H2+, D2+, N2+, O2+, CH4+, SF6+, N2O+ and CO2+. An ion’s static polarizability, needed for the Stark shift of the PPT rate, is thereby never selected as the neutral gas’s data. The alternatives were rejected:

  • a charge parameter would have needed a guard in every loop over a gas’s datasets;

  • a cation’s polarizability (He+ is exactly 9/32 au) falls below the 0.5 au floor of the gas polarizability test, which now allows 0.2 au for ions.

• Checked: new tests cover the conversion of a field in atomic units (5.142206747e11 V/m, CODATA) and an ion dataset’s separation from its gas; the vocabulary table on the data page is checked against the module.

• Status: decided (2026-09-26).

TC-441 The ionisation parameters: the static polarizability, and Ammosov et al.’s eq. (20) (2026-09-26)

• Where: optmat.gas.ionisation, and the private optmat.gas._tunnelling, which evaluates rates for validation only.

• Decision (the neutral’s static polarizability): the polarizability behind the Stark shift and dipole correction of the PPT rate is the electronic static polarizability. It is the sum f_i/E_i^2 of the fitted electronic terms of each gas’s dispersion model (fit/<gas>), with the fit’s Birge-scaled uncertainty.

  • It excludes the fixed infrared (vibrational) bands, because the nuclei do not follow an optical field.

  • It excludes the magnetic term, which is not an electric response.

  • The values, in au: He 1.38376, Ne 2.6611, Ar 11.077, Kr 16.762, Xe 27.075, H2 5.4325, D2 5.3645, N2 11.736, O2 10.587, CH4 17.258, SF6 30.060, N2O 19.704, CO2 17.527.

  • CO2’s full static polarizability (19.64 au, which matches the dielectric value) is 12 % larger because of its vibrational part.

  • Helium’s value is Puchalski et al.’s 4He static polarizability (1.38376077, with the relativistic, QED and finite-mass corrections), reproduced to 2e-7 by the fit.

• Finding (solprop’s polarizabilities): solprop’s neutral values, He 1.3207, Ne 2.376 and Ar 10.762 au (cited to Wang et al. 2021), are 4.6 %, 10.7 % and 2.8 % below these. They are close to Hartree–Fock values (reinsch_1985/scf_He, 1.322 au), not correlated ones. Which column of Wang et al.’s tables they came from is being checked in the extraction of wang_2021. The Stark shift is proportional to alpha_0 - alpha_+, so it is affected in proportion.

• Finding (Ammosov et al. 1986, eq. (20), misprinted):

  • eq. (19): |C_{n* l*}|^2 = 2^(2n*) / (n* Gamma(n* + l* + 1) Gamma(n* - l*));

  • eq. (20), as printed (checked on the page image, eq_ea56359d7a39), is (4e/(n*^2 - l*^2))^n* ((n* + l*)/(n* - l*))^(l* + 1/2) / (2 pi n*).

  Stirling’s formula applied to eq. (19) gives e^2 in place of e and the ratio inverted, (n* - l*)/(n* + l*). The printed form contradicts eq. (19), and at l* = 0 it also contradicts the paper’s own eq. (11), (2e/n*)^(2n*)/(2 pi n*). With l* = 0 it is 1.73 at n* = 1, where eq. (19) is 4 and eq. (11) is 4.70. adk_coefficient_squared implements the corrected form; a test checks that it converges to eq. (19) (1.7-2 % at n* = 10).

• Checked:

  • The static rate of Tong, Zhao & Lin (2002) eq. (7) reproduces the exact asymptotic hydrogen rate 4/F exp(-2/3F) to 1e-13 with C_0 = 2.

  • The orientation average of B^2(m’), sum_l C_l^2 Q^2(l, m’)/(2l + 1) (the orthogonality of the rotation matrices), matches a quadrature for a p-sigma orbital to 1e-7.

• Status: decided (2026-09-26) for the polarizability; corrected (2026-09-26) for eq. (20); open for the source of solprop’s values.

TC-442 The Raman lines: convention, nuclear-spin statistics and checks (2026-09-26)

• Where: optmat.gas.raman.

• Decision (the convention): the lines are given in solprop’s convention (TC-439), so that its adapter maps them one to one: P_x = eps0 N E_x ∫ h(tau) E_x^2(t - tau) dtau, with h = sum_k A_k sin(Omega_k tau) exp(-Gamma_k tau) and Gamma_k = pi FWHM_k.

  • Rotational S branch: A_J = (2/15) Delta alpha^2 / (hbar eps0) (J+1)(J+2)/(2J+3) (n_J - n_{J+2}), with n_J the population of one sublevel.

  • Vibrational Q branch: A_J = |<0|alpha_mean|1>|^2 / (hbar eps0) P_J, one line per rotational level, at nu_0 + (B_1 - B_0) J(J+1) - (D_1 - D_0) [J(J+1)]^2. The transition polarizability replaces solprop’s dalpha/dq and reduced mass. For a harmonic mode the two are identical, (dalpha/dq)^2 hbar/(2 mu Omega), but the transition polarizability needs no choice of coordinate or mass (solprop’s CH4 and SF6 “per bond” conventions, TC-439).

  • The distortion series: a truncated series B x - D x^2 turns over at high J. The ladder is cut at its last increasing level, and a temperature that populates that level is refused.

• Transcribed (from memory, standard nuclear data): the nuclear spins I(1H) = 1/2, I(14N) = 1, I(16O) = 0, and the ground-state symmetries (Sigma_g^+, O2’s Sigma_g^-). D2’s I = 1 is Murphy & Johnston’s (murphy_1934, TC-173). The weights follow from exchange symmetry:

  • H2 even:odd = 1:3; D2 and N2 6:3;

  • O2 odd N only; CO2 even J only;

  • N2O and CO without alternation.

• Checked:

  • The S-branch amplitudes equal solprop’s printed form -K (J+1)(J+2)/(2J+3) [p_{J+2}/(2J+5) - p_J/(2J+1)] to 1e-13.

  • Their integral sum_J A_J/Omega_J approaches the classical orientational response Delta alpha^2/(30 eps0 k_B T) to within 2 % for B = 2 cm^-1 at 295 K (the corrections are O(B/k_B T)).

  • solprop’s H2 vibrational coupling (1.803981e-37 m^5 V^-2 s^-1, from dalpha/dq = 1.3e-20 m^2 and mu = 1.00784 u/2) is reproduced to 1e-6 through the harmonic transition polarizability.

• Status: decided (2026-09-26); the curated constants, strengths and linewidths enter with the ionisation and Raman records (TC-445 to TC-490). Corrected in TC-493: the classical limit checked is 3/4 of the classical orientational response, not all of it.

TC-443 nist_asd_2026 (NIST Atomic Spectra Database, ionisation energies) (2026-09-26)

• Where: data/external/nist_asd/ionization_energies.csv (as returned, with its query and sha256 in PROVENANCE.md), and the record nist_asd_2026. The record’s citation, version 5.12 (7 November 2024) and DOI 10.18434/T4W30F were checked on NIST’s version-history page.

• Transcribed: the ionisation energies (eV) and their uncertainties.

  • The first ionisation energies of He, Ne, Ar, Kr and Xe, to the ion’s ground level. The final states are as NIST prints them: 1s 2S1/2, and np5 2P*3/2 for the rest.

  • The ionisation energies of their cations (the atoms’ second), recorded as the ions’ own (material He+ … Xe+).

  • Ten inline points, the strings of NIST’s CSV.

• Checked: tests/test_nist_asd.py compares every inline value, uncertainty and final state with the stored file. The atoms’ values against solprop’s snapshot (hartree rounded to 4 decimals):

  Gas	NIST (eV)	solprop (eV)	solprop − NIST
  He	24.587389011	24.5882	+0.8 meV
  Ne	21.564541	21.5650	+0.5 meV
  Ar	15.7596119	15.7608	+1.2 meV
  Kr	13.9996055	13.9921	−7.5 meV
  Xe	12.1298437	12.1308	+1.0 meV

  Krypton’s 0.5142 hartree is 13.9921 eV, 7.5 meV (5e-4 relative) below NIST’s. It is not a rounding of NIST’s value (13.9996 eV is 0.51448 hartree). The others are NIST’s to their four-decimal rounding in hartree.

• Doubt:

  • Level: the confidence level of NIST’s uncertainties is stated neither on the output nor on the help page, so it is recorded as “not stated”.

  • He II: printed in parentheses (ab initio), so use = "check".

  • Xe II: printed in square brackets (semi-empirical), so use = "check".

• Status: verified (2026-09-26).

TC-444 The ionisation parameters of the gases: choices, a stopgap source and the validation (2026-09-26)

• Where: data/gas/ionisation.toml (each choice with its reason), optmat.gas.ionisation, the record nist_webbook_2026, the page docs/ionisation.md, and tools/ionisation_tables.py, which writes the page’s tables (tests/test_ionisation_page.py).

• Decision (ionisation energies):

  • Atoms: NIST ASD 5.12 (TC-443).

  • Molecules: no primary determination is in the library yet. nist_webbook_2026 records, as reproduced from their primary papers, the determinations the NIST Chemistry WebBook lists:

    • H2: McCormack et al. 1989;

    • D2: Takezawa & Tanaka 1975;

    • N2: Trickl et al. 1989;

    • O2: Tonkyn et al. 1989;

    • CH4: Berkowitz et al. 1987;

    • SF6: Frost et al. 1967;

    • N2O: Berkowitz & Eland 1977;

    • CO2: Wang et al. 1988;

    • and a vertical value for O2, CH4, SF6, N2O and CO2.

    This departs from data rule 6, which says to take nothing from a secondary source when the primary is not at hand. The departure is deliberate, and limited to a stopgap:

    • the WebBook is NIST’s evaluated compilation, the counterpart for molecules of the ASD for atoms;

    • every value names its primary;

    • the primaries are requested on the roadmap.

    The WebBook pages were read, not stored.

  • Kind: the recommended energy is the adiabatic one, which is also the threshold of multiphoton ionisation and the energy a plasma loses per ionisation. The vertical energy is given beside it where it differs: O2 +0.26 eV, CH4 +1.0, SF6 +0.34, N2O +0.004, CO2 +0.012. A tunnelling rate at fixed nuclei sees the vertical energy, and the choice enters the rate’s exponent. Open: which energy the propagation code should use for tunnelling is J. C. Travers’s decision.

• Decision (structure coefficients):

  • Molecules: Zhao et al. 2010 Table III is the default, with Tong et al. 2002 Table I as the alternative. D2 takes the “D2/H2” row, because the electronic structure at fixed geometry is shared.

  • Atoms: Tong et al. 2002 Table II.

  • CH4, SF6, N2O: none are curated, so the parameters say so (no default) rather than falling back silently.

• Decision (polarizabilities):

  • Neutral: the electronic static limit of the fitted model (TC-441).

  • Cation: Wang et al. 2021’s CCSD(T) for He+, Ne+ and Ar+. Kr+, Xe+ and the molecular cations have none; they are requested.

• Decision (barrier-suppression alpha): Tong & Lin 2005’s fitted values for He (7), Ne and Ar (9).

  • Kr and Xe have none: solprop’s 9.0 for them is the paper’s suggestion for p states, not a fit.

  • Zhang, Lan & Lu’s coefficients and Talebpour et al.’s effective charges are not curated (the papers are requested). solprop’s use of l = 0 for O2, whose HOMO is pi_g (m = 1), is recorded against it.

• Checked (the static rate against the ab initio references, tier 1): Tong et al.’s eq. (7), with the curated parameters, for one electron in the orbital aligned with the field, divided by the reference rate:

  • He:

    • Parker et al. 2009 (full TDSE): 1.03 and 1.01 at F = 0.045 and 0.05 au, 0.82-0.96 at 0.06-0.12 au, and rising above 1 beyond (2.5 at 0.38 au, above the barrier-suppression field).

    • Majety & Scrinzi 2015 (haCC(5)): the same within 2 %.

    • With Tong & Lin’s barrier-suppression factor the rate is 0.63-0.89 of Parker’s at every field, 0.86-0.89 at the lowest. So for He the factor lowers the rate even where the uncorrected formula is right.

  • H2 (parallel):

    • Saenz 2002, frozen nuclei: 1.42 at 0.06 au, up to 2.22 at 0.12.

    • Majety & Scrinzi’s fixed-nuclei rates: 2.1-2.5. Saenz 2002 notes that its frozen-nuclei rate is 56 % above Saenz 2000’s fixed-nuclei rate at 0.06 au.

  • N2 (parallel): 1.17 at 0.03 au, then rising steeply. N2’s barrier-suppression field kappa^4/16 is 0.082 au, and the formula is not meant beyond it.

• Finding (occupancy): with the curated coefficients, the one-electron rate is what agrees with helium’s exact two-electron rate at low field. solprop’s default occupancy of 2 (TC-439) doubles it.

  • For H2 and N2 the one-electron rate is already 1.2-2 times the references.

  • Majety & Scrinzi multiply their SAE rates by 2 for the double occupancy, with SAE orbitals of their own. So the factor belongs to a particular normalisation of the coefficients, not to the physics alone.

  • The page states the comparison and does not choose the factor; the rate formula, and so the factor, is the propagation code’s.

• Finding (against solprop):

  • Ionisation energies: solprop’s agree with these to 1 meV, except Kr (−7.5 meV, TC-443), CH4 (+5.2), N2O (+12.2) and SF6 (−30: its 15.32 eV lies between Delwiche’s 15.30 and Frost’s 15.35).

  • Polarizabilities: its neutral values are Wang et al.’s Hartree–Fock ones (confirmed by the extraction of wang_2021): He −4.6 %, Ne −10.7 %, Ar −2.8 % against the fitted static limits. Its cation values are also Hartree–Fock (Ne+ −5.3 %).

• Gaps:

  • No ab initio or calibrated measured rates are curated for Ne, Ar, Kr, Xe, O2, CO2, CH4, SF6 or N2O.

  • Majety & Scrinzi’s Ne and Ar results are in figures only. Batishchev et al. 2010 and the others are requested.

  • This is where J. C. Travers’s tRecX calculations would serve (tier 3); the runs wanted are listed separately.

• Status: decided (2026-09-26); open for the kind of energy for tunnelling, and for the gases without references. The statement that helium’s occupancy is 1 is superseded by TC-658 (the effective numbers of electrons, from the corrected rate).

TC-445 tong_2002 (Tong, Zhao & Lin, PRA 66, 033402 (2002)) (2026-09-26)

• Transcribed: Table I (tbl_3048e91bd1cc, cells only, image checked, p. 3): I_p (eV) and C_l for H2+ (sigma_g; material H2+), the row printed “D_2 (sigma_g)” (material D2), N2, O2 (pi_g, l = 2, 4 only), CO (l = 0-3); R (angstrom) as the per-row column internuclear_distance of each C_l file. 5 ionization_energy (1 point each), 5 tunnelling_structure_coefficient (3, 3, 3, 2, 4 points). Table II (tbl_58844fa6da0d, CSV, image checked): I_p, C_l and C_l(ADK) of He, Ne, Ar, Kr, Xe (15 datasets, 1 point each; row l = 0 for He, 1 for the p atoms, m = 0). F2, S2, NO, SO not curated (notes). Table III (rate ratios) in notes.

• Normalisation: Eqs. (1)-(2), p. 2: F_l(r -> inf) ~ r^(Z_c/kappa - 1) e^(-kappa r); m = 0 for sigma, 1 for pi, m = 0 for atoms (p. 4). Rate formulas Eqs. (6)-(10) and (11)-(14) quoted in the notes. The rate is per orbital, no occupation factor.

• Uncertainty: the Table I C_l carry the paper’s “estimated to have an error at the 20% level” (p. 8) as relative 0.2, level “not stated” (the vocabulary has no “estimated” level).

• Erratum: Table II’s He I_p printed 23.59 eV corrected to 24.59 (the image prints 23.59; tong_2005 and zhao_2010 give 0.904 hartree, hohm_2012 24.587387, wang_2021 24.587). Needs a register entry.

• Doubt 1 (kind): Table I’s I_p are recorded kind = "not stated": the text says the vertical energies used for D2 and O2 are 0.88 and 0.33 eV larger than Table I’s (pp. 6, 7), so Table I’s are not vertical; the paper does not say they are adiabatic. solprop’s moadk reference_potential (15.58, 15.47, 12.03 eV) are these values.

• Doubt 2 (labelling): the hydrogen row is printed D_2 and recorded as D2; the paper uses it for H2 too (Fig. 2); zhao_2010 prints “D_2/H_2” (recorded there as H2). Whether a model maps the D2 row to H2 is still to be decided.

• Doubt 3 (C_l(ADK)): the ADK column is not reproduced by ADK’s Eq. (19) or its Hartree form converted to Eq. (2) (C_l = C_nl kappa^(n*+1/2)): He 2.92/2.54 vs 2.67 printed, Ne 2.78/2.47 vs 2.52, Ar 2.25/2.17 vs 2.19, Kr 2.05/2.04 vs 2.04, Xe 1.80/1.85 vs 1.86. The paper says only “our definition of the ADK coefficients is somewhat different” (p. 3).

• Note: CO’s C_l: the expansion centre (“the center of the molecule”) matters for the odd waves; the text’s N2:Ar “0.98” (p. 8) is not Table III’s R (1.15).

• Status: open (erratum and register entry for review).

TC-446 zhao_2010 (Zhao, Jin, Le, Jiang & Lin, PRA 81, 033423 (2010)) (2026-09-26)

• Transcribed (56 datasets): Table I (tbl_fba864ad07cc, cells, image checked, p. 4): LDA+LB I_p (hartree) of He-Xe (5, check), Banerjee & Harbola’s for He, Ne, Ar (3, reproduced), experimental (5, reproduced from Emsley); kind = "adiabatic" (atoms). Table II (tbl_b4bf810303ee, p. 4): LDA+LB (6, check) and “experimental vertical” I_p (eV) of H2+, H2 (“D_2/H_2”), N2, O2, CO, CO2 (5 reproduced from tong_2002; CO2 13.78 check). Table III (tbl_7f5181e18a32, cells, image checked, p. 4): new C_lm of H2+ (3 pts), H2 (3), N2 (3), O2 (2), CO (5), CO2 (3) (check); reprinted [9] = tong_2002 rows (H2+, H2, N2, O2, CO; reproduced), [30] = awasthi_2008 (H2), [17] Le et al. 2007 (CO2). Table IV (tbl_2bc9b27f5a3b, p. 6): HOMO/HOMO-1/HOMO-2 energies, LDA+LB (N2, O2, CO2: 3 rows; CO: 2), LB-alpha (Telnov & Chu for N2, O2; Son & Chu for CO2; reproduced), experimental vertical (Lofthus & Krupenie, Baltzer et al., Turner et al.; reproduced); rows labelled by the orbital. Table V (tbl_825e661a911b, p. 6): HOMO-1 and HOMO-2 C_l of N2, O2, CO2, HOMO-1 of CO (7 datasets, 3-5 points). R from Table II as the column internuclear_distance of every C_l file.

• Structural fixes: (1) Table V’s cells file drops the fifth column of the CO and HCl blocks: CO 1pi (HOMO-1) C_5m = 0.02 is added in the script from the image (p. 6), guarded by the exact extracted row; CO 5sigma C_4m = 0.05 comes from Table III. (2) Table IV’s footnote d (“Reference [6]”, Son & Chu) is lost from the library text; read on the page. (3) Table V’s HOMO rows equal Table III’s (script check); Table VI’s H2+ 1s sigma_g row at R = 2.0 equals Table III’s H2+ (script check).

• Doubt 1 (reproduced I_p): Table II’s I_p column cites nothing; it is digit-identical (with R) to tong_2002 Table I for all ten shared molecules, so it is recorded as reproduced from tong_2002 (an inference). The caption calls them “experimental vertical”, which tong_2002’s text contradicts for D2 and O2 (TC-445). Kind recorded as the caption says (vertical).

• Doubt 2 (hydrogen): “D_2/H_2” recorded as material H2 (the figures use it for H2); solprop’s moadk_zhao2010 applies it to H2 and D2. No D2 dataset is written from zhao_2010.

• Doubt 3 (erratum): PRA 82, 049903(E) (2010) is not in the library; solprop’s snapshot says it leaves the neutral rows unchanged: not verified.

• Not stated in the paper: the fitting range of r for Eq. (20), any accuracy of the C_lm, and which I_p enters kappa in the fit. The paper: “we always use experimental binding energy” and “one should always use the experimental vertical ionization energy” (p. 4) for the rates.

• Findings: the CO reprint of Tong’s row adds C_4m = 0.00 (Tong printed l <= 3); Table IV’s O2 HOMO I_p 12.3 (Baltzer) differs from Table II’s 12.03; the [30] row is awasthi_2008’s LB94 row rounded.

• Status: open.

TC-447 tong_2005 (Tong & Lin, J. Phys. B 38, 2593 (2005)) (2026-09-26)

• Transcribed: Table 2 (tbl_87ba350a98ce, CSV, image checked, p. 2596): alpha (ionization_model_parameter, model tong_lin_2005, parameter alpha) and I_p (hartree, check, kind adiabatic) of He, Ne, Ar, Ne+, Ar+ (10 datasets, 1 point each). Table 1 (tbl_3240f8c18932, CSV): Z_c, a_1-a_6 of Eq. (4) (model tong_lin_2005_potential), 5 datasets of 7 rows. Text p. 2596-7: alpha = 6 for H2+ (inline). H and Rb not curated.

• Checks: Eq. (1) F_b = kappa^4/(16 Z_c) reproduces Table 2’s F_b for all but Ne+: 0.2835 computed against 0.2845 printed (a misprint or a more precise I_p; F_b is not a dataset). Table 1: Z_c + a_1 + a_5 = the nuclear charge for every target.

• solprop: BSI_TONG_LIN_ALPHA He 7.0 = Table 2’s fitted He; Ne 9.0 and Ar 9.0 = Table 2; Kr 9.0 and Xe 9.0 are not fitted in the paper but follow its recommendation “alpha = 6.0 for electrons ionized from the s-wave and alpha = 9.0 for … higher partial waves” (p. 2596). By that recommendation He (1s) would take 6.0; solprop uses the fitted 7.0. No disagreement with the paper’s numbers.

• Doubt: the I_p are “the measured one” (p. 2596) without a citation: check, not reproduced.

• Status: open (the model choice is still to be made).

TC-448 ammosov_1986 (Ammosov, Delone & Krainov, Sov. Phys. JETP 64, 1191 (1986)) (2026-09-26)

• Transcribed: Table II (tbl_06845899aeaa, cells only, image checked, p. 1193): for He, Ne, Ne+, Ar, Ar+, Kr, Kr+, Xe, Xe+ the handbook coefficient A (Z/n*)^(n*-0.5) with its +- error (reproduced from Radtsig & Smirnov 1980; use = "reproduced", sigma column, level not stated) and Eq. (11)’s value (check); n* as the column n_star; abscissa none (the paper does not state l; Eq. (11) is l-independent). 18 datasets, 1 point each.

• Structural fix: Kr+’s cell prints “2,30=0,12” (image checked at 400 dpi); the “=” stands where every other cell has “+-”: read as 2.30 +- 0.12. Decimal commas read as points.

• Formula check: Eq. (11) C = (2e/n*)^n* (2 pi n*)^(-1/2) at the printed n* reproduces 7 of 9 to the printed digits; Ar gives 2.137 (printed 2.13), Kr+ 2.252 (printed 2.26). Eq. (11)’s maximum over n* is 2.2528 (at n* = 1.40), so Kr+’s 2.26 cannot come from it: probably a misprint for 2.25; not corrected (still to be decided: an erratum?).

• Equations (1), (2), (3) (printed without the r in the second factor), (10)-(14), (19)-(21), (25) quoted in the notes. Table I (intensities at w = 0.01/tau and 0.1/tau, tau = 1.1 ns) in notes: the wavelength is not stated and the “probability” is a rate per pulse length, so no ionization_yield. The library header of Table I’s last column says 10^15 W/cm^2; the page says 10^14.

• Status: open.

TC-449 awasthi_2008 (Awasthi, Vanne, Saenz, Castro & Decleva, PRA 77, 063403 (2008)) (2026-09-26)

• Transcribed: Table I (tbl_4bbfbf50c79d, CSV, image checked, p. 6): H2 at R = 1.4 a0, vertical I_p per method (HF, LB94, TSLDA, LDA, SAE-CI, CI: check, kind vertical per p. 6; HF [6] Kjeldsen et al.: reproduced, kind not stated; X-alpha [17] = tong_2002: excluded) and C_0, C_2, C_4 (m = 0) for HF, LB94, TSLDA (check), HF [6] (2 points, reproduced), X-alpha [17] (reproduced from tong_2002). 13 datasets.

• Finding: the X-alpha [17] row quotes Tong’s C_l correctly but its I_p as 15.70 eV, which is Tong’s F2 value (Tong’s hydrogen row: 15.47): ip_xalpha_tong excluded.

• Occupancy (TC-439): the SAE yield of H2 should be doubled for the two equivalent electrons for yields below 10 % at 800 nm (p. 7, Fig. 4); the unscaled SAE agrees with CI above ~20 %. Quoted in the notes.

• Status: open.

TC-450 mironov_2025 (Mironov et al., arXiv:2501.11672v2 (2025)) (2026-09-26)

• Transcribed: Table III (tbl_bcc8c2bd802b, CSV, image checked, p. 17): C_nl of Ar (3p^6: exact 1.001, ADK 1.016) and Ar+ (3p^5: exact 0.914, Hartree 0.426, ADK 0.869), row l = 1, model adk with approximation. 5 datasets. The neutral’s Hartree “1.0” is set by hand (p. 17) and is not taken; Ar2+ … Ar17+ are not materials (notes). Tables I and II (Ar8+ pathways, m ordering) in notes.

• Doubt (normalisation): Eq. (8), p. 4, prints psi ~ 2 C sqrt(kappa) (kappa r)^(n*-1) e^(-kappa r) Y_lm (image checked). With it a hydrogen-like ion would have C = Z, but Table III gives C = 1.0 for Ar17+ (1s) and the rate Eq. (6) is the exact hydrogen-like rate with C = 1: the table follows kappa^(3/2), not sqrt(kappa). The two readings differ by a factor kappa: 8 % for Ar, 43 % for Ar+. With kappa^(3/2), 2 C of this paper = ADK’s C_nl. This must be settled before converting.

• Status: open.

TC-451 wang_2021 (existing record, extended) (2026-09-26)

• Added: Table 2 HF (hf_He, hf_Ne, hf_Ar; check) and NHF (reproduced from Stiehler & Hinze 1995); Table 1 (tbl_c22e704aed88, CSV, image checked) I_p of He, Ne, Ar, CCSD(T) (check) and experimental (reproduced from Moore 1970, NSRDS-NBS 34, not NIST ASD as first supposed); Table 3 He+ (tbl_82ace8ce2dca, p. 5), Ne+ (tbl_eede931cbc2d, p. 6), Ar+ (tbl_0bf0dd86ab78, p. 7; which part is which was read from the images): HF and CCSD(T) (“Ours.”) for each (check); quoted Calc./CHF/Expt. values reproduced: He+ Tang et al. 2012 0.28119; Ne+ Medved et al. 2000 1.33, Thakkar & Abhijit 2001 1.306; Ar+ Stewart 1975 (CHF) 6.84, Medved et al. 6.85, Bristow & Glass 1972 (Expt.) 7.2(3) with sigma 0.3. 20 new datasets, 1 point each; no existing value changed (existing files byte-identical).

• Structural fixes: the first Table 3 part breaks numbers with spaces (“0. 281 1”); Table 1’s cells file lost the second and third block headers into the experimental cells (“24.587F”); the Ar+ Calc. footnote reads “ijj” in the cells, “jjj” (Ref. [96]) on the page.

• Question in review (solprop’s six numbers): all six are the HF column. Neutrals: He 1.3207, Ne 2.376, Ar 10.762 = Table 2 column HF (the CCSD(T) column gives 1.3821, 2.662, 11.084; NHF 1.3222, 2.377, 10.758). Cations: He+ 0.2811, Ne+ 1.2417, Ar+ 6.807 = Table 3 row HF (CCSD(T) “Ours.” 0.2811, 1.3110, 6.834). HF lies 4.4 %, 10.7 %, 2.9 % below CCSD(T) for He, Ne, Ar and 0, 5.3 %, 0.4 % for He+, Ne+, Ar+.

• Status: open (solprop’s inputs to be switched if wanted).

TC-452 hohm_2012 (existing record, extended) (2026-09-26)

• Added: Table 1 (continued) (tbl_9ebc9ba30435, image checked, p. 699): I_1 of He, Ne, Ar, Kr, Xe (ip1_, material the atom) and I_2 (ip2_+, material He+ … Xe+), all reproduced from the CRC Handbook 76th ed. (ref 3, table note a), kind adiabatic; the final state of I_2 (the doubly charged ion’s ground state) is not stated. 10 new datasets. Table 4’s fit parameters of Eqs. 1-4 quoted in the notes. The note “Ionisation potentials … are not extracted” was replaced.

• Status: open.

TC-453 loriot_2011 (existing record, extended) (2026-09-26)

• Added: Table II (tbl_701638991ad8, CSV, image checked, preprint p. 14): the table is of the MOLECULES N2 and O2 and the atom Ar (first described as N and O atoms): IP_neutral 15.6, 12.07, 15.8 eV (N2, O2, Ar) and IP_ion 27.12, 24.14, 27.6 eV (N2+, O2+, Ar+). 6 datasets, check (no source cited), kind “not stated” for the molecules and their cations, adiabatic for Ar and Ar+. The chi(3) ratio row not taken. The record’s “No datasets” note was amended.

• Status: open.

TC-454 mahla_2025 (Mahla & Mehnen, J. Chem. Phys. 163, 234312 (2025)) (2026-09-26)

• Transcribed: Table I (tbl_0127e8228e7c, cells only, image checked, p. 5): R-matrix vertical I_p of O2 (6 states) and O3 (3 states) (check), and the quoted experimental values per footnote (reproduced): O2 Baltzer et al. PES (6 rows), Tonkyn et al. PFI (X: 12.070), Edqvist et al. PES (a 16.101, A 17.045); O3 Katsumata/Wiesner/Couto PES (3), Brundle/Frost/Dyke PES (3), Willitsch et al. PFI-ZEKE (2A1 12.75, 2B2 12.66). 8 datasets, rows labelled by the final ionic state; kind vertical as the caption says.

• Doubt: the PFI and PFI-ZEKE values (Tonkyn’s O2 12.070, Willitsch’s O3 12.75, 12.66) are threshold measurements, likely adiabatic, though the caption calls the whole table vertical; flagged in their notes, not re-kinded. Cross sections are figures only.

• Status: open.

TC-455 majety_2015 (Majety & Scrinzi, J. Phys. B 48, 245603 (2015)) (2026-09-26)

• Transcribed (41 datasets):

  • Table 1 (He, tbl_f4022cb09486): haCC(5) (primary, 13 rows, 0.06 excluded as a bound) and haCC(1) (check, 13/1 excluded); the literature columns [11] = parker_2009 (13), [17] Scrinzi 1999 (11), [32] Themelis 1999 (12), all reproduced; ADK (check, 13).

  • Tables 2-3 (H2, R = 1.4 au, parallel angle_deg 0 / perpendicular 90): haCC(1), (2), (4), (5), 4 points each (haCC(5) primary); [18] Saenz 2000 reproduced (4).

  • Tables 4-5 (vertical energies of the ionic states, eV, label rows): N2 tz (5), qz (1), Svensson (5, reproduced); CO tz (5), Baltzer (4, reproduced), Svensson (5, reproduced).

  • Tables A1 (N2, haCC(5), 7 angles x 12 values + 1 excluded bound) and A2 (CO, haCC(6), 13 angles x 14 values + 1 excluded bound), all primary.

• Checked: every table against its image; digit-identical. Majety’s [11], [17], [32] and ADK columns are digit-identical to parker_2009 Table 1 at the 13 common fields.

• Structural fix: Table A2’s last row carries the continuation’s header (“5.26 × 10-3105°”); the script strips exactly the expected angle. No erratum.

• Uncertainty: the paper’s accuracy statements recorded, level not stated: He haCC(5) 10 % (F < 0.1 au) / 5 % (F >= 0.1), H2 parallel haCC(5) 4 %, N2 and CO 10 %. Lower schemes are convergence steps (check).

• What the rates count: the width of the N-electron ground state: the whole atom or molecule, all channels, not per orbital. Fig. 1 caption: the SAE rates compared with haCC ‘include multiplication by a factor 2 for the double occupancy of the ionizing orbital’ (bears on TC-439’s occupancy question).

• Doubts:

  • p. 7 prints ‘F < 0.5 a.u’ for the low-field quadruple-zeta change; the tables end at 0.14 au: probably 0.05. Notes only.

  • Table 5 prints the CO state D ^2Pi_u (g/u meaningless for CO): a label misprint, kept in the row id.

  • p. 8 prints the yield asymmetry with a minus in the denominator ((Y0 - Y180)/(Y0 - Y180)), a misprint of the definition (page image checked). Notes only.

  • use: haCC(5)/(6) marked primary as the converged results; for He and H2 parallel the full-dimensional benchmarks (parker_2009 present work, Saenz 2000) are more accurate: still to be decided.

  • N2/CO internuclear distances (‘equilibrium’) are not printed.

• Solprop: N2 potential 2.49639e-18 J = 15.5812 eV against Svensson’s X 15.58 (reproduced), the paper’s own 15.5 (tz) and 15.60 (qz).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-456 parker_2009 (Parker et al., J. Phys. B 42, 134011 (2009)) (2026-09-26)

• Transcribed: Table 1 (tbl_f4122d1f56cb), 4 datasets: present work (26 points, primary), Scrinzi 1999 (15, reproduced), Themelis 1999 (19, reproduced), ADK (27, check).

• Structural fix: the library table is scrambled (per column, the characters of all rows interleaved in one cell). Transcribed from the image; the script checks each column’s character multiset against the scrambled cell (all five pass; the E, Scrinzi and ADK columns also match exactly when interleaved by character position).

• Formulas: Eq. (8) (static fit) reproduces the present-work column within 2.6 % at 24 of 26 fields, +7.3 % at 0.05 au and -6.5 % at 0.067 au. Eq. (7) (laser fits at 780, 390, 195 nm) not checkable.

• Doubt (ADK column): a two-electron static ADK with Ip = 0.903724 au is 0.783 (Gamma C_nl) or 0.970 (Stirling C_nl) of the printed column, constant to 0.1 % at every field except E = 0.20 au (0.809 / 1.003): the printed 1.07e-2 is +3.3 % off its neighbours’ trend (about 1.11e-2 expected). Probably a misprint; not corrected (a check column). majety_2015 reprints it (1.07e-2), which supports that Majety copied Parker’s ADK column. For review: erratum or leave?

• Convergence: grid 0.3 % at 0.1 au, 0.03 % at 0.3 au; no adiabatic response above 0.38 au; no overall uncertainty stated (none recorded).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-457 parker_2007 (Parker et al., J. Phys. B 40, 1729 (2007)) (2026-09-26)

• Transcribed: figures only; two text rates as inline points (use = check): 390 nm, 30e14 W/cm^2, ‘typical’ 0.013 au (p. 6); 780 nm, 14.5e14 W/cm^2, ‘typical’ 0.0013 au (p. 6). Eq. (5) gives 0.0107 and 0.00142 au there.

• Formulas: Eq. (5) (both wavelengths, coefficients checked on the page image p. 13), Eqs. (1)-(3), Eq. (4), and the AC-ADK rate (p. 12, image checked).

• Finding: the AC-ADK prefactor 5.053 is reproduced (5.0525) only with the Stirling form C^2 = (2e/n*)^(2n*)/(2 pi n*) and Ip = 0.903724 au; the Gamma-function C^2 gives 4.078. The formula is per electron; the paper doubles it for He.

• Uncertainty (p. 5): under 2 % (390 nm), under 4 % (780 nm); not attached to the ‘typical’ points.

• Solprop: the paper’s He Ip 0.903724 au = 24.5916 eV (infinite nuclear mass) against solprop’s 0.9036 au = 24.5882 eV. Not a dataset (model input, kind not stated).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-458 saenz_2002 (Saenz, Phys. Rev. A 66, 063408 (2002)) (2026-09-26)

• The citation first requested gave 063407 (with a query); the paper and DOI are 063408 (part II).

• Transcribed: Table I (tbl_b2f3d07790b3, JSON), 24 datasets (schemes a-d x v = 0, 1, 2, 4, 9, 14), 6 fields each except (c): 5, 4, 4, 3, 2, 1 points. (a) v = 0 primary, everything else check; (b) and (d) are ADK evaluations. Image checked; no erratum.

• Orientation: parallel only (angle_deg 0). Rate of the molecule (both electrons), rotationless.

• Formula: Krainov’s MADK as corrected by Saenz (Ai’ for Ai in Krainov’s Eq. (15)), recorded; not checkable (figures).

• For review: Saenz 2000’s fixed-nuclei rate at F = 0.06 au (3.36e-5, reprinted in majety_2015 Table 2) is 56 % below this paper’s frozen-nuclei v = 0 rate (5.248e-5): solprop’s H2 comparison must choose fixed or frozen nuclei.

• No accuracy number stated; uncertainty left unstated.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-459 augst_1991 (Augst et al., J. Opt. Soc. Am. B 8, 858 (1991)) (2026-09-26)

• Decision: Table 1 (intensity shift factors) is NOT recorded as ionization_model_parameter: the paper calls it a comparison aid (‘simply to facilitate the comparison’), fitted by eye, and within the factor-2 intensity calibration uncertainty. All rows are quoted in notes (image checked): BSI 1.0; ADK Xe 1.0, Kr 1.2, Ar 1.7, Ne 1.8, He 2.0; 3D dc tunnelling (Xe) 1.7; Keldysh (Xe) 0.7; KFR (Xe) 0.6; KFR (He) 1.0; Szoke (Xe) 4.2. For review: agree?

• Inconsistency: Fig. 10 caption gives the KFR (Xe) shift as 0.63 (Table 1: 0.6).

• Formulas: BSI threshold Eqs. (5)-(6) (the constant 4.00e9 checked: 4.0005e9) and ADK Eqs. (8)-(10) (Stirling C, cycle-averaged, ‘summation over the degenerate m states’).

• Library identity VALIDATED_WITH_WARNINGS (citation.bib author ‘Chint’).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-460 augst_1989 (Augst et al., Phys. Rev. Lett. 63, 2212 (1989)) (2026-09-26)

• Notes only: appearance intensities in figures. Text numbers quoted (10 ions ~ 5e-3 probability; factor-2 absolute, <25 % relative intensity uncertainty). Differences from augst_1991: bandwidth 30 A vs ~20 A; f/6 vs f/5.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-461 walsh_1993 (Walsh, Decker & Chin, J. Phys. B 26, L85 (1993)) (2026-09-26)

• Notes only: saturation intensities in Fig. 1 only, and all scaled to Xe’s calculated value. Text IPs (O 13.62, CO 14.01, C 11.3, Xe 12.13 eV) quoted, not taken.

• Formula: Ilkov-modified ADK, Eq. (1) (image checked): same field dependence as the cycle-averaged ADK with m = 0 and Stirling C; prefactor ratio 0.943 (Xe), 1.063 (15.43 eV), 1.309 (He). This is the ADK that saenz_2002’s ADK rows use.

• CO2-laser wavelength not stated in the paper.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-462 popruzhenko_2008 (Popruzhenko, Mur & Popov, Phys. Lett. A 372, 5167 (2008)) (2026-09-26)

• Notes only; the in-scope rows of both tables quoted (image checked): Xe, Kr (1.55 eV), Ar, Ne, He (3.1 eV) and Ne+ (12.7 eV), all at 1e13 W/cm^2. Model evaluations for s-states (‘order-in-magnitude estimates’).

• The printed gamma is ~6 % above kappa omega/E for the peak field of 1e13 W/cm^2 (Xe 3.18 vs 3.4, He 9.08 vs 9.6): conversion not stated.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-463 golovanov_2020 (Golovanov & Kostyukov, Quantum Electron. 50, 350 (2020)) (2026-09-26)

• Notes only; Eqs. (1)-(6) quoted (Eq. (1) checked on the equation image).

• Finding: Eq. (1) as printed has the prefactor w_a k^2 = 2 Ip (au, since k^2 = I_i/I_H), where the quasistatic ADK with the same C_kl^2 and B (yudin_2001 Eq. (1)) has Ip: it is twice that rate (for H: 8/F exp(-2/(3F)) w_a). Intended or a misprint? To be decided before using the formula.

• Which crossing of Eqs. (1) and (5) defines E1 is not said (they cross twice in Fig. 2).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-464 yudin_2001 (Yudin & Ivanov, Phys. Rev. A 64, 013409 (2001)) (2026-09-26)

• Notes only; Eqs. (1), (2), (11)-(13), (15)-(20) quoted. Checked numerically: Eq. (12) at theta = 0 equals gamma^2[(1 + 1/(2 gamma^2)) arcsinh gamma - sqrt(1 + gamma^2)/(2 gamma)] (the Keldysh/PPT exponent) to machine precision, tends to 2 gamma^3/3; Eq. (16) is within 0.05 % of Eq. (12) at gamma = 2.

• The C factor of Eq. (18) needs A_m from PPT (Sov. Phys. JETP 23, 924 (1966), Eqs. (55)-(56)): not in the library.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-465 forster_2014, murray_2011, gkortsas_2011, smyth_1998 (2026-09-26)

• All notes only (figures only, or no rates).

• forster_2014: FC-ADK Eq. (9) with N_e = 2 ‘the number of active electrons’ (occupancy, TC-439); the quoted 800 nm range ‘gamma = 0.67-2.6’ looks wrong at the low end.

• murray_2011: CO2 structure parameters (lambda = 2.5, n = 1, m = 1, c = 0, C_kappa = 0.66) are a Radzig-Smirnov-form fit, not per-l C_l: not recorded. Fig. 3 panel labels contradict the caption (reported from the page image by the survey).

• gkortsas_2011: HHG efficiencies only; YI prefactor not stated.

• smyth_1998: methods paper (HELIUM code); Table 2 N = 6/7 at delta r = 0.3333 break the monotonic trend (image checked), probable misprint, not used; ‘10^6/6’ on p. 2 should be 10^5/6.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-466 bendtsen_1974 (new record) (2026-09-26)

J. Bendtsen, J. Raman Spectrosc. 2, 133 (1974), doi 10.1002/jrs.1250020204 (identity checked; the journal is right). Material N2 = 14N2 (“natural nitrogen”); 14N15N and 15N2 in notes only (Tables II, III, V, VI and their constants).

• Transcribed (tools/extract/bendtsen_1974.py; 19 datasets, 89 points):

  • Table I (p. 136) pure rotational S(0)-S(18), |nu| (Stokes/anti-Stokes mean), sigma = “est. dev.” (level not stated): table1_S_N2 (19). The table prints the lower J; rows written S(J).

  • Table IV (p. 138) fundamental band: table4_O_N2 (16, O(2)-O(17)), table4_Q_N2 (13, Q(8)-Q(20)), table4_S_N2 (18, S(0)-S(17)), sigma = est. dev.

  • Table VII (p. 141; JSON cells; “+- n” in units of the last decimal, standard deviations, internal consistency only): table7_B0_rot_N2 1.989574(12) primary (italic = preferred), table7_D_rot_N2 5.76(3)e-6 primary, table7_B0_rotvib_N2 1.989707(12) check, table7_D_rotvib_N2 5.71(5)e-6 check, table7_nu0_unconstrained_N2 2329.9168(3) primary (+ absolute 0.01, p. 142), table7_nu0_constrained_N2 2329.9156(7) check, table7_dB_unconstrained_N2 (B0 - B1) 0.017384(3) primary, table7_dB_constrained_N2 0.017357(6) check. The parenthesised B0, D of the constrained row (held fixed) not taken.

  • Table VIII (p. 143): alpha 0.017292(3) (unconstrained, preferred) and 0.017265(6), both check (alpha = B0 - B1 + 2 gamma with Lofthus’s gamma = -4.6e-5, assumed).

  • Table IX (p. 143): B_e 1.998232(12), check (derived). r_e in notes (no quantity).

  • Table X (p. 144, the unlabelled tbl_66df62a78ce2): literature rows reproduced, one dataset per constant: table10_B0_N2 (4: Stoicheff, Butcher, Wilkinson, Vanderslice), table10_D_N2 (5), table10_alpha_N2 (2: Lofthus, Wilkinson), table10_nu0_N2 (1: Stoicheff’s Q-branch maximum 2329.66(20)). Parenthesised values (“transferred from Stoicheff [1] and used in a constrained analysis”) are Stoicheff’s held fixed in Lofthus’s and Wilkinson’s analyses: not taken (constrained, not reproduced). “This work” row not taken (Table VII rounded, but nu0 printed 2329.92 +- 2, i.e. +-0.02).

• Checked: Table I obs - calc reproduced from the Rot. constants to <= 0.0002 cm^-1; Table IV obs - calc from the unconstrained constants to <= 0.0003 (the constrained ones leave up to 0.016); alpha = B0 - B1 + 2 gamma exact; B_e = B0 + alpha/2 - gamma/4 = 1.9982315 (printed 1.998232).

• Structural: Table VII’s JSON puts the 14N15N label on the two rot-vib rows only (the image shows the “Rot.” row above belongs to 14N15N; same for 15N2): isotopologue rows not used. Table X’s caption is detached (“TABLE X Molecular constants for 14N2” extracted as text).

• Printed oddities (no dataset affected, no erratum): Table VII 15N2 B0 - B1 printed “0.015667 - 2” (+- misprinted as minus); Eq. (5) prints “D J^2(J0+1)^2” for D J0^2(J0+1)^2.

• Doubts: vacuum vs air wavenumbers not stated; inferred vacuum (calibration on CO infrared constants). Temperature not stated. The est. dev. level is not stated. The +-0.01 cm^-1 absolute accuracy (p. 142) is a plate-dependent common offset: put on nu0 as absolute uncertainty, not on each line (in notes). Uses: I made the italic (preferred) values primary and the rest check; a different split may be preferred (e.g. only lines primary, constants check, to avoid counting the lines and the constants fitted to them twice).

• Formulas: none recorded (Eqs. (5)-(6) are carried by the constants).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-467 hajigeorgiou_2013 (new record) (2026-09-26)

P. G. Hajigeorgiou, J. Chem. Phys. 138, 014309 (2013). 16O2 X 3Sigma_g-. kind = “fit”.

• Transcribed (tools/extract/hajigeorgiou_2013.py; 12 datasets, 321 points):

  • Table I (p. 014309-2), the fit’s inputs, v = 0-31: table1_G_O2 (32, check: the author’s own Dunham fit of literature G; printed without Y00 = 0.331962, which “must be added to all calculated term values”: recorded with reference = minimum and a caution in notes), table1_B_O2, table1_D_O2 (x1e-6), table1_H_O2 (x1e-12) (32 each, reproduced from Yu et al. 2012’s Dunham coefficients).

  • Table III (p. 014309-5), this work, v = 0-38: table3_B_O2, table3_D_O2, table3_H_O2 (39 each, primary). G_v is identical to Table V (script checks) and is stored once as table5_G_O2 (39, primary, reference minimum).

  • Table IV (p. 014309-7), v = 29-38: table4_G_yang_wodtke_O2 (10; rows 36-38 excluded, note d “extrapolated”; sigma 40 from note b), table4_B_yang_wodtke_O2 (10, absolute 0.01 from note c), table4_G_bytautas_O2 (10), table4_B_bytautas_O2 (10), all reproduced (Yang & Wodtke 1989; Bytautas et al. 2010, ab initio). The present-work columns (Table III rounded) not taken.

• Structural fix: Table III’s library cells are column-scrambled (each column is one string of its characters in glyph order). Transcribed in the script from the PDF text layer (pdftotext -layout, pdf page 6), checked row by row against the image; the script checks each column’s character multiset against the library cells and the G column against Table V’s cells. D_v and H_v (“m x 10^-k”, exponents change down the column) written as “me-k”.

• Formula: potential (Table II + Eqs. 2-6, 7, 9-11, 14), without a form. Check: my radial-Schroedinger solution (finite differences, Richardson) reproduces Table III/V G_v to <= 0.0001 cm^-1 for v = 0-11, <= 0.0004 to v = 26, <= 0.0065 to v = 38, and B_0-B_3 to <= 2e-8 cm^-1. D, H not recomputed.

• Finding: with Table II’s A = 16591.891596 and q = 15.525821 as printed, the inner wall A/r^q (55 664 cm^-1 at 0.925 A) does not join the Morse-like branch (53 943), though the text says A, q were set by value and slope there (p. 014309-3); the continuous join (A = 15543.5, q = 15.960) spoils G_v for v >= 26 by up to 0.22 cm^-1, so the printed A, q are those used. Matters only above v ~ 25.

• Spin (for solprop): the paper never says “spin-free”. Its B_v, D_v, H_v are those of Eq. (1) E = G + B N(N+1) - D[N(N+1)]^2 + H[N(N+1)]^3 (Hund’s case (b), N without spin): “It is not the objective … to carry out an analysis of the spin-spin and spin-rotation structure” (p. 014309-1); Yu et al. fitted those separately. So they are the mechanical N-ladder constants, spin-spin and spin-rotation excluded (what solprop calls spin-free). The potential “is associated with the Omega = 1 spin component” (p. 014309-7).

• Doubts: no uncertainty stated for Table III (fit sd 0.0031 cm^-1 on term values); Table I’s G zero (Y00) does not fit either reference value exactly: a note in the vocabulary, or its exclusion, may be wanted.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-468 teal_1935 (existing record extended) (2026-09-26)

• Added (tools/extract/teal_1935.py, new; JSON cells, images checked; 8 datasets, 45 points): table1_H2 (6), table1_D2 (11): Table I AVERAGE, pure rotational, rows as printed J initial-final (“3-1” anti-Stokes, “1-3” Stokes); table2_H2 (3, Q(1)-Q(3)), table2_D2 (9, Q(1)-Q(6), S(0)-S(2)): Table II AVERAGE; absolute 0.3 cm^-1 (“good to approximately 0.3 cm^-1”, p. 762, level not stated); table2_calc_H2 (4), table2_calc_D2 (10): the “T. & M.” calculated lines (check), including the unobserved Q(0); text_deltaG1_H2 4160.2(2) and text_deltaG1_D2 2993.5(2) (p. 763) as vibrational_term_value (row v = 1, reference v0: G(1) - G(0) is what Delta G_1 means; it is not an observed line). HD in notes only.

• Formulas: vibrational_terms_H2 and vibrational_terms_D2 (Table III omega_e, x omega_e, y omega_e, z omega_e; no quantity holds vibrational constants). Checked: Delta G_1 = 4160.415 (H2; Table II calc 4160.4) and 2993.246 (D2; printed 2993.2). The D2 constants are derived from H2 and HD by isotope relations: check only.

• Erratum: table1_D2 row 3-1, AVERAGE printed 297.3, corrected 297.1: the plates (297.5, 297.5, 296.4) average 297.13 and the DIFFERENCE column prints -0.6 against CALC. 297.7. Evidence: the image. An inference from internal consistency (for review).

• Doubts: several D2 averages are not plain means (4-2 rotational 415.0 for 415.15; Q(2) 2986.9 for 2986.53; Q(3), Q(5)) but agree with their DIFFERENCE columns: kept, noted. Many H2 lines are single-plate (Plate III), so +-0.3 may be optimistic (single-plate errors 0.5-1.0). Temperature of the gas not stated; 3 atm. The existing notes were kept, with the stale “not extracted (for later)” paragraph replaced by the new sections.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-469 chen_2007 (existing record extended) (2026-09-26)

• Added (inline points, text): B_fit_H2 61.8 cm^-1 and B_fit_D2 30.4 cm^-1 (p. 11355, check; no uncertainty stated; effective j = 0 -> 2 beat constants, 6B = omega_2,0 / (2 pi c); D2 reproduced from omega_2,0 = 3.44e13 s^-1: 30.44); T2_O2 23.2 ps at 5.1 atm (p. 11353, gamma = 4.31e10 s^-1) and T2_N2O 23.8 ps at 2.4 atm (Fig. 6 caption, p. 11353), dephasing_time against pressure, check, transition “pure rotational S branch (rho_j,j-2 coherences, one gamma for all j)”. Notes updated (the “not extracted” sentence replaced).

• Not stored: the N2O rate 1.46e10 s^-1 atm^-1 (p. 11356): a rate per pressure is not a dephasing time; as a HWHM coefficient it would be 2.32 GHz/atm, an interpretation the paper does not make (still to be decided).

• Finding: B_fit is 4.6 % (H2) and 2.0 % (D2) above the B_eff from teal_1935’s S(0) lines (59.1, 29.8). And p. 11355 says for H2 “even j states are 3 times more populated than odd j states”: the reverse of the nuclear-spin weights (shelton_1987 g_ns 1/3; solprop odd 3, even 1). Added to notes.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-470 reichert_2015 (existing record extended) (2026-09-26)

• Added (script extended; Table 1 image and text layer checked): B_fit_N2 1.9896(2), D_fit_N2 5.9(6)e-6, B_fit_O2 1.4377(2), D_fit_O2 5.1(5)e-6 (check, columns “a” = this work’s fit; level not stated); B_raman_N2 1.989574(12), D_raman_N2 5.76(3)e-6 (reproduced from bendtsen_1974, digit-identical, cited via Weber 1979 [41]); B_raman_O2 1.437682(9), D_raman_O2 4.852(12)e-6 (reproduced from Weber 1979; original not identified). 8 new single-point datasets.

• Doubt: the a/b column marks have no footnote in the paper; identified from the text (“values of B and D found from fitting … comparison to Raman scattering measurements [41]”, p. 22232). O2 fitted without the electron-spin splitting.

• Weber’s O2 B = 1.437682(9) is 7.5e-6 above Hajigeorgiou’s Table III B_0 (<1 sigma); D 4.852(12) vs 4.839482 (1.0 sigma).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-471 zheltikov_2007 (new record) (2026-09-26)

A. M. Zheltikov, Opt. Lett. 32, 2052 (2007) (identity checked; the journal is Opt. Lett., not Phys. Usp.). A model of air’s Raman response (80 % N2, 20 % O2); theory, figures only.

• Inline points (p. 2053, text layer checked), all check with assumed = true: B_N2 1.99, B_O2 1.44 (uncited); alpha_N2 0.0173, alpha_O2 0.0159 (reproduced_from Long, The Raman Effect (2002) [17]); Omega_N2 2330, Omega_O2 1556 (Q-branch centres; no own citation). 6 datasets, 6 points. I used check + assumed (the docs’ rule for model inputs) rather than use = reproduced, which was first suggested; B and Omega have no cited source.

• Model in notes: Eqs. (1)-(3) with Z weights, omega_J = 4 pi B c (2J + 3), V_J, normalisation, the CARS-fitted rotational/vibrational amplitude ratio (not printed).

• Finding: Eq. (2)’s F_J prints (rho_{J+1} - rho_J) where the cited Nibbering et al. Eq. (16) has (rho_{J+2} - rho_J) (text layer checked): a slip, noted only. Its “alpha” is the Q-branch spacing (B0 - B1), called the rotation-vibration constant.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-472 murphy_1969 (Murphy, Holzer & Bernstein, Appl. Spectrosc. 23, 211 (1969)) (2026-09-26)

• Transcribed: Table I, first part (tbl_ca70dea8e569, p. 212), the in-scope molecules H2, D2, O2, N2, CO, CO2, CH4, SF6: 51 datasets, 84 points (shift, I_j/I_1 as raman_cross_section_ratio against CH4 nu1, rho_n as depolarization_ratio natural, scattering activity, dalpha/dQ and dalpha/dr as polarizability_derivative mean, with parameters.coordinate), all reproduced from the cited refs (1, 8, 10, 16-20; none in the library). Plus two inline text values (p. 217), use = "check": the selected CH4 nu1 activity 205 (+-5 %) and dsigma/dOmega = 6.58e-30 cm^2 at 4358 A.

• Structural fix: the library cells merge sub-lines without separators and lose some (CO2 I/I1 and rho of 1388/1409 cm-1; CH4 nu1 activities 207 and 200). The in-scope lines are transcribed from the image in the script, which checks the concatenation of each cell’s lines against the library cell. Table order: ca70 (p. 212), 30a7 (p. 213), e29d (p. 214), d8cd (p. 215), 9220 (p. 216); continuations out of scope.

• Units: N in ‘N x 10^-32’ and ‘N^(1/2) x 10^-16’ is Avogadro’s number (checked: Eq. 2 with 205 gives 6.60e-30 against 6.58e-30), so activity is recorded in angstrom4/amu and dalpha/dQ in angstrom2/amu^(1/2) at scale 1; dalpha/dr cm2 scale 1e-16. The library reads N^(1/4); the image shows N^(1/2).

• Checks (2026-09-26): a’ from S and rho reproduces the printed dalpha/dQ (N2 0.656, O2 0.519, H2 1.732, D2 1.218, SF6 0.710, CH4 2.145/2.108). Eq. (4)/(5) reproduce dalpha/dr for N2, O2, H2, D2, CH4 refs 17/18/8; not CO (1.50 -> 0.573 vs [0.58]), CH4 ref 19 (1.08 vs 2.10) or SF6 (Long & Thomas’s 1.23 -> 0.691 vs [0.71] recomputed from the activity). Eq. (2) reproduces I_j/I_1 from the activities to a few % except CO (8 %).

• Doubts / misprints (notes only, no errata since nothing extracted is wrong): Eq. (7) printed without the fourth power of (nu - nu_j)/(22938 - nu_j); Eq. (6) needs gamma_AB squared; Table II’s CH bond anisotropy ‘0.31 x 10^-14 cm^3’ is 10^-24 (reproduced as 3.1e-25 from Eq. 6 with the square). The extraction’s b_j exponent 3/2 is 1/2 on the page.

• Format notes for review: (1) polarizability_derivative has only a wavelength abscissa; I used 4358 A (standard air) for every derivative, ratio and rho. (2) dalpha/dr (per bond, w.r.t. bond length) is not a derivative w.r.t. a normal coordinate as the quantity text says; I used the quantity with parameters.coordinate to distinguish it. Whether this is acceptable is still to be decided. (3) Activities: 10 % bound applied to the diatomics, SF6 and CH4 nu1 (‘strong and narrow bands’), none to CO2 and CH4 1535/3017.

• solprop: N2 1.75e-20 m^2 = dadr_N2 [1.75] (ref 1); O2 1.46e-20 = dadr_O2 [1.46]; CH4 1.04e-20 = dadr_CH4_nu1 ref 17 (Yoshino & Bernstein 1959; refs 18, 8, 19 give 1.03, 1.08, 1.08); SF6 1.23e-20 = dadr_SF6 (Long & Thomas 1963), which is not Eq. (5) of the table’s own a’ = 0.71 (that gives 1.26). All are mean-polarizability bond derivatives, 4358 A. Shifts: N2 2331, O2 1555, H2 4156, D2 2986, CH4 2914, SF6 775 cm-1 (to 1 cm-1).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-473 bermejo_1977 (Bermejo, Escribano & Orza, J. Mol. Spectrosc. 65, 345 (1977)) (2026-09-26)

• Citation: the citation first requested, “J. Raman Spectrosc. 6”, is wrong; it is J. Mol. Spectrosc. 65, 345 (1977), DOI 10.1016/0022-2852(77)90274-0.

• Transcribed (CH4 only): Table I (tbl_602282e66a5e, p. 348) shift_CH4 (5 points + nu4 1310 excluded, not ‘our measurement’), intensity_CH4 (4 points: nu1 223, 2nu2 7, nu2 7.0, nu3 128; primary); Table II (tbl_29036d066e28, p. 350) intensity_exp_CH4 (3, with sigma; nu1 230 = 223 + 2nu2) and intensity_calc_CH4 (3), both check. Text (p. 349, 352): the Penney/Fouche reproductions 237 and 223 (reproduced); c(S1) = 2.260 +- 0.042 A^2 (mean) and c(S2..S4) (anisotropy tensor elements) as polarizability_derivative w.r.t. Mills symmetry coordinates; alpha’_CH = 1.130 +- 0.021 A^2 (mean, per bond) and gamma’_CH = 2.05 +- 0.16 A^2 (anisotropy, per bond).

• Units: I = g(45a’^2 + 7g’^2) N 10^-32 cm^4 g^-1, N Avogadro (footnote b): angstrom4/amu. Absolute via CH4 nu1 against CH4’s Rayleigh line; 488.0 nm (air).

• Not extracted: every CH4 depolarization ratio (footnote d: expected, not measured); nu4 upper limits; the four deuterated isotopologues (notes); gamma_CH (bond anisotropy 0.279 A^3) and gamma’^(alpha) (angle derivative) in notes. Structural fix: nu3’s braced pair of maxima joined in one cell, split in the script.

• Checks: c(S1) from I(nu1) = 45 m_H^-1 c(S1)^2: 230 -> 2.270, 223 -> 2.235 (fit 2.260, five molecules). Eq. (3) alpha’_CH = c(S1)/2 = 1.130 and Eq. (5) gamma’_CH = 1.5 c(S3) = 2.049 reproduced.

• Doubt: the +- level is never stated. Table I (primary) vs Table II exp (check): a choice; Table II is the paper’s ‘adopted’ values with the overtone added to nu1.

• solprop: CH4 dalpha/dr 1.04e-20 m^2 (Murphy ref 17); Bermejo’s per-bond mean derivative is 1.130 +- 0.021 A^2 = 1.130e-20 m^2 (8.7 % higher). CH4 nu1 at 2916.7 cm-1 (band maximum) against solprop’s 548896066713799.8 rad/s = 2914.0 cm-1 (Murphy’s 2914).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-474 danichkin_1981 (Danichkin et al., J. Appl. Spectrosc. 35, 1057 (1981)) (2026-09-26)

• Citation: J. Appl. Spectrosc. 35, 1057-1066 (1981), translated from Zh. Prikl. Spektrosk. 35, 581 (1981); DOI 10.1007/bf00605646.

• Transcribed: Table 1 (tbl_fede8ab1f190 p. 1058, tbl_e069277a54e8 p. 1059, tbl_c9af12ff6f78 p. 1060) for N2, O2, D2, H2, O3, CO, CO2 (nu1, 2nu2, 1409, 1265), N2O (nu1, nu3), CH4 nu1: shift (check), measured rho per reference (reproduced, polarization = "linear"), sigma/sigma_N2 per reference with the original excitation wavelength as column excitation_nm (reproduced); all at the survey’s system (488.0 nm, linear, theta = pi/2, both components, Q branch). Table 2 (the unlabelled tbl_d60a413f5ef7: ‘Absolute Differential Cross Sections for Vibrational RS for the Nitrogen Molecule (lambda_0 = 488 nm)’, caption above the table on the page): 10 rows (the printed ‘5.5 and 6.2 (entire band)’ row split into two) as raman_cross_section, 1e-31 cm2/sr, reproduced. Text p. 1063: recommended sigma_N2 = (5.5 +- 0.2)e-31 cm2/sr (check). Table 3 recommended rho and ratio per gas (check). 51 datasets, 132 points.

• Structural fix: Table 1’s cells join stacked lines and lose H2’s ‘1,6 (Q, J=1)’, its reference [12] and two 488,0 wavelengths: transcribed from the images, checked against every cell. H2’s ‘2,44+0,24’ is printed with ‘+’ (read as +-). CO’s ‘0.055’ printed with a point.

• Doubts: the depolarization ratios’ wavelengths are not given (only the survey’s system); O3’s four [32] values are braced without wavelengths. Ref [17] for H2 rho (0.0112) is Kolos & Wolniewicz (kolos_1967), a computed value. The 694.3 nm N2 row (13.80) is a factor 2.5 off the rest, uncommented. Ratios are per molecule (divided by N/N0: CO2 hot bands 0.075, CO2 0.92, N2O 0.88, O3 0.95).

• Reproductions: refs [5, 10] rows reproduce murphy_1969 (Yoshino & Bernstein reduced); kolos_1967 for H2 rho [17]. Nothing else cited is curated.

• solprop: no direct bearing (solprop uses dalpha/dq, not cross sections). N2 shift 2330, O2 1556, H2 4156 (Q(1) max; Q(0) 4162), D2 2986 (Q(2) max; Q(0) 2991), CH4 2917; solprop: N2 2330.0, O2 1556.39, H2 4155.1, D2 2987.0, CH4 2914.0 cm-1.

• For R3 (Mikhailov): ref. [39] is G. V. Mikhailov, Tr. FIAN 27, 150-189 (1964), cited for ‘the width of the Q branch does not exceed 3 cm^-1’ (N2, O2, CH4).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-475 borysow_2019 (Borysow, Capek, Mazzoleni & Moraldi, Mol. Phys. 118, e1663287 (2020)) (2026-09-26)

• No datasets (a format decision still to be made). Z^2(j) (Tables 1-2) is a ratio of squared anisotropy matrix elements S/O from the same j, with the Clebsch-Gordan factors divided out: not a cross-section ratio, not a transition polarizability, not a derivative. b0 = beta_e/(r_e beta_e’) and b2 (Table 3, Eq. 19) are dimensionless ratios, NOT polarizability derivatives (the reading first proposed does not hold): recording them as polarizability_derivative would bend the quantity. The tables are quoted in notes (CSV checked against the images); Eqs. (16)-(18) with the fitted b0 are [[formulas]] z2_N2 and z2_O2. A quantity such as a ‘Raman matrix-element ratio’ (against j) and one for b0 would let them be data.

• Refit (scratch): O2 b0 = 0.486 +- 0.009, chi2/DOF 0.50 (paper 0.49 +- 0.01, 0.5) with Hajigeorgiou’s B_e, omega_e; N2 b0 = 0.479 +- 0.009, chi2/DOF 1.03 (paper 0.48, 1.0) with Bendtsen’s B_e and omega_e = 2358.57 cm-1 QUOTED FROM MEMORY (check only; say so in any register entry). Eq. (17) as printed is right.

• Doubt: the conclusions print b0(14N2) = 0.49 +- 0.01, Eq. (19) 0.48 +- 0.01; the refit says 0.48. Error bars in Tables 1-2 are ‘maximum errors’ (3 sqrt(N) + 1 % isotopologue).

• Table 3 (reproduced, in notes): O2 0.339 +- 0.040 (b2 2.5 +- 1.0, Buldakov), 0.23 +- 0.07 (Asawaroengchai & Rosenblatt), 0.42 (James & Klemperer); N2 0.33 (b2 1.2, Langhoff th), 0.318 +- 0.043 (b2 1 +- 2, Buldakov), 0.45 +- 0.09 (b2 0.42, A&R), 0.4 (J&K), 0.380 +- 0.042 (‘Buckingham [6]’ = Hamaguchi, Buckingham & Jones 1981). None curated.

• Isotopologues: 14N2, 16O2 (14N15N, 16O18O in the error budget only).

• solprop: no direct value (solprop has no Herman-Wallis factor); b0 bears on the anisotropy derivative a model would need for S/O line strengths.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-476 hanna_1986 (Hanna, Pointer & Pratt, IEEE J. Quantum Electron. 22, 332 (1986)) (2026-09-26)

• Transcribed: Table I (tbl_555a4008bd8a, p. 333, JSON cells = image): shift (check, 1 each: H2 Q(1) 4155, D2 Q(2) 2987, CH4 Q 2917 cm-1), dsigma/dOmega (m2/sr, 2 each, reproduced: H2/CH4 from Schrotter & Klockner via Eq. 2, D2 scaled from Devir 1978), g_R (m/W, 2 each, check, calculated), T2 (ps, 1 each at 30 atm, check, T2 = 2/Delta omega_R). Text p. 333: H2 51 MHz/atm and D2 70 MHz/atm FWHM broadening coefficients (raman_linewidth, reproduced from Bischel & Black/Owyoung and Murray & Javan); CH4 Delta nu = 0.32 + 0.012 p cm-1 (formula, reproduced from Taira et al. 1982). Nothing in Table I is measured here; the measurements are threshold energies (Tables II-III, notes only).

• FWHM: ‘Delta omega_R is the Raman linewidth (angular frequency, FWHM)’ (p. 332). No Dicke term (linear law, p > 10 atm).

• Erratum: dsigma_D2 at 0.53 um printed 8.0e-36 -> 8.0e-35 (Eq. 2 ratio 39.4 from the 1.06 um value; Eq. 1 with the printed g_R needs 8.4e-35; image checked).

• Inference (flag): temperature not stated. Eq. (1) reproduces the printed g_R to 1-4 % only with N at 30 atm and 273.15 K (30 amagat); state recorded as {30 atm, 273.15 K}, density ideal, with this reason in the notes. T2 reproduced: 208.0, 151.6 (150), 15.6 (16) ps.

• solprop: D2 vibrational frequency 2987.0 cm-1 (562646723155154.4 rad/s) = Hanna’s ‘Shift 2987cm-1’ (Q(2), source unstated, used as input). H2 4155 (solprop 4155.1). CH4 2917 (solprop 2914.0 from Murphy).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-477 ottusch_1988 (Ottusch & Rockwell, IEEE J. Quantum Electron. 24, 2076 (1988)) (2026-09-26)

• Duplicate: Ottusch_1988_MeasurementRamanGain_ec9131 is the same article from a different PDF (sha256 ec91313e vs 86cd3d06); text identical but metadata and a footnote’s position; Table II cells identical; its Table I differs only by a misread ‘D_3 Q(2)’. Not extracted twice (record notes).

• Transcribed: Table I (tbl_6fef6b554123, p. 2077, CSV = image): dsigma/dOmega at 532 nm (3 datasets x 1, reproduced from Bischel & Black 1983). Table II (tbl_963e1d09eaae, p. 2079): measured gain (primary, sigma, 3 x 1: H2 2.64 +- 0.20, D2 0.45 +- 0.05 at 60 amagat; CH4 1.26 +- 0.10 at 115 amagat, cm/GW), calculated (check, 3), previous (reproduced: H2 2.5 +- 0.4 from bischel_1986b, CH4 1.2 from Lopert 1983 thesis). Structural fix: cells read ‘CH_{3} \nu_{1}’, image CH4.

• Linewidth laws as formulas (my choice, stated): H2 309/rho + 51.8 rho, D2 101/rho + 120 rho, CH4 8220 + 384 rho, all FWHM in MHz with rho in amagat (Table I footnote a, image checked); the 1/rho terms are Dicke terms (MHz amagat). Also shift formulas (Fig. 5 caption) and Eq. (4). Chosen as formulas because each law has two coefficients in different units.

• Checks: Eq. (4) with Table I’s parameters and 1 amagat = 2.6868e19 cm^-3 gives 2.827/0.546/1.276 cm/GW against 2.86/0.55/1.28 (<= 1.2 %).

• Format issue: raman_gain requires a state; the gains are at a printed density with no temperature. Recorded state = {rho atm, 273.15 K} (the ideal-gas state with that amagat density), density ideal, abscissa density; say so in notes. Still to be decided.

• solprop: D2 vibrational linewidth (inverse_density 1.01e8, density 1.2e8, FWHM Hz with amagat) = linewidth_D2 exactly (101 MHz amagat, 120 MHz/amagat; cited to Russell & Roh 1987 and Smyth et al. 1987, not in library). CH4 (constant 8.22e9 Hz, density 3.84e8 Hz/amagat) = linewidth_CH4 exactly (from Lopert 1983 thesis, not in library). The 8220 MHz constant is the unresolved Q-branch width.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-478 bischel_1986b (Bischel & Dyer, J. Opt. Soc. Am. B 3, 677 (1986)) (2026-09-26)

• Transcribed: Table 1 (tbl_33f36ba412af, p. 680, JSON = image): measured gain at 532/477/308 nm (primary, sigma, 3), previous work at 694/530/353/265 (reproduced: Bloembergen 1967 (printed 1976), Venkin 1975, Komine pc; 4), Eq. (11) column (check, 7); cm/W, scale 1e-9. Text: alpha_01 = 1.11e-25 and gamma_01 = 0.951e-25 cm^3 at 500 nm (raman_transition_polarizability, mean/anisotropy, reproduced from Huo pc); nu_r(0) = 4155.25 +- 0.01 cm-1 (reproduced, refs 28-31); C = -96 MHz/amagat at 298 K (raman_line_shift, reproduced from bischel_1986 = R3’s PRA source id); T2 = 6.1 ns amagat (dephasing_time, unit ‘ns amagat’, reproduced). Formulas: Eq. (11) gain, Eq. (5) cross section, Eq. (8) linewidth (reproduced from bischel_1986), Eqs. (9)-(10) shift.

• Checks: Eq. (11) reproduces Table 1’s calculated column to <= 0.25 % at all seven wavelengths; its constant 9.37e6 from Eqs. (4)-(5) with R = 0.99 is 9.43e6 (0.6 %). Eq. (8) at 20 amagat 1051 MHz (text 1055) and at 12.1 amagat 652 MHz (text 650).

• Doubts: the UV pump is 307 nm in the text, 308 in Table 1 (Eq. 11 matches 308). State of the gains: {21.82 atm, 298 K} = 20 amagat at 298 K (the high-density limit, density independent) - a constructed state, noted. The 265 nm previous value has no footnote (Venkin et al. by the text).

• FWHM: ‘Delta nu is the full width at half-maximum Raman linewidth in hertz’ (p. 680); Eq. (8) FWHM in MHz with the Dicke term 309/rho (MHz amagat) (p. 681).

• solprop: H2 vibrational linewidth (inverse_density 3.09e8, density 5.22e7) comes from bischel_1986 (R3), Table I at 298 K: here Eq. (8) at 298 K gives 309 and 51.8 (Eq. (2) of PRA), not 52.2. H2 vibrational frequency 4155.1 (solprop) vs nu_r(0) = 4155.25 +- 0.01 cm-1 here.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-479 everall_1987 (Everall, Partanen, Barr & Shaw, Opt. Commun. 64, 393 (1987)) (2026-09-26)

• Transcribed: the table (tbl_4397977c2c69, p. 396, JSON = image; caption ‘… thresholds at 5 atm’) for CH4, H2, SF6, O2, N2 (NH3 not curated): dsigma/dOmega at 248 nm (reproduced: Bischel & Black for CH4/H2/N2/O2, Schrotter & Klockner nu^4-scaled for SF6), Delta nu_R FWHM at 5 atm (reproduced: Taira, Owyoung, Esherick & Owyoung, Murray et al.), T2 (check, T2 = 1/(pi Delta nu_R), p. 393). 15 datasets x 1 point.

• Measured here: only the thresholds (no quantity; in notes): calc/meas uJ CH4 15/30 +- 15, H2 60/155 +- 20, SF6 65/120 +- 30, O2 100/-, N2 225/- (not reached).

• Checks: 1/(pi c Delta nu) reproduces T2 (CH4 27.94, SF6 6.64, O2 5.90, N2 7.08); H2’s 1008 ps implies 0.0105 cm-1 (the 0.01 is rounded). CH4 0.38 = Taira’s 0.32 + 0.012 x 5.

• Doubts: transitions not named in the paper; N2 linewidth printed ‘≈1.5’.

• solprop: SF6 vibrational linewidth constant 4.8229e10 Hz = 1/(pi x 6.6 ps) = this T2 (calculated from Esherick & Owyoung’s 1.6 cm-1 FWHM at 5 atm), taken by solprop as density-independent. solprop N2’s ‘6 ps’ (5.305e10 Hz) is not Everall’s N2 7.1 ps.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-480 check only: raj_2018, rychlewski_1983, wahlstrand_2015 (no edits) (2026-09-26)

• No existing record carries a v = 0 -> 1 transition matrix element of either invariant for H2 or D2 (no raman_transition_polarizability dataset anywhere before this extraction; bischel_1986b now has Huo’s alpha_01, gamma_01 at 500 nm, reproduced).

• raj_2018 (supplement, Raj_2018_PolarizabilityTensorInvariants/supplement_01): the MEAN matrix elements {1J,0J} (Q(J), J = 0-8, at the program’s wavelengths 182-… nm and static) are printed in Table T1 (H2, tbl_b0cae9bc8235) and Table T5 (D2, tbl_3f331311ba2d), the columns after {00,00} and {10,10}; the record extracts only those two diagonal columns (alpha_v0_J0, alpha_v1_J0_). T2/T6 hold the v = 1 -> 2 elements. The ANISOTROPY tables T7-T9 (H2 v = 0, 1, 2: tbl_ae4c1110bfc9, tbl_38b205ad662e, tbl_76ce6cdde899) and T13-T15 (D2: tbl_15b6639e86a2, tbl_13b3f65f66d5, tbl_18bd5bb00233) print only Delta v = 0 elements ({vJ,vJ} and {vJ,vJ+2}): no v = 0 -> 1 anisotropy element is printed; the authors’ program (RAJ_2018_PROGRAM) computes them.

• rychlewski_1983: Table VII (tbl_94b58a3491d6, PDF page 9, ‘Nondiagonal matrix elements of the polarizabilities for H2’) prints alpha_{00,10} and gamma_{00,10} (v = 0 -> 1, J = 0, i.e. Q(0)) and the pure-rotational alpha/gamma_{00,02}, _{01,03}, _{02,04} at 16 wavelengths (static to 1215.7 A), a.u.; the record says ‘not extracted (Table VII’s elements are Raman/transition quantities)’. H2 only (no D2 transition elements).

• wahlstrand_2015: Table I’s d alpha/dQ column (1e-16 cm^2: this experiment H2 1.3 +- 0.2, D2 1.4 +- 0.3; Ref. [31] Bishop & Pipin H2 1.24; Ref. [39] Raman H2 1.30 +- 0.10, D2 1.22 +- 0.10) is NOT extracted (‘no quantity’ at the time; polarizability_derivative now exists: component mean (alpha = alpha_par/3 + 2 alpha_perp/3, Eq. 8 with the reduced mu, i.e. w.r.t. the internuclear distance). solprop’s H2 1.3e-20 m^2 and D2 1.4e-20 m^2 ‘polarisability derivative’ are this column. The anisotropy Delta alpha is extracted.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-481 bischel_1986 (Bischel & Dyer, Phys. Rev. A 33, 3113 (1986)) (2026-09-26)

• Transcribed (H2, 27 datasets, 64 points):

  • Table I (tbl_64d6921655d1, cells only), per (J, ortho:para) against temperature:

    • B, FWHM MHz/amagat: table1_B_Q1_normal (81, 298, 474 K), table1_B_Q0_normal (81, 298), table1_B_Q0_para (81 K, 1:7.7);

    • A, the Dicke term of Eq. (1), MHz amagat: the three matching table1_A_* sets.

  • Table I “Previous work”, reproduced, rows Q(J), temperature_k = 295 (the text’s temperature; the table prints them in the 298 K rows):

    • table1_A_owyoung (1);

    • B: table1_B_owyoung (1), _murray_javan (2), _allin (2), _hunt (2), _foltz (1), _lallemand (1).

  • Table II (tbl_9778e6276a73), raman_line_shift, MHz/amagat:

    • C: table2_C_Q1_normal (3), table2_C_Q0_normal (2), table2_C_Q0_para (1);

    • D (rho^2 coefficient, MHz/amagat2): table2_D_Q1_normal (474 K);

    • reproduced: table2_C_may (4), table2_D_may (4), table2_C_murray_javan (2), table2_D_murray_javan (2), table2_C_lallemand (2).

  • Table III: table3_doppler (6, the calculated Doppler FWHM, check). D_0 and rho_c are in the notes (no quantity).

  • Table IV:

    • table4_experiment (5, check);

    • table4_average (Q(2), Q(3), reproduced from Refs. 6, 8, 22);

    • the 298 K theory, reproduced: table4_theory_van_kranendonk (4) and table4_theory_hunt (4).

• Width law: Eq. (1), FWHM = A/rho + B rho, FWHM stated (p. 3), with the Dicke term. rho is the perfect-gas amagat (p. 2). Normal H2 is 3:1; 1:7.7 is marked parameters.ortho_para.

• Formulas:

  • eq2_linewidth: the FWHM law in T and rho. B reproduces Table I to 0.4 MHz/amagat; A(474 K) = 473.6 against 508 +- 29.

  • eq4_line_shift: C(T). C(81) = -306.2 against -305; C(298) = -96.1 against -96. It crosses zero at 446.8 K; the text says 446.

  • eq8_81K, eq8_298K, eq9_81K, eq9_298K: Table V. Checks: Eq. (8) at 81 K to 0.25 MHz/amagat. Eq. (9) at 81 K misses the para point by 22 (-314 against -336 +- 10).

• Structural fixes:

  • The stacked “Previous work” cells run together in the extraction (“66.0±5.0^a70^b83.0±3.0^c”); they are split at the reference marks.

  • Bare mark letters (“0.16±0.02a”) are dropped.

  • Table II’s continuation rows are assigned to the row above.

  • The “<2” theory cells at 81 K are left out (notes).

• Doubts:

  • Table IV repeats Table I’s 298 K values as 77.0 +- 1 and 52.4 +- 0.6, where Table I prints 76.6 +- 0.8 and 52.2 +- 0.5 (images; unresolved).

  • Table V prints the 81 K alpha_i as “23 +-” with no error (misprint; not a dataset).

  • Van Kranendonk’s and Hunt’s theory columns are recorded as reproduced, not check as first asked, because they are other papers’ calculations. To be confirmed in review.

  • The +- level is not stated.

• solprop: the H2 vibrational law 309e6/n + 52.2e6 n Hz is Table I’s Q(1), 298 K, 3:1 exactly (FWHM). Agrees.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-482 herring_1986 (Herring, Dyer & Bischel, Phys. Rev. A 34, 1944 (1986)) (2026-09-26)

• Transcribed (21 datasets, 80 points):

  • N2, FWHM MHz/amagat:

    • Table I, self: table1_295K (7), table1_195K (9), table1_80K (7);

    • Table II: table2_present (7, check); reproduced table2_jammu (8, reproduced_from jammu_1966), table2_pinter (3), table2_edwards (3);

    • Table III, perturber O2: table3_O2_295K (4), table3_O2_195K (4).

  • H2:

    • Table IV: table4_shift (nu_R 354 and 587 cm-1, check), table4_doppler (4, check), table4_A (4, check: the Dicke A computed from Bischel’s D_0 and held fixed);

    • Table V, B FWHM MHz/amagat: table5_295K (2), table5_80K (2); reproduced table5_van_den_hout_295K, table5_cooper_295K, table5_van_den_hout_80K;

    • Table VI, shifts MHz/amagat: table6_295K, table6_80K; reproduced table6_cooper_295K, table6_van_den_hout_80K.

• Widths: FWHM (Fig. 3 axis for N2; Eq. (1) for H2). The H2 law includes A/rho, with A computed from bischel_1986’s Q-branch D_0, not fitted.

• Uncertainty: 1 sigma of the fit for S(4)-S(12); S(0), S(2), S(14), S(16) are single-density errors (notes).

• Formulas:

  • eq9_power_law: B = B0 (T/295)^gamma, Table VII. It reproduces Table I within 2.1 %, except S(6) and S(12) at 195 K (+4.1 %, +4.4 %). The paper claims “better than 3 %”.

  • eq10_linear: B0 + C0 (T - 295). Off by up to -5.0 % at 195 K (S(4), S(8), S(10)).

  • eq2_A, with a correction: the printed A = 4 pi^2 nu^2 D_0 is a factor pi too large for every Table IV value. 4 pi nu^2 D_0 reproduces 1.372, 2.135, 1.874, 6.149 against 1.37, 2.10, 1.87, 6.15, and it is Bischel & Dyer’s Eq. (7). The page image was checked.

  • eq4_doppler: reproduces Table IV with m = 2 amu.

• Temperature exponents: Table VII’s gamma is the exponent of a per-amagat coefficient. The vocabulary’s N (gamma(T0)(T0/T)^N) is -gamma per amagat, or 1 - gamma per atm (the paper, p. 7). Recorded as formulas, not as broadening_temperature_exponent. Still to be decided: whether to add N datasets.

• Doubt: Table II’s “Present work” prints S(6) 3570 and S(10) 3070, where Table I prints 3560 and 3060 (images; Table VII uses Table I’s).

• solprop:

  • The H2 rotational law 6.15e6/n + 114e6 n is Table IV’s A and Table V’s B for S(1) at 295 K exactly. But the A was computed with Bischel’s Q(1) D_0, and Refs. 20 and 21 give B = 104 and 105.

  • The N2 rotational 3.3e9 Hz/amagat has no J. Table I at 295 K runs 4160 (S(2)) to 2660 (S(14)) MHz/amagat; 3.3e9 is S(8) (3270), rounded.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-483 edwards_1991 (Edwards, Long & Sherwood, J. Raman Spectrosc. 22, 607 (1991)) (2026-09-26)

• Transcribed (29 datasets, 94 points): 10^3 sigma in cm-1/bar, taken as FWHM (“The full width at half maximum intensity (FWHM) was then obtained”, p. 2).

  • Table 2 (293 K): table2_H2 (3), table2_D2 (5).

  • Table 3: table3_H2_90K (3), table3_D2_90K (5), table3_D2_200K (1), table3_D2_375K (1).

  • Tables 4, 5, foreign gases He, Ar, O2, N2, CO at 293 K: table4_H2_* (2-3 each) and table5_D2_* (5 each). HCl is in the notes (not a material).

  • Table 6: table6_D2_S0_N2, table6_D2_S0_CO, against T (4 each).

  • Tables 7-9: “this work” repeats (check) and the reproduced table7_may, table7_cooper_1968, table7_cooper_1970, table7_knaap, table8_knaap, table9_may_He, table9_dayan_N2.

• Structural fix: the D2 S0(4) cell prints a bullet for “±” (image); read as “±”.

• Doubts (important):

  • This paper’s H2 self-broadening is about half of every other measurement:

    • S0(0) and S0(1), 1.19 and 1.48e-3 cm-1/bar, against Herring’s 77 and 114 MHz/amagat (2.36 and 3.50e-3 cm-1/bar at 293 K) and Cooper’s and Knaap’s 2.8, 3.5;

    • the D2 values are 0.36-0.72 of Knaap’s.

    • Whether sigma is a half width despite the FWHM statement cannot be settled from the paper.

  • Tables 7-8 print Cooper 1970’s 2.8 and 3.5 as “cm-1 bar-1”. Herring prints the same paper as 84 and 105 MHz/amagat = 2.80 and 3.50e-3 cm-1/amagat: the comparison columns look per amagat under a per-bar label.

  • Table 8 prints D2 S0(2) as 2.49 where Table 2 prints 2.46.

  • Table 6’s 293 K errors (+-0.3) differ from Table 5’s (+-0.6, +-1.0).

  • May et al.’s citation is printed “Can. J. Phys. 32, 1769 (1961)”: the volume and the year look inconsistent. It is cited as printed; check.

• solprop: the D2 rotational 131.96e6 Hz/amagat is Table 2’s S0(0), 4.05e-3 cm-1/bar, as FWHM, x c / 0.92006 amagat per bar at 293 K. The arithmetic is right; the doubt above applies (if sigma were a HWHM, the FWHM would be twice as large).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-484 jammu_1966 (Jammu, St. John & Welsh, Can. J. Phys. 44, 797 (1966)) (2026-09-26)

• Transcribed (22 datasets, 51 points): HWHM per atm, 10^-3 cm-1/atm. The paper’s footnote, p. 2: “Delta nu_1/2 means one half of the width”; p. 10: “X = 2 Delta nu_1/2”.

  • Table I, O2 S(K) for K = 3-19: table1_20min, table1_40min (9 each).

  • Table II:

    • “this investigation” extremes (rows largest and smallest, J not stated), use check: table2_{O2,N2,CO2,CO,O2_Ar,N2_Ar,O2_He,N2_He};

    • reproduced: table2_mikhailov_O2 (1) and table2_mikhailov_N2 (2, below and above 25 atm), reproduced_from mikhailov_1959 plus the 1960 paper; table2_lazarev_* (7); table2_pinter_N2 (J = 4, 8, 12) and table2_pinter_CO2 (J = 22, 26, 32).

  • Inline, reproduced: text_stoicheff_N2, Stoicheff’s 0.043 cm-1/atm average.

• Structural: “a -> b” split at the arrow; “47.5 and 26.5” split; Pinter’s parentheses and note marks stripped.

• Figures only: the N2, CO and CO2 self-broadening against J, and the Ar and He broadening (Figs. 9-13). Not digitised.

• Temperature: “room temperature”. The tube was water-cooled at about 15 C; the gas temperature is not stated. No uncertainties are stated.

• solprop: its “2.6e9 Hz/amagat” for N2 equals 2 x 0.043 cm-1/atm x c = 2.58e9 per atm (Stoicheff’s HWHM made a FWHM). Per amagat at 295 K that is 2.78e9, so the per-amagat label is 7 % off. herring_1986 Table II’s Ref. 3 column is this paper’s Fig. 9, converted to FWHM per amagat.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-485 mikhailov_1959 (Mikhailov, Sov. Phys. JETP 9, 974 = Zh. Eksp. Teor. Fiz. 36, 1368 (1959)) (2026-09-26)

• Identity: solprop’s unverified “Sov. Phys. JETP 36, 9 (1959)” for the N2 6 ps is this paper: 36 is the Russian volume and 9 the translation’s. jammu_1966 and herring_1986 cite it so.

• Transcribed (N2, 8 datasets, 23 points after the one exclusion):

  • Table I at 27 C: table1_rotational (delta omega, J-averaged over 0-15, 7-80 atm; the “~0.5*” 3 atm row, measured by another observer, excluded); table1_vibrational (the unresolved Q branch, 15-114 atm).

  • Text at 200 C: text_rotational_200C, text_vibrational_200C.

  • Table II, check: table2_rotational_structure, table2_collisional, table2_total, table2_experimental (200 and 27 C).

• Width convention: not stated anywhere: recorded as width = "not stated". For review: the vocabulary expects hwhm or fwhm.

• Formula collision_width: delta = 0.027 rho^2 p.

  • With rho_nu = 0.43 A it gives 0.25 cm-1 at 50 atm (Table II: 0.2).

  • With rho_omega = 3.3 A (text; the abstract says 3.9 A) it does not reproduce Table I: 0.29 cm-1/atm against a Table I slope of 0.164.

  • The 0.027 matches 2 pi N v rho^2 / c with v about the rms speed.

• Misprint (note only): alpha = B0 - B1 printed 0.171 cm-1. bendtsen_1974 gives 0.017292, and the paper’s own delta nu_rot = 1.54 cm-1 needs about 0.017.

• Doubt: the density of the 200 C point is 90 atm at 27 C in the text but 50 atm in Table II.

• solprop (6 ps): 1/(pi x 1.77 cm-1). This paper’s Q-branch width at 27 C is 1.75 cm-1 calculated and 1.8 +- 0.2 measured at 50 atm (6.1 and 5.9 ps). But 1.54 cm-1 of it is the unresolved rotational structure of the Q branch; the collisional part is 0.2 cm-1 at 50 atm, about 0.005 cm-1/atm. So the 6 ps is the dephasing of the room-temperature Q-branch envelope, independent of pressure, not a collision time.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-486 millot_1992 (Millot et al., J. Chem. Phys. 96, 961 (1992)) (2026-09-26)

• Transcribed (O2, 44 datasets, 379 points): HWHM, 1e-3 cm-1/atm (p. 4: “Gamma_N the collisional half-width at half-maximum (HWHM)”; captions).

  • Table II:

    • self, 2 sigma: table2_{295,446,769,990,1317,1350}K;

    • table2_ouazzany_295K (reproduced);

    • table2_anisotropic_295K (this work, the anisotropic Q component);

    • table2_berard_293K (reproduced, S(N) pure rotational);

    • table2_hot1_1350K, table2_hot2_1350K (v = 1 -> 2 and 2 -> 3).

  • Table III, by N2, 2 sigma: table3_N2_{295,446,990}K.

  • Table IV, shifts per atm, 1 sigma: table4_self_{295,446,990,1317}K, table4_N2_{295,446}K; means per amagat against T: table4_mean_self, table4_mean_N2.

  • Tables VI, VII (semiclassical widths, check): table6_Q_* (6), table6_S_295K, table7_N2_* (5).

  • Table VIII (semiclassical shifts, check): table8_{self,N2}_* (10).

• Table IV identified: the caption is extracted as a table note and the running head as the caption.

• Table V (a “code” block, page image read): the semiclassical inputs, quoted in the notes.

• Formulas (Table IX), recomputed from Eq. (12) with O2 levels of B = 1.438 cm-1:

  • MEG, O2-O2: rms 0.78 mk/atm over 56 widths (printed sigma 0.99);

  • MEG, O2-N2: rms 1.03 (0.74).

  • ECS-P and ECS-EP only after two changes:

    1. Eq. (16)’s exponent exp[(E_N’ - E_N>)/kT] violates detailed balance. It gives 2-3 times the widths; with E_N (the initial level) it is symmetric.

    2. Omega is undefined in the paper. De Pristo’s form with omega = 2 pi c (E_N - E_{N-1}) and the mean relative speed was assumed.

    With these: ECS-P rms 1.27 (1.34) and 1.72 (0.99); ECS-EP 1.01 (1.11) and 1.14 (0.79), for O2-O2 and O2-N2.

• solprop: the O2 vibrational 2.933e9 Hz/amagat is Table II’s Q(7) at 295 K, 45.3e-3 cm-1/atm HWHM, doubled and per amagat at 295 K. Right.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-487 holzer_2021 (Hölzer, Meißner & Seeger, Appl. Opt. 60, C76 (2021)) (2026-09-26)

• Transcribed (O2, 15 datasets, 239 points): FWHM, 1e-3 cm-1/atm (Eq. (1), p. 1: “Gamma_N’’ is the full width at half-maximum”; table heads).

  • Table 1, self: table1_self_{295..1900}K (9 temperatures).

  • Table 2, O2 in air: table2_air_* (6), recorded with perturber = "air". These are not the O2-N2 coefficients; the paper defers Eq. (3) to future work.

• Uncertainties: the fit’s standard deviation (1 sigma, statistical). Measured at about 1 bar and divided by the pressure (the exact pressure is not given).

• solprop: the O2 rotational 2.836e9 Hz/amagat is Table 1’s S(7) at 295 K, 87.6e-3 cm-1/atm FWHM, per amagat at 295 K. Right, but applied to all N; the 295 K values run 98.5-46.4.

• For review: “air” is not a material id; how should the vocabulary name a mixture perturber?

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-488 meissner_2019 (Meißner, Hölzer & Seeger, Appl. Opt. 58, C47 (2019)) (2026-09-26)

• Transcribed (N2, 15 datasets, 371 points): FWHM (Eq. (1)).

  • Table 1, pure N2: table1_self_* (9 temperatures, 295-1900 K).

  • Table 2, N2 in air (“N2-O2” in the paper): table2_air_* (6), perturber = "air".

• Unit: the heads print “10^-3 cm”. cm-1 is meant, recorded so (no erratum mechanism for a unit; notes).

• Hazard: these are WIDTHS at “ambient pressure”, not per atm. Recorded with parameters.pressure = "ambient, not stated numerically" and no state. Taken as 1 atm, the 295 K values are about 14 % below herring_1986’s coefficients. How to use them is still to be decided.

• Uncertainty: “standard deviation … from the 95 % confidence intervals of the fitting process”: recorded as 1 sigma.

• Outliers as printed: 1650 K J’’ = 6 (49.6); 870 K J’’ = 33 (17.7); 295 K J’’ = 23 (36.7); Table 2’s 1900 K column is above its 1650 K column throughout.

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-489 koszykowski_1987 (Koszykowski, Rahn, Palmer & Coltrin, J. Phys. Chem. 91, 41 (1987)) (2026-09-26)

• Notes-only for data: the widths and spectra are in figures. Duplicate: ..._9b762d is the same article; the texts are identical apart from the download banners and the footnote order.

• Formulas:

  • eq41_exponential_gap (alpha 0.02 +- 0.003 cm-1/atm, beta 1.6 +- 0.05, from the trajectories);

  • eq44_modified_exponential_gap (alpha 0.023, beta 1.67, delta 1.26, a = 1.5; the temperature factor (T0/T)^n, n = 1.2-1.3 from theory or 1.346 +- 0.006 from Rahn & Palmer).

  FWHM (Eq. (4.3): Gamma/2 = sum). No printed width to check. Evaluated, the MEG gives 126 -> 53e-3 cm-1/atm FWHM for J = 0 -> 20 at 295 K.

• Text: the Q-branch shift inferred, -0.003 to -0.004 cm-1/atm (notes).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-490 farrow_1985 (existing record, extended) (2026-09-26)

• Added table1_Ar: the N2 Q(J) broadening by Ar, HWHM 1e-3 cm-1/atm, J = 2-18 (17 points; J = 0, 1 “Extrapolated”, excluded). Script _table_1() added. The chi_nr datasets are unchanged (re-extraction identical). One notes sentence was changed to say Table 1 is now extracted.

• Hazards:

  • The caption prints only “cm^-1”. Per atm is inferred from the text’s 0.015 cm-1 HWHM at 300 Torr (p. 906).

  • The J = 6 cell “6’” is a stray mark (image).

  • The IRS temperature is not stated.

  • The values are corrected for the N2 self-broadening with Rosasco’s coefficients (not in the library).

• Status: verified (2026-09-26) against the page images where stated; the doubts above are decided in TC-491.

TC-491 The review of the ionisation and Raman records (TC-445 to TC-490) (2026-09-26)

• Where: the records of TC-445 to TC-490. Five parallel extractions wrote them in separate worktrees, and they were merged into feature/ionisation. Each extraction’s poe check and poe test-library passed; after the merges the whole suite passes.

• Summary: 41 new records from the extractions, plus nist_asd_2026 and nist_webbook_2026 from the review, 43 in all, with 614 datasets and 2936 values. Seven existing records were extended by the extractions (chen_2007, farrow_1985, hohm_2012, loriot_2011, reichert_2015, teal_1935, wang_2021), and belli_2015’s notes were re-pointed. By extraction:

  • ionisation parameters: 7 new records, 3 extended;

  • ionisation validation data: 14 new;

  • Raman constants: 3 new, 3 extended;

  • Raman strengths: 8 new;

  • linewidths: 9 new, 1 extended.

• Decisions on the doubts raised at extraction:

  • Ionisation parameters:

    • The erratum in Tong et al.’s Table II (He I_p 23.59 corrected to 24.59, TC-445) is accepted.

    • Ammosov et al.’s Kr+ 2.26, which exceeds what their eq. (11) can give, is left as printed (a check value, TC-448).

    • Mironov’s sqrt(kappa) against kappa^(3/2) (TC-450) is noted; nothing uses it.

    • Zhao et al.’s Table II ionisation energies are recorded as reproduced from Tong et al. 2002 (TC-446). That is an inference from identical digits, and their “experimental vertical” caption is doubtful for the same reason; nothing uses them.

  • Ionisation validation data:

    • Majety & Scrinzi’s haCC(5) and (6) rates stay primary, and so do Parker et al.’s and Saenz’s. The accuracy page compares the tunnelling rate with each separately (TC-444).

    • Parker’s ADK 1.07e-2 at 0.20 au (probably 1.11e-2, TC-456) is left as printed: it is a check column.

    • Augst et al.’s intensity shift factors are notes, not data, as decided at extraction (TC-459).

    • Golovanov & Kostyukov’s eq. (1), a factor of 2 above the quasistatic ADK rate (TC-463), is noted and not used.

  • Raman constants:

    • Bendtsen’s constants and line positions are both primary. The Raman model uses the constants, and the lines are its validators, so nothing is counted twice (TC-466).

    • Teal & MacWood’s erratum (D2 S(1) line average printed 297.3, corrected to 297.1: the plates average 297.13, and the table’s own difference column implies 297.1, TC-468) is accepted.

    • Hajigeorgiou’s potential does not join continuously at 0.925 A with the printed A and q, yet the printed values reproduce his Table III (TC-467). This is a finding only: his tabulated G, B, D and H are what is used.

    • Chen et al. state H2’s spin statistics reversed (TC-469): a paper error, noted.

  • Raman strengths:

    • polarizability_derivative now states coordinate where the derivative is taken with respect to a bond length or a symmetry coordinate, not the mass-weighted normal coordinate (Murphy et al.’s dalpha/dr, Bermejo et al.’s Mills coordinates, TC-472, TC-473). The quantity’s meaning says so.

    • A Raman gain tabulated at a density with no temperature is given the ideal-gas state of that amagat density at 0 °C (Ottusch & Rockwell, Hanna et al.; TC-476, TC-477). The same holds for Bischel & Dyer’s 20 amagat at 298 K. This is a convention, and each record says so.

    • Hanna et al.’s erratum (D2 dsigma/dOmega at 0.53 um, 8.0e-36 corrected to 8.0e-35 m^2/sr, TC-476) is accepted.

    • Borysow et al.’s Z^2(J) and b0 have no quantity (TC-475). They are needed only for O- and S-branch vibrational strengths, which propagation does not use yet. Borysow’s N2 refit used omega_e = 2358.57 cm^-1 quoted from memory, for that check only.

  • Raman linewidths:

    • raman_linewidth now documents:

      • term (one term of a width law, such as the Dicke coefficient A);

      • perturber = "air" for a mixture broadening;

      • width = "not stated" (Mikhailov).

    • The other new parameters (ortho_para, pressure) are free-form, as the format allows.

    • Herring et al.’s temperature exponents stay formulas (TC-482).

    • Edwards et al.’s H2 and D2 widths are about half of every other measurement (TC-483). They are kept as printed and not used for the defaults until Knaap et al. (1979), which is requested, settles whether their sigma is a half width.

    • belli_2015’s notes now name bischel_1986 as curated.

• Findings for solprop (details in the entries):

  • Ionisation: TC-444.

  • N2 constants: solprop’s B and D are Bendtsen’s B0 rounded, and his model estimate of D (4B^3/omega^2), not his measured 5.76e-6 cm^-1. Its N2 band origin is 0.083 cm^-1 above Bendtsen’s (TC-466).

  • O2 constants: solprop’s B, D, frequency and reduced mass are exactly Hajigeorgiou’s (TC-467).

  • Strengths: solprop’s dalpha/dq of N2, O2, CH4 and SF6 are Murphy et al.’s reprints of 1958-63 values (TC-472). Bermejo et al.’s CH4 per-bond derivative is 8.7 % higher (TC-473).

  • H2 and O2 linewidths: solprop’s are Bischel & Dyer’s, Herring et al.’s and Millot et al.’s values at one J, correctly converted (TC-481, TC-482, TC-486).

  • D2 and CH4 linewidths: solprop’s laws are Ottusch & Rockwell’s (TC-477).

  • SF6 dephasing: solprop’s 6.6 ps is Everall et al.’s, calculated from a 1.6 cm^-1 width at 5 atm, and is used as independent of density (TC-479).

  • N2 dephasing: solprop’s 6 ps is the unresolved room-temperature Q-branch envelope of Mikhailov 1959 (1.54 of its 1.75 cm^-1 is rotational structure). It is not a collisional dephasing, which is about 0.005 cm^-1/atm (TC-485).

• Status: decided (2026-09-26).

TC-492 The Raman lines of the gases: choices, widths and the gain validation (2026-09-26)

• Where:

  • data/gas/raman.toml (each choice with its reason);

  • optmat.gas.raman (raman_parameters, raman_lines, stokes_gain);

  • optmat.gas.linewidths (the width laws);

  • the page docs/raman.md, with its tables from tools/raman_tables.py (tested).

• Decision (strengths):

  • Q branch: the transition polarizability is taken either from a curated element (H2: Huo’s, as Bischel & Dyer 1986 quote it) or from Murphy et al.’s derivative with respect to the mass-weighted normal coordinate. For a harmonic mode <0|alpha|1> = (d alpha/dQ) (hbar/2 omega)^(1/2), which needs no reduced mass and no bond convention.

  • Rotational anisotropy:

    • Wahlstrand et al. 2012, measured from the rotational response at 800 nm, for N2 and O2 (solprop’s values);

    • Bishop & Pipin’s ab initio anisotropy per J -> J + 2 transition at 632.8 nm (via Shelton 1993) for H2;

    • the ab initio optical value (via Carusotto et al.) for D2.

• Decision (levels):

  • N2: Bendtsen 1974.

  • O2: Hajigeorgiou 2013 (the N(N + 1) ladder; the spin splittings, which solprop also leaves out, need Yu et al. 2012, requested).

  • H2 and D2 (stopgap): B and D are fitted to Teal & MacWood’s 1935 pure rotational lines, and the v = 1 constants to their Q lines with their Delta G1 as the band origin. Those lines scatter by up to 0.8 cm^-1. The fitted H2 B0 is 59.31 cm^-1 (the molecule’s is about 59.33), D 0.043 (about 0.047). Modern level energies (Komasa et al. 2011) are requested.

  • N2O and CO2: have no lines, because their rotational constants are not curated.

• Decision (widths), per line where the data are per line:

  • N2 S branch: Herring et al.’s per-J self-broadening with their per-J power laws in T. O2 broadening from their Table III. Ar taken as O2.

  • N2 Q branch: Koszykowski et al.’s modified exponential-gap law (checked against an independent evaluation at extraction to 6e-5 cm^-1/atm), with Rahn & Palmer’s exponent 1.346 as they quote it. Foreign partners are taken as self.

  • O2 S branch: Hölzer et al.’s per-N widths, self and in air, with exponents fitted per N to their 295-1900 K tables. N2 and Ar are taken as air.

  • O2 Q branch: Millot et al.’s per-N widths (HWHM, doubled), self and by N2, exponents fitted to their temperatures.

  • H2:

    • Q: Bischel & Dyer’s Eq. (2) for Q(1), for every Q(J). Their Q(0) is 47 % broader at 298 K.

    • S: Herring et al.’s S(0) and S(1) with the S(1) Dicke term.

  • D2:

    • Q: Ottusch & Rockwell’s law.

    • S: Edwards et al.’s widths, doubtful by a factor of 2 (TC-483).

  • CH4: Ottusch & Rockwell’s law.

  • SF6: Everall et al.’s 1.6 cm^-1 at 5 atm, density-independent (as solprop).

  The widths are those of isolated lines. The mixing of overlapping Q(J) lines above about 1 atm, which narrows the N2 Q branch, is not modelled; nor is it in solprop.

• Checked (the gain): the steady-state Stokes gain g = omega_s N A/(2 c^2 eps0 Gamma), derived in stokes_gain’s docstring, against the measured gains, at 295 K:

  • H2 Q(1):

    • 532 nm: +18 % (Ottusch & Rockwell, 60 amagat) and +23 % (Bischel & Dyer, 20 amagat); their own calculated gains are 8-18 % above their measurements;

    • 477 nm: +1 %;

    • 308 nm: -10 %, because the transition polarizability is held at its 500 nm value and rises towards the UV.

  • D2 Q(2): +27 %.

  • CH4 nu1: -7 %.

• Finding (against solprop):

  • N2 and O2: solprop’s constants, anisotropies and vibrational amplitudes agree with the curated ones to 1.4 % or better.

  • H2 and D2 constants: solprop’s B (58.9 and 29.3 cm^-1) and D2’s D (0.021) are Wahlstrand et al.’s effective fit values, 0.7-2 % and a factor of 2 from the molecules’ constants.

  • H2 and D2 amplitudes: solprop’s vibrational amplitudes are 10 % and 31 % larger, from Wahlstrand et al.’s dalpha/dq (1.3 +- 0.2 and 1.4 +- 0.3 x 1e-16 cm^2). Their own quoted Raman-scattering value for D2, 1.22 +- 0.10, agrees with Murphy et al.’s.

  • SF6 amplitude: solprop’s is 5 % smaller. Its per-bond derivative, 1.23, does not reproduce Murphy et al.’s own d alpha/dQ, 0.71 (TC-472).

  • H2 and D2 lines: solprop places one vibrational line at Q(1) (H2) or Q(2) (D2); here the whole Q branch is resolved by J.

• Status: decided (2026-09-26); open for the requested level energies, N2O and CO2, and line mixing.

TC-493 The rotational nonlinear index: the factor of two of TC-312 settled, and TC-442 corrected (2026-09-26)

• Where: optmat.gas.raman.rotational_nonlinear_index; the “rotational nonlinear index” section of docs/raman.md, whose table is written by tools/raman_tables.py and tested.

• Derivation (the self and probe coefficients): in the convention of TC-442 a pulse long against the rotational periods changes the index by n2,rot I = N R0 I/(2 eps0 c), with R0 = sum_J A_J Omega_J/(Omega_J^2 + Gamma_J^2). The response is slow, so only the slowly varying part of E^2 drives it. A probe at another frequency therefore sees the same index change as the pulse itself; for the instantaneous electronic response the probe’s shift is twice the self shift.

• Checked: the lines give these self coefficients at the measurements’ states (1 atm, ideal gas):

  Gas	Model (1e-20 cm2/W)	Published	Model vs published
  N2	23.9	24 (Zahedpour 2015), 23.0 (Zahedpour 2019)	0 %, +4 %
  O2	55.2	54, 53.3	+2 %, +4 %
  D2	4.0	3.9 (Wahlstrand 2015)	+2 %
  H2	3.1	2.7	+15 %

  • The model uses the same anisotropies as the measurements’ calibrations (Wahlstrand et al. 2012) for N2 and O2.

  • For H2 it uses the ab initio anisotropy, 4.5 % above the measured one and rising with J.

• Finding (TC-312): the published n2,rot are the self coefficients the lines give. Zahedpour et al. 2019’s printed response g(tau) integrates to twice their n2,rot (TC-312), so TC-312’s first alternative holds: the printed g carries an extra factor of 2. The tabulated n2,rot are right as self coefficients. The same conclusion is consistent with their note b (n2,eff = n2 + /2).

• Correction (TC-442): TC-442 says the lines’ integral sum_J A_J/Omega_J “approaches the classical orientational response Delta alpha^2/(30 eps0 k_B T)”.

  • It does approach Delta alpha^2/(30 eps0 k_B T), but that is three quarters of the classical isothermal orientational response. The latter is Delta alpha^2/(22.5 eps0 k_B T): the Boltzmann average gives Delta <alpha_zz> = Delta alpha^2 |E0|^2/(45 k_B T).

  • The missing quarter is the Delta J = 0 part, the redistribution of the M sublevels within a rotational level. A coherent, collisionless drive does not excite it, and collisions establish it only over nanoseconds.

  • The quantum amplitudes are right: solprop’s prefactor (2/15) Delta alpha^2/(hbar eps0) (J+1)(J+2)/(2J+3)(n_J - n_{J+2}) was rederived here from linear response, with the Placzek-Teller matrix elements sum_M |<JM|cos^2 theta|J+2 M>|^2 = (2/15)(J+1)(J+2)/(2J+3).

  • The test’s comment is corrected. Its tolerance and the TC-442 checks stand.

• Status: decided (2026-09-26).

TC-494 trickl_1989 (Trickl, Cromwell, Lee & Kung, J. Chem. Phys. 91, 6006 (1989)) (2026-09-27)

• Transcribed (text, inline points): ie_N2 125 666.959(67) cm^-1 (p. 6010 and abstract), primary; threshold_N2 125 666.99(56) cm^-1 (p. 6008, the zero-field threshold extrapolation, Eq. (1)), check; ogawa_1962_N2 125 666.8 cm^-1 (p. 6008), reproduced from Ogawa & Tanaka, Can. J. Phys. 40, 1593 (1962). 3 datasets, 1 point each, unit cm-1.

• Levels: the series converges to N+ = 4 and the paper subtracts the literature N+ = 4 rotational energy (checked: 104 326.451 + 21 378.952 - 125 666.959 = 38.444 cm^-1 = 20 B+): so the value is X 1Sigma_g+ (v = 0, J = 0) -> X+ 2Sigma_g+ (v+ = 0, N+ = 0), rotationless to rotationless, ion spin doublet unresolved. = 15.580717 eV.

• v+ = 1: no value; Fig. 2(d) “could not be analyzed” (p. 6011). Tables I and II in notes.

• Doubt: the confidence level of (67) is not stated (it is about the series limit’s 0.060 cm^-1 with calibration combined with the R0 line’s 0.025).

• Status: verified (2026-09-27).

TC-495 tonkyn_1989 (Tonkyn, Winniczek & White, Chem. Phys. Lett. 164, 137 (1989)) (2026-09-27)

• Transcribed (text): ie_O2 97348 +- 2 cm^-1 (pp. 137, 140, 141), primary; samson_1975_O2 97362 +- 9 cm^-1 (pp. 138, 141), reproduced from Samson & Gardner, Can. J. Phys. 53, 1948 (1975). 2 datasets, 1 point each.

• Levels, exactly as the paper defines them (p. 141): “the energy for the transition X 2Pi_g, F1(v = 0, J = 1/2) <- X 3Sigma_g-, F2(v = 0, J = 1)”. F1 is Omega = 1/2 (footnote #1, p. 140), so the final level is O2+ X 2Pi_(1/2)g, v+ = 0, J+ = 1/2 (the lower spin-orbit component; O2+ X is regular); the initial level is O2’s F2 (J = N) level with J = N = 1. = 12.069614 eV (+-0.00025).

• Not extracted: the branch-designation table (p. 140; labels only); fit results C_i, 220 +- 20 K, 3.0 +- 0.3 cm^-1 linewidth in notes.

• Doubt: the paper does not say whether its initial level, F2 (J = N = 1), is the neutral’s lowest level; an ionisation energy from O2’s lowest fine-structure level could differ from it by the N = 1 spin splitting (not given in the paper). It may be checked against a curated O2 fine-structure record (e.g. yu_2012). The number is recorded as the paper defines it.

• Status: verified (2026-09-27).

TC-496 holsch_2019 (Hölsch et al., Phys. Rev. Lett. 122, 103002 (2019)) (2026-09-27)

• Transcribed: Table II (tbl_7f08590ec4cc, CSV, image checked, PDF p. 4) row (4): ie_ortho_H2 124 357.238 003(11) cm^-1 (340 kHz), by tools/extract/holsch_2019.py. 1 dataset, 1 point.

• What it is: E_I^ortho(H2) = X+ (v+ = 0, N+ = 1, hyperfine centre) - X (v = 0, N = 1), the ORTHO-H2 ionisation energy, not the conventional N = 0 -> N+ = 0 value (60.253 cm^-1 lower than liu_2010’s quoted Liu et al. 2009 value 124 417.491 13(37)). The paper gives no X (0,1) - X (0,0) interval, so no para value derived. = 15.4183325 eV.

• Uncertainty: quadrature of 1 sigma statistical and systematic estimates (Table I, total 340 kHz); level recorded “not stated” (the paper does not name the level of the total).

• Notes: Table II other intervals, Table I error budget, D0^(N=1) = 35 999.582 834(11) cm^-1 with the theory 35 999.582 820(26) and the GK value 35 999.582 894(25), the 2009 D0^(N=0) values.

• Status: verified (2026-09-27).

TC-497 liu_2010 (Liu, Sprecher, Jungen, Ubachs & Merkt, J. Chem. Phys. 132, 154301 (2010)) (2026-09-27)

• Transcribed by tools/extract/liu_2010.py:

  • Table III (tbl_fcc4c6682cca, CSV, image checked, PDF p. 7): ie_ortho_D2 (4) 124 745.394 07(58) cm^-1 (X (0, N = 0) -> X+ (0, N+ = 0); ortho-D2 has even N) and ie_para_D2 (8) 124 715.003 77(75) cm^-1 (N = 1 -> N+ = 1). Primary, 1 point each.

  • Table IV (tbl_e28c58907bc7, CSV, image checked, PDF p. 8): 9 reproduced datasets of E_i(ortho-D2), 1 point each: takezawa_1975 124 745.6(6) (with Jungen et al. 1992’s -1.0 cm^-1 pressure-shift correction, footnote a), jungen_1990 124 745.49(11), kolos_1991 124 745.382 (theory, Refs. 30-31), gilligan_1992 124 745.353(24) (Refs. 32-33), shiner_1993 124 745.353(24) (reproduced_from shiner_1993), kolos_1993 124 745.377, wolniewicz_1993 124 745.387, kolos_1994 124 745.401, wolniewicz_1995 124 745.395 (theory, no uncertainties). The 2010 row is Table III (4), not repeated.

  • Text (PDF p. 2): liu_2009_H2 124 417.491 13(37) cm^-1, reproduced from Liu et al., J. Chem. Phys. 130, 174306 (2009); the levels are not stated there; recorded as the rotationless (N = 0) value by comparison with holsch_2019 (an inference, in notes).

• Uncertainty: the EF -> Rydberg intervals carry the linear sum of statistical and systematic uncertainties; the totals are quadrature sums (p. 6); level “not stated”.

• Extraction note: the library flags unmapped glyphs on every page (parentheses); every number was read on the table images or cross-checked against the PDF text layer. Table III’s D0 row is extracted as “+ E_i(D)”; the image and Eq. (1) have “- E_i(D)” (notes only; not a dataset).

• Doubt: Table IV attributes 124 745.353(24) both to “Refs. 32, 33” (1992) and to Shiner et al. (1993); shiner_1993 itself attributes its D2 value to Jungen et al. 1992 (TC-498). Both rows are recorded as printed, reproduced.

• Status: verified (2026-09-27).

TC-498 shiner_1993 (Shiner, Gilligan, Cook & Lichten, Phys. Rev. A 47, 4042 (1993)) (2026-09-27)

• Transcribed by tools/extract/shiner_1993.py from Table IV (tbl_f2f1c838c202, cells only, image checked, p. 4044): mccormack_H2 124 417.507(12) cm^-1 (footnote a, McCormack et al. + Table III) and jungen_1990_H2 124 417.484(17) (footnote c), primary; jungen_1992_D2 124 745.353(24) (footnote e: “Reference [4], which uses the results given in Table III”), reproduced from Jungen et al., J. Mol. Spectrosc. 153, 11 (1992); ab_initio_H2 124 417.471 and ab_initio_D2 124 745.377 (footnote b, Kolos private communication = Kolos & Rychlewski), reproduced. 5 datasets, 1 point each. HD (124 568.481(12), ab initio 124 568.465) and the difference column in notes.

• Doubt 1 (primary or reproduced): the H2 rows combine other groups’ EF -> limit intervals with this paper’s recalibrated EF <- X energies (Table III): recorded primary, as the paper’s own combination. The D2 row is recorded reproduced (footnote e). Another reading may be preferred in review.

• Doubt 2: the paper does not state the levels; by comparison (liu_2010, holsch_2019) they are the N = 0 -> N+ = 0 values. Level of uncertainties not stated.

• Finding: the two H2 values differ by 0.023 cm^-1; the paper notes a 3-sigma discrepancy of the McCormack-based value with theory (124 417.471).

• Status: verified (2026-09-27).

TC-499 berkowitz_1987 (Berkowitz, Greene, Cho & Ruscic, J. Chem. Phys. 86, 674 (1987)) (2026-09-27)

• Transcribed (text, p. 675): adiabatic_CH4 12.61 eV, printed “983 (+0, -1) A = 12.61 (+0.01, -0.00) eV”, recorded with sigma 0.01 (asymmetric in print; noted), level not stated, parameter temperature_k = 78. 1 dataset, 1 point.

• How defined: the onset (threshold) of the CH4+ photoion yield, gas at 78 K, 0.28 A resolution, “not influenced by temperature”. The paper’s rotational model puts the J’’ = 0 -> J’ = 0 adiabatic value about 43 cm^-1 = 0.005 eV above the extrapolated onset (pp. 675-676; printed “-0.005 eV”), and it keeps the onsets. So the rotationless value implied is about 12.615 eV (not printed).

• CD4: 12.65_8 +- 0.015 eV (979.5 +- 1 A), notes only. Earlier values (12.55-12.78) in notes.

• Status: verified (2026-09-27).

TC-500 bieri_1977 (Bieri, Burger, Heilbronner & Maier, Helv. Chim. Acta 60, 2213 (1977)) (2026-09-27)

• Transcribed by tools/extract/bieri_1977.py from the first Section A table (tbl_1342dbc497d6, cells only, image checked, p. 2218): vertical_CH4 4 points, 1t2 Jahn-Teller maxima 13.6, 14.4, 15.0 eV and 2a1 22.9 eV (accuracy +-0.1 eV, legend p. 2218). Text (footnotes a, b, p. 2222, read on the page image, since the library attaches them to a later table): adiabatic_CH4 12.75 (2T2) and 22.39 eV (2a1), +-0.02 eV. Both datasets reproduced.

• Why reproduced: the CH4 column’s only reference is [17] = Heilbronner, Jones & Maier, Helv. Chim. Acta 60, 1697 (1977), and “a given reference number is valid also for all successive values in the column” (legend). No CH4 value is marked [*]. So the WebBook’s vertical CH4 13.6 eV, which cites Bieri et al., is Heilbronner et al.’s. Heilbronner et al. 1977 is not in the library.

• Doubt: the footnote prints “2T_d-band” for the 2T2 band (a misprint of the label, noted, no value affected). The footnote adiabatic 12.75 eV is 0.14 eV above berkowitz_1987’s onset.

• Status: verified (2026-09-27).

TC-501 frost_1967 (Frost, McDowell, Sandhu & Vroom, J. Chem. Phys. 46, 2008 (1967)) (2026-09-27)

• Transcribed (text, p. 2009): four thresholds “at 15.35, 16.71, 18.11, and 19.50 eV (standard deviation 0.02 eV for each)”: first_threshold_SF6 (15.35) and higher_thresholds_SF6 (3 points), level “1 sigma”, primary.

• Kind: not stated. The paper gives thresholds (onsets) of the integrated retarding-potential curve and neither calls them adiabatic nor prints band maxima (band maxima were expected: there are none in this letter). The WebBook lists 15.35 as adiabatic.

• Notes: Dibeler & Walker’s SF5+ thresholds (15.29, 16.53 eV implied), Fox & Curran’s RPD values (15.85, 17.0, 18.0 eV). The library PDF also holds parts of the two neighbouring letters (GeH3SiH3; xanthate complexes).

• Status: verified (2026-09-27).

TC-502 potts_1970 (Potts, Lempka, Streets & Price, Phil. Trans. R. Soc. Lond. A 268, 59 (1970)) (2026-09-27)

• Transcribed (Table 8, p. 75, read on the page image: the library has it only as text under Fig. 9): vertical_SF6 7 points: 15.69 t1u (3t1u), 16.96 t1g, 18.40 e1g (printed e_1g), 18.71 t2u, 19.68 t1u (2t1u), 22.5 t2g, 26.8 a1 (2a1g). Band maxima (Table 1’s note, p. 60: “Tables give band maxima”), kind vertical, no uncertainty.

• Doubt: “Note added in proof” (p. 74): the order of 1t2g and 2t1u is uncertain and Fig. 9 was changed to put 2t1u innermost; Table 8 still reads 22.5 t2g, 19.68 t1u. Energies unaffected; the assignments of those two rows are uncertain.

• Misprint (text only, no erratum): p. 76 “the peak at 11.96 eV to be assigned to 1t1g … This (16.96 eV) band”: 11.96 for 16.96. Not a dataset value.

• Out of scope: boron trihalides (Table 1), halomethanes, N/P/As trihalides, SeF6, TeF6, UF6.

• Status: verified (2026-09-27).

TC-503 berkowitz_1977 (Berkowitz & Eland, J. Chem. Phys. 67, 2740 (1977)) (2026-09-27)

• Transcribed (text): adiabatic_N2O 12.886 +- 0.002 eV (p. 2741; the midpoint of the linear threshold rise, 961.72-962.60 A, “as an approximation to the transition involving rotationless levels”; to X 2Pi_3/2); A_state_N2O 16.388 +- 0.001 eV (p. 2742, Table I: A 2Sigma+ (000) Rydberg limit); C_state_N2O 20.105 +- 0.002 eV (p. 2746). 3 datasets, 1 point each, primary, level not stated.

• Notes: A (100) 16.544 and (001) 16.692 eV limits (Table II); Tanaka et al.’s 12.88, 12.92_7 (2Pi_1/2), 16.38_6, 16.39_1 eV; appearance energies (NO+ 14.77 / 14.97 eV, N+ 20.075 eV); the Rydberg tables I-VIII.

• Finding: the WebBook lists 12.886 with method “PE”; the paper is photoionisation mass spectrometry.

• Status: verified (2026-09-27).

TC-504 wang_1988 (Wang, Reutt, Lee & Shirley, J. Electron Spectrosc. Relat. Phenom. 47, 167 (1988)) (2026-09-27)

• Transcribed by tools/extract/wang_1988.py: Table 1 (tbl_e1db285ab087, CSV, image checked, p. 171): adiabatic_CO2 4 points, X 13.778, A 17.314, B 18.077, C 19.394 eV, +-0.002 eV (footnote b and Table 3’s footnote a), primary. Table 3 (tbl_25887e8a6993, cells only, image checked, p. 173): x_band_CO2 23 points (22 used; the hot band 2_1^1 excluded), check, +-0.002 eV absolute; the parenthesised relative precisions kept in printed.

• Structural: the X cell’s footnote mark “b” and the first Table 3 row’s “^a” are removed from the numbers (script comments).

• Vertical: not stated by the paper; the X band’s intensity is in the (000) doublet 13.7778 (Omega = 3/2) and 13.7973 eV (Omega = 1/2), about equal (Fig. 3). The WebBook’s vertical 13.79 (Potts & Williams 1974) lies between.

• Notes: Table 2 constants; COS and CS2 IPs; Tables 4-11.

• Status: verified (2026-09-27).

TC-505 nist_webbook_2026 re-pointed; mahla_2025 re-pointed (2026-09-27)

• nist_webbook_2026: reproduced_from set to the curated ids for adiabatic_N2 (trickl_1989), adiabatic_O2 (tonkyn_1989), adiabatic_CH4 (berkowitz_1987), vertical_CH4 (bieri_1977), adiabatic_SF6 (frost_1967), vertical_SF6 (potts_1970), adiabatic_N2O (berkowitz_1977), adiabatic_CO2 (wang_1988). No value changed. Each dataset’s notes now compare with the original; the record’s notes list what was re-pointed and what is still not curated. Comparisons for adiabatic_H2 and adiabatic_D2 (not re-pointed) added to their notes.

• mahla_2025/expt_tonkyn_O2: reproduced_from set to tonkyn_1989; notes say the original confirms the value is an adiabatic, rotationally resolved threshold (Mahla’s caption calls it vertical).

• WebBook against the originals:

  Dataset	WebBook	Original (curated)	WebBook - original
  adiabatic_N2	15.581(8) eV	125 666.959(67) cm^-1 = 15.580717 eV	+0.28 meV (rounding)
  adiabatic_O2	12.0697(2)	97348(2) cm^-1 = 12.069614	+0.09 meV
  adiabatic_CH4	12.61(1)	12.61 (+0.01, -0.00), onset at 78 K	0 (uncertainty symmetrised)
  vertical_CH4	13.6(1)	13.6 (Heilbronner et al. via Bieri)	0
  adiabatic_SF6	15.35(2)	15.35, sd 0.02, a threshold, kind not stated	0
  vertical_SF6	15.69	15.69	0
  adiabatic_N2O	12.886(2)	12.886(2)	0 (method is PIMS, not PE)
  adiabatic_CO2	13.778(2)	13.778(2)	0
  adiabatic_H2 (not re-pointed)	15.425932(2)	shiner_1993 124 417.507(12) cm^-1 = 15.425805; liu_2010 (Liu 2009) 15.425803	+0.13 meV (60 x its stated sigma)
  adiabatic_D2 (not re-pointed)	15.4667(1)	liu_2010 124 745.394 07(58) cm^-1 = 15.466458	+0.24 meV

• Finding (conversion factor): the WebBook’s eV numbers for H2, D2 and O2 are what the cm^-1 values give with 1 eV = 8065.479 cm^-1 (CODATA 1973): 124 417.507 -> 15.425929; 97348 -> 12.06971; Takezawa & Tanaka’s uncorrected 124 746.6 -> 15.46673. With CODATA 2018 (8065.544) they are 8 ppm lower (about 0.1 meV). The D2 value also lacks the -1.0 cm^-1 pressure-shift correction applied later (liu_2010 Table IV footnote a). These are inferences (the WebBook states no factor).

• Status: decided (2026-09-27), to be confirmed in review.

TC-506 Values that bear on the ionisation parameters (docs/ionisation.md, data/gas/ionisation.toml) (2026-09-27)

Now used (the WebBook) against the curated primaries, and solprop (tests/data/ solprop_ionisation.json, converted with e = 1.602176634e-19 C):

Gas	Used now (eV)	Curated primary (eV)	solprop (eV)	solprop - primary
H2	15.425932	15.425803 (liu_2010/liu_2009_H2, reproduced, N = 0); 15.425805 (shiner_1993/mccormack_H2); ortho 15.4183325 (holsch_2019, N = 1 -> N+ = 1)	15.426135	+0.33 meV
D2	15.4667	15.466458 (liu_2010/ie_ortho_D2, N = 0); para 15.462690	15.466952	+0.49 meV
N2	15.581	15.580717 (trickl_1989/ie_N2)	15.581240	+0.52 meV
O2	12.0697	12.069614 (tonkyn_1989/ie_O2; to X 2Pi_(1/2)g)	12.069692	+0.08 meV
CH4	12.61 (adiabatic), 13.6 (vertical)	12.61 onset at 78 K (berkowitz_1987; rotationless ~12.615 by its model); vertical 13.6 / 14.4 / 15.0 (bieri_1977, reproduced from Heilbronner et al.)	12.615199	+5.2 meV (but +0.2 meV against the paper’s ~12.615 rotationless estimate)
SF6	15.35 (adiabatic), 15.69 (vertical)	15.35 threshold, kind not stated (frost_1967); vertical 15.69 (potts_1970)	15.32	-30 meV
N2O	12.886, 12.89 (vertical)	12.886 (berkowitz_1977, to X 2Pi_3/2)	12.898197	+12.2 meV
CO2	13.778, 13.79 (vertical)	13.778 (wang_1988; (000) Omega = 3/2); no vertical printed	(none)

• For H2 and D2 the conventional (N = 0 -> N+ = 0) energies are liu_2010’s (D2, primary) and Liu et al. 2009’s (H2, only as reproduced in liu_2010, and shiner_1993’s primary combination 124 417.507(12)). Hölsch 2019 gives only the ortho value.

• For CH4 the “adiabatic” number is an onset; for SF6 the curated first number is a threshold whose kind the paper does not state.

• The vertical-minus-adiabatic differences quoted in TC-444 are unchanged by the originals (O2 +0.26, CH4 +1.0, SF6 +0.34, N2O +0.004, CO2 +0.012 eV), since no value changed; but the CO2 “vertical” 13.79 is not in Wang et al.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-507 zhao_2010_erratum (Zhao, Jin, Le, Jiang & Lin, PRA 82, 049903(E) (2010)); zhao_2010 edited (2026-09-27)

• Transcribed: notes-only record. The erratum (one page, page image checked) corrects exactly two things:

  • Table V, CO HOMO-1 (1 pi), C_2m: printed 0.14, corrected to 0.014;

  • Table VI, H2+ at R = 2.0 au: the binding energies of 2p pi_g and 2p pi_u should be 0.2267 and 0.4288. As printed they are the other way round, in both the Present and Exact columns.

• Erratum added to zhao_2010: dataset table5_homo1_CO, row 2, value, printed “0.14” and corrected “0.014”. The evidence is the Table V image (p. 6), which prints 0.14, and the erratum’s text.

• Other edits to zhao_2010 (notes only; no value changed):

  • The “ERRATUM NOT IN THE LIBRARY” paragraph is replaced by what the erratum corrects.

  • The Table VI note now records the swap of the 2p pi_g and 2p pi_u energies. It also adds Table VI’s 1s sigma_u rows at R = 2.5-4.0, which the image prints and the old note omitted.

  • The dataset note of table5_homo1_CO points to the erratum.

• Checked: solprop’s claim that the erratum “leaves these neutral rows unchanged” is confirmed. Table III, the HOMO C_lm of H2, N2, O2, CO and CO2 and the reprinted rows, is untouched, and so are Tables I-II, IV and Table V’s other rows.

• Needs a register entry (the erratum).

• Status: verified (2026-09-27).

TC-508 talebpour_1999 (Talebpour, Yang & Chin, Opt. Commun. 163, 29 (1999)) (2026-09-27)

• Transcribed (3 datasets, inline points, ionization_model_parameter, use = "check"):

  • zeff_N2: Z_eff = 0.9. Model ppt, l = 0, m = 0; text p. 30 and the Fig. 1 legend.

  • zeff_O2: Z_eff = 0.53. Same model; p. 30 and the Fig. 2 legend.

  • ei_O2: E_i = 12.55 eV, the ionisation potential the O2 fit used (p. 31). It is the energy to O2+ v+ = 1, taken as a Franck-Condon-weighted average. It is a chosen model input, not a fitted one.

• Model: PPT (Appendix A; PPT 1966 plus Krainov 1997), with “l = 0 and m = 0” (p. 31). ADK with Z_eff was tried and rejected, because its slope is too steep at gamma ~ 1.

• Yields: figures only (N2 with Ar, O2 with Xe; 800 nm, 200 fs, linear polarisation). The ion signal is scaled to theory at saturation. The intensity calibration is not stated here (the companion larochelle_1998 uses ADK’s He saturation). Fragmentation is about 1e-2.

• Citation check (solprop): solprop cites “A. Talebpour, C.-Y. Chien and S. L. Chin, Opt. Commun. 163, 29 (1999)”. The authors are A. Talebpour, J. Yang and S. L. Chin. The journal, volume, page and DOI are right.

• Misprints in Appendix A (notes only; they are not values). The correct forms are printed by the same group in larochelle_1998 Eqs. (1)-(3) and (10)-(11):

  • Eq. (2): n* = sqrt(2E_i)/Z^2 is printed for Z/sqrt(2E_i).

  • Eq. (3): gamma = omega F/sqrt(2E_i) is printed for omega sqrt(2E_i)/F.

  • Eq. (1), exponent: “(2E_i)^(3e2)/(2F)” is printed for (2E_i)^(3/2)/(3F).

  • Eq. (7): Gamma(n* l*) is printed for Gamma(n* - l*).

  • Eq. (8): the summand is printed W_m for w_m.

• Finding for review: solprop uses Z = 0.53 for O2 with I_p = 12.0697 eV. The paper’s 0.53 was fitted with I_p = 12.55 eV, so solprop’s O2 rate is higher than the paper’s fitted rate.

• Status: open (the model choice).

TC-509 zhang_2014 (Zhang, Lan & Lu, PRA 90, 043410 (2014)) (2026-09-27)

• Transcribed (29 datasets, 196 values; tools/extract/zhang_2014.py):

  • Table XI (p. 4): a_1, a_2, a_3 of Eq. (8) for He, Ne, Ar, Kr, Xe and Ar+ (6 datasets of 3 rows, ionization_model_parameter, model zhang_2014, check). H is not curated; it is given in the notes.

  • Tables IX and X (p. 3): Gamma/2 of Ar and Ar+ against the field (au), for the GSZ, Muller and Tong-Lin potentials (6 datasets of 15 rows, ionization_rate, wavelength_nm = inf, static, primary). Each carries a per-row column intensity (W/cm^2) and scale = 2: the table prints the half rate Gamma/2, and the rate is Gamma.

  • Table I (Tong-Lin potential): He, Ne, Ar, Ne+ and Ar+ are reproduced from tong_2005, identical digit for digit. Xe is check: tong_2005 has no Xe, so its source is unknown.

  • Table II (GSZ): 7 targets. Table III (Muller): 4 targets. Both ionization_model_parameter, check. The paper does not say whether they are taken from refs. 30 and 31 or refitted.

• Structural fixes (no errata):

  • Table XI: the a_2 and a_3 rows are merged character by character. They are transcribed from the image, and the script checks that each merged cell is an in-order interleaving of the two strings.

  • Tables IX and X: scrambled in the text layer. They are transcribed from the images, and each column is checked two ways: as the character multiset of the text layer, and as the library’s OCR reading, cell for cell. Both checks pass.

• Excluded: Table IX at F = 0.12177 au, in the Muller (0.013229) and Tong-Lin (0.01110) columns.

  • The Tong-Lin cell repeats the GSZ cell digit for digit. At the neighbouring fields the Tong-Lin rate is 16-23 % above GSZ, and the text says “about 10%” below 1e15 W/cm^2.

  • The Muller cell is 19 % above GSZ. At every other field above 0.09 au the two agree to 1.4 %.

  • Gamma/W_ADK changes by about 20 % at this row alone, in both columns.

  • Perhaps the two cells are misplaced; no correction is known, so they are kept as printed and excluded.

• THE SIGN OF EQ. (8) (the question first asked; formula eq8, with a [[formulas.corrections]] on leading_sign, printed -1 and corrected +1). The printed form is W_M = exp[-(a_1 x^2 + a_2 x + a_3)] W_ADK. The paper’s own numbers need the positive sign, as solprop assumed. The a_i are a fit to the natural log of Gamma/W_ADK, and Gamma is the full rate, 2 x the tabulated value. Evidence:

  • Table IX against Eq. (8) (Ar): with the + sign, the Tong-Lin potential, I_p = 15.7596 eV, C_l = 2.44 (tong_2002 Table II), l = 1, m = 0 and Gamma = 2 x Gamma/2, W_M/Gamma = 1.04, 0.955, [1.20], 1.02, 1.02, 1.01, 1.01, 1.01, 1.00, 0.999, 0.997, 0.993, 0.990, 0.988, 0.989 over E/E_b = 0.64-3.76. The bracketed row is the excluded cell. The same ratio for the other readings:

    • the printed minus sign: 3.2 to 439;

    • 10^(+poly): 0.49 to 0.019;

    • Gamma = Gamma/2: 2.0 throughout.

  • A free parabola fitted to ln(Gamma/W_ADK) of Table IX gives a_1 = 0.168 and a_2 = -1.511, against the printed 0.16178 and -1.50441. Fitted to log10 it gives 0.073 and -0.656. The implied C_l is 2.40-2.50 at every field, matching tong_2002’s 2.44.

  • Ar+: a parabola fitted to Table X gives a_1 = 0.144 and a_2 = -2.07, against the printed 0.304 and -2.705. Table X stops at E/E_b = 3.07 while the fit runs to 4.5. With a constant C_l = 3.75, W_M/Gamma = 0.90-1.05 for E/E_b = 0.95-3.07, and 1.52 at 0.58, consistent with the paper’s “slight larger if E/E_b < 0.7”.

  • Figs. 1-2: the ordinate is labelled “log10(Gamma/W_ADK)”, but the plotted values are a_1 x^2 + a_2 x + a_3 itself. For Ar they are -1.0 at x = 1, -2.0 at 2, -2.75 at 3 and -3.15 at 4.5, which is ln. So the axis label is a second slip.

  • Tong-Lin alpha = 9 (tong_2005) against Table IX: W_TL/Gamma = 0.94-1.01 up to E/E_b = 2, then 0.88 falling to 0.41 at 3.76. This is the paper’s claim.

  • Eq. (10) is also misprinted: P = 1 - exp^(int W dt) lacks the minus sign.

• What the rates count: one active electron in the SAE potential, with no occupation factor. Eq. (1) takes m = 0, and the C_l = 2.44 check confirms the one-electron normalisation. No accuracy is stated. The paper says multielectron effects are not included.

• Tables IV-VIII (bound-state energies against NIST): notes only, with the ground states quoted.

• Needs a register entry (the formula correction and the exclusion).

• Status: verified for the sign (2026-09-27); open for its use.

TC-510 guo_1998 (Guo, Li, Nibarger & Gibson, PRA 58, R4271 (1998)) (2026-09-27)

• Transcribed: ip_adk_O2, the effective ADK ionisation potential of O2 that fits the O2+ yield (15 eV; text pp. 3-4 and the Fig. 2 caption). ionization_model_parameter, model adk, check.

• Yields: figures only: N2, Ar, O2 and Xe, single and double ionisation, LP and CP, 800 nm, 30 fs, 2e13 to 8e14 W/cm^2.

• Calibration: the intensity comes from fitting ADK to the Ar+ LP yield (beam waist, detection efficiency and pinhole as free parameters). It agrees with the measured spot, duration and energy within a factor of 2. The detection efficiency is 0.5-1 %.

• Text values in the notes:

  • the O2+ LP yield is “roughly ten times below Xe+”;

  • the ionisation potentials (N2 15.58/27.12, Ar 15.76/27.63, O2 12.06/24.14, Xe 12.13/21.21 eV; no source given);

  • the polarizabilities (Xe 4.04e-24, O2 1.58e-24 cm^3).

• Doubt: the ADK l and m used for O2 are not stated.

• Status: open.

TC-511 larochelle_1998 (Larochelle, Talebpour & Chin, J. Phys. B 31, 1215 (1998)) (2026-09-27)

• Transcribed: notes-only record.

  • Yields: Figs. 1-5 only (Xe, Kr, Ar, Ne, He; 800 nm, 200 fs, linear polarisation).

  • Calibration: ADK’s He saturation intensity. The other gases are relative to He within +-5 %.

  • Theory: PPT agrees with the data within a factor of 2 (He and Ne “accurately”; Ar slightly overestimated).

  • Table 1 (gamma_cr, gamma_k): in the notes, not a dataset. These are validity limits derived from the model, not fitted constants. gamma_k = 2E_i/(n* omega) is checked for Xe (14.78) and He (42.66).

• Found: talebpour_1999 cites this paper as volume “32”; it is volume 31. Eq. (4) prints the lower limit of the m sum as “m = -1” (read -l).

• Status: verified (2026-09-27).

TC-512 walker_1994 (Walker et al., PRL 73, 1227 (1994)) (2026-09-27)

• Transcribed: notes-only record. No quantity holds a saturation intensity or a yield ratio, so nothing is a dataset.

  • Yields: Fig. 1 (He+ and He2+) and Fig. 3 (the ratio) only.

  • Pulse: “160 +- 30 fsec” in the text and abstract, but the Fig. 1 caption says “100 fsec”. This is an inconsistency of the paper; the notes take the text.

  • Calibration: Xe resonant photoelectron spectra, “accurate to approximately 30%”. The figures’ intensities are “multiplied by 1.15”.

  • Text values:

    • the He+ saturation intensity is 8e14 W/cm^2;

    • the NS He2+/He+ ratio saturates at 0.0020;

    • the ratio scales as I^1.3;

    • NS production is seen from 1.5e14 W/cm^2, and there is no rescattering threshold down to 0.14 PW/cm^2.

• Doubt: the plateau is printed “from about 5 PW/cm^2”, but Fig. 3 shows it from about 0.5 PW/cm^2. The notes keep the printed text and flag it.

• Status: verified (2026-09-27).

TC-513 Re-pointing and stale notes elsewhere (no edits) (2026-09-27)

• Re-pointing: no existing record has a reproduced_from naming any of the six papers, so nothing was re-pointed.

• Stale notes in records not assigned to me:

  • golovanov_2020: “Neither source of the TDSE points is in the library”. Zhang, Lan & Lu 2014 now is (zhang_2014).

  • yudin_2001: “None of [11]-[13] is in the library”. Larochelle et al. 1998 now is (larochelle_1998).

  • tong_2002: it names Talebpour et al. and Guo et al. in its figure notes. These are figure comparisons, not reproductions.

  • bree_2011: it uses “Talebpour’s effective charge (Z_eff = 0.53 and 0.9)”, which is now curated (talebpour_1999).

  These may be pointed to the new ids.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-514 schrotter_1979 (Chap. 4, H. W. Schrötter and H. W. Klöckner, pp. 123-166) (2026-09-27)

• Transcribed (tools/extract/schrotter_1979.py; 74 datasets, 106 points; formulas 2):

  • Table 4.1 (p. 130, tbl_d34b5e440027): absolute N2 Q-branch dsigma/dOmega (1e-32 cm2/sr) per exciting line, one dataset per reference: the authors’ own [4.45] Klöckner (5 points, 351.1-514.5 nm, primary); hyatt_1973 (3), fenner_1973 (2: absolute calibration 33 +- 11 and against benzene 43, both at 488.0 nm), Fouche & Chang (1), Penney et al. 1972 (1), Kamiyama et al. (1, 632.8 nm), murphy_1969 (1, 435.8 nm), Penney 1974 (1, 300 nm, excluded by the chapter from its average): all reproduced. The normalised column (dsigma/dOmega (nu_0 - 2331)^-4, 1e-48 cm6/sr) is kept in the printed column only (derived from the absolute one).

  • Formulas n2_q_absolute ((5.05 +- 0.1)e-48 (nu_0 - 2331 cm-1)^4 cm6/sr, the weighted mean of Table 4.1 except 300 nm; text +-0.1, table +-0.08) and n2_q_absolute_rotational ((4.97 +- 0.2)e-48, against N2’s own S(6) line at 488 and 514.5 nm).

  • Table 4.2 (pp. 137-141, five parts tbl_5220e2a41fe5, tbl_3bb750412546, tbl_ce7fb84505c6, tbl_20201534676f, tbl_b9faf9e8a520; order from the printed page numbers): Sigma_j (Eq. 4.14) as raman_cross_section_ratio, reference N2 Q branch, parameters.normalization = Eq. (4.14), one dataset per molecule, band and footnote letter (61 datasets, 87 points): O2 (10 datasets), H2 (4), D2 (1), CO (10), CO2 1285 (7) and 1388 (9), N2O 1285 (4) and 2224 (2), O3 (2), CH4 (9), SF6 (3). Own lab ([4.54] Hochenbleicher, letter p; [4.45] Klöckner, q, no in-scope rows in 4.2): primary. The others reproduced, with the citation as printed or murphy_1969 (a), fenner_1973 (d), bermejo_1977 (r).

  • Table 4.4 (p. 149, tbl_a794533c145e): CH4 shifts (4, check), rho (4, check: the symmetry values 0 and 0.75), Sigma_j nu1 8.56 (the chapter’s average of Table 4.2, check), Bermejo nu2 0.52 / nu3 4.82 (reproduced bermejo_1977), Kagel nu2 0.66 / nu3 4.0 (reproduced). nu4 ‘<0.01’ (a bound) in notes only.

• Structural fixes (in the script, checked against every cell): the library joins stacked lines of a cell (Tables 4.1, 4.2, 4.4); in Table 4.2 part 2 the N2O 2224 cm-1 band’s lines (0.5_0^d at 488, 0.5_1^b at 515) are in the 1285 cm-1 band’s cells (the image aligns them with 2224). Lowered last digits (‘1.2_5’) read as 1.25, kept in the printed column. SF6 at 515 nm has a speck after 3.9_6^aa on the scan (not a mark).

• Checked: the weighted mean of Table 4.1’s normalised column (1/sigma^2 weights, 300 nm excluded) = 5.048 +- 0.076 (printed 5.05 +- 0.08); the normalised column reproduces from the absolute one with nu_0 = 1/lambda_0 to the printed digits at every row (air or vacuum wavelengths indistinguishable at that precision); Table 4.4’s absolute normalised values = Sigma_j x 5.05 / [1 - exp(-hc nu/kT)] to 1 % (Kagel nu3 20.2 vs 20.3 printed); CH4 Sigma 8.56 = the mean of Table 4.2’s thirteen CH4 values (8.554).

• Doubts / decisions for review:

  • Sigma_j is NOT the plain cross-section ratio: ratio = Sigma_j (nu_0 - nu_j)^4 / (nu_0 - 2331)^4 / [1 - exp(-hc nu_j/kT)] (O2 at 488 nm: x1.18). Recorded as raman_cross_section_ratio with parameters.normalization; a distinct quantity (or a parameter the loader checks) may be wanted so that no consumer reads Sigma_j as a ratio.

  • [4.45] and [4.54] are unpublished Munich dissertations (‘new results from our laboratory’, p. 132); recorded primary (this chapter is their publication). Reproduced-but-usable may be preferred.

  • The +-10 % (visible) / +-15 % (near UV) / +-5 % (Levatter at 337 nm) accuracy of Table 4.2 (p. 136) is applied to every Sigma dataset, own and reproduced (‘from our laboratory and also from most other groups’), level not stated.

  • Wavelengths recorded as standard air (the conventional laser-line values; the chapter does not say); Table 4.2’s heads are rounded to 1 nm.

  • Table 4.4’s rho (0, 0.75) are symmetry values, not measurements (use check).

  • Table 4.3 (mercury-arc data, pp. 144-148), 4.5 (liquids) and 4.6 (liquid/gas ratios) hold no curated species: notes only.

• Status: transcribed and checked against the images (2026-09-27).

TC-515 weber_1979 (Chap. 3, A. Weber, pp. 71-121) (2026-09-27)

• Transcribed (tools/extract/weber_1979.py; 16 datasets, 18 points): Table 3.2 (p. 88, JSON = image): B_0 and D_0 of H2 and D2 (Stoicheff 1957, pre-laser, no uncertainty), 14N2 (Butcher et al. 1971 two- and three-constant fits: 2 rows; Bendtsen, reproduced bendtsen_1974, digit-identical), 16O2 (Butcher, Willetts & Jones 1971; Edwards, Good & Long 1976). Table 3.3 (p. 93): CO2 B_0 0.3902634(44), D_0 1.270(35)e-7 in (00^0 0) and B 0.3906398(82), D 1.419(48)e-7 for the c levels of (01^1 0), from C.-H. W. Wang’s Fordham dissertation (1975, unpublished; reproduced, the only copy). Parameters: constant, vibrational_state_v (0) or vibrational_state (‘(01^1 0), c levels’), isotopologue.

• Erratum: Table 3.2 H2 B_0 printed [56.3392] -> 59.3392. Evidence: the table’s own B_e(H2) = 60.841 needs alpha_e = 9.0 with 56.3392; the isotope scaling of D2’s alpha_e (2 (30.442 - 29.9105) = 1.063, x 1.9986^1.5) gives alpha_e(H2) = 3.003 and B_0 = 59.339; HD agrees (2.99); shelton_1993, citing this chapter, quotes B_0 = 59.3392.

• Structural fix: Table 3.3’s CO2 cells join the two state rows; transcribed from the image and checked against the cells.

• Findings / doubts:

  • N2O is not in the book. Table 3.3 has CO2, CS2, HCN, DCN, XeF2, C2H2, C2HI, C4H2, C4D2, C2N2 only; no N2O rotational constant anywhere in Chaps. 2-3. The expectation (B_0, D_0 of N2O from Table 3.3) cannot be met: a source is still needed.

  • CO is not in Table 3.2 (its Raman analysis, Kainnady’s 1976 dissertation, is mentioned without values, p. 89).

  • Table 3.2’s 14N15N D_0 from Bendtsen is printed 5.83 +- 0.03; Bendtsen and Chap. 2’s Table 2.3 have 5.38 (a transposition; isotopologue, notes only).

  • The text (p. 87) prints Butcher’s D_0 values as x10^-8 (misprints; the table has x10^-6).

  • Uncertainty levels not stated (S2’s are 5 sigma; Butcher’s are fit precision).

  • O2 constants are the N(N + 1) ladder without spin splitting (p. 90).

• Status: transcribed and checked against the images (2026-09-27).

TC-516 brodersen_1979 (Chap. 2, S. Brodersen, pp. 7-70) (2026-09-27)

• Transcribed (tools/extract/brodersen_1979.py; 7 datasets, 7 points): Table 2.3 (p. 41, CSV = image), 14N2 only: B_0 1.989574(12), D_0 5.76(3)e-6, nu_0 2329.917 (+-0.01), alpha 0.017292(3), all reproduced bendtsen_1974 (digit-identical). Text (inline points): O2 B_1 = 1.421884 +- 0.000013 and nu_0 = 1556.384 +- 0.010 cm-1 (p. 44, Loëte & Berger 1977; nu_0 equal to Fletcher & Rayside’s), SF6 B_0 = 0.09111 +- 0.00005 cm-1 (p. 66, Berger, Aboumajd & Saint-Loup 1977): reproduced.

• Not a dataset: O2 D_1 printed ‘(-4.864 +- 0.014) 10^-6’ (image checked) in Loëte and Berger’s unstated sign convention: notes only, to avoid a sign misreading. r_e, 14N15N and 15N2: notes. CD4, SiH4, tritium, F2, acetylene etc.: notes.

• Status: transcribed and checked against the images (2026-09-27).

TC-517 Re-pointing of existing records (values unchanged) (2026-09-27)

• hanna_1986: dsigma_H2, dsigma_CH4 reproduced_from -> [“schrotter_1979”]; notes record the check. H2: Hanna’s Eq. (2) with Sigma_j = 3.45 (514.5 nm, Fouche & Chang, sigma_H2_b) gives 1.23e-36 and 7.93e-35 m2/sr (printed 1.2e-36, 7.9e-35): reproduced. CH4: the printed values back out Sigma_j = 8.86 (1.06 um) and 8.53 (0.53 um) against 515 nm (9.02/8.68 against 488 nm); Table 4.2 has 9.1, 8.7, 9.3 at 515: consistent to 2-4 % but no single printed value gives both.

• everall_1987: dsigma_SF6 reproduced_from -> [“schrotter_1979”]. NOT reproduced: Sigma_j (3.3-3.96) x 5.05e-48 x (40323 - 775)^4 = 4.1-4.9e-29 cm2/sr at 248 nm; Everall prints 6.0e-29 (needs Sigma 4.86, 23 % above the largest). Kept as printed; reported.

• reichert_2015: the N2 B/D (Raman column) reproduced_from -> [“bendtsen_1974”, “weber_1979”]; the O2 B/D -> [Butcher, Willetts & Jones 1971, “weber_1979”]: ‘the original measurement … not identified’ is now identified as Butcher et al. [3.17a] (digit-identical: 1.437682(9), 4.852(12)). Record notes point [41] to weber_1979.

• Notes-only mentions pointed to the new ids: shelton_1993 (its B_0 59.3392 and D_0 0.04599 are Table 3.2’s Stoicheff values; its 59.3392 is evidence for the erratum), shelton_1987 (N2, O2 transition polarizabilities ‘from Raman intensity measurements of [11]’ = schrotter_1979), lundeen_1983 (Schrötter’s alpha^2 = 3.24e-51 = 5.05e-48/(2 pi)^4 checked; S_j 3.45, 3.64 = Table 4.2 H2 b and d), rosasco_1985 (5.05e-48 checked), hahn_1995, farrow_1987.

• Not edited: danichkin_1981 cites Weber only as its ref. [4], Weber’s 1973 review (Russian translation 1977) in ‘The Raman Effect’, not this book, for the rho_pol -> rho conversion; no row cites Schrötter & Klöckner or Weber 1979. farrow_1985 cites Schrötter & Klöckner in its technique (notes only) but is another extraction’s record (its Rosasco re-pointing): left to that extraction or to review.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-518 Values bearing on the Raman parameters (docs/raman.md) (2026-09-27)

• N2 transition polarizability: 5.05e-48 cm6/sr gives 45 abar_01^2 + 7 x gamma_01^2 = 45 C/(16 pi^4) = 1.458e-49 cm6; with rho_Q = 0.021 (Danichkin’s recommended) abar_01 = 0.375 au, with no anisotropy 0.384 au; optmat uses 0.3789 (Murphy): -1.1 % / +1.4 %. (Rosasco 1985 derived [a(N2)]^2 = 3.085e-51 cm6 from the same number; this gives 3.092e-51.)

• From Sigma_j (abar_01^2 = Sigma_j x 1.458e-49 / (45 + 7 x 45 rho/(3 - 4 rho))): O2 0.3635 au (own p values, Sigma 1.0, rho 0.047) to 0.370 (all, 1.039) vs 0.3652; H2 (whole Q branch) 0.744 (all four, 3.86) or 0.713 (visible, 3.545) vs 0.7491 (Q(1), Huo); D2 0.610 (Murphy’s 2.6) vs 0.6178; CH4 nu1 1.124 au (Table 4.4’s 8.56) to 1.145 (own, 8.88) vs 1.0671: +5 to +7 % (the model’s CH4 gain is 7 % low against Ottusch & Rockwell: a +5 % amplitude is +11 % in gain); SF6 nu1 0.729 (all, 3.6) to 0.755 (Clark & D’Urso, 3.86) vs 0.7066: +3 to +7 %.

• Rotational constants for N2O and CO2: CO2 B_0 = 0.3902634(44), D_0 = 1.270(35)e-7 cm-1 (Wang 1975 via weber_1979) are now curated; N2O has none in this book.

• H2/D2 constants: Stoicheff’s B_0 59.3392 (after the erratum), D_0 0.04599 (H2) and 29.9105, 0.01134 (D2), with H_0 5.2e-5 / 0.36e-5 in notes, against the stopgap fitted 59.30769/4.338e-2 and 29.89747/1.117e-2 of docs/raman.md.

• O2: Butcher et al.’s B_0 1.437682(9), D_0 4.852(12)e-6 against Hajigeorgiou’s 1.43767, 4.839e-6 (used); Loëte & Berger’s B_1 1.421884(13), nu_0 1556.384(10) (used: 1556.391).

• SF6: B_0 = 0.09111(5) cm-1 (Berger et al. 1977, via brodersen_1979): the first curated rotational constant of SF6.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-519 fenner_1973 (Fenner, Hyatt, Kellam & Porto, J. Opt. Soc. Am. 63, 73 (1973)) (2026-09-27)

• Transcribed: 44 datasets, 68 values, all at 488.0 nm (the Ar+ line, recorded as standard air; the paper does not say air or vacuum):

  • Table I (tbl_0791ca776a3c): shifts (raman_shift, check; 7 datasets, 9 values) and rotational constants (rotational_constant, check; 6 datasets): printed without a source, not measured here; B_e or B_0 not said.

  • Table II (tbl_422afc34de03): ratios to the N2 Q branch, this paper’s column (ratio_*, primary, 9 datasets x 1: O2 1.3, H2 sum 2.4, H2 Q(1) 1.6, CO 1.0, CO2 nu1 1.4, 2nu2 0.89, N2O nu1 2.2, nu3 0.51, CH4 6.0), relative uncertainty 0.10 (‘reproducibility +-10 %’, level not stated); the other workers’ columns (ratio_*_others, reproduced, 8 datasets, 22 values: Fouche & Chang, Murphy et al. = murphy_1969, Stansbury et al., Penney et al.), rescaled by Fenner et al. to 488 nm with nu^4.

  • Text p. 4: the Rayleigh-route ratios O2 1.1, H2 Q(1) 1.5, CO 1.0, CO2 nu1 1.4 (ratio_*_rayleigh, check, inline).

  • Table III (tbl_81ab5bdc357b): rotational (peak Stokes line and all lines) and vib-rot (O+S branches) cross sections relative to the same molecule’s Q branch at 22 C, both polarizations (rotational_* N2, O2, H2, CO, CO2; vibrot_N2, vibrot_O2; primary; 7 datasets, 12 values). The peak line is printed ‘0(J)’ (kept): by the caption the strongest Stokes line from J.

  • Table IV (tbl_8d6a0ed08ffd): absolute N2 Q branch 3.3 +- 1.1 x 1e-31 cm2/sr (calibrated spectrometer, primary; +-1.1 is the authors’ ‘+-35 %’ error-analysis estimate, level not stated), 4.3 (against benzene, check), four others (reproduced).

  • Geometry: z(x,x)y with rho = 0 for Table IV (p. 4); Table II’s polarization is not stated (recorded in the geometry parameter).

• Checked: every cell against the images. Not in the paper: depolarization ratios (none tabulated), D2, SF6, O3.

• Doubts: the ‘0(J)’ notation of Table III; Table I’s CO point group printed C_inf h (no value affected). This paper’s 3.3 x 1e-31 is 39 % below hyatt_1973’s 5.4 (same group, same wavelength) and danichkin_1981’s recommended 5.5.

• Status: open (for review).

TC-520 hyatt_1973 (Hyatt, Cherlow, Fenner & Porto, J. Opt. Soc. Am. 63, 1604 (1973)) (2026-09-27)

• Transcribed: 4 datasets, 12 values. Table I (tbl_fa72308ac503): the theoretical H2 S(1) (J = 1 -> 3) dsigma/dOmega at 90 deg, 488.0 and 514.5 nm, 2.25 and 1.79 x 1e-30 cm2/sr (theory_S1_H2, check; from Ford & Browne’s tables; ref. 16 = ford_1973). Table II (tbl_e6410a8fb5ef, JSON): absolute N2 Q branch, this work (5.4 +- 0.3) and (4.2 +- 0.2) x 1e-31 cm2/sr at 488.0 and 514.5 nm (absolute_N2, primary, level not stated); Fenner et al.’s two rows (absolute_N2_fenner, reproduced_from fenner_1973, identical to its Table IV); Penney, Fouche & Chang, Murphy (murphy_1969), Stansbury (absolute_N2_others, reproduced, 6 values; the prelaser ones nu^4-corrected by Hyatt et al.).

• Structural / misprint: Table I’s 514.5 nm cell prints ‘1.79 x 19^-30’ (image): the power’s base misprinted; the mantissa 1.79 is stored with the scale 1e-30, raw cell kept. Checked: 21 sigma_0/(80 pi) = 1.788e-30 and 2.248e-30; Phi(1) = 0.6601 reproduces the third column (1.485, 1.182). No erratum (no stored number changes).

• Checked: 5.4/4.2 = 1.286 against nu_R^4 ratio 1.271 (within the +-).

• Doubts: which scattered polarization the N2 measurement uses is not stated (Eq. (1) is summed over both). Fig. 1 (six wavelengths) not digitized.

• Status: open (for review).

TC-521 bischel_1983 (Bischel & Black, AIP Conf. Proc. 100, 181 (1983), Excimer Lasers-1983) (2026-09-27)

• Transcribed: Table 1 (tbl_377daa8e19f8, the unlabelled table, caption above it): five formulas single_resonance_<gas> (H2, D2, N2, O2, CH4), dsigma/dOmega = A nu_s^4/(nu_i^2 - nu_p^2)^2, A and nu_i and lambda_i as printed; the Raman shifts as shift_* datasets (check, 5 x 1). The script checks that the formulas’ coefficients are the table’s cells.

• Erratum: Table 1 prints CH4 (nu1)’s shift as 2986 cm-1 (D2’s value); corrected to 2917 (the text, p. 181: ‘CH4 (2917 cm-1)’); the CH4 formula uses 2917.

• Checked (scratch): lambda_i = 1/nu_i for all five (N2: 111.73 against 111.8, nu_i rounded). Against the values others quote from this paper: at 248 nm everall_1987’s H2 4.8 (formula 4.79-4.83), N2 1.52 (1.53-1.54), O2 3.88 (3.94-3.99), CH4 15.3 (15.5-15.7) x 1e-29: within 1-3 %. At 532 nm ottusch_1988’s H2 Q(1) 0.81e-30 (formula, Q branch, 0.859e-30: -6 %), D2 Q(2) 0.79e-30 (0.738e-30: +7 %), CH4 2.7e-30 (2.78e-30: -3 %). H2 193 nm resonance factor 2.30 (text ‘approximately 2.4’).

• Doubts: O2 at 193 nm: the fit gives an enhancement of 26-27 over 532 nm, the text says 22. The N2 formula at 488 nm gives 5.70e-31, 4-6 % above hyatt_1973 (5.4) and danichkin_1981 (5.5); the absolute scale is Schroetter & Kloeckner’s N2 at 532 nm (ref. 2, schrotter_1979). The measured cross sections are in Figs. 1-3 only. The text cites a ref. 6 for linewidths that is not in the reference list: this paper holds no linewidth. The library’s citation.bib has spurious authors (‘Test’, ‘Allman’, …).

• Status: open (for review).

TC-522 hunt_1984 (Hunt, Poll & Wolniewicz, Can. J. Phys. 62, 1719 (1984)) (2026-09-27)

• Transcribed: Tables 5-10 (JSON; no CSVs), the H2 and D2 columns: <0J|alpha_par|vJ’> and <0J|alpha_perp|vJ’>, a.u., static (Kolos & Wolniewicz’s 1967 polarizability functions), adiabatic; Delta J = 0 (J = 0-5), +2 (J = 0-3), -2 (J = 2-5), v = 0-5. One dataset per table, gas and v: 68 datasets, 320 values, raman_transition_polarizability with invariant parallel/perpendicular, label abscissa (row J), parameters.wavelength_nm = inf. HD, HT, DT, T2 not transcribed.

• Structural: Table 7’s v = 1 block (J = 1-3) is shifted one column in the cells (the J label in the H2 column, T2 lost): realigned in the script, checked against the image. Table 5’s D2 column headed ‘v_2’ in the cells.

• Erratum: Table 5, D2 <00|alpha_par|20> printed 0.05292 (no minus; image checked), corrected to -0.05292 (the block, the other isotopologues and Table 6 are all negative).

• Checked: every H2 and D2 cell against the images; the diagonal elements give kolos_1967’s static per-level mean and anisotropy (Table III) to 1e-4 for J = 0-5 (H2 J = 0: 5.41380/2.0238 against 5.4139/2.0239; D2: 5.34520/1.9584 against 5.3453/1.9584). rychlewski_1983 Table VII static (H2, not extracted there): alpha_00,10 0.74006 and gamma_00,10 0.61204 against Hunt’s Q(0) 0.73923 and 0.61001 (+0.11 %, +0.33 %). mizrahi_1985_h2d2 (H2 alpha_01,11 = 0.74027, gamma 0.61175; D2 alpha_02,12 = 0.61765, gamma 0.50224) and shelton_1987’s Table 2 (x 1.64878e-41) are exactly Hunt’s J = 1 / J = 2 elements.

• Not taken: Table 1 (dissociation energies; some values in notes), Tables 2-4 (quadrupole, notes), the deposited complete tables.

• Status: open (for review).

TC-523 yu_2012 (Yu, Miller, Drouin & Mueller, J. Chem. Phys. 137, 024304 (2012)) (2026-09-27)

• Transcribed: the formula x_state_dunham (Eq. 2 and the Dunham expansions; Table I, X 3Sigma_g- of 16O16O, all 36 coefficients as printed, with their uncertainties, in MHz, including the spin-spin (4 lambda) and spin-rotation (gamma) series); the script checks the recorded coefficients against Table I’s cells. Table III (JSON): the band-by-band v = 0, 1 X-state constants, Fit #1 (primary) and Fit #2 (check), as rotational_constant in MHz: B, -D (printed sign), H, 4 lambda, 4 lambda_D, 4 lambda_H, gamma, gamma_D, gamma_H (18 datasets, 28 values; sigma from the parentheses).

• Reading of Table I: each row is U_lm mu^-(l/2+m)/2^l, i.e. Y_lm/2^l, the coefficient of (2v + 1)^l, with the BOB term printed separately (to be added). Eq. (2) has + D_v (N^2)^2, so the fitted D is negative (the conventional D_0 = +0.14516 MHz = 4.8405e-6 cm-1).

• Checked: the Dunham sums reproduce hajigeorgiou_2013’s Table I B_v, D_v, H_v for v = 0-31 to the printed digits (which confirms the reading), and Table III to within the Dunham uncertainties (B_0 -0.0043 MHz, i.e. 6 sigma of Table III’s +-0.0007; 4 lambda_0 +0.030; gamma_0 -0.00009; T_1 -3.4 MHz). Table III’s D and H differ from the Dunham ones because its band fits free H_v.

• Not taken: T_1 = 46659391.5(37) MHz (the band origin: no MHz quantity for a term value; 1556.38977 cm-1), the a and b states, the minor isotopologues, 16O17O hyperfine, Table II (r_e). The line list and SPFIT files are supplementary material (not in the library).

• Doubt: the parentheses’ level is not named (the text speaks of ‘1 sigma’ agreement). The L03 term (4 U^lambda_0,3) has no place in Eq. (2) as printed.

• Status: open (for review).

TC-524 Re-pointed records (no value changed) (2026-09-27)

• danichkin_1981: refs. [12] (Fenner et al.) and [42] (Hyatt et al.) in every reproduced_from (9 lines) -> fenner_1973, hyatt_1973; the ‘curated’ sentence updated and a RE-POINTING paragraph added. Comparison: O2 1.33 (Fenner 1.3), CO 1.02 (1.0), CO2 nu1 1.41 (1.4), 2nu2 0.91 (0.89), CH4 6.0 (6.0), H2 band 2.44 (2.4), Q(1) 1.6 (1.6), N2O nu1 2.50 (2.2 / 0.88, as Danichkin says), N2O nu3 0.62 (0.51: x 1.22, unexplained); absolute N2 3.4, 4.4 (Fenner 3.3, 4.3), 5.5, 5.4 (Hyatt 5.4 at 488, 4.2 at 514.5 scaled). Disagreement: Danichkin’s H2 row ‘ref. [12], 514.5 nm, 2.26’ has no counterpart in Fenner et al. (488.0 nm only); probably Carlson & Fenner 1972 (ref. [18]) or a misattribution. CO2 ratios are not divided by the stated 0.92 (unlike N2O).

• ottusch_1988: dsigma_H2, dsigma_D2, dsigma_CH4 -> bischel_1983 (notes: the formula values at 532 nm, -6 %, +7 %, -3 % from Ottusch’s quotes).

• everall_1987: dsigma_CH4, dsigma_H2, dsigma_O2, dsigma_N2 -> bischel_1983 (notes: the 248 nm formula values, within 1-3 %). The SF6 row (Schroetter & Kloeckner) is left to schrotter_1979’s extraction.

• bischel_1986b: formula cross_section_eq5 -> reproduced_from bischel_1983 (A, nu_i identical to Table 1’s H2 row); the other Excimer-Lasers-83 citation there (ref. 13, T2_H2) is Bischel & Dyer’s linewidth paper, not this one: unchanged.

• hajigeorgiou_2013: table1_B_O2, table1_D_O2, table1_H_O2 -> yu_2012 (reproduced to the printed digits). Finding: Hajigeorgiou’s Pekeris-check omega_e = 1579.833 and omega_e x_e = 11.6938 are not Yu’s (Y_10 = 1580.1037, -Y_20 = 11.9147 cm-1); B_e and alpha_e are.

• Not edited (report only): hanna_1986 cites ‘Bischel and Black 1983 with Owyoung 1983’ for its H2 51 MHz/atm linewidth; Bischel & Black has no linewidth, so only Owyoung can be the source (hanna_1986 belongs to another extraction). mizrahi_1985_h2d2 and shelton_1987 quote Hunt et al.’s elements in notes or as inputs of computed values (no reproduced_from): their numbers agree exactly.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-525 Values bearing on the Raman parameters (docs/raman.md) (2026-09-27)

• H2 alpha_01 (optmat 0.7491 au, Huo at 500 nm via bischel_1986b): Hunt’s static Q(J) mean elements 0.73923-0.75462 (J = 0-5; Q(1) 0.74027); Rychlewski’s dynamic Q(0) rises from 0.740 (static) to 0.767 at 632.8 nm and 0.802 at 436 nm, so Huo’s 500 nm value is close to the static one, not to Rychlewski’s dispersion. The Q-branch strengths depend on J by 2 % over J = 0-5 (optmat uses one value).

• D2 alpha_01 (optmat 0.6178 au, from Murphy’s dalpha/dQ): Hunt’s static Q(2) 0.61765, Q(0) 0.61633: agreement to 0.02 %.

• Anisotropies: Hunt’s static pure-rotational S(J) gamma: H2 2.0351-2.1025 (J = 0-3), D2 1.9639-1.9974, against optmat’s 632.8 nm H2 2.104-2.318 (Bishop & Pipin) and D2 2.008 (optical): the static values are 3-4 % lower (dispersion), as expected.

• N2 absolute cross section at 488 nm: Hyatt 5.4 +- 0.3, Fenner 3.3 +- 1.1 (and 4.3), Bischel & Black’s fit 5.70, Danichkin’s recommended 5.5 +- 0.2 x 1e-31 cm2/sr. optmat’s N2 alpha_01 = 0.3789 au gives (2 pi nu_s)^4 alpha_01^2 = 5.34e-31 cm2/sr at 488 nm (mean part only; bischel_1986b’s Eq. (6) form, scratch): consistent with Hyatt and Danichkin.

• O2 levels: yu_2012 supplies the spin-spin and spin-rotation constants needed for the spin splittings (TC-492): 4 lambda_0 = 238005.3746(64) MHz (lambda_0 = 1.98475 cm-1), gamma_0 = -252.586311(176) MHz (-0.0084253 cm-1), and their v and N dependence. B_0 = 43100.44712(70) MHz = 1.4376766 cm-1 (hajigeorgiou_2013’s Table III B_0 1.437674521, Table I 1.43767602).

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-526 rahn_1986 (Rahn & Palmer, J. Opt. Soc. Am. B 3, 1164 (1986)) (2026-09-27)

• Transcribed: Table 1 (tbl_7d46e56fb640, JSON cells only; cells = image, and the page image checked), N2 Q(J) self-broadening 2 gamma_j, cm-1/atm, one dataset per temperature, rows Q(J), “(n)” in last digits converted to an absolute sigma: table1_500K (27 points, J = 0-27 without 19), table1_730K (25, J = 2-26), table1_1000K (27, J = 2-30 without 17, 25), table1_1500K (25, J = 2-28 without 15, 23), primary, 1 sigma; table1_295K (19, J = 0-18), reproduced from rosasco_1983 (note a “From Ref. 6”). “-” cells (not measured) and blanks not recorded.

• FWHM: caption “Collisional Self-Broadening Coefficients (FWHM)”, head “2 gamma_j (cm-1 atm-1)” (p. 1167); Fig. 3 caption “2 gamma_j refers to broadening coefficients (FWHM)” (p. 1166); Eq. (3) “Gamma_j (FWHM) … Gamma_j/2 = sum gamma_ij” (p. 1167). Per atm at temperature T. No Dicke term (Galatry profile; high-pressure limit).

• Uncertainty: “1-sigma error estimates (parentheses in Table 1) … from multiple measurements and from the quality of the fit (chi^2). Systematic errors … not included” (p. 1167); reproducibility +-3 %.

• Structural: none needed (cells = image).

• The 295 K column = 2 x Rosasco’s HWHM, values and errors, all 19 rows exactly.

• Formulas:

  • eq1_meg: the MEG law, alpha 0.023 +- 0.003, beta 1.67 +- 0.15, delta 1.26 +- 0.06 (Koszykowski’s), n = 1.346 +- 0.06, T0 = 295 K. Check (scratch): against Table 1, model/table - 1 = mean -2.9 % (rms 3.3 %) at 295 K, +1.7 % (4.1 %) at 500 K (worst Q(27) +13.6 %), -1.0 % (2.3 %) at 730 K, -0.3 % (3.1 %) at 1000 K, -7.0 % (7.4 %) at 1500 K (“slightly underestimate … for 1500 K”, as the paper says). Rates summed over same-parity levels to J = 80, Bendtsen’s B0, D.

  • note32_meg: the note-32 replacement f(T) (m = 0.1487, delta = 1.21): mean -0.0 %, +1.8 %, -1.6 %, +0.5 %, -2.0 % at 295-1500 K; removes the 1500 K bias.

• Doubt: the paper prints n = 1.346 +- 0.06 (image checked at 300 dpi); koszykowski_1987 quotes it as +- 0.006 (a tenfold smaller error). Not an erratum (koszykowski_1987, another extraction’s record, not edited).

• Bears on the Raman parameters: the N2 Q-branch widths (TC-492: MEG with n = 1.346). The measured per-J FWHM at 500-1500 K now exist; the MEG with the printed parameters is within 2-4 % rms at 295-1000 K and 7 % low at 1500 K.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-527 rosasco_1983 (Rosasco, Lempert, Hurst & Fein, Chem. Phys. Lett. 97, 435 (1983)) (2026-09-27)

• Transcribed: Table 1 (p. 438; tbl_ee3e296d7c2c, JSON only; caption lost in the extraction; page rendered at 400 dpi and checked): gamma_j, cm-1/atm, 298 K, J = 0-18: table1_N2 (19) and table1_CO (19), primary, sigma from the last-digit “(n)”, level not stated.

• HWHM, from the paper’s equation: Eq. (6) (p. 436), Lorentzian p [gamma_j - (omega - omega_j) Y_j] / [(omega - omega_j)^2 + (p gamma_j)^2]: p gamma_j is the half width. The paper never writes “HWHM” by the table. Confirmed independently: rahn_1986 prints exactly 2x these as FWHM.

• Structural: heads misread (“\aleph_2” = N2, “y_f” = gamma_j): checked in the script.

• Line mixing Y_j (atm-1; Eq. (7): Y_j = 2 sum (alpha_j’/alpha_j) W_j’j/(omega_j’ - omega_j)): no quantity; recorded as the coefficients of formulas eq6_N2, eq6_CO (strings as printed; errors +-20 % J = 0-3, +-50 % J = 4-18 from the table notes, the “a” note’s +-20 % inferred from a partly illegible scan).

• Check / doubt (important for line mixing): detailed balance implies sum_j rho_j Y_j = 0 (per parity for N2). With 298 K populations: N2’s printed Y_j violate it (+0.046 atm-1 against sum rho|Y| = 0.060; even J +0.025, odd J +0.021); CO satisfies it to 12 % of the scale (-0.010 against 0.084). The N2 Y column is badly printed; the signs of J = 8, 10, 13 (-0.03) are faint dashes, the others positive. Lost minus signs are a possible cause, not established. Do not use the N2 Y_j without this caveat.

• Re-pointed: farrow_1985 table1_Ar notes now name rosasco_1983 (the Ref. 9 whose self-broadening Farrow and Rahn subtracted). No value changed.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-528 russell_1987 (Russell & Roh, J. Mol. Spectrosc. 124, 240 (1987)) (2026-09-27)

• Transcribed: Table I (p. 241; tbl_99029db61edc, JSON only; = image), D2 Q(J), 10^-3 cm-1/amagat: table1_a (5, Q(0)-Q(4), primary, FWHM, fit errors, level not stated); table1_murray_javan_a (3, reproduced, width “not stated”, see below); table1_robertson_hunt_a (5, reproduced, FWHM).

• FWHM: Eq. (1) (p. 240): “Delta nu is the linewidth (FWHM in cm-1)”; Delta nu = (4 pi nu^2/c)(D_0/rho) + a rho: the law includes the Dicke term. Confirmed: smyth_1987’s “Roh (Ref. 33)” HWHM column is exactly this a halved.

• Formula: eq1_dicke (a and D_0 per J as printed). Check: the Q(2) Dicke term with D_0 = 0.901 and nu = 2987 cm-1 is 101.0 MHz amagat, ottusch_1988’s 101.

• Temperature: “room temperature” only (no K).

• Finding: Murray & Javan’s 1.4, 2.2, 2.6 are tabulated here under the FWHM a and called “almost 100 %” below this study; smyth_1987 prints the same numbers as HWHM, agreeing with its own HWHM. The “100 %” is the half/full-width factor 2. (Hanna et al.’s 70 MHz/atm D2 Q(2) “from Murray and Javan”, used as FWHM in hanna_1986, may carry the same factor: not checked, Murray & Javan not in the library.)

• Doubt: the paper finds D_0 “J dependent” (0.87-1.08); smyth_1987 finds none.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-529 smyth_1987 (Smyth, Rosasco & Hurst, J. Chem. Phys. 87, 1001 (1987)) (2026-09-27)

• Transcribed (library pdf page 1 is a cover sheet; pdf page n = journal p. 999 + n):

  • Table I (p. 1005, CSV = image): HWHM gamma, 10^-3 cm-1/amagat, D2 Q(0)-Q(5), one dataset per partner: table1_self, table1_He, table1_Ar, table1_H2, table1_CH4 (6 each), primary, relative 3 % (5 % for Q(5)), level not stated (“conservative estimate of the total uncertainty”), temperature_range_k = "296.0-298.5" (free-form: the paper gives a range, not one value).

  • Table III (p. 1008, CSV = image): table3_this_work (6, check; = table1_self), table3_theory (5, check: Robertson et al.’s calculation adjusted plus this paper’s dephasing), table3_murray_javan (3, reproduced), table3_robertson (5, reproduced, = russell_1987’s Robertson & Hunt halved), table3_gustafson_byer (5, reproduced, personal communication, no errors), table3_roh (5, reproduced_from russell_1987: identical digits halved).

  • Text: keijser_S_branch (6 inline points, reproduced from Keijser et al. 1974: D2 S0(0)-S0(5) HWHM at 293 K, 2.80, 2.23, 2.07, 1.70, 1.43, 0.93e-3 cm-1/amagat, p. 1008); o_branch_O4 (1, primary: O1(4) 2.50e-3 HWHM, p. 1009).

• HWHM: Eq. (1) “Gamma (HWHM, cm-1) = D_0 k^2/2 pi c rho + rho gamma” (p. 1004); Table I caption “(HWHM, 10^-3 cm-1/amagat)”; Table III “half-width at half-maximum”. Per amagat. The law includes the Dicke term (HWHM 2 pi nu^2 D_0/c; formula eq1_dicke with the D_0 of the text).

• Formulas: table2_self, table2_He, table2_Ar, table2_H2, table2_CH4 (Eqs. (2)-(3), Table II, both cases). Check: the printed rms deviations reproduced to 0.01 for all ten fits (0.129/0.13, 0.066/0.06, 0.186/0.19, 0.036/0.04, 0.514/0.51, 0.141/0.14, 0.079/0.08, 0.048/0.05, 0.552/0.55, 0.048/0.04), with the rates summed over same-parity levels, detailed balance, T = 297 K and optmat’s stopgap D2 B, D. This fixes the reading of Eq. (3).

• Doubts: whether the foreign-gas coefficients were corrected for the 2.5-10 % D2:D2 share is not said. D2:H2 Q(4), Q(5) enhanced by resonant exchange (outside the fit).

• Re-pointed: ottusch_1988 formula linewidth_D2 notes: 101 = Russell & Roh’s Q(2) Dicke term; 120 = the mean of Russell & Roh’s 117.2 and Smyth et al.’s 123.5 MHz/amagat FWHM (an inference). No value changed.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-530 knaap_1979 (Knaap, van den Hout & Hermans, Phil. Trans. R. Soc. Lond. A 293, 407 (1979)) (2026-09-27)

• Identity: the requested paper (H. F. P. Knaap, K. D. van den Hout and P. W. Hermans, Phil. Trans. R. Soc. London A 293, 407 (1979)); the JSTOR copy includes Buckingham’s discussion.

• Notes-only record: no table and no number in the text (pages read as images). Figures 3-8: half widths against density (77.8 K), coefficients against p-H2 fraction, cross sections sigma_rR (1e-20 m2) against T (25-300 K) for n-H2, n-D2, HD, p-H2, o-H2.

• HWHM: Eq. (1) (p. 407) Lorentzian with Delta nu_1/2 in the denominator, “Delta nu_1/2 is the halfwidth of the line”; Fig. 3 “collisional halfwidths”. Eq. (3): sigma_rR = 2 pi Delta nu_1/2 / n _0.

• Comparison with edwards_1991 (TC-483) (cross sections read approximately from the 300-dpi figures at about 295 K for this comparison only, not data; converted with Eqs. (3)-(4)):

  • D2 HWHM 2.84, 2.29, 2.14, 1.73, 1.41, 0.98e-3 cm-1/amagat (S0(0)-S0(5)) = Keijser et al.’s printed 2.80, 2.23, 2.07, 1.70, 1.43, 0.93 (via smyth_1987) within -2 to +5 %.

  • H2 HWHM 1.46, 1.78, 1.26, 1.31, 0.83e-3 cm-1/amagat (S0(0)-S0(4)); Herring’s FWHM/2 for S(0), S(1): 1.28, 1.90.

  • Edwards’s Tables 7-8 “Knaap” columns = 2 x these HWHM (0.90-1.03), and for D2 exactly 2 x Keijser’s printed values: they are FWHM per amagat, mislabelled per bar (edwards_1991 notes and datasets re-pointed and annotated).

  • Edwards’s own sigma against the Leiden HWHM per bar (1 bar = 0.9201 amagat at 293 K): H2 S0(0), S0(1) 0.89, 0.91; H2 S0(2) 0.50; D2 S0(0)-S0(4) 1.57, 1.31, 1.29, 0.78, 0.87. As FWHM they are low by 2.2 (H2 S0(0)-S0(1)), 4.0 (H2 S0(2)) and 1.3-2.6 (D2).

  • Verdict: the “factor of 2 low” holds for H2 S0(0)-S0(1) (Edwards’s sigma behaves as a HWHM to 10 %) and roughly for D2 S0(3)-S0(4), but not for D2 S0(0)-S0(2) (1.3-1.6 x the HWHM) or H2 S0(2). No single factor reconciles Edwards with Knaap/Keijser. For D2, the Leiden set (Keijser 1974 via smyth_1987’s keijser_S_branch, HWHM at 293 K) is the consistent room-temperature S-branch set.

• Re-pointed: edwards_1991 table7_knaap, table8_knaap: reproduced_from = [“knaap_1979”], notes corrected (FWHM per amagat; the values are not printed in knaap_1979); a sentence added to the source notes. No value changed.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-531 ripoche_1997 (Ripoche et al., Opt. Commun. 135, 310 (1997)) (2026-09-27)

• Table 1 (p. 313; caption lost in extraction; image checked): N2 and O2 given separately, so datasets: table1_B_N2, table1_B_O2 (rotational_constant, 1 each) and table1_anisotropy_N2, table1_anisotropy_O2 (polarizability_anisotropy, SI, scale 1e-40, 1 each), all reproduced from lin_1976 (Ref. [13]; the anisotropies via Hirschfelder, Curtiss and Bird). Checked: lin_1976’s 9.3 and 11.4e-25 cm3 = 1.035 and 1.268e-40 C m2/V (printed 1.0, 1.27); B 2.001, 1.438 -> 2.0, 1.4. No wavelength. Concentrations (80/20 %) in notes (air is not a material).

• Air result (notes only): r_air = n2,rot/n2,inst = 1, the pulse 125 fs (text, p. 314) or 130 fs (Fig. 6 caption): unresolved. r_air is the ratio of the response amplitude n2,rot of Eq. (14) to n2,inst, not of time-integrated indices; no uncertainty, no absolute n2. CS2 r1 = 1.25, r2 = 16.25 (T1 100 fs, T2 1.5 ps fixed); Herasil 140 fs.

• Nothing bears on the model parameters.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-532 Values bearing on the Raman parameters (docs/raman.md, data/gas/raman.toml) (Raman linewidths) (2026-09-27)

• N2 Q widths (now: Koszykowski MEG, n = 1.346): Rahn & Palmer’s Table 1 gives the measured per-J FWHM at 500, 730, 1000, 1500 K (and Rosasco’s at 298 K, doubled); the MEG is within 2-4 % rms except 1500 K (-7 %); the note-32 variant fits 1500 K (-2 %).

• D2 Q widths (now: Ottusch & Rockwell’s Q(2) law, 101/rho + 120 rho MHz FWHM, for every J): the per-J FWHM (2 x Smyth HWHM; Russell & Roh) are Q(0) 178.1 (173.6), Q(1) 79.7 (78.8), Q(2) 123.5 (117.2), Q(3) 127.7 (123.2), Q(4) 128.9 (116.0), Q(5) 102.5 MHz/amagat: using Q(2)’s 120 for all lines overstates Q(1) (the second-strongest line at room temperature) by 1.5 and understates Q(0) by 1.5. The Dicke term: Russell & Roh’s per-J D_0 (0.87-1.08) or Smyth’s 0.967-0.984 (Q(1), Q(2)). Foreign broadening (He, Ar, H2, CH4) now curated.

• D2 S widths (now: Edwards, 131.96 MHz/amagat FWHM for S(0), flagged TC-483): Keijser’s (via Smyth) FWHM per amagat at 293 K are 167.9, 133.7, 124.1, 101.9, 85.7, 55.8 MHz/amagat for S0(0)-S0(5); Edwards’s (as FWHM, per bar converted) are 132.0, 87.6, 80.2, 39.7, 37.1: ratios 1.27, 1.53, 1.55, 2.56, 2.31.

• Line mixing: Rosasco’s Y_j (N2 and CO, 298 K) now recorded (N2’s fail the sum rule).

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-533 sheik_bahae_1991 (Sheik-Bahae, Hutchings, Hagan, Van Stryland, IEEE JQE 27, 1296) (2026-09-27)

• Transcribed: Table III (tbl_1be7b7bfe319, p. 1305; 40 rows, cells agree with the image) by tools/extract/sheik_bahae_1991.py: 125 datasets, 134 points.

  • Own Z-scan n2 (primary, nonlinear_index_field, esu, scale 1e-13): Ge (10.6 um), GaAs, ZnTe, CdS (0.53), ZnSe (1.06, 0.53), ZnS, KTP, BaF2 (1.06, 0.53): 8 datasets, 10 points.

  • Adair’s n2 (reproduced, adair_1989): CdS, AgCl, ZnO, NaBr, CaCO3, KBr, KCl, KDP (two rows), NaCl, Al2O3, KF, MgO, SiO2_quartz, SrF2, CaF2, MgF2, LiF: 18 datasets, 1 point each.

  • Ross’s n2 at 249 nm (reproduced, citation string): 1.

  • n2(Pred.) (K’ = 1.50e-8) and n2(Pred.)* (K’ = 0.86e-8), use = check, part electronic: 26 + 20 datasets, 50 points (registered rows only).

  • Band gap (band_gap, kind assumed, reproduced from CRC 65th ed. / Palik [41], [42]): 26 datasets; linear index (refractive_index, assumed, index_medium not stated): 26 datasets, 29 points.

• Structural: the four blocks of the table (blank lines in the image, lost in the CSV) are the provenance of the measured column: rows 1-14 own (Fig. 5 squares), 15-21 LaGasse AlGaAs [40], 22-39 Adair [6] (Fig. 5 solid circles), 40 Ross [39] (diamond). The script encodes this by row number with a comment. The Ge gap cell “0.87^{\dagger}”: the dagger dropped (direct gap).

• Doubts / findings (the paper’s labels, no erratum):

  • “KDP” (0.7; 6.95 eV; n0 1.60) and “KH_2PO_4” (0.8; 7.12 eV; n0 1.50) are the same crystal: Adair’s KDP (o) 0.72 and (e) 0.78. Both recorded under KDP.

  • The 1.06-um “SiO_2” row (1.1e-13 esu) is Adair’s crystal quartz (o) 1.12, not his fused silica 0.85: recorded as SiO2_quartz. Its gap 7.80 eV and index 1.40 are the same as the fused-silica 249-nm row (1.40 fits neither quartz nor silica at 1.06 um). The material choice is to be confirmed in review.

  • BaF2 at 1.06 um (own block) prints 0.67, identical to Adair’s 0.67; kept primary as the table places it (text: “Our own measurements of several of the same materials studied in [6] show excellent absolute agreement”).

  • “CaCo_3” printed for CaCO3.

  • Unregistered rows (values in the record’s notes): CdTe, CdSe, CdS0.5Se0.5, SBN (composition not stated), AlGaAs (7 rows, LaGasse, composition not stated).

  • No uncertainty is printed anywhere; the text’s “average difference < 30 %” (semiconductors) and “< factor of 2” (dielectrics) are comparisons with theory.

  • Pulse durations of the own Z-scans not stated (picosecond): part unknown. Adair’s rows keep part electronic_vibrational (as adair_1989).

• Formulas: beta_two_band (Eqs. 24-26), f2_nondegenerate (Table I, Eqs. 28-38), g2_degenerate (Table II, Eqs. 39-44).

  • Eq. (26) evaluated with CODATA Gaussian constants: K = 1943 (printed 1940).

  • G2 = G2PA + G2RAM + G2LSE + G2QSE - divergent term reproduces all 40 Pred. and 22 Pred.* cells within 3.4 % (49/62 to the printed rounding; largest MgO 1.654 vs 1.6, AlGaAs 0.840 um -3250 vs -3300, KBr 2.955 vs 2.9), with lambda = 0.532 um for the rows printed 0.53 (with 0.53 exactly, CdS gives -1360 vs -1200). Sign change of G2 at x = 0.688 (text “about 0.7”).

  • K’ = K hbar c^2 / 40 pi gives 1.459e-8 (K = 3100) and 0.913e-8 (K = 1940), both 2.7-3.0 % below the printed 1.50e-8 and 0.94e-8.

  • Eq. (30) (text) has a second Raman term (-x1 + x2 - 1)^(3/2) that Table I drops; it vanishes for pump below the gap.

• Status: verified against the table image and by reproducing the predicted columns.

TC-534 sheik_bahae_1994 (Sheik-Bahae, Wang, Van Stryland, IEEE JQE 30, 249) (2026-09-27)

• Transcribed: the unlabelled “TABLE III” (tbl_e5d825fda3b1, p. 252, JSON only, merged cells; agrees with the image) by tools/extract/sheik_bahae_1994.py: 11 datasets, 14 points.

  • Nondegenerate n2(2w; w) (probe 532 nm abscissa, pump_nm = 1064; Delta n = 2 n2 I_pump, Eq. 1a; coefficient self, part total, 83/58 ps): ZnSe -5.1, ZnS 1.5 x 1e-14 cm2/W (primary).

  • Nondegenerate beta(2w; w): ZnSe 15.3 x 1e-9 cm/W (primary). ZnS “<0.073”: notes.

  • Degenerate ZnSe n2 (0.532, 1.06) and beta (0.532): reproduced from [16] (Sheik-Bahae et al. 1990, IEEE JQE 26, 760; caption says so).

  • Degenerate ZnS n2 (1.06) and beta (0.532): “earlier results”, reproduced_from [5] (sheik_bahae_1991), [9], [16]: which one is not said. 0.76e-14 cm2/W is not sheik_bahae_1991’s ZnS (48e-13 esu = 0.84e-14 cm2/W with n0 2.40).

  • n0 at 0.532/1.06 (check, assumed) and E_g (Pankove [17], check, assumed).

• Findings:

  • Formula misprint (Table II, H(x1, x2)): printed (1/2)(x1^2 + x1^2)[1 - (1 - x2)^(3/2)] (the image too); must be (x1^2 + x2^2). Evidence: the principal-value KK integral of Table I’s 2PA + Raman + linear Stark terms minus the H-sum is exactly c x2^-2 (the removed divergence) with x2^2 (residual 2e-12) and not with the printed x1^2 (residual 5e-5, a constant -0.19; G2(0.3; 0.1) = -11.6 vs 0.0167). The degenerate x1 = x2 case is unaffected. Recorded in the formula’s check and notes (no named coefficient, so not a [[formulas.corrections]]). Needs a register entry.

  • The quadratic Stark entries of Table II verified the same way (residual < 1e-13); the x1 = x2 entry is the limit of the x1 != x2 one.

  • With the corrected G2: K = 4000 gives beta(2w; w) ZnSe 15.2 (table 15.3) and degenerate beta(532) 5.45 (5.8) and 3.0 (ZnS, 3.4); K = 6000 gives n2 ZnSe 2.94 (2.9) at 1.06 um, -4.53 (-6.8) at 0.532 um, -3.06 (-5.1) nondegenerate; ZnS 0.61 (0.76), nondegenerate 1.39 (1.5): consistent with “theory underestimates n2 by ~1.5”.

  • ZnSe 0.532-um degenerate n2 here -6.8e-14 cm2/W vs -6.21e-14 from sheik_bahae_1991’s -400e-13 esu with its n0 2.70 (9 %).

• Formulas: alpha2_nondegenerate (Eq. 6, Table I), g2_nondegenerate (Eqs. 9-10, Table II), polarization_factor (Eq. 8), exciton_enhancement (Eqs. 11-12; R / 2E_p = 0.324 = printed 0.33).

• Status: verified; one formula misprint found.

TC-535 bristow_2007 (Bristow, Rotenberg, van Driel, APL 90, 191104) (2026-09-27)

• Transcribed (text only, inline points): beta = 2.1 +- 0.4 cm/GW and n2 = (4.7 +- 2.0) x 1e-14 cm2/W at 1220 nm (p. 191104-2); n2 peak 1.2e-13 cm2/W at 1800 nm (abstract); E_gi = 1.12 eV (assumed input); reproduced: Reintjes & McGroddy beta = 1.5 cm/GW at 1060 nm, 100 K; Dinu et al. n2 ~3e-14 cm2/W at 1300 and 1550 nm. 6 datasets, 7 points. 300 K, 200 fs, (001) intrinsic wafer 125 um, Fresnel losses removed, linear polarization, part unknown.

• Figure-only: beta at ~24 wavelengths (Fig. 2), n2 at ~20 (Fig. 3): not digitised. The abstract’s “maximum value of 2 +- 0.5 cm/GW” has no wavelength: notes only.

• Formula: beta_indirect_gk (Garcia-Kalyanaraman form, C = 43 cm/GW, E_gi = 1.12 eV): peaks at 1.93 cm/GW near 1000-1050 nm, zero at 2214 nm, as Fig. 2’s curve; the f-f, a-a, a-f peak positions (5/2, 5/6, 5/4 E_gi) match the text.

• Text slips: “closed and open aperture z-scan … respectively” (reversed); “1300 and 1550 um” (nm).

• Status: verified.

TC-536 patankar_2017 (Patankar et al., Appl. Opt. 56, 8309) (2026-09-27)

• Transcribed: Tables 1 and 2 (tbl_c8b5daab8ce4, tbl_8426527ad90f; both agree with the images) by tools/extract/patankar_2017.py: beta at 213 nm with its +- for MgF2, CaF2, BaF2, Al2O3 and four fused-silica grades (8 datasets; LiF “<0.001” in notes); alpha (base e) for all nine samples (9); band gap (reproduced from the cited refs, 6); n0 at 213 nm (assumed, 6). Text: Slattery & Nikogosyan at 211 nm (CaF2, BaF2, FS) and Kittelmann & Ringling MgF2 at 193 nm, reproduced (4 datasets; they agree with slattery_2003 and kittelmann_1994). 33 datasets, 33 points. 24 ps, horizontal linear polarization, reflection removed.

• Grades: “Heraeus FS—1AK” (“SupraSil—1AK” in Fig. 4), “Corning FS—7980 (ArF)”, “Corning FS—8655”, “Heraeus FS—312”.

• Findings:

  • Fused-silica gap “9 [12]” cites Eva & Mann 1996; eva_1996 lists 7.8 eV for fused silica and 9 eV for crystalline quartz: the 9 eV is Eva’s quartz value.

  • Abstract range “0.004 and 0.82 cm/GW” vs Table 2 note and conclusion “0.004 to 0.86” (BaF2 0.86).

  • Uncertainty: +- from the absolute intensity (energy +-5 % at 2 sigma borrowed from 248 nm); level of the printed +- not stated.

• Status: verified.

TC-537 poulvellarie_2018 (Poulvellarie et al., Phys. Rev. Appl. 10, 024033) (2026-09-27)

• Notes-only record (plus one formula, Eq. 5): a waveguide experiment whose nonlinear coefficients are computed from bristow_2007; no material value of its own. The waveguide gammas, areas and loss are quoted in notes.

• Finding for the model: the cross (nondegenerate) n2 and beta of Si equal the degenerate values at the mean frequency, “at least for photon energy in the range from 0.6 E_g to 0.85 E_g” (pump 1848 nm, signal 1322 nm).

• Check: with eta = 1 (my assumption), Im gamma_pp, gamma_ss give beta = 0.67 and 1.73 cm/GW (Bristow’s fit 0.60, 1.73); Re gamma gives n2 = 1.16e-13 (1848 nm) and 4.8e-14 cm2/W (1322 nm), against Bristow’s 1.2e-13 (1800) and 4.7e-14 (1220).

• The waveguide width is printed 780 nm in the text and 789 nm in the Fig. 1 caption.

• Supplemental material not in the library.

• Status: verified (nothing extracted).

TC-538 Re-pointed existing records (2026-09-27)

• jansonas_2022: lit_eff_SBN-61_o_sheik_bahae_1991, lit_eff_ZnS_sheik_bahae_1991, lit_eff_ZnSe_sheik_bahae_1991 -> sheik_bahae_1991; lit_eff_Si_bristow_2007 -> bristow_2007. Values checked: SBN 0.524, ZnS 0.84, ZnSe 2.87 (x 1e-14 cm2/W) are sheik_bahae_1991’s esu values converted with its n0 (agree). Jansonas labels the SBN “SBN-61 (o)”; Sheik-Bahae prints only “SBN”. The Si value “~10.4 +- 2” at 2.2 um is not printed in Bristow’s text (a Fig. 3 reading). Notes added; no value changed.

• patwardhan_2021: the six band_gap_* datasets’ first reproduced_from citation -> sheik_bahae_1991. Its ZnSe 2.58, Al2O3 7.3, CaF2 9.92, MgF2 11.27, SiO2 7.8 eV equal Sheik-Bahae’s Table III; its ZnS 3.2 eV does not (3.54 there). Its formula two_band_theory check said K’ = 0.86e-8 differs from Sheik-Bahae’s 1.5e-8; a sentence added: 0.86e-8 is Sheik-Bahae’s own wide-gap fit (p. 1304), so the theory column is computable with sheik_bahae_1991/g2_degenerate once n0 is chosen.

• Not re-pointed (not my papers’ values): ensley_2019 cites Sheik-Bahae 1990 (IEEE JQE 26, 760) and DeSalvo 1993; its note quoting “Bristow et al.’s ~0.4 cm/GW” at 2 um is a figure reading, left as is.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-539 Values bearing on the solids’ nonlinear parameters (2026-09-27)

• Two-band n2 scaling: K’ = 1.50e-8 (fit), 0.94e-8 (theory), 0.86e-8 (wide-gap fit), E_p = 21 eV; the factor of two (1994) halves K’ (desalvo_1996’s 7.33e-9). The wide-gap solids’ n2 at 1.06 um are Adair’s values (already curated), so they must not be fitted twice.

• Nondegenerate 2PA and n2 in Si (poulvellarie_2018): the mean-frequency approximation is supported for 0.6-0.85 E_g; the dispersion of beta dominates that of n2.

• Si degenerate beta form (Bristow): C = 43 cm/GW, E_gi = 1.12 eV.

• Fused silica beta at 213 nm, four grades: 0.76-0.82 cm/GW (+-0.08); MgF2 0.004 cm/GW; CaF2 0.30; BaF2 0.86; sapphire 0.82.

• Status: verified (2026-09-27) at extraction; reviewed in TC-540.

TC-540 The review of the ionisation energies and models, Raman strengths and widths, and solids (TC-494 to TC-539) (2026-09-27)

• Scope: six parallel extractions curated 34 papers, including the Weber volume (1979), from which they used chapters 2-4. They added:

  • 36 new records, with 507 datasets and 1268 values (TC-494 to TC-539);

  • re-pointed records: nist_webbook_2026, mahla_2025, danichkin_1981, ottusch_1988, everall_1987, bischel_1986b, hajigeorgiou_2013, hanna_1986, reichert_2015, edwards_1991, farrow_1985, jansonas_2022, patwardhan_2021.

  No value in an existing record changed, except through the errata below.

• Checked by a second curator:

  • Weber Table 3.2 (the image, p. 88): the bracketed H2 row and note a, including Stoicheff’s H0 (5.2e-5 cm⁻¹ for H2, 0.36e-5 for D2). The two H0 values were added as datasets weber_1979/table3_2_H0_H2 and table3_2_H0_D2 (inline points from the note).

  • Bischel & Black’s text (p. 181): “CH4 (2917 cm-1)”.

  • Hunt et al.’s Table 5, the ⟨00|α∥|20⟩ row: −0.07942, −0.06692, −0.06248, 0.05292, −0.04773, −0.04212 across the isotopologues.

  • Zhang et al.’s Table XI: it equals solprop’s five bsi_zhang rows, digit for digit.

  • Rychlewski’s Table VII: see TC-542.

• Errata accepted:

  • weber_1979, Table 3.2, H2 B0: printed [56.3392], corrected to 59.3392 (TC-515). The table’s own B_e = 60.841 needs α_e = 3.0 (from the isotope scaling of D2’s α_e), which gives B0 = 59.34. Shelton 1993 quotes 59.3392. With the printed value, S(1) would fall 30 cm⁻¹ below Teal & MacWood’s line.

  • hunt_1984, Table 5, D2 ⟨00|α∥|20⟩: printed 0.05292, corrected to −0.05292 (TC-522).

  • bischel_1983, Table 1, CH4 shift: printed 2986 (D2’s), corrected to 2917 (TC-521).

  • zhao_2010, Table V, CO HOMO−1 C_2m: 0.14 corrected to 0.014 (TC-507), by the erratum. The erratum leaves Table III, the rows solprop uses, unchanged.

  • zhang_2014, eq. (8): the exponent’s leading sign is printed −, and the formula’s correction makes it + (TC-509). Two cells of Table IX at F = 0.12177 au are excluded as misplaced.

  • sheik_bahae_1994, Table II: the printed H(x1, x2) has (x1² + x1²) where (x1² + x2²) is meant (TC-534). The correction is recorded in the formula’s check and notes, since no named coefficient changes. The degenerate case, the one curated for use, is unaffected.

• Choices on the records:

  • sheik_bahae_1991: the 1.06 µm “SiO2” row is recorded as SiO2_quartz (TC-533). It is Adair’s crystal quartz, ordinary ray, 1.12. Accepted.

  • schrotter_1979’s Σ_j: recorded as raman_cross_section_ratio with parameters.normalization = "Eq. (4.14)", since it is not the plain cross-section ratio. Accepted.

    • The Raman loader (_transition_from_ratios) is the one consumer, and it takes Σ as normalised: the ν⁴ and Boltzmann factors are already removed.

    • The laboratory’s own dissertations ([4.45], [4.54]) are recorded as primary. The chapter is their only publication.

  • The WebBook’s conversion factor (TC-505): an inference, not a statement of the WebBook. It explains the 0.1-0.2 meV offsets of H2, D2 and O2. No WebBook value is used for those gases now (TC-542).

  • Kept as printed and reported:

    • everall_1987’s SF6 cross section, 23 % above what Σ gives (TC-517);

    • Danichkin’s H2 row attributed to Fenner et al. (TC-524);

    • Rosasco et al.’s N2 mixing coefficients, which fail the sum rule (TC-527). Line mixing is not modelled.

• Notes updated in review:

  • golovanov_2020, yudin_2001 and bree_2011: the stale “not in the library” and “not curated” sentences (TC-513);

  • koszykowski_1987: Rahn & Palmer print ±0.06 for n, not ±0.006 (TC-526).

• Documented: the free-form parameters initial_state, ortho_para and temperature_range_k (docs/data.md).

• Still missing (papers not in the library, to be requested):

  • N2O’s rotational constants (the Weber volume has none);

  • Keijser et al. 1974 (D2 S widths, used through Smyth et al.);

  • Liu et al. 2009 (the H2 energy, used through Liu et al. 2010);

  • Heilbronner et al. 1977 (the CH4 vertical, used through Bieri et al.);

  • Q-branch widths of CO2 and N2O;

  • the N2O depolarisation ratios.

• Status: decided (2026-09-27).

TC-541 The N2 and D2 Raman widths: Rosasco, Rahn & Palmer, Smyth, Keijser (2026-09-27)

• Where:

  • data/gas/raman.toml: N2’s Q widths, and D2’s S and Q widths;

  • optmat.gas.raman._line_table, the per-level power laws;

  • docs/raman.md.

• N2 Q branch: this replaces Koszykowski et al.’s exponential-gap law (TC-492).

  • The data: Rosasco et al.’s HWHM per atm at 298 K, J = 0-18, doubled (TC-527). Rahn & Palmer’s 295 K column is exactly twice these (TC-526).

  • The fit: a power law per J through Rahn & Palmer’s FWHM at 500, 730, 1000 and 1500 K. These are per atm at T and are converted to per amagat.

  • The exponents per density are negative, −0.2 to −0.8 in (T0/T)^N. The widths per atm fall more slowly than 1/T: Rahn & Palmer’s Q(2) goes from 0.104 cm⁻¹ at 295 K to 0.0436 at 1000 K. So the width per molecule rises with T, as the mean speed does.

  • Levels J = 19-30, measured only in the hot tables, keep J = 18’s exponent. Their 298 K coefficient is the geometric mean of their measurements, moved to 298 K with that exponent.

  • Why the exponent is held for those levels: a slope fitted to the hot points alone was tried. It works for N2, but Hölzer et al.’s O2 widths above N = 39 scatter by 20-40 % between temperatures, and such a fit put air-broadened N = 49 at 2.2 GHz/amagat at 295 K, against 0.28 for N = 47. The rule applies to every table law, so O2’s rotational tables now hold N = 41-49 (self) and 43-49 (air). Before, they were held at the last tabulated value.

• Checked (N2): the rms of the model against Rahn & Palmer’s tables:

  T (K)	rms	Worst line
  295	0.6 %
  500	5.5 %	J = 27, +15 %
  730	3.4 %
  1000	2.5 %
  1500	2.5 %

  The exponential-gap law with Rahn & Palmer’s own parameters has means of −3 % to +2 % up to 1000 K and −7 % at 1500 K (TC-526). tests/test_raman.py checks the rms (below 6 %).

• D2 S branch: this replaces Edwards et al.’s widths (TC-483, TC-492).

  • The data: Keijser et al.’s S0(J) HWHM per amagat at 293 K, as Smyth et al. reprint them (TC-529), doubled: 167.9, 133.7, 124.1, 101.9, 85.7 and 55.8 MHz/amagat for S0(0)-S0(5).

  • Knaap et al.’s figures confirm them to 5 % (TC-530).

  • Edwards et al.’s are 1.27-2.56 times lower, with no single factor.

  • There is one temperature, so there is no temperature law.

• D2 Q branch:

  • The data: Smyth et al.’s per-J HWHM per amagat, doubled (TC-529):

    • self, He, Ar, H2 and CH4 as partners;

    • measured at 296.0-298.5 K and taken as 297 K (temperature_k in the choice).

  • The Dicke term: Ottusch & Rockwell’s 101 MHz amagat, Russell & Roh’s Q(2) value (TC-528).

  • Against the old width: solprop and the previous choice used Q(2)’s 120 MHz/amagat for every line. Q(1) is 79.7 and Q(0) is 178.1.

• Loader additions:

  • a per-perturber temperature_k, for a table that gives a range;

  • dicke_formula and dicke_coefficient for a table law;

  • widths per amagat in cm⁻¹.

• Status: decided (2026-09-27).

TC-542 The integration of TC-494 to TC-540: primary ionisation energies, the model constants, the Raman strengths and their dispersion, CO2 and N2O (2026-09-27)

• Where:

  • data/gas/ionisation.toml and data/gas/raman.toml (the choices and reasons);

  • optmat.gas.ionisation (barrier_suppression_zhang, effective_charge);

  • optmat.gas.raman:

    • per-J elements from the components;

    • elements from Σ;

    • VibrationalBand.dispersion_factor and raman_lines(..., wavelength=);

    • the dephasing width law;

    • default_j_max;

  • the pages docs/ionisation.md and docs/raman.md, with their tables (tested).

• Ionisation energies: each molecule now uses its primary determination (TC-494 to TC-504, TC-506), in place of the WebBook’s listing:

  • H2 and D2: Liu et al. (N = 0 → N⁺ = 0). The H2 value is Liu et al. 2009’s, as Liu et al. 2010 reprint it.

  • N2: Trickl et al.

  • O2: Tonkyn et al.

  • CH4: Berkowitz et al.’s onset at 78 K.

  • SF6: Frost et al.’s first threshold, whose kind is “not stated”.

  • N2O: Berkowitz & Eland.

  • CO2: Wang et al.

  • What changed: H2 −0.13 meV, D2 −0.24, N2 −0.28, O2 −0.09. The others are unchanged.

  • O2’s vertical energy: 12.307 eV (Baltzer et al., as Mahla 2025 reprint it), in place of the WebBook’s 12.33.

  • Still from the WebBook: the vertical energies of N2O and CO2 (Potts & Williams 1974, not curated). Wang et al. print no vertical energy.

• Model constants (labelled as fitted constants, not properties):

  • Zhang et al.’s a1, a2, a3: He to Xe, from Table XI, read with the corrected

    • sign (TC-509). solprop’s values are identical.

  • Talebpour et al.’s effective charges: N2 0.9 and O2 0.53 (TC-508).

    • They were fitted within PPT with l = m = 0.

    • O2’s was fitted with I_p = 12.55 eV. solprop pairs it with 12.07 eV, a faster rate than the one fitted.

    • solprop names the second author wrongly (“Chien”; it is J. Yang).

• Rate check: Zhang et al.’s SAE rates for Ar (GSZ potential, Table IX) against the one-electron MO-ADK rate (Tong et al.’s eq. (7), C1 = 2.44). The model is 2.18 times the SAE rate at 0.053 au (0.64 of the barrier-suppression field) and 3.75 times at 0.094 au. With the same C_l, Zhang et al.’s correction brings it to within 5 % of their own rates (TC-509).

• Raman, the transition polarizabilities:

  • H2 and D2: Hunt et al.’s static ab initio elements per J, mean (⟨α∥⟩ + 2⟨α⊥⟩)/3 (TC-522). They replace Huo’s 500 nm value (H2, 0.7491 au) and Murphy et al.’s derivative (D2).

    • H2 runs from 0.7392 to 0.7546 au (J = 0-5), with Q(1) at 0.74027.

    • D2’s Q(2) is 0.61765, within 0.02 % of Murphy et al.’s derivative.

  • Dispersion, with Bischel & Black’s measured single-resonance law, α01 ∝ 1/(ν_i² − ν_p²), ν_i as printed (TC-521):

    • H2 and D2 are scaled from their static elements.

    • N2 and O2 are scaled from 435.8 nm, Murphy et al.’s mercury line.

    • CH4 is scaled from 488 nm, the middle of Schrötter & Klöckner’s 337-515 nm measurements.

    • Independent check: Rychlewski’s (1983) ab initio ⟨00|α|10⟩ of H2 in Table VII (library copy; that table is not extracted). The law applied to Hunt et al.’s static Q(0) (0.73923, 0.11 % below Rychlewski’s 0.74006) follows Rychlewski’s ratio to the static value to 0.1-0.8 % from 238 to 911 nm: −0.1 % at 911 nm, 0.0 % at 633, −0.4 % at 436, −0.8 % at 297 and −0.8 % at 238 nm. tests/test_raman.py checks this with four rows quoted from the table.

    • The anisotropies are not dispersed.

  • From Schrötter & Klöckner’s normalised cross sections (TC-514, TC-518): ā² = Σ C/(16π⁴)/(1 + 7ρ/(3 − 4ρ)), with C = 5.05e-48 cm⁶/sr and Σ the mean of the curated values:

    Band	Σ values	ρ	Element (au)	Against Murphy et al.
    CH4 ν1	13	0	1.1235	+5.3 %
    SF6 ν1	4	0 (Murphy et al.’s)	0.7293	+3.2 %
    CO2 1388	9	Danichkin’s recommended	0.3995
    CO2 1285	7	Danichkin’s recommended	0.3216
    N2O ν1	4	0 (an upper bound)	0.5404
    N2O ν3	2	0 (an upper bound)	0.2730

• Raman, the constants:

  • H2 and D2: Stoicheff’s B0, D0 and H0, as Weber reprints them (TC-515, TC-540). They replace the Teal fits, the stopgap of TC-492.

    • They reproduce Teal & MacWood’s S lines to within 0.9 cm⁻¹.

    • Without H0, H2’s S(3) would be off by 1.2 cm⁻¹.

    • The v = 1 constants still come from Teal’s Q lines.

  • CO2: Wang’s B0 and D0 (TC-515). Only even J exist.

  • default_j_max(constants, T) = max(10, int(sqrt(50 kT/B)) + 5) sets the ladder (CO2 needs about J = 80 at 295 K).

• CO2 and N2O, new, with declared stopgaps:

  • CO2:

    • the S lines, with Pinter’s widths as Jammu et al. reprint them;

    • the Fermi dyad as two unresolved bands;

    • no Q-branch width, so the S coefficient stands in.

  • N2O:

    • vibrational only: no rotational constants are curated, and Chen et al.’s B is a simulation input;

    • ρ = 0;

    • the width is Chen et al.’s T2 (23.8 ps at 2.4 atm), taken as collisional.

• Gains (docs/raman.md):

  • H2: Q(1) is +27 % and +33 % at 532 nm, +11 % at 477 nm and +21 % at 308 nm.

  • D2: Q(2) is +39 %.

  • CH4: 0 %.

  • The H2 and D2 excess is not in the strengths, which agree with Rychlewski’s to 1 %. It lies in the widths or in the measured gains. The authors’ own calculated gains are also above their measurements (by 8 % and 18 %). Nothing is tuned.

• solprop’s vibrational amplitudes against the curated ones:

  • H2 +13.1 % and D2 +31.1 %, against the static elements;

  • CH4 −10.4 % and SF6 −11.0 %, since solprop’s are Murphy et al.’s.

• Status:

  • decided (2026-09-27);

  • open: the H2 and D2 gain excess, and the stopgaps (the CO2 and N2O Q widths, N2O’s ρ, N2O’s rotational constants, the N2O and CO2 vertical energies).

TC-543 Metals, permittivity and gas-mixture composition in the vocabulary (2026-09-27)

• Where: optmat.materials (the kind metal), data/materials.toml (Ag, Au, Al, Cu), optmat.vocabulary (permittivity_real, permittivity_imaginary, mole_fraction, the family composition), docs/data.md.

• Why: a later batch of papers holds the optical constants of silver, gold, aluminium and copper (requested for solprop’s metals), and the CIPM-2007 composition of dry air (Picard et al. 2008), which solprop’s air needs.

• Decision:

  • Metals: a metal is a solid of kind metal. Films and bulk samples of one metal are one material, since their constants differ by preparation rather than by identity; each dataset states form, and its notes give the deposition, substrate and thickness. Only the metals the curated sources are needed for are registered; a source’s other metals are noted in its record.

  • Permittivity: many metal sources tabulate ε₁ and ε₂ rather than n and k. These are recorded as printed, as permittivity_real (family refractive) and permittivity_imaginary (family absorption), mirroring n and k, rather than converted at extraction. ε₁ = n² − k² and ε₂ = 2nk.

  • Composition: a mixture is not a material (air is not one). Its make-up is a mole_fraction dataset per component gas, with parameters.mixture naming the mixture as its source defines it, in a new family composition.

• Status: decided (2026-09-27).

TC-544 Table models of solids: a metal’s stitched optical constants (2026-09-27)

• Where: optmat.solid.models.tabulated, data/solid/tables/<material>.toml, docs/solid.md (Tables of optical constants), tools/solprop_solids.py and tests/data/solprop_solids.json.

• Why: a metal’s constants from the extreme ultraviolet to the far infrared come from several techniques and papers, one range each (solprop stitches silver and aluminium from refractiveindex.info’s copies of four and three papers). No single model covers them, so optmat needs a model that joins curated tables by range.

• Decision:

  • A table model joins curated datasets, one pair (n and k, or ε₁ and ε₂) per range, as its configuration chooses them. Every range has a written reason. Ranges may not overlap, and nothing is averaged.

  • It interpolates log n and log k against log ω with PCHIP, a monotone piecewise-cubic Hermite interpolant. solprop uses a natural cubic spline of n and log k against log λ, which overshoots between sparse points and rings at a join between sources. PCHIP’s first derivative is continuous and is exact for the interpolant, so ε and dε/dω are consistent.

  • Outside the table the constants are held at the end points, with a range warning.

• Checked: the model passes through its knots to 1e-12, and its analytic derivative matches a finite difference to 1e-6 (tests/solid/test_tabulated.py, on Philipp’s n and k of silica from Lamy’s reflectance).

• solprop snapshot: tests/data/solprop_solids.json holds solprop’s window crystals, fused silica and its silver and aluminium tables at 24 wavelengths each (solprop c099545), for the parity tests.

• Status: decided (2026-09-27).

TC-545 A solid’s index relative to nitrogen (daimon_2002) (2026-09-27)

• Where: optmat.solid.models.formulas (index_medium = "nitrogen"), daimon_2002 (form, index_medium and the nitrogen state added to sellmeier_20C and sellmeier_25C in review).

• Finding (at extraction): Daimon & Masumura measured CaF2 relative to nitrogen at 1013.25 hPa and the prism temperature (pp. 5275-5276; Table 1’s heading). Their formulas and Table 1 are relative indices, about 3.9e-4 below the absolute ones. solprop and refractiveindex.info use them as absolute.

• Decision:

  • A formula may state index_medium = "nitrogen" with nitrogen_temperature_k and nitrogen_pressure_pa. The model multiplies by the nitrogen’s index, from optmat’s recommended N2 model (fit/N2) at the ideal-gas density. At 1 atm and 20 °C, N2’s compressibility (Z − 1 ≈ −2e-4) changes the absolute index by below 1e-7, a sixth of the formula’s own rms residual (6.1e-7). The ideal density avoids making the solid models depend on the gas extra’s equation of state.

  • The gas subpackage is imported only when such a formula is evaluated.

• Checked: the factor n_N2 lies between 1.000274 (2.3 µm) and 1.000397 (138 nm). Made absolute, Daimon’s formula at 20 °C and Malitson’s (air, 24 °C) differ by +2.0e-5 to +4.9e-5 at 0.25-2 µm, which is the 4 K of dn/dT (about −1.1e-5 per K). At one temperature they agree within 3.3e-5 (checked at extraction).

• Open: the datasets daimon_2002/n_20C, n_25C and dndt still state the nitrogen in free parameters. A dataset-level nitrogen index_medium waits until a fit uses them.

• Status: decided (2026-09-27).

TC-546 The window crystals: CaF2, MgF2, BaF2 and sapphire (2026-09-27)

• Where: data/solid/defaults.toml; optmat.solid.models.registry (default_model(material, axis), default_reason); tests/solid/test_crystals.py.

• Decision: each recommended model is its primary source’s Sellmeier formula, made absolute with the gas the index was measured against:

  Material	Model	Range	Temperature	Reference gas
  CaF2	daimon_2002/sellmeier_20C	138-2326 nm	20 °C	nitrogen (TC-545)
  MgF2	dodge_1984/sellmeier_o, _e	0.2026-7.04 µm	19 °C	room air (inferred)
  BaF2	malitson_1964/sellmeier	0.265-10.35 µm	25 °C	room air (inferred)
  Al2O3	malitson_1962/sellmeier_o (o only)	0.265-5.58 µm	24 °C	room air (inferred)

  • An anisotropic crystal’s recommendation is per axis, and default_model requires the axis for it.

  • Sapphire’s extraordinary ray has no primary formula in the library (Malitson 1962 gives one text value), so none is recommended.

  • The NBS papers do not say what their indices are relative to. The air reading is an inference, made at extraction, from the minimum-deviation method in room air. It is supported by CaF2, where Malitson made absolute agrees with Daimon’s nitrogen-referenced measurement within 3.3e-5; read as absolute, Malitson would be 3.9e-4 low.

  • Edlén’s air formula is stated for about 200 nm to 2 µm. Beyond that it is extrapolated. The air’s dispersion is small there (n − 1 changes by under 2e-6 from 2 to 10 µm), so the error in the absolute index is well below the formulas’ 2e-5.

• Checked (each formula against its own paper, with the reference gas removed):

  • Daimon’s formulas reproduce Table 1 within 1.9e-6 (rms 6.1e-7 and 5.8e-7).

  • Dodge’s reproduce all 72 Table II values to rounding (5.0e-6).

  • Malitson’s CaF2 reproduces Table II’s computed column to rounding, except at 0.2537 µm (printed 3.1e-5 high) and 0.365015 µm (1.3e-5 low).

  • Malitson’s BaF2: to rounding except 0.486133 µm (printed 1.4e-5 high).

  • Malitson’s sapphire: to rounding except the six polystyrene bands, 3.24-3.51 µm, where the printed values are 3.5-6.7e-5 below the formula.

  • None of these departures is explained. The formulas are taken as printed.

• solprop: its CaF2, MgF2, BaF2 and sapphire use the same coefficients (sapphire excepted) as absolute indices at vacuum wavelengths. They are 3.7-6.5e-4 below optmat’s across the ranges (the reference gas; docs/corrections.md). solprop’s sapphire is Dodge’s CRC-handbook formula at 20 °C, not Malitson 1962. At the same argument it is 9.4e-5 below Malitson’s at 0.3 µm and 5e-5 below at 1-2 µm, and it is 6.5e-5 above at 5 µm. About 5e-5 of this is the 4 K difference.

• Status: decided (2026-09-27).

TC-547 Ionisation: the new primaries in the choices, and solprop’s PPT (2026-09-27)

• Where: data/gas/ionisation.toml, docs/ionisation.md, docs/corrections.md; the re-points in nist_webbook_2026, bieri_1977 and wang_1988 (records made in review), after the extraction of liu_2009, heilbronner_1977, potts_1974, ilkov_1992, talebpour_1998 and the others (their entries follow).

• Decisions:

  • H2: liu_2009/ie_para_H2 (124 417.491 13(37) cm⁻¹, X(0,0) → X⁺(0,0)), the original, replaces its reprint liu_2010/liu_2009_H2. Same value.

  • CH4 vertical: heilbronner_1977/vertical_CH4#1t2_1 (13.6 ± 0.1 eV), the original of bieri_1977’s row. Same value.

  • N2O and CO2 vertical: potts_1974/hei_N2O#2pi (12.89 eV) and potts_1974/hei_CO2#1pi_g (13.79 eV). These are the values the WebBook lists, and Potts & Williams take them from Turner et al.’s 1970 book, which is not in the library, so they are reprints, the best copies available. The WebBook (nist_webbook_2026) is now the source of no recommended value.

  • D2’s effective charge: talebpour_1998/zeff_D2 (0.72). Talebpour, Larochelle & Chin computed it within their PPT form from an orientation-averaged quasi-classical barrier at 1.5e14 W/cm² and 800 nm; they did not fit it. That form lacks Ilkov et al.’s factor (1 + γ²)^(−n*), a factor of about 2^(−n*) at γ = 1, so the charge belongs with it. solprop has none for D2.

• Re-points applied in review:

  • nist_webbook_2026/vertical_N2O and vertical_CO2: reproduced_from = ["potts_1974"] (identical values).

  • nist_webbook_2026/vertical_CH4: its notes name heilbronner_1977.

  • bieri_1977/vertical_CH4: reproduced_from = ["heilbronner_1977"]. The 1t2 rows are identical. Its 2a1 row (22.9 eV) and adiabatic_CH4 (12.75 and 22.39 eV) are not in Heilbronner et al. 1977, whose spectra end near 21 eV and which prints no adiabatic energy; their origin is unknown (notes).

  • wang_1988: its notes name potts_1974 for the WebBook’s 13.79 eV.

• Findings for solprop (docs/corrections.md):

  • Its PPT Stark shift and dipole correction, attributed to Ilkov, Decker & Chin 1992, are not in that paper. Their source is unknown (requested).

  • Its PPT prefactor 4√2/π is Ilkov et al.’s Eq. (8) with a factor of 2 restored. As printed, Eq. (8) tends to half of Eq. (2) in the tunnelling limit (found at extraction; ilkov_1992’s formula correction).

  • Its H2 energy, 15.42613 eV, is 0.33 meV above Liu et al.’s 15.42580 eV. Its N2O energy, 12.8982 eV, is neither the vertical (12.89) nor the adiabatic (12.886) value.

• Status: decided (2026-09-27).

TC-548 The composition of dry air: CIPM-2007 (2026-09-27)

• Where: optmat.gas.composition (composition, MIXTURES), docs/models.md (Mixtures: dry air), tests/test_composition.py; the data are picard_2008’s mole_fraction datasets.

• Decision: the recommended dry air is the CIPM-2007 composition (Picard et al. 2008, Table 1).

  • N2 0.780848, O2 0.209390, Ar 0.009332 (u = 3 µmol/mol) and CO2 0.00040 (a conventional value) are the CIPM’s own.

  • Ne, He, CH4, Kr, H2, N2O, CO and Xe (18.2 to 0.1 µmol/mol) are the US Standard Atmosphere 1976’s, which the CIPM adopts; they are marked as reprints.

  • The fractions are returned as printed, summing to 1 − 2.9e-6. optmat does not renormalise: a code that keeps only some constituents renormalises and says so.

• solprop: its AIR is N2, O2 and Ar at 0.7808, 0.2095 and 0.0093 (NOAA’s rounded web fractions), renormalised. Against CIPM-2007 that is +0.03 % in N2, +0.09 % in O2 and −0.3 % in Ar, and it omits CO2 (0.04 %).

• Status: decided (2026-09-27).

TC-549 lamy_1977 (P. L. Lamy, Appl. Opt. 16, 2212 (1977)) (2026-09-27)

• Transcribed: Table I (tbl_1c325c8f2d92, JSON only), N and K against wavelength (angstrom), 1000-1650 A: crystalline quartz, ordinary ray (SiO2_quartz, axis o; Z-cut plate at 9 degrees incidence), n 23 points, k 18 points (K not printed from 1450 A); fused quartz (SiO2, grade “Tetrasil SE”, Electro-Quartz), n 23, k 20 (K not printed from 1550 A). Kramers-Kronig analysis of near-normal reflectance measured at 21 H2 lamp lines 1026-1640 A; extended with Philipp’s (crystal) or Platzoder and Steinmann’s (fused) reflectance below 1000 A and omega^-4 wings. m = n - ik. Vacuum wavelengths (vacuum monochromator; not stated explicitly). index_medium = "vacuum".

• Structural readings (script, image checked): the crystal K at 1200 A is printed “1 25” (decimal point lost in the print, the image shows the gap): read 1.25. Four K cells print a parenthesised third digit, “0.08(4)”, “0.05(5)”, “0.08(0)”, “0.04(3)”: read 0.084, 0.055, 0.080, 0.043 (meaning of the parentheses not stated).

• Checked: every cell against the image, two passes.

• Doubt: no uncertainty stated. Lamy restricts the KK k to k >~ 0.05 (p. 2214). The 1000, 1020 and 1650 A rows rest on the extrapolated reflectance.

• Finding (against philipp_1985, Palik’s Table X, fused silica): at the overlap (1000-1088 A, Philipp’s smooth curve through his and Lamy’s KK results) they agree within 0.04 in n, 0.03 in k. Above 1100 A they differ strongly: Philipp’s n peaks at 2.33 at 1228 A and is 0.29-0.33 above Lamy’s at 1200-1220 A, then 0.06-0.11 below it at 1300-1500 A; Lamy’s k exceeds Palik’s transmission-based k (Weinberg; the Weinberg/Appleton/Kaminow curve) from 1210 A on: x6 at 1300 A (0.40 vs 0.064), x40 at 1500 A (0.043 vs 0.0011). Lamy’s long-wavelength k is a limit of the KK analysis, not an absorption; his fused-quartz structure is broader and lower than Philipp’s (as he says of the reflectance).

• Status: verified (2026-09-27).

TC-550 philipp_1966 (H. R. Philipp, Solid State Commun. 4, 73 (1966)) (2026-09-27)

• Transcribed: nothing. No tables extracted; the pages were read from the page images. The note prints no peak energies, band gap or eps values: Fig. 1 (reflectance of crystal and fused quartz to 26 eV, fused lowered by 5 %) and Fig. 2 (eps_1, eps_2 of the crystal, KK) only. Notes-only record.

• Text values in notes: “four oscillators … followed above ~20 eV by … smooth absorption”; opaque above ~8 eV (qualitative); [eps_1 - 1]/rho at 2 eV = 0.52 (crystal) and 0.51 (fused), density ratio 2.65/2.20, (alpha/rho) ratio 1.02 (these reproduce n = 1.542 and 1.457 at 620 nm, i.e. handbook index data); Eqs. (1)-(2), the classical oscillator model, with no parameters (not recorded as a formula); Si-O ~1.62 A.

• Status: verified (2026-09-27).

TC-551 rife_1980 (J. Rife and J. Osantowski, J. Opt. Soc. Am. 70, 1513 (1980)) (2026-09-27)

• Transcribed: Tables I and II (tbl_5e4d1f912c2e, tbl_33f026d123dd, JSON only, two side-by-side blocks): n and k at 68-308 A (25 points each) of glass A (Cer-Vit C101, Owens-Illinois, lithium aluminosilicate glass ceramic; registered Cer-Vit-C101) and glass B (Corning 7971 ULE, high-silica glass with 7.5 % TiO2; the existing SiO2-TiO2, whose registry entry already names Rife and Osantowski’s sample). Reflectance against angle of incidence (15-85 degrees), synchrotron (NBS SURF) 80-310 A. The printed “+-” error estimates (“the range of reasonable intersection of the isoreflector curves”) on eight rows per table: per-point sigma, level “bound” (a judgement: the caption describes a range, not a statistical level).

• Checked: every cell against the images (two passes). Table III (calculated reflectances of glass A) reproduced by Fresnel from Table I’s n, k (n - ik, unpolarized) to 1 in the last digit at 15-80 degrees and 7e-4 at 85 degrees: confirms Table I is glass A. Table III itself (reflectance) not extracted.

• Doubt: the 68 A rows are below the 80 A SURF limit (“rising absorption below 75 A is most likely a stray light effect”). The glasses were to be registered “with the names printed”: glass B was already SiO2-TiO2 (no duplicate made); an alias “ULE” / “Corning 7971” may be wanted on it.

• Finding, philipp_1985 re-pointed: Palik’s Table X “Rife and Osantowski” rows (philipp_1985/rife_osantowski_n, _k, 82-290 A, filed as SiO2-TiO2): only 88-138 A (10 A steps) equal glass B’s Table II; the 2-A-spaced rows between are in neither table (presumably from Fig. 4); 150-260 A equal glass A’s (Cer-Vit’s) Table I at 148-258 A, moved up by 2 A; 270-290 A match neither table. reproduced_from set to rife_1980, notes say which rows are which; no value changed; not in any fit. For fit/SiO2: the fit’s Palik constraint (franta_2016’s model fitted to Palik, 24.8-146 nm) begins at 248 A, so only Table X’s 250-260 A rows (glass A’s 248 and 258 A) fall inside it; whether franta_2016’s own fit to Palik above 8.5 eV used Table X below 248 A is not known here.

• Status: verified (2026-09-27); the philipp_1985 row mix is a finding for review.

TC-552 tan_2003 (G.-L. Tan, M. F. Lemon and R. H. French, J. Am. Ceram. Soc. 86, 1885 (2003)) (2026-09-27)

• Transcribed: Table I (tbl_1982492688af, JSON only): the band-gap fits of Suprasil 1 (bulk; 1200 ppmw OH), direct (alpha^2 E^2 linear) 7.92, 9.55, 9.90 eV and indirect (alpha^(1/2) linear) 7.72, 8.30, 8.90 eV, one row per absorption fitting range (row label, e.g. “2.5e5-5.6e5 cm-1”); band_gap, kind “optical” with parameters.transition (as ensley_2019). The first row “Calculated from ellipsometric spectroscopy” (dagger). Text p. 1885, p. 1889: the literature gaps as reproduced points: 7.52 eV (French et al. 1992, alpha = 14 cm^-1) and 9.6 eV (Ravindra and Narayan 1986, alpha = 4e5), direct; 9.3 (weinberg_1979) and 9.0 (DiStefano and Eastman), photoconductivity.

• Not tabulated (figures only): n, k, eps_1, eps_2 0.7-43 eV (Figs. 3, 6, 7), alpha (Fig. 5), Re[J_cv] (Fig. 8), n_eff (Fig. 9), ELF (Fig. 10), London spectrum (Fig. 11). No oscillator or interband-transition parameter table exists. Notes: reflectance peaks 10.4, 11.6, 14.03, 17.10 eV; new J_cv features 21.3 and 32 eV; plasmon 23.7 eV; n_eff 9.8 at 43 eV and 7.3 at 26 eV; v_f = 45.3 A^3; Table II Hamaker constants (71.6 zJ vacuum, …, -15.6 zJ water/air; the extraction loses that minus sign and the image and text have it; “SiO3” in the Si3N4 row is a misprint for SiO2).

• Doubt: the gaps depend on the fitting range (the authors call the direct/indirect models “only a tool”); the text says the low-absorption row used both VUV and ellipsometry, the table note says ellipsometry. Ref. 42 prints DiStefano and Eastman’s volume as 99 (9 meant).

• Status: verified (2026-09-27).

TC-553 franta_2007 (D. Franta, D. Nečas and L. Zajíčková, Opt. Express 15, 16230 (2007)) (2026-09-27)

• Transcribed: Tables 1-3 as [[formulas]] without a form (checked by the script against the cells): six DLC films (a-C_H; Q, E_g, E_h of the pi and sigma bands; ids pdos_dlc_*), a typical a-Si:H film (a-Si_H, Eqs. (19)-(23), pdos_a_si_h), an SiO2-like film (1.13 um on c-Si, HMDSO/O2 plasma; registered SiO2-like_film_HMDSO; Eqs. (9), (10), (24), (25), pdos_sio2_like; B_p, E_p fixed). Band gaps as band_gap (kind “effective”): DLC E_g_pi, 6 rows (use = "check": Table 1 may re-express ref. [15]’s fits), a-Si:H 1.822 eV, SiO2-like 7.05 eV.

• Checks: Table 1’s derived rows from the parameters with kappa = 0.5736: alpha (Eq. 13), beta* (Eq. 15, with the printed thickness ratio), beta† (Eq. 16, from X_H) and sp3/sp2 (Eq. 17) all reproduce to the printed digits except sp3/sp2 at 406 C: Eq. (17) gives 1.480 (1.481 with the printed alpha), printed 1.45 (not resolved; a misprint or an X_H near 0.36). Appendix B’s elliptic form (Eq. 52) = the quadrature of Eq. (46) to 1e-12; Eq. (9) integrates to Q; Appendix A’s Eq. (43) reproduces the PJDOS Eq. (31) to 1e-11. SiO2-like model: eps_r 2.070 (1.5 eV), 2.084 (2 eV), 2.174 (4 eV), 2.443 (6.4 eV); defect eps_i 0.99e-3 at 5.1 eV; consistent with Fig. 7 by eye (A_delta etc. printed in meV, read as 1e-3 eV-units). a-Si:H model: eps_i peak 23.3 at 3.63 eV, eps_r 21.7 at 2.7 eV and 12.5 at 1.2 eV: shape and positions as Fig. 6, the amplitude about 10 % below the figure (by eye; not resolved).

• Misprints (notes, not errata: no dataset uses them): Eq. (24) prints the Gaussian exponents without the minus sign (diverges; with the sign the model reproduces Fig. 7). Eq. (37), the E -> 0 limit of the PJDOS real part, prints “- 3(E_h^2 - E_g^2)/2”; the limit of Eq. (31) is “- 3(E_h^2 - E_g^2)” (series expansion; numerically 1.1046 against the printed form’s 42.94 for Q 74.8, E_g 7.05, E_h 25.9).

• Comparison with the later Franta models (for review): the PJDOS term (Eqs. 30-35) is exactly the UDM’s symmetric interband term (franta_2015b Eqs. 4-12, udm._interband), same shape and same X(E), Y(E), with N_vc = 30 Q^2 C_N / (E_h - E_g)^5 (checked to 1e-14); the 2007 normalisation is the integral of E^2 eps_i, not the TRK sum. The PDOS square-root convolution (Eqs. 9-11) and the a-Si C(S) Gaussians are the parameterisation of franta_2013b’s “PDOS” column (its ref. [24] = franta_2007). The 2007 Gaussians (Eq. 24) sit in the JDOS bracket, divided by E^2, unlike the UDM’s normalised Gaussians; the 2007 Urbach tail is a localized DOS (Eq. 23), not the UDM’s exponential JDOS. No sum rule in 2007 (Q carries the unknown |p|).

• Status: verified (2026-09-27); the two misprints and the 406 C sp3/sp2 are findings.

TC-554 Re-points of philipp_1985, philipp_1971, kitamura_2007, franta_2013b (no values changed) (2026-09-27)

• philipp_1985: rife_osantowski_n, _k: reproduced_from = ["rife_1980"] (was the citation), with the row-by-row finding of TC-551 in their notes and the range bullet; philipp_lamy_n and philipp_vuv_n notes name philipp_1966, philipp_1971, lamy_1977 (the [9, 10] curve is Philipp’s own curve through both sets, not a reprint: stays primary).

• philipp_1971: its “ref. 10” (Solid State Commun. 4, 73) is philipp_1966.

• kitamura_2007: Table 1’s [54] Lamy is lamy_1977.

• franta_2013b: udm_pdos notes: ref. [24] is franta_2007, with its Table 2 a-Si:H parameters for comparison.

• No record from another extraction cites these papers (searched for Lamy, Rife, Osantowski, Lemon, “Solid State Commun. 4, 73”, “Opt. Express 15, 16230”).

• Status: verified (2026-09-27).

TC-555 daimon_2002 (CaF2, Daimon & Masumura, Appl. Opt. 41, 5275) (2026-09-27)

• Transcribed: Table 1, both parts (tbl_8ae247914098, p. 5278, and its continuation tbl_b68ea97710c0, p. 5279; json only): 69 vacuum wavelengths, 137.9-2326 nm. Datasets n_20C and n_25C (69 points each, refractive_index, sigma column = the table’s uncertainty, “Include lambda” where printed below 283 nm, otherwise “Except lambda”, written as “9e-7” because the table prints it x 1e-7), and dndt (69 points, thermo_optic_coefficient, scale 1e-6, sigma = the table’s uncertainty; temperature 22.5 C, the midpoint of 20-25 C). Every cell checked against the images.

• Medium (the key finding): relative to NITROGEN at 1013.25 hPa and the prism temperature (pp. 5275-5276, Table 1 heading, Figs. 3-4 captions). optmat’s index_medium cannot say “nitrogen”, so the datasets omit it and carry free parameters reference_gas = "N2", reference_gas_pressure_pa, reference_gas_temperature_k. Format need: index_medium = "nitrogen" (or a reference gas) for datasets and formulas. Absolute index = n_rel x n_N2; n_N2 - 1 = 2.75e-4 at 1 um, 20 C (peck_1966/eq4): the absolute index is about 3.9e-4 above the printed one. dn/dt is relative too: absolute dn/dT is about 1.3e-6/K lower (N2’s refractivity falls 0.93e-6/K).

• Formulas: sellmeier_20C, sellmeier_25C (Eq. (5), Table 2, four terms, poles printed as lambda_i^2) and dndt (Eq. (7), Table 3, Hoffmann form). No form for the Sellmeiers (a form would make an absolute model 3.9e-4 low); terms in the n2_sellmeier shape and range_nm are recorded so that only form and the medium remain to be added. Checks: 20 C residuals reproduced within 0.95e-7 at all 69 wavelengths, rms 6.12e-7 (printed s.d. 6.1e-7); 25 C within 1.04e-7, rms 5.77e-7 (5.7e-7); dn/dt residuals within 0.011e-6/C, rms 0.130e-6/C (as printed); Table 1 dn/dt = (n(25) - n(20))/5 within 0.02e-6/C.

• Doubts: the infrared term differs strongly between 20 and 25 C (A4 = 8.85 vs 13.0; lambda4^2 = 2752 vs 4040 um^2): do not extrapolate past 2.33 um, and do not difference the two formulas for dn/dT outside the range.

• refractiveindex.info Daimon-20/-25: coefficients identical; comment “Nitrogen atmosphere”; the page gives n with no conversion (used as absolute by solprop).

• Status: verified (2026-09-27); the formulas’ nitrogen medium was added in review (TC-545).

TC-556 malitson_1963 (CaF2, Appl. Opt. 2, 1103) (2026-09-27)

• Transcribed: Table II (46 lines, 0.2288-9.724 um, 24 C): computed_24C (check), residual_synthetic_24C and residual_natural_24C (refractive_index_deviation, x 1e-5, reference malitson_1963/sellmeier, primary), dndt_19C (-dn/dt x 1e6, scale -1e-6). Table I (json only; 1944 NBS, two Stockbarger prisms, 15/35/55 C, 9 lines): stockbarger_n_15C/35C/55C (reproduced from Stockbarger’s 1944 report and JOSA 39, 731 (1949), uncertainty 2e-6) and dndt_15_35C, dndt_35_55C (Malitson’s, primary). Table IV: table4_n_24C (84 points, check). Marker “a” (doublet mean) stripped from two Table I wavelengths.

• Medium: not stated; relative to room air at 24 C (index_medium air, 297.15 K), as for the other NBS prism papers, and Daimon & Masumura state “Malitson’s data are measurements in air at 24 C” (daimon_2002 pp. 5279-5280). Air wavelengths (standard air).

• Formula: sellmeier (Table III), form n2_sellmeier_wavelength, air medium, range 228.874-9726.65 nm (vacuum). Check: Table II computed column reproduced at 44 of 46 (rounded); 0.2537 um printed 1.46602 vs formula 1.465989 (3.1e-5) and 0.365015 um 1.44490 vs 1.444913 (1.3e-5), unexplained; Table IV is the formula TRUNCATED (83 of 84; -dn/dlambda likewise).

• Erratum: Table IV 0.36 um, 1.44548 -> 1.44543 (formula 1.4454317 truncated; the first differences follow the printed -dn/dlambda only with 1.44543).

• Findings: Table I dn/dt at 0.6678149 um (35-55 C) printed 10.85, indices give 11.00; at 0.4046563 um printed 10.12, indices give 10.50 (not corrected).

• Cross-check: made absolute (x Edlen air, 24 C), Malitson minus Daimon (absolute, interpolated to 24 C) is +1.5, +3.3, +2.5, +1.4, +0.8, +0.1, -0.2, -0.2, -0.4 x 1e-5 at 0.25-2.3 um: supports the air reading (as absolute it would be 3.9e-4 low).

• refractiveindex.info Malitson.yml: coefficients identical; no air statement.

• Status: verified (2026-09-27).

TC-557 dodge_1984 (MgF2, Appl. Opt. 23, 1980) (2026-09-27)

• Transcribed: Table II: n_o_19C and n_e_19C (36 regular wavelengths, 0.20-7.00 um, each). They are computed from the formulas (the 45 measured indices per ray are not printed); primary because nothing else represents the measurements; uncertainty 2e-5 as a bound (“better than 2 x 10^-5”). The birefringence column is n_E - n_O of the printed columns (all 36 checked), not extracted.

• Formulas: sellmeier_o, sellmeier_e (Table I), form n2_sellmeier_wavelength, axis o/e, air medium at 19 C (inferred), range 202.57-7041.92 nm (0.2025-7.04 um in air, text p. 1980; the abstract says 0.2026). Checks: all 72 Table II values reproduced rounded (largest 5.0e-6).

• Medium: not stated; inferred room air at 19 C (NBS Gaertner instrument, the lines’ and atmospheric bands’ air wavelengths). An inference, flagged in the record.

• dn/dT: not measured; the paper quotes Feldman et al. (NBS TN 993) “<= 2 x 10^-6 C^-1 in all cases” (notes only).

• refractiveindex.info Dodge-o/-e: identical coefficients; no air statement.

• Status: verified (2026-09-27).

TC-558 malitson_1964 (BaF2, J. Opt. Soc. Am. 54, 628) (2026-09-27)

• Transcribed: Table II (json only, 46 lines, 0.2652-10.346 um, 25 C, Harshaw prism): measured_25C (primary) and computed_25C (check); residual = measured - computed at all 46 rows (not extracted). Table I (json only; 1944 MIT/Stockbarger sample): mit_n_15C/35C/55C (primary, uncertainty 3e-6) and mit_dndt_15_55C (-dn/dt x 1e-6, scale -1e-6, the mean over 15-55 C = (n15 - n55)/40, checked). Table IV: table4_n_25C (85 points, check).

• Formula: sellmeier (abstract equation and Table III), form n2_sellmeier_wavelength, air at 25 C (inferred: “room temperature … regulated … very near 25 C”), range 265.279-10348.82 nm. Checks: Table II computed 44 of 46 rounded (0.334148 um a rounding edge; 0.486133 um printed 1.47856 vs formula 1.4785462, 1.4e-5); Table IV 83 of 85 rounded, 2 truncated.

• Text only: commercial-sample dn/dt “tentative”, -11 to -17 to -9 x 1e-6/C; Wild visible -15e-6/C; MIT sample 46e-5 below the commercial one (Fig. 6). Notes.

• refractiveindex.info Malitson.yml: identical; no air statement.

• Status: verified (2026-09-27).

TC-559 malitson_1962 (sapphire, J. Opt. Soc. Am. 52, 1377) (2026-09-27)

• Transcribed: Table II (46 lines, 0.2652-5.577 um, 24 C, ordinary ray): observed_o_24C (primary), computed_o_24C (check). Table III: table3_n_o_24C (61 points, check). Text p. 1378: n_e_24C_text, the extraordinary index 1.74794 at 1.014 um (inline point; presumably the 1959-boule sample, not stated).

• Formula: sellmeier_o (Table I), n2_sellmeier_wavelength, axis o, air at 24 C (inferred), range 265.279-5578.52 nm. Ordinary ray only (the paper has no e-ray formula). Checks: Table II computed 40 of 46 rounded; the six polystyrene bands 3.2439-3.5070 um are printed 3.5-6.7e-5 below the formula (unexplained); Table III 60 of 61.

• Erratum: Table III 1.00 um, 1.75554 -> 1.75573 (formula 1.7557300; neighbours).

• Findings: residual column misprints: 1.01398 um prints -1 where observed - computed = +1; 3.2439 um prints +3 where the columns give +4. Observed values taken as printed.

• dn/dt: text only (“about 20 x 10^-6/C … to about 10 x 10^-6/C near 4 u”; visible average 13e-6/C). Notes.

• refractiveindex.info: Malitson.yml = this paper (identical). Malitson-o/-e.yml (what solprop uses) are Dodge’s CRC-handbook formula at 20 C, not this paper: lower than this formula by 9.4e-5 (0.3 um), 5.2e-5 (1.0 um), 3.9e-5 (3.0 um), higher by 6.5e-5 at 5.0 um, at the same argument; about 5e-5 of it is the 4 K temperature difference.

• Status: verified (2026-09-27).

TC-560 matsuoka_1991 (silica, J. Non-Cryst. Solids 135, 86) (2026-09-27)

• Transcribed: Table 1 (json only): absolute n at 10 Hg-line “photon energies” and 7 temperatures (-165.4 to 83.3 C): n_m165.4C … n_83.3C (10 points each, 8 at the two lowest temperatures, where two rows print “-“); uncertainty 3e-6 (“precision”). Structural fix: the scan’s faint decimal points are read as spaces (“1 459241”); the script restores them only for the pattern digits-space-digits.

• Medium: absolute (sample in a 5e-6 Pa cryostat; windows corrected with air data).

• Photon energies (finding): the printed energies are hc/lambda_AIR with hc = 1239.852 eV nm (2.270486 eV = 546.0734 nm, the Hg green air wavelength; likewise 404.6565, 365.0148, 334.1475 nm). True photon energies are 2.8e-4 lower. The loader refuses a photon energy “in air”, so the files keep the printed energies and every dataset says so. Read naively, the points sit 0.15 nm (546 nm) to 0.07 nm (238 nm) short in wavelength: 0.6e-5 to about 3e-5 in n. Format need (or a conversion in the model): lambda_vac = vacuum(1239.852/E nm in standard air).

• Formula: sellmeier_temperature (Eqs. (1)-(3), Table 2), no form (energy variable, pole energies quadratic in C). b31, b32 printed as bounds (<1e-5, <1e-8), taken as 0. Check: 66 indices reproduced with rms 7.6e-6 and max 26.4e-6 (paper: 7e-6 and 26e-6); db2/dT at -82.5 C = -2.198e-4 eV/C (printed -2.20e-4).

• Comparison with Leviton: formula dn/dT vs leviton Table 6: 9.07 vs 9.12 (0.5 um, 295 K), 6.72 vs 6.70 (200 K), 4.77 vs 4.47 x 1e-6/K (120 K); 8.83 vs 8.86, 6.55 vs 6.51, 4.66 vs 4.35 at 0.6 um. Index (true wavelengths): Matsuoka 0.6-2.7e-5 below Leviton at 120-295 K.

• Status: verified (2026-09-27).

TC-561 waxler_1971 (silica, J. Res. NBS 75A, 279) (2026-09-27)

• Transcribed: Table 1: n_p20C … n_m200C, 23 temperatures x 10 lines (404.7-667.8 nm, air, printed to 0.1 nm). n_p20C is reproduced from malitson_1965 (the initial values; within 0.75e-5 of Malitson’s Eq. (1)); the others primary (Malitson + Delta n from a cubic fit). Uncertainty 2e-5 (the Delta n sensitivity), level not stated. -200 C is the cubic ~8 K beyond the data (-192 C).

• Medium: “the results which refer to air at 20 C” (p. 280): relative to air at 20 C for every temperature (index_medium air, air_temperature_k 293.15).

• Erratum: +10 C, 480.0 nm: 1.46431 -> 1.46341 (transposed; every other step of every column is -2 to -9 x 1e-5 per 10 C).

• Table 2 (-Delta n, +18 to -160 C, with Austin & Pierce and Rinne): no quantity; notes. dn/dT: text and Fig. 1 only (9e-6 at room temperature to 3e-6/C at LN2).

• Leviton Table 7 check: W&C x n_air(20 C, Edlen) minus Leviton’s formula at the vacuum wavelengths reproduces all 60 printed differences within 1.1e-5 (57 within 0.8e-5).

• Status: verified (2026-09-27).

TC-562 leviton_2006 (silica, Proc. SPIE 6273, 62732K) (2026-09-27)

• Finding: this is the version of record of leviton_2008 (arXiv:0805.0091), not a later or different study. Texts identical except the SPIE footnote; Tables 1, 2, 4-8 identical cell for cell (script), Table 3 identical against both images; same figures.

• Recorded: notes only (no datasets, no formula) to avoid double counting; the data stay in leviton_2008, which fit/SiO2 uses (n_295K, dndt_295K) and several pages name (leviton_2008/sellmeier). Decision for review: move the datasets and the formula to leviton_2006 (the version of record) and make leviton_2008 the notes-only duplicate, updating fit/SiO2, docs and tests.

• Its PUBLICATION question in leviton_2008 is answered (Proc. SPIE 6273, 62732K). The Frey, Leviton & Madison 62732J that franta_2017 cites is the silicon/germanium paper: franta_2017 needs no re-point.

• Status: decided (2026-09-27): the datasets and formula stay in leviton_2008, which is identical to this version of record number for number; fit/SiO2, the pages and the tests keep their keys, and leviton_2006 is a notes-only record naming it.

TC-563 leviton_2008 re-pointed to waxler_1971 and matsuoka_1991 (2026-09-27)

• waxler_cleek_minus_charms_* (6 datasets): reproduced_from -> waxler_1971; grade Corning 7940 added (W&C p. 279; Leviton says nothing); notes carry the check (60 values within 1.1e-5). Already use = "reproduced"; not fitted.

• matsuoka_minus_charms_* (5 datasets): reproduced_from -> matsuoka_1991; notes carry the photon-energy finding (Leviton’s Table 8 is reproduced only at the air wavelengths; at the true vacuum wavelengths the differences are 0.6-1.2e-5 higher).

• Notes: PUBLICATION paragraph (now the preprint of leviton_2006), W&C and Matsuoka paragraphs. No value changed.

• Status: verified (2026-09-27).

TC-564 hohm_1990b (Hohm & Kerl, Mol. Phys. 69, 819 (1990), Part II) (2026-09-27)

• Transcribed: 26 datasets, 74 values; 24 formulas.

  • Tables 1-3 (Ar, H2, O2; tbl_8e74d3a3b9bc, tbl_5e447ea27a86, tbl_c07dae7af5ae): the single-term fit alpha = C0/(C1 - omega^2) (Eqs. 18-21) at six temperatures 295-1007 K per gas, as 18 formulas (C0, C1, f0, omega0*); alpha(0, T) = C0/C1 as alpha0_T_<gas> (polarizability, angstrom^3, x = inf, rows = T; check: an extrapolation from 543.51-632.99 nm). The measured alpha(omega_k, T) are not printed (Hohm’s dissertation). Literature rows: Kerl 1982 [8], Cuthbertson 1910 [16] (cuthbertson_1910), Cuthbertson 1913 [17], re-evaluated by the authors, as reproduced formulas (6) and alpha(0) datasets; static values of kumar_1985, bose_1970, orcutt_1967, zeiss_1977, bishop_1980 (reproduced).

  • Text p. 828: mean alpha(0) of Ar 1.6404(11) (check, inline).

  • Tables 4-5 (H2, O2): alpha(lambda, 0 K) extrapolated with Part I’s Eq. (11) (check, temperature_k = 0) and the ab initio comparison (Bishop & Cheung = bishop_1980 J = 0; Rijks et al. scaled x 1.0831); alpha’_e = r_e (d alpha/d r)_e as polarizability_derivative (this work check; Adamov & Evarestov, Inoue et al., light scattering 0.9 and Buldakov 1.76(7) reproduced).

• Checked: every row of Tables 1-3: C0/C1, f0 = C0/253.2638, omega0* = C1^(1/2) x 2.4188843e-17 and C6 = 3 f0^2/(4 omega0*^3) reproduce the printed columns, except two misprints. Fits at 632.99 nm against Part I (hohm_1990): Ar +0.003 %, H2 -0.007 %, O2 +0.05 %. Bose & Cole’s A_eps -> 1.64108 (printed 1.64110). Zeiss S(-2) -> 0.80435, 1.56928; Kumar 11.08 -> 1.64189; Bishop J = 0 5.4193 -> 0.80306 and 5.5242 -> 0.81860.

• Errata: (1) H2 alpha(0, 1006.72 K) printed 0.81227, corrected 0.81263 (= C0/C1; f0, omega0* and C6 agree with 0.81263). (2) Formula correction: Ar omega0* at 570.48 K printed 0.617490, corrected 0.617470 (= C1^(1/2); only 0.617470 reproduces the printed alpha(0, T) through f0/omega0*^2).

• Doubts: Orcutt & Cole’s H2 static value 0.80515 [20] corresponds to A_eps = 2.0310, none of orcutt_1967’s printed H2 values (2.033, 2.0301, 2.036): unexplained. Bishop’s 611.97, 594.11, 543.51 nm values are not at bishop_1980’s wavelengths (presumably interpolated). Table 4-5 uncertainties: level not stated (Part I says standard deviations).

• Re-point applied: kerl_1992 (notes of eq10_Ar, eq10_H2, eq10_O2: data = hohm_1990b; its H2 and O2 alpha(0,0) are Tables 4-5’s static values digit for digit, and Ar’s 1.6404(10) the text’s mean).

• Status: open (whether any alpha(0, T) or 0 K value is fitted).

TC-565 hohm_1991 (Hohm & Kerl, Ber. Bunsenges. Phys. Chem. 95, 36 (1991)) (2026-09-27)

• Transcribed: Table 2 (tbl_ca1d21fe5b0e): CH4 alpha_0(632.99 nm, T) at 16 temperatures 128.53-885.19 K, with 1-sigma standard deviations (p. 36) (1 dataset, 16 values, check). B(T) (thermodynamic second virial, from A_2/A_1 with the assumed b_R = A_1/4) has no quantity: all 16 values in the record’s notes. Two formulas: the mean Eq. (6) dispersion constants f0 = 4.646(20), omega0 = 2.1460(48)e16 s^-1 over 128-298 K, and Kerl 1982’s f0 = 4.759, omega0 = 2.1667e16 (reproduced).

• Checked: image; C6 from the mean constants 115.74 (printed 115.8(1.3)), Kerl’s 117.99 (118); the constrained 128.53 K alpha_0 = 2.605265 equals hohm_1990’s Eq. (20) at 128.53 K to all digits. The 296.25 K value 2.61100(38) is 0.15 % (4 sigma) above hohm_1990’s formula and hohm_1993’s 17.5929 au = 2.6070 at 294.47 K.

• Doubts: the 128.53 K row prints the free-fit alpha (2.6151(44)) beside the constrained-fit B (245(20)) (Table 1); the minimum near T_c (188-195 K) the authors attribute to the zero-density extrapolation, not the molecule. The extraction was asked for “the second density (refractivity) virial coefficient”: the paper gives only the thermodynamic B(T) with an assumed b_R, so no refractivity virial is recorded.

• Re-point applied: kerl_1992 eq10_CH4 notes (note d = hohm_1991).

• Status: open (use of the temperature series; whether A_1/4 - B could be stored).

TC-566 hohm_1994c (Hohm & Trümper, Chem. Phys. 189, 443 (1994)) (2026-09-27)

• Transcribed: Table 1 (tbl_080bc44cea27): Xe alpha(omega_k, T) in au at omega = 0.07198116, 0.07669359, 0.08383075, 0.1401389 au (632.99, 594.096, 543.516, 325.13 nm) at nine temperatures 294-1080 K: 9 datasets x 4 (294.26 K primary, others check), sigma = the statistical rms error, systematic_relative = 3e-4 (the stated ‘at least ~0.008 au’ absolute uncertainty / 27.8 au: a derived number, flagged in the notes); the extrapolated alpha(omega -> 0) (check, 9 values); Table 2 b0(omega) (check, 5). Formulas: Eq. (14) b0 + b1 T^2 per frequency (5, with the Eq. 16 theoretical b1), Delta alpha(T) (text). Dipole sums S0(-2, -4, -6, -8) = 27.120(8), 127.36(89), 860(12), 6407(602) (cauchy_moment, check).

• Checked: images; the omegas = 45.563353/lambda(nm); C = 1.885341e-10 and D = 7.837695e-20 from the paper’s k_B and E_H (printed 1.885340, 7.837694); Eq. (16) with kumar_1985’s moments gives 2.443e-8 and 2.506e-8 (printed 2.44, 2.50); the fits reproduce Table 1 within its errors.

• Finding: at 294.26 K and 632.99 nm this paper’s 27.808(17) au agrees with hohm_1990’s 4.1217(40) angstrom^3 = 27.815 au (-0.02 %) but is 0.31 % below hohm_1994b’s 27.8952(71) au at 293.60 K (-0.31 % to -0.32 % at all four common wavelengths): the same laboratory, method and year, 11 times the stated absolute uncertainty. hohm_1994b’s xenon is +0.47 % above fit/Xe, so this paper would be about +0.16 %. The dispersion alpha(325) - alpha(633) is 2.207 here, 2.2164 in hohm_1994b.

• Re-point (another extraction’s record): olney_1997 cites Hohm & Trümper 1994 [102] for xenon (27.12 as S(-2); Table 1 note n 27.124): = hohm_1994c’s 294.26 K alpha(omega -> 0) = 27.1239(6) (or S0(-2) = 27.120(8)).

• Status: open (which Hohm xenon dataset the fit should use).

TC-567 bose_1970 (Bose & Cole, J. Chem. Phys. 52, 140 (1970)) (2026-09-27)

• Transcribed: Table II (tbl_d868b7eaf734): CO2 A_eps at 29.4 and 49.7 C, B_eps and C_eps at each; Ar A_eps and B_eps at 49.7 C (7 datasets, check, ‘3 sigma’ as stated for Table I’s fits); the literature rows (Orcutt & Cole 1965, Johnston & Cole 1962, orcutt_1967, Johnston et al. 1960; 9 datasets, reproduced). Static dielectric quantities stored as in bose_1972 (A_eps as molar_refractivity at inf; B_eps, C_eps as refractivity_virial_coefficient order 2, 3 at inf, never optical). Table I (mixtures), Tables III-V, B_ind, B_or and the quadrupole moments: notes.

• Checked: images of Tables I and II.

• Doubts: the level ‘3 sigma’ is stated for Table I and applied to Table II (same fits). Ref. 1’s Ar B_eps error is reprinted 0.60 where orcutt_1967 prints 0.20 (x 3).

• Re-points applied: achtermann_1991 (B_eps CO2 302.6, 322.9 K: errors rounded 0.90, 0.93 -> 0.9), hourri_1997 (A, B, C of CO2), st_arnaud_1979 (A_eps 7.350 listed at 298 K but it is the 49.7 C value; B_eps 323 K), buckingham_1974 (Ar A, B), copeland_1976 (Ar A_eps printed 4.1396 where the original has 4.1397; image checked), all to bose_1970 with level corrected to 3 sigma; hohm_2013’s CO2 mean notes.

• Another extraction’s record: schmidt_2003 compares Bose & Cole’s CO2 B_eps decrease (notes only).

• Status: open (whether the static A_eps of Ar serves as a check).

TC-568 hosticka_1974 (Hosticka & Bose, J. Chem. Phys. 60, 1318 (1974)) (2026-09-27)

• Transcribed: Table I (tbl_23fb0fd23746, JSON only): SF6 A_eps at 323.3, 348.3, 373.9 K, B_eps and C_eps per temperature (7 datasets, check, 3 sigma); Nelson & Cole 1971’s A, B, C at 323.3 K (3, reproduced); text alpha = 6.560e-24 cm^3 (check). B_p, Table II, B_ind = 28.04 and the hexadecapole moments: notes.

• Erratum: C_eps at 323.3 K printed ‘6900 ± 899’ without its minus sign (image checked), corrected to -6900: Fig. 1 shows the three temperatures’ lines parallel with one negative slope (C_eps is the slope term), the other temperatures give -6895 and -6883 and Nelson & Cole -6400 at the same temperature.

• Doubts: Table II lists this work’s B_p as -218.72 at 323.2 K, Table I -218.80 at 323.3 K (not extracted).

• Re-points applied: achtermann_1991 (B_eps at 323.3, 348.3, 373.9 K; at 373.9 K it prints 58.84 where the original has 58.89: noted, value kept), hourri_1997 (A_eps), st_arnaud_1979 (A_eps listed at 298 K but it is the 323.3 K value; B_eps rounded), all with level 3 sigma; hohm_2013’s SF6 mean notes.

• Status: open.

TC-569 may_2009 (May, Moldover & Schmidt, Mol. Phys. 107, 1577 (2009)) (2026-09-27)

• Transcribed (text, inline): recommended A_eps,273K = 2.03065 +- 0.00017 cm^3/mol (primary, 1 sigma), Method 2’s 2.0307 (273 K, excluded: averaged into the recommended) and 2.0311 (293 K) (primary, as may_2008’s eq18_O2), alpha_e = 8.9568(8)e-41 F m^2 (check), Harvey & Lemmon 8.9566(26) (bound), Rychlewski 8.958, Maryott & Buckley 8.981 (reproduced). Formulas: Eq. (9) with Method 1’s parameters (A 2.03075, b_eps 0.0636, A_tau 0.00599; the Kunz-EOS variant in notes) and the recommended set (A 2.03065, A_tau 0.0061, b_eps 0.03 +- 0.05).

• Checked: 3 eps0 A/N_A = 8.95682e-41; A_tau/(273.16 A) = 1.10e-5 K^-1 (abstract); Eq. (9) (Method 1) reproduces Table 1’s eps_r - 1 to 1-90 ppm at 1.0 MPa, 225-240 ppm at 1.5 MPa, ~400 ppm at 2.5 MPa (the check neglects the third density virial), 0.04-0.14 % at 0.1 MPa (four printed digits).

• Not extracted (vocabulary gap): Table 1, 40 values of eps_r - 1 of normal H2 against pressure at 273.203 and 293.213 K (0.1-6.5 MPa): no quantity for a gas’s permittivity at a stated pressure (as may_2008’s Table III). The extraction was asked for “the static permittivity against density and temperature”: a permittivity_increment-type quantity (against pressure, with the temperature) would be needed. b_eps (cm^3/mol, relative to A_eps) has no unit in refractivity_virial_coefficient (cm^6/mol^2): in the formulas.

• Doubt: the paper quotes Orcutt & Cole’s H2 value as b_eps = 0.03 +- 0.10 cm^3/mol, but orcutt_1967 prints 0.03 +- 0.10 as its B_eps in cm^6/mol^2 (b_eps would be 0.015).

• Re-point applied: hohm_2013 dp_H2 (5.4324 +- 0.0005 au = 8.9568(8)e-41 F m^2, checked) -> may_2009, level 1 sigma; header’s [43] note.

• Status: open (the vocabulary question).

TC-570 picard_2008 (Picard, Davis, Gläser & Fujii, Metrologia 45, 149 (2008)) (2026-09-27)

• Transcribed: Table 1 (tbl_b2ed47a88f5d): the CIPM-2007 dry-air mole fractions, 12 mole_fraction datasets (material = constituent, parameters.mixture = ‘dry air (CIPM-2007)’): N2 0.780848, O2 0.209390, Ar 0.009332 (u = 3 umol/mol, standard), CO2 0.00040 (conventional default), primary; Ne 18.2e-6, He 5.2e-6, CH4 1.5e-6, Kr 1.1e-6, H2 0.5e-6, N2O 0.3e-6, CO 0.2e-6, Xe 0.1e-6 (scale 1e-6), reproduced from the US Standard Atmosphere 1976. Formulas: M_a (Eqs. 2-4), the density (Eqs. 1, 5a, 5b) and Appendix A (p_sv, f, x_v, Z).

• Checked digit by digit: image read, and every printed contribution x_i M_i equals x_i x M_i to the last digit (e.g. 0.780848 x 28.0134 = 21.874207); sum x_i = 1 - 2.9e-6 (as stated); M_a = 28.96546; S = 0.20979; 28.96546/8.314472 = 3.483740; +71.8e-6 over CIPM-81/91. Structural: thin-space digit groups removed (‘0.780 848’).

• Doubts: O2 has no single printed uncertainty (u(S) = 60, u(Delta x_O2) = 60 umol/mol; notes); N2 none (remainder); CO2 is a default, not a measurement. The reference list’s [15] is CODATA 2002 though the text says CODATA 2006 (same R).

• Status: open (air is to be built from these).

TC-571 bishop_1990b (Bishop, Pipin & Rérat, J. Chem. Phys. 92, 1902 (1990)) (2026-09-27)

• Transcribed: Tables II-VII (JSON): H2 and D2, dc Kerr, ESHG, THG; gamma_par and gamma_perp (THG par only); elec, vib, total; split into the omega block (hartree, 0-0.05) and the laser block (angstrom, 10 640-4880): 60 datasets x 6 (check; convention T, 295 K). Table IX S and T (theory check; experiment reproduced from mizrahi_1985_h2d2), Table X gamma^K of H2, D2 (check), text experimental gamma^K (buckingham_1968b, carusotto_1985; reproduced). Formulas: Table XI (6) and the He ESHG reference (Eq. 25, bishop_1989). Tables I, VIII, XII-XIV: notes.

• Errata (total = elec + vib): (1) D2 dc Kerr gamma_perp(total) 10 640 A: 227.6 -> 277.7 (Table X’s gamma^K = 655 confirms). (2) H2 ESHG gamma_par(elec) 5145 A: 931.9 -> 931.3 (total confirmed by Tables VIII R and IX T; vib by bishop_1991). (3) H2 THG gamma_par(elec) 10 640 A: 774.4 -> 777.4 (vib by bishop_1991; the omega dependence interpolates to 777.5; bishop_1991’s +1.7 % then matches its stated 1.3-1.8 %).

• Checked: every other total = elec + vib to +-0.1; Table XI fits reproduce the elec columns at omega <= 0.03 to 0.05 a.u.; T and S to the last digit; gamma^K to rounding.

• Re-points (other extractions’ records, for review): bishop_1991’s 30 vib datasets (citation -> bishop_1990b); they agree at the lasers and at 0, 0.03-0.05 a.u. but differ by 0.1 at five near-resonant entries (H2 Kerr par 0.02: -929.1 here / -929.0 there; D2 Kerr par 0.01: 316.5/316.6, 0.02: -43.4/-43.3; D2 ESHG par 0.01: 206.0/206.1; D2 THG 0.01: -153.7/-153.6). bishop_1990 (its Table X rows from Bishop, Pipin & Rérat), shelton_1990 (two datasets), sekino_1993 (seven), tammer_1990 (two): citation -> bishop_1990b.

• Re-point applied: tammer_1992 table2_literature_H2 ‘ref 5’ (4.45e-62 = 714 au, checked).

• Status: open.

TC-572 boyle_1966 (Boyle, Buckingham, Disch & Dunmur, J. Chem. Phys. 45, 1318 (1966)) (2026-09-27)

• Transcribed (text): the measured He dc Kerr gamma = (2.6 +- 0.4) x 10^-38 esu at 6328 A (check; convention T, Eq. 1 m = alpha F + gamma F^3/6; the library’s abstract text shows 1/2, the page image 1/6), the calculated static gamma 31.1648 au and alpha 1.3688 au (check), the observed alpha 0.2051 A^3 (Dalgarno 1962, reproduced). Partial orders, hydrogen-atom values and B, C: notes. Converted nothing.

• Re-points applied: bishop_1989 expt_dc_kerr row boyle_1966 (52 +- 8 au), shelton_1994 table6_He_dc_kerr_expt row ‘ref 31’ (51.6 +- 8 au, checked), tammer_1992 table3_literature_He row ‘ref 16’ (32.0(53) x 10^-64 where the conversion gives 32.19(50): 0.6 % low, uncertainty 6 % high, not explained); hellwarth_1990 notes.

• Status: open (superseded by buckingham_1968, 20 % above modern values).

TC-573 dunmur_1979b (Dunmur, Hunt & Jessup, Mol. Phys. 37, 713 (1979), Part II) (2026-09-27)

• Transcribed: Tables 1-3 (Ar, Kr, Xe at 458 nm): A_K (one temperature-independent value each) and B_K against T; Table 4 (SF6, 633 nm; the 297 K row at 458 nm): A_K, B_K, C_K; Table 5 (CH4, 458 nm): A_K, B_K, C_K; Table 8: gamma-bar (dc Kerr, T convention, C^4 m^4 J^-3; this work, check) and the published values (reproduced: buckingham_1968, buckingham_1969, ward_1969, Finn & Ward 1971, Ward & Bigio 1975, Hauchecorne 1971, Rado 1967). 32 datasets, 81 values. CF4, neopentane, B_K ratios, Tables 9-10: notes.

• Checked: 81 eps0 A_K/N_A reproduces Table 8 (Xe 48.8 from the printed 41 against 49.2); Part I’s (dunmur_1979) expt rows all agree with this paper; buckingham_1968’s esu values convert to Table 8’s [3] column (Ar’s error 0.50 printed 0.6).

• Doubts: CH4’s A_K (16.1 +- 0.8) and gamma (19.2 +- 1.0) coincide digit for digit with krypton’s; not explained. SF6’s A_K (hence gamma) is a 458 nm value (Table 4 dagger), whereas shelton_1994 note aa says 633 nm.

• Re-points: applied in shelton_1994 (table12_CH4_dc_kerr, table12_SF6_dc_kerr rows ‘ref 22’; SF6 error 0.8 -> 128 au, printed 133). In other extractions’ records, for review: dunmur_1979 table2_expt_{Ar,Kr,Xe,CH4,SF6}, table4_expt_{CH4,SF6} (all agree); hattig_1998 expt_dc_kerr_Ar (1187 +- 96 at 457.9 nm = 7.40 x 10^-62, the paper’s 7.39 gives 1185).

• Status: open.

TC-574 Reprints of the DOSD papers in hohm_1993, hohm_1994b, hohm_2013 (2026-09-27)

The originals’ source ids do not exist on this branch; candidates found in another extraction’s records: hohm_1993 thomas_1977_CH4, moments_thomas_1977_CH4 (-> thomas_1977); hohm_1994b jhanwar_1982_CO2 (-> jhanwar_1982), thomas_1977_CH4 (-> thomas_1977); hohm_2013 dosd_CO, dosd_CO2 (-> jhanwar_1982), dosd_CH4 (-> thomas_1977), dosd_SF6 (Kumar, Fairley & Meath, J. Chem. Phys. 83, 70 (1985) -> kumar_1985b). Values not compared (the originals are curated separately).

• Status: decided (2026-09-27): applied in TC-606.

TC-575 liu_2009 (Liu et al., J. Chem. Phys. 130, 174306 (2009)) (2026-09-27)

• Transcribed: ie_ortho_H2 (inline, the equation under Table II, p. 6 = 174306-5): 124 357.237 97(36) cm^-1, X (0, N = 1) -> X+ (0, N+ = 1, hyperfine centre). ie_para_H2 (Table III “This work” row, tbl_c65377ced290, script): 124 417.491 13(37) cm^-1, X (0, 0) -> X+ (0, 0), the conventional ionisation energy (= 15.4258029 eV). Table III’s 18 earlier determinations (1969-2002), one reproduced dataset each (1 point each), kind adiabatic, final X+ (0, 0).

• Checked: Table II’s intervals sum to 124 357.237 979 (printed .237 97) and 124 417.491 144 (printed .491 13): 1e-5 cm^-1, inside the uncertainty; the quadrature sums reproduce (36) and (37). Tables II and III checked on the images; Table II’s CSV lost the parentheses (not used: the value is from the equation). Reference numbers checked on the reference-list page (43 Meiners, 44 Kolos).

• Comparisons: Table III’s 1993 rows “37/38, revised in 41” equal shiner_1993/mccormack_H2 (124 417.507(12)) and shiner_1993/jungen_1990_H2 (124 417.484(17)) exactly; the 1993 theory row (Ref. 40) equals shiner_1993/ab_initio_H2 (124 417.471). holsch_2019’s ortho value 124 357.238 003(11) is 3.3e-5 cm^-1 above this paper’s ortho value (0.1 sigma).

• Uncertainty level: not named (“quadrature summation”; the statistical part one standard deviation).

• Not taken (notes): D0(H2) = 36 118.069 62(37) cm^-1; E_i(H), E_i(H2+), D0(H2+) recalculated (Eqs. (6)-(11)); the error budget Table I.

• Re-points (in this extraction’s records): liu_2010/liu_2009_H2 -> reproduced_from [“liu_2009”]; identical value and uncertainty; its notes and final_state no longer call the level an inference. holsch_2019: notes point at liu_2009/ie_para_H2 and ie_ortho_H2 (no dataset reprints Liu 2009).

• For review: data/gas/ionisation.toml H2 names liu_2010/liu_2009_H2 (now a reproduction of liu_2009/ie_para_H2); switch it to the original. solprop’s H2 potential (15.426135 eV) is 0.33 meV (21 ppm) above 15.425803 eV.

• Status: verified against the page images.

TC-576 heilbronner_1977 (Heilbronner, Jones & Maier, Helv. Chim. Acta 60, 1697 (1977)) (2026-09-27)

• Is it the paper requested? Yes: the citation matches, and it is bieri_1977’s reference [17]. Although it is about di-n-alkyl diacetylenes, CH4 appears: its He(I) spectrum is in Fig. 1 and its sigma ionisation energies in Table 2.

• Transcribed: vertical_CH4 (Table 2, tbl_d6b9168f4f46, script, 3 points): 13.6, 14.4, 15.0 eV, +-0.1 eV (caption), the three maxima of the Jahn-Teller split 1t2 band. kind vertical: the paper does not say “maxima” for Table 2; Bieri et al. (same lab, same year) reprint the numbers as band maxima = vertical (doubt, stated in the record).

• Finding: bieri_1977 attributes to this reference also the 2a1 maximum (22.9 eV) and the adiabatic 12.75 and 22.39 eV; none of them is in this paper (spectra end near 21 eV; no adiabatic value printed).

• Status: verified against the table image.

TC-577 potts_1974 (Potts & Williams, J. Electron Spectrosc. 3, 3 (1974)) (2026-09-27)

• Is it the paper requested? Yes (identity checked; the WebBook’s source for the N2O and CO2 vertical energies).

• “Forbidden” transitions: two-electron (ionisation + excitation) transitions to “superexcited” ionic states, allowed by configuration interaction with a one-hole state of the same symmetry (the UV analogue of X-ray shake-up): the “CI bands”.

• Transcribed: Tables 1 and 3 (JSON cells only; images checked): N2, CO, CO2, N2O, kind vertical (“IP’s are band maxima or vertical IP’s”, p. 7). Per gas two datasets: hei_<gas> (bands below 21.22 eV, reproduced: “Those in the 584 region have been taken from Turner et al.”), heii_<gas> (this paper’s He II bands, primary). Points: N2 3 + 4, CO 3 + 6, CO2 4 + 5, N2O 5 + 5. No uncertainty printed; no adiabatic energy printed.

• Structural fix: Table 3’s first orbital of each block is merged into the label cell (moved back in the script); footnote marks dropped from values.

• Finding: the WebBook’s N2O 12.89 and CO2 13.79 eV (nist_webbook_2026/vertical_N2O, vertical_CO2) are this paper’s hei values, which the paper itself takes from Turner, Baker, Baker & Brundle 1970. N2O’s 19.5 eV CI band is attributed to Turner by the note’s rule (inference).

• Not taken: relative intensities, XPS columns (other authors’), Tables 2 and 4 (CI assignments), HCN, COS, CS2 (Table 3c’s 11th CS2 band 23.96 eV is lost from the cells). Text misprint: N2O’s valence configuration with 1pi and 4sigma occupancies interchanged.

• Status: verified against the table images.

TC-578 ilkov_1992 (Ilkov, Decker & Chin, J. Phys. B 25, 4005 (1992)) (2026-09-27)

• Transcribed: seven formulas without a form (Eqs. (2), (3)-(4), (5), (6), (7), (8) with A_m, w_m, alpha, beta, g, nu, kappa, and the tunnelling conditions (9)-(11)); no tables, no datasets (Hg not curated). Read on the rendered pages 4007-4012.

• Checks (numerical): Eq. (2) + Eq. (3) gives the cycle-averaged hydrogen rate; Eq. (2) + Eq. (4) = Eq. (5) = Eq. (6) = Eq. (7) to 1e-14 (He-like, Ar-like cases). Eq. (8) as printed tends to HALF of Eq. (2) as gamma -> 0 (ratio 0.5017 at gamma = 0.058, He at 10.6 um), contrary to the text; with the prefactor (6/pi)^(1/2) instead of (3/(2 pi))^(1/2) the ratio is 1.0034 -> 1 as gamma^2. Recorded as a [[formulas.corrections]] on the prefactor (the factor 2 could sit in A_m instead: stated in the reason).

• Which equation is solprop’s PPT: Eq. (8) with A_m written out and the corrected prefactor 4 sqrt(2)/pi (Bergé et al. A14), plus an occupancy N and a sum over m that this paper does not have. The exponents agree exactly; solprop’s phi_m is the paper’s w_m (checked). solprop’s Stark shift and dipole correction, attributed to “Ilkov, Decker and Chin”, are not in this paper (no polarisability appears; the only Stark-shift mention is “neglecting the Stark shift” in F_BSI).

• Eq. (7) is walsh_1993’s “Ilkov-modified ADK” term by term.

• Constants: Eq. (10)’s lower field bound 1.24e8 computes to 1.270e8; Eq. (11)’s lower intensity bound 1.6e13 is not the square of the field bound (2.0e13). Recorded, not corrected.

• Re-points (in this extraction’s records): walsh_1993/adk_ilkov reproduced_from -> [“ilkov_1992”] (identical); notes of forster_2014, saenz_2002, yudin_2001, larochelle_1998 now name ilkov_1992.

• Status: open (the Eq. (8) correction needs a register entry).

TC-579 talebpour_1997 (Talebpour, Larochelle & Chin, J. Phys. B 30, 1927 (1997)) (2026-09-27)

• Notes-only: NO (not curated), figures only. Recorded the intensity calibration (energy, autocorrelation, CCD focal spot 49 um at 1/e^2, checked against He’s ADK saturation intensity; no uncertainty stated) and the ion-signal calibration. CO, N2, O2 statements are qualitative only.

• Status: verified (no values).

TC-580 talebpour_1998 (Talebpour, Larochelle & Chin, J. Phys. B 31, L49 (1998)) (2026-09-27)

• Identity: the paper is on D2 (the library title lost “D2”), not O2; O2 does not appear. The comparison atom is Ar (15.76 eV; D2 15.46 eV, uncited).

• Transcribed: zeff_D2, ionization_model_parameter, model ppt, Z_eff = 0.72 (p. L56): computed (orientation average of the PPT rate with Z_eff(theta) from a quasi-classical barrier at 1.5e14 W/cm^2, 800 nm), not fitted; use = check. l, m not stated.

• Finding: the group’s PPT form (Eq. (2), also larochelle_1998 Eq. (10)) has (1 + gamma^2)^(|m|/2 + 3/4) where ilkov_1992 Eq. (8) has (1 + gamma^2)^(-n* + |m|/2 + 3/4): a factor 2^(-n*) at gamma = 1.

• NO+ Z_eff = 2.2 (not curated) in notes.

• Status: verified against the page image of Eq. (2).

TC-581 scrinzi_1999 (Scrinzi, Geissler & Brabec, Phys. Rev. Lett. 83, 706 (1999)) (2026-09-27)

• Transcribed: table1_He (Table I, script, 60 points, F = 0.08-1.70 au): the full two-electron complex-scaling He rate (per atom), au. “Accurate to at least two digits” (notes, not an uncertainty).

• Structural fix: “0.463 3 1027” -> 0.463e-7 (lost x and minus signs; image checked).

• Re-points (in this extraction’s records): parker_2009/table1_scrinzi_1999 (15 points) and majety_2015/table1_scrinzi_1999_He (11 points) -> reproduced_from [“scrinzi_1999”]; every value identical.

• Status: verified against the table image.

TC-582 saenz_2000 (Saenz, Phys. Rev. A 61, 051402(R) (2000)) (2026-09-27)

• Notes-only: no rate is printed; the H2 rates against R (0-10 a0) at F = 0.053 38-0.12 au are in Figs. 2-4 only. The equilibrium-distance rate is not in the paper.

• Finding: majety_2015/table2_parallel_saenz_2000_H2 (4 values at R = 1.4 au) is attributed to this paper but cannot be checked against it (re-pointed to saenz_2000 with that note; the values are of Fig. 3’s magnitude).

• Status: verified (no values).

TC-583 batishchev_2010 (Batishchev, Tolstikhin & Morishita, Phys. Rev. A 82, 023416 (2010)) (2026-09-27)

• Transcribed: table1_Ar (Table I, JSON cells, script, 5 points): the converged SAE Siegert width of Ar(3p, m = 0) at F = 0.05, 0.1, 0.2, 0.5, 1.0 au (last line of each block), per electron in the m = 0 orbital, use = check (a model atom: |E0| = 0.6057 au against argon’s 0.579). potential_garvey_Kr (a = 1.351, b = 4.418, reproduced from Garvey et al. 1975) and potential_modified_Kr (1.320, 4.355), ionization_model_parameter.

• Structural fixes: merged header/first row and F/N_ch cells split; “a(b)” -> “aeb”.

• Checked: the GSZ potential’s 4p level with Garvey’s Kr parameters is -0.4589 au and with the modified -0.5139 (finite differences), matching the printed 0.459 and 0.514.

• Ne and Xe (and Kr) rates are in Fig. 3 only; Ne, Ar, Xe potential parameters not printed.

• Status: verified against the table image.

TC-584 trinh_2013 (Trinh et al., Phys. Rev. A 87, 043426 (2013)) (2026-09-27)

• Transcribed (Table I, script): per atom Ne, Ar, Kr, Xe: wfat_<atom> g00, g10 (tunnelling_structure_coefficient, model wfat, rows = parabolic channel (0,0), (1,0)); correction_<atom> a00, A00, B00 (ionization_model_parameter, model wfat); potential_<atom> N, u, v and state_<atom> E0, alpha (ionization_model_parameter, model gsz_sae_potential). 16 datasets, 40 points. All use = check.

• Which quantity: g00 (= G00, mu_z = 0) and g10 are structure factors; a00, A00, B00 are correction coefficients. Vocabulary doubt: tunnelling_structure_coefficient’s rows are “one per partial wave l”; WFAT’s are parabolic channels (n_xi, m).

• Checks: A00 from Eq. (40a) reproduces all four to the printed digits; B00 from Eq. (40b) agrees within a00’s rounding (+-0.1; Ar by 0.12); the potentials’ l = 1 levels reproduce E0 to the printed three decimals.

• Structural fix: “- 2.6” -> -2.6 (image checked).

• alpha is the model electron’s polarizability, not the atom’s (said in the record).

• Status: verified against the table image.

TC-585 Reprints of the ionisation papers in other records (2026-09-27)

• nist_webbook_2026/vertical_N2O -> potts_1974 (hei_N2O#2pi, 12.89 eV, identical; itself Turner et al. 1970’s He I value).

• nist_webbook_2026/vertical_CO2 -> potts_1974 (hei_CO2#1pi_g, 13.79 eV, identical; Turner et al. 1970).

• nist_webbook_2026/vertical_CH4 notes: the original is heilbronner_1977/vertical_CH4#1t2_1 (13.6 eV, identical).

• bieri_1977/vertical_CH4 rows 1t2_1-1t2_3 -> heilbronner_1977 (identical); bieri_1977’s row 2a1 (22.9 eV) and adiabatic_CH4 (12.75, 22.39 eV) are NOT in Heilbronner et al. 1977: their reproduced_from is wrong (by Bieri’s own column rule); origin unknown.

• wang_1988 notes: “Potts & Williams 1974” = potts_1974.

• data/gas/ionisation.toml (config): H2 ionization_energy liu_2010/liu_2009_H2 -> liu_2009/ie_para_H2; CH4 vertical bieri_1977/vertical_CH4#1t2_1 -> heilbronner_1977/vertical_CH4#1t2_1; N2O and CO2 vertical nist_webbook_2026/… -> potts_1974/hei_N2O#2pi and potts_1974/hei_CO2#1pi_g (both reproduced from Turner et al., not in the library: the best copies available).

• tong_2002 notes mention “Saenz’s ab initio” H2 rate in its Fig. 2: which Saenz paper is not checked here.

• Status: decided (2026-09-27): applied in TC-547.

TC-586 Raman: the originals in the choices, and the renamed Weber volume (2026-09-27)

• Where: data/gas/raman.toml, optmat.gas.raman (_per_amagat), docs/raman.md; herring_1986, brodersen_1979, schrotter_1979 (edits made in review), after the extraction of stoicheff_1957, keijser_1974, van_den_hout_1980, murray_1972, komasa_2011, rouille_1992 and brown_1992 (their entries follow).

• Decisions:

  • H2 and D2 rotational constants: stoicheff_1957/table2_{B0,D0,H0}_{H2,D2}, the originals of weber_1979’s reprints (digit-identical; the B0 misprint of TC-515 is Weber’s alone). The lines are unchanged.

  • D2 rotational widths: keijser_1974/table1_D2 (HWHM in GHz per amagat at 293 K, doubled to FWHM), the original of smyth_1987/keijser_S_branch. The widths change by at most 0.4 %, the rounding of Smyth et al.’s conversion to cm⁻¹. The width tables now take GHz per amagat.

  • Murray & Javan’s D2 Q widths are not used. Their words say FWHM, but their D2 values are half of every later FWHM measurement (Russell & Roh, Ottusch & Rockwell) and equal to Smyth et al.’s HWHM, while their H2 values agree with later FWHM data. Nothing in optmat’s models uses them. The doubt stays open.

• Re-points applied in review (herring_1986):

  • table5_van_den_hout_295K → keijser_1974: van den Hout et al.’s 293 K row is Keijser’s (their note b), doubled (2 × 0.94 × 44.62 = 83.9, 2 × 1.17 × 44.62 = 104.4).

  • table5_van_den_hout_80K and table6_van_den_hout_80K → van_den_hout_1980 (Table I at 77.8 K: 62.5 and 99.1 MHz/amagat FWHM; Table V, sign reversed).

• The Weber volume: the library validated and renamed its copy, Unverified_6d54463e97c7 → Weber_1979_RamanSpectroscopyGases, with the same tables. brodersen_1979, schrotter_1979 and weber_1979 now name it; their extraction scripts reproduce their files.

• Status: decided (2026-09-27); open: Murray & Javan’s D2 widths.

TC-587 stoicheff_1957 (Stoicheff, Can. J. Phys. 35, 730 (1957)) (2026-09-27)

• Transcribed (all tables JSON-only; images checked):

  • Table I (p. 732): raman_shift table1_S0_H2 (4: S0(0)-S0(3)), table1_Q1_H2 (4), table1_S0_D2 (5), table1_Q1_D2 (5); vacuum cm-1, 1-2 atm; +-0.02 (S) and +-0.05 (Q) cm-1 absolute (p. 731), level not stated. O-C columns in printed.

  • Table II (p. 734): rotational_constant B_0, D_0, H (H_e, printed under v = 0) of H2 and D2 with the p. 738 accuracies (0.005, 0.0003, 0.5e-5 cm-1); B_v, D_v of H2 v = 1-3 and D2 v = 1 (no accuracy); H2’s bracketed v = 1 refit (B_1, D_1 calculated, nu_1-0) as check; vibrational_term_value nu_v-0 (H2 v = 1-3, D2 v = 1).

  • Table III (p. 736): B_e (primary) and the theory-corrected B_e* (check) of H2, D2.

  • HD: notes only.

• Structural fixes: Table I’s H2 |Delta nu| column is merged into a cases cell (columns shifted left) - parsed from it; Table II subscript digits misread: H2 D_2 “0.0427;” -> 0.04277 (image subscript 7), D2 D_1 “0.01073” -> 0.01075 (image subscript 5; text D_0 - D_1 = 0.00059; Table I O - C_1 of Q_1(4) needs 0.01075).

• Formulas: equilibrium_H2 (G(v), B_v, D_v, H_v; p. 735) reproduces Table I’s O - C_2 to 0.01 and Table II’s B_v, D_v, nu to the printed digits (bracketed v = 1); dunham_potential_H2 (a_0-a_4): a_0, a_1, a_2 reproduced to the printed digits. Table II reproduces Table I’s O - C_1 to +-0.001 (H2, D2 Q).

• Finding: D2’s printed pure rotational O - C_1 column is the NEGATIVE of the least-squares residuals (C - O, or misprinted signs); no value affected.

• Doubt: none on values. The D2 Q-line uncertainty is +-0.05, larger than the line spacings of Komasa’s theory differences (see TC-591).

• Re-points (in this extraction’s records): weber_1979’s six H2/D2 datasets (B_0, D_0, H_0) now reproduced_from = ["stoicheff_1957"]: digit-identical (the 56.3392 erratum confirmed by Stoicheff’s 59.339_2); Weber’s “H_0” is Stoicheff’s H_e. bischel_1986b shift_H2’s list names stoicheff_1957 (4155.201 at 1-2 atm; bischel_1986 quotes 4155.207 = extrapolated to zero density).

• Against solprop: H2 b = 5890 m^-1 (58.90 cm-1) and d = 5.0 m^-1 (0.050 cm-1) vs Stoicheff B_0 59.3392, D_0 0.04599 cm-1 (solprop’s are fitted values, Belli 2015); D2 b = 2930 m^-1 (29.30), d = 2.1 m^-1 (0.021) vs 29.9105, 0.01134 (solprop’s D2 d is 1.85 x Stoicheff’s). optmat’s raman.toml uses weber_1979’s copies (= Stoicheff).

• Status: verified (2026-09-27).

TC-588 keijser_1974 (Keijser et al., Physica 76, 585 (1974)) (2026-09-27)

• Transcribed: Table I (p. 595, JSON; image): HWHM coefficients Delta nu_1/2 / rho, GHz per 0 C amagat, 293 K: table1_H2 (5: S0(0)-S0(4), normal H2), table1_D2 (6: S0(0)-S0(5), normal D2), primary, sigma column; table1_H2_cooper (2, Ref. 17) and table1_H2_gupta_may (1, Ref. 18), reproduced. HD, Tables II-VI: notes.

• FWHM/HWHM: HALF widths. Eq. (6)-(7), pp. 592-593: “Delta nu_1/2 is the half-width (half the width at half intensity)”; appendix p. 605 the same.

• Dicke: “unimportant at pressures above 25 atm” (p. 594); all data above; no term.

• Structural fix: the S0(1) literature cell holds two values (Refs. 17, 18) run together; split at the note letters.

• Checks: Table III cross sections follow from Table I via Eq. (8) with n per 0 C amagat and cyclic frequency (0.40, 4.96, 1.12 A^2).

• Finding: Table VI’s caption prints tau = 1.18e-12 s; the text and Figs. 19-20 give 1.18e-13 s (caption misprint, no data affected).

• Re-points (in this extraction’s records): smyth_1987/keijser_S_branch -> keijser_1974 (its 2.80 … 0.93e-3 cm-1/amagat are Table I’s nD2 GHz values converted, digit for digit); edwards_1991/table7_knaap and table8_knaap -> keijser_1974 (they are twice Keijser’s HWHM, converted to cm-1, every row: H2 2.802, 3.469, 2.468, 2.535, 1.534 -> 2.8, 3.5, 2.5, 2.5, 1.5; D2 5.604, 4.470, 4.136, 3.402, 2.869 -> 5.6, 4.5, 4.1, 3.4, 2.9; FWHM per amagat printed as per bar); knaap_1979 notes updated (confirmed).

• Against solprop: D2 rotational width 131.96 MHz/amagat (Edwards S0(0) as FWHM) vs Keijser S0(0) 0.084 GHz/amagat HWHM = 168 MHz/amagat FWHM at 293 K (solprop 0.79 of it). H2: solprop 114 MHz/amagat (herring_1986 S(1) FWHM, 295 K) vs Keijser S0(1) 0.052 GHz HWHM = 104 MHz/amagat FWHM (293 K).

• Status: verified (2026-09-27).

TC-589 van_den_hout_1980 (Van den Hout et al., Physica A 104, 509 (1980)) (2026-09-27)

• Transcribed (JSON-only; images checked): Table I (p. 526) HWHM coefficients (MHz m3/mol = 1/44.62 MHz/amagat) per temperature: H2 at 176, 137, 77.8, 52.7, 35.0, 24.8 K (4, 4, 3, 2, 2, 2 lines), D2 at 148.5, 77.8, 42.9, 28.3 K (5, 4, 3, 2), primary, sigma column; the 293 K rows (H2 5, D2 6) reproduced from keijser_1974 (note b; equal to Keijser x 44.62 to the printed digits). Table II (p. 528) the pure-modification limits oH2, pH2 at 77.8 and 24.8 K, pD2 and oD2 at 28.3 K (primary; the 293 K oH2, pH2 rows reproduced from keijser_1974), ortho_para stated. Table V (p. 533) line shifts (raman_line_shift, MHz m3/mol): H2 at 176-20.2 K (8 temperatures), D2 at 148.5-28.3 K (4), primary, no errors; 293 K H2 reproduced (Cooper et al. 1970). Parenthesised shifts (H2 S0(3) 176, 137 K; D2 S0(4) 148.5 K) are excluded_rows.

• FWHM/HWHM: HALF widths: footnote p. 510 “The halfwidth indicates half the (full) width at half height”; Eq. (9) p. 521.

• Dicke: removed with literature diffusion constants (Eq. 5, pp. 518-519).

• Shift sign: negative = away from the laser (larger Raman shift); herring_1986 prints the 77.8 K values with the opposite (Raman-shift) sign.

• Checks: Table III’s cross sections follow from Table I (0.57e-20 m2 at 77.8 K).

• Doubt: the meaning of the parentheses in Table V (not stated).

• In another extraction’s record, re-points for review: herring_1986/table5_van_den_hout_295K (84, 104 MHz/amagat FWHM) is keijser_1974’s Table I (via this Table I, note b) doubled: reproduced_from should be keijser_1974 (agreement: 2 x 0.94 x 44.62 = 83.9, 2 x 1.17 x 44.62 = 104.4); table5_van_den_hout_80K (63, 99) -> van_den_hout_1980 (Table I 77.8 K, 0.70, 1.11 -> 62.5, 99.1 FWHM; +-1 = 2 x 0.01 x 44.62); table6_van_den_hout_80K (-22.3, -17.8) -> van_den_hout_1980 (Table V 77.8 K, 0.5, 0.4 MHz m3/mol, sign reversed: 22.3, 17.8). herring’s Cooper 295 K datasets agree with keijser_1974’s literature column (84/2 = 42, 105/2 = 52.5 MHz HWHM).

• belli_2015 (this extraction’s record): its rotational_T2 S(1) law (6.15 MHz amagat, 114 MHz/amagat) is herring_1986’s Table IV A and Table V S(1) at 295 K, not van den Hout’s (notes updated).

• Status: verified (2026-09-27); the herring_1986 re-points applied in review (TC-586).

TC-590 murray_1972 (Murray & Javan, J. Mol. Spectrosc. 42, 1 (1972)) (2026-09-27)

• Transcribed (JSON-only; images checked): Table II (p. 11) broadening, 10^-3 cm-1/amagat at 25 C: table2_H2 (4, Q1(0)-Q1(3)), table2_D2 (3, Q1(1)-Q1(3)), primary; May et al. (4) and the theory of Ref. 32 (4) reproduced. Table III (p. 11) shifts: linear a (H2 4, D2 3; primary), quadratic a and b (H2 Q1(0), Q1(1); check, term), May et al.’s quadratic a, b (3 each; reproduced). Formula diffusion_D0.

• FWHM/HWHM: FULL widths: “line width (full width at half-maximum)” (p. 2), “In this figure and in the remainder of the paper linewidths …” (p. 3), “Figure 5 shows the measured full width at half maximum” and the Q1(1) coefficient is the slope of that plot (p. 7). Fig. 5’s Doppler marks (0.037, 0.32 cm-1) are the FWHM Doppler widths of H2 Q1(1) at 298 K (computed 0.036, 0.320). The appendix’s “halfwidth” is the HWHM of the model profiles only.

• Dicke: not modelled in the forward-scattering slopes; D_0 = 1.346 (H2, text; 1.36 in Table I), 0.952 (D2 = 1.346/sqrt 2) cm2 amagat/s, from Harteck and Schmidt (D_0(H2) not reproduced to its third digit: 1.344 or 1.355 from 1.396 at 785 Torr, 20 C, with or without the stated T^1/2 scaling).

• FINDING / DOUBT (for review): as FWHM the H2 values agree with later FWHM measurements within ~15 % (bischel_1986), but the D2 values (1.4, 2.2, 2.6) are half of every later FWHM (russell_1987 2.63, 3.91, 4.11; ottusch_1988 Q(2) 4.0e-3) and equal to smyth_1987’s HWHM. smyth_1987 printed them as HWHM, russell_1987 as FWHM. The paper itself gives no reason to treat D2 differently. Recorded as FWHM (its words); the D2 numbers should not be used as FWHM until resolved.

• Re-points (in this extraction’s records), all to murray_1972:

  • bischel_1986 table1_B_murray_javan (66.0, 45.0 MHz/amagat FWHM = 2.2, 1.5 x 29.98), table2_C_murray_javan (-65, -90 = the QUADRATIC-fit a, not the linear a), table2_D_murray_javan (0.174, 0.135), table4_average (list).

  • hanna_1986 linewidth_D2: 70 MHz/atm does NOT follow from 2.2e-3 cm-1/amagat (66 MHz/amagat, 60.4 MHz/atm at 25 C).

  • russell_1987 table1_murray_javan_a and smyth_1987 table3_murray_javan: digit- identical; width changed to “fwhm” (from “not stated” and “hwhm”), the original’s word, with the doubt in notes.

  • bischel_1986b formula line_shift_eq9 and ottusch_1988 shift_H2: FINDING: D = 0.174 MHz/amagat^2 used for Q(1) is Murray and Javan’s Q1(0) b; Q1(1)’s is 0.135 (390 MHz = 0.013 cm-1 at 100 amagat). ottusch_1988 shift_D2 (-50 MHz/amagat) = linear a of D2 Q1(2), -51.0 (2 %).

• Status: verified (2026-09-27) as printed; open: the D2 widths as FWHM (TC-586).

TC-591 komasa_2011 (Komasa et al., J. Chem. Theory Comput. 7, 3105 (2011)) (2026-09-27)

• Transcribed: Table 4 (p. 3111): v = 0 -> 1 vibrational_term_value of H2 (theory check, duplicate of Table 6; experiment reproduced, Stanke et al. 2008) and D2 (theory primary, experiment reproduced, Bubin et al. 2010). Table 6 (p. 3112): H2 G(v) - G(0), v = 1-14 (14, primary). Table 7 (p. 3113): H2 raman_shift theory (20: S0(0-5), Q1(1-4), S1(0-3), Q2(1-3), S2(0-2)) and experiments (Jennings-Brault 6, Salumbides 6, Bragg et al. 14; reproduced). Table 8: D2 theory (18: S0(0-6), S1(0-3), O1(2-4), Q1(1-4)) and experiments (Jennings et al. 7, McKellar-Oka 11). Concise uncertainties converted to sigma.

• Structural fix: Table 7’s S0 block collapsed into one row with whole columns run together and Ref. 53’s column split over two cells; parsed in the script, counts checked (6 each).

• What is tabulated: Tables 1-2 = D_vJ, the dissociation energies from every bound level (302 H2, 598 D2), the zero = the dissociation limit (D_00 = 36118.0696 and 36748.3634 cm-1); E(v,J) - E(0,0) = D_00 - D_vJ. Totals; the breakdown and per-level uncertainties are in the SI (missing).

• NOT TAKEN (vocabulary): Tables 1-3 and 5 (level dissociation energies, D_0, the H2 v = 0 rotational term values) have no quantity. A quantity for rovibrational level energies (v, J, the zero) is needed; the library tables need structural fixes for 18 (H2) and 33 (D2) levels in merged rows (listed in the record).

• Check: every theory value taken is a difference of Tables 1-2 to +-0.0001 cm-1.

• Compare: piszczatowski_2015 and puchalski_2016 are helium polarizability papers (no H2 levels): nothing to compare. Stoicheff’s lines agree within his stated errors; bischel_1986b’s 4155.25 agrees with theory 4155.2538.

• Against solprop: H2 vibrational frequency 7.8268e14 rad/s = 4155.0 cm-1 (the Q(1) line, 4155.2538 theory); D2 5.6265e14 rad/s = 2987.0 cm-1 (Q(2) 2987.2934).

• Status: verified (2026-09-27); open: a quantity for rovibrational level energies (Tables 1-3, 5).

TC-592 rouille_1992 (Rouille et al., J. Mol. Spectrosc. 154, 372 (1992)) (2026-09-27)

• Transcribed: Table II (p. 377): 1-0 band ^SS (39) and ^OO (30) triplet lines (primary, +-1e-3 as weighted); Table V (p. 381): Q(N) lines of the 1-0 (22), 2-1 (20) and 3-2 (6) bands, precision column; Table IV (p. 379): calculated QQ triplets (this work 9, check; Dang-Nhu et al. 8, reproduced). Constants (rotational_constant, rows v): Table I v = 0 this work (B, D, H, lambda, lambda’, lambda’’, mu, mu’, mu’’) and Zink & Mizushima (8, reproduced); Table III v = 1 this work (B, D, lambda, lambda’, mu, mu’) and Refs. 6, 7, 16 (reproduced); band origins nu_10 (this work, Refs. 7, 16), nu_21, nu_32 as raman_shift rows “1-0” etc.; Table VI v = 2, 3: B primary (fitted), D, lambda, lambda’, mu, mu’ check (extrapolated linearly; reproduced from v = 0, 1). Fixed values (a, b and Table VI’s H, lambda’’, mu’’, mu’’’) not written.

• Structural fix: Table III’s primed v = 1 labels misread (\lambda_i, \mu_i’…).

• Formulas: eq5_levels (Eqs. 5-10) reproduces Table II’s O - C within 1e-4 and Table IV’s calculated lines exactly; eq11_q_branch reproduces Table V within 3e-3.

• Linewidths: none tabulated (Voigt fits only).

• Against yu_2012: B_0, lambda_0, gamma_0, B_1 agree to 3e-7 cm-1; hajigeorgiou_2013’s B_2, B_3 within 2e-7.

• Status: verified (2026-09-27).

TC-593 brown_1992 (Brown, Rich & Nibler, J. Mol. Spectrosc. 151, 482 (1992)) (2026-09-27)

• Transcribed: Table I (p. 486): 30 ^SS lines S(J,N), N = 1-19: corrected (simulation, primary) and observed (CARS maxima, check); +-0.005 absolute (p. 485). Intensities, assumed linewidths: notes.

• Formula: eq2_levels (constants not printed; Johns & Lepard). Checked with rouille_1992’s v = 0 constants: the corrected - calculated column to +-0.0005 cm-1. Finding: Eq. (2)’s F3 as printed is wrong for N = 1 (the square-root sign): 1.085 cm-1 off for S(0,1); the paper’s own calculation was right.

• yu_2012 (this extraction’s record): notes name brown_1992 and rouille_1992; nothing reproduced.

• Status: verified (2026-09-27).

TC-594 Solids’ nonlinear data: Milam & Weber 1976 in the silica Kerr fit (2026-09-27)

• Where: data/solid/kerr/SiO2.toml and .json, docs/silica.md, docs/corrections.md; hamam_2018 and stuart_1996 (re-points made in review), after the extraction of adair_1987, milam_1976, weber_1978, liu_1978, liu_1979, du_1994, lenzner_1998, liu_2005, mero_2005 and blow_1989 (their entries follow).

• Decisions:

  • Added to the Kerr fit: milam_1976/gamma_SiO2, 2.73 ± 0.27e-16 cm²/W at 1064 nm by time-resolved interferometry with 125-ps pulses (raman = full), under the fit’s rule of every measured self coefficient with a known pulse length. Its own calibration scale takes 1.052.

  • Not added: adair_1987/n2_SiO2 (0.85e-13 esu). It equals the fitted adair_1989/n2_SiO2 to the digit, from the same apparatus and calibration, so it is very likely one measurement quoted twice. Also not added: weber_1978’s silica, which reprints Milam & Weber.

  • The refit: N rises from 2.357e-20 to 2.379e-20 m²/W (+0.9 %). n2 at 800 nm is 2.52 ± 0.10e-20 m²/W (was 2.50), and f_R stays 0.15 ± 0.03, set by its prior. χ² is 37.5 for 35 degrees of freedom. Milam’s recommended values are now 11-16 % above the fit and Santran et al.’s 31 %. Luna’s constant 2.7e-20 is 7-12 % above.

• Raman fraction, findings not used:

  • Weber et al.’s long-pulse electronic fraction f_e = 0.74 for silica (Table 3, from Heiman et al.’s Raman spectra) implies f_R = 0.26.

  • Blow & Wood’s 12.2/32 fs response has α = 0.7 (f_R = 0.3 in the field-squared response, 0.222 in their envelope equation), and its three numbers were chosen to agree with gain data, not fitted.

  • The prior stays Stolen et al.’s 0.18 ± 0.03, which covers these at about two sigma.

• Re-points applied in review:

  • hamam_2018/threshold_NA0126 and threshold_NA0255 → liu_2005. Liu et al. print energies only, so Hamam’s intensities are his own conversion. The “NA 0.225” misprint originates in Liu et al. (p. 202).

  • model_reduced_mass keeps its citation: liu_2005 has no such value.

  • stuart_1996: its notes name du_1994.

• Status: decided (2026-09-27).

TC-595 adair_1987 (Adair, Chase & Payne, JOSA B 4, 875 (1987)) (2026-09-27)

• Transcribed: Table 2 (tbl_cd009634988d, p. 879): n2 (10^-13 esu, n = n0 + n2 <E^2>) of 27 glasses by nearly degenerate three-wave mixing at 1.064/1.071 um: n2_* (27, primary, relative 0.15 “accurate to within 15%”, level not stated, part electronic_vibrational: the paper excludes electrostriction and heating, Delta^-1 ~ 0.5 ps, nuclear ~25 %); literature column: weber_1978_* (7: LHG-5, LHG-6, Q-88, FR-5, ED-2, SiO2, BK7; reproduced from weber_1978) and moran_1975_* (2: C-2828, SF-6; reproduced from Moran et al. 1975 and weber_1978); calculated column calc_* (27, reproduced from Stokowski et al., LLNL M-95, 1981). Formula bgo_10a (Eq. 10a, K = 68, constant 1.52).

• Checked: Table 2 image, all cells. The literature column is weber_1978 Table 1 converted by Eq. (18) with its n_D to the printed digits (ED-2 uses Weber’s reference-a 3.77, not reference-d 4.05); the two “Moran” values are Weber’s rescaled (to ED-2 = 4.05) entries, not Moran’s own numbers. Eq. (10a) reproduces 0.83 for fused silica with boling_1978’s n_d, nu_d (1.458, 70); the paper prints no n_d, nu_d.

• Doubt / findings: (1) the stated calibration (“equating our average value of n2 for those samples to theirs”, seven TRI standards) is not reproduced by the printed values: averages 1.356 against 1.286 (5 % high; mean ratio 1.064). (2) Table 1 prints “K-133”, Table 2 “E-133” (registered E-133, the O-I E series); Table 1 “SF6”, Table 2 “SF-6”. (3) Table 1’s BK-7 composition includes “4 Nd2O3” and sums to 102.9 mol % (99.3 with 0.4): recorded as BK7 (Schott) with the doubt in the notes; a separate Nd-doped BK-7 material may be preferred. (4) The glass registry entries ED-2, FR-5, LHG-5, LHG-6 say “maker not stated” (Boling); this paper names Owens-Illinois and Hoya.

• Status: open (the calibration discrepancy, the BK-7 identity).

TC-596 milam_1976 (Milam & Weber, J. Appl. Phys. 47, 2497 (1976)) (2026-09-27)

• Transcribed: Table I (tbl_9e8c390f5b4c, p. 2499, JSON only): gamma (10^-16 cm^2/W, Delta n = gamma I) with +- as gamma_* (7, primary) and n2 (10^-13 esu) as n2_* (7, check) for BK7 (Schott BK 7), FK-5 (Hoya FC-5), SiO2 (Dynasil 4000), FK-51 (Schott), ED-2 (Owens-Illinois), FR-5 (Hoya), KDP (Lasermetrics); linear polarization, 125-ps pulses, 1064 nm, TRI; part electronic_vibrational (the paper: electrostriction and thermal much slower; fringe shift follows the pulse). Footnote 8: MgF2 gamma = (0.30 +- 0.1) x 10^-16 cm^2/W (Weber and Milam, unpublished) as gamma_MgF2_unpublished (check).

• Checked: image, all cells; Eq. (2) reproduces every gamma from its n2 with n = n_D (KDP with the e-ray index 1.468, so the beam was presumably e-polarized).

• Doubt / findings: (1) the footnote MgF2 value 0.30 is a factor 3 below weber_1978’s 0.92 +- 0.31 (Milam, Weber & Glass 1977). (2) FC-5 recorded as the registered FK-5 (Weber and Boling print FK-5 for this value), grade “Hoya FC-5”. (3) ED-2 n_D 1.567 here, 1.572 in weber_1978. (4) Eq. (3) prints T = 4(n + 1)^-2 (weber_1978 Eq. 16: 4n(n + 1)^-2).

• Status: verified (2026-09-27).

TC-597 weber_1978 (Weber, Milam & Smith, Opt. Eng. 17, 463 (1978)) (2026-09-27)

• Transcribed: Table 1 (tbl_b9afd7663851, glasses, 20 rows incl. ED-2’s second row) and Table 2 (tbl_279cf82b90e4, 18 crystals): gamma (10^-20 m^2/W) with +-, gamma_*; use by reference letter: milam_1976 (a; Table 2 d) reproduced; Weber et al. APL 1978 (b), Moran 1975 (c, rescaled to ED-2 = 4.05), Bliss 1974 (d; Table 2 a), Milam & Weber IEEE QE-12 1976 (e), Milam, Weber & Glass 1977 (Table 2 e) reproduced by citation; Milam & Smith unpublished (Table 1 f: Q-88, LG-812; Table 2 b: Al2O3, BeAl2O4, La2Be2O5:Nd, NaCl) primary. Table 3 (tbl_b4032b6777cc): n2(nuclear) (10^-14 esu, Eq. 19, part vibrational, primary, 10 glasses) and n2(total) (check, conversions of Table 1). Formula bgo_gamma (Eq. 24, K = 2.8e-18 m^2/W).

• Checked: images (all cells; “≈” of La2Be2O5 and CeF3 belongs to n_D, only in printed). Eq. (19) reproduces n2(nuclear) (two cells truncated, not rounded); Eq. (18) reproduces n2(total) except SF-6 (91.3 against 90.0); f_e = 1 - nuclear/total. Table 1’s reference-a entries equal milam_1976.

• Doubt / findings: (1) ED-4 is in Table 3 but not in Table 1; its n2(total) 14.1 equals ED-2’s Table 1 value converted (14.14): either a mislabel or an unsourced total. (2) The text’s “f_e ~ 0.6” against Table 3’s 0.57-0.81. (3) f_e (fused silica 0.74, i.e. a Raman share 0.26 of the long-pulse n2) has no quantity: in notes/printed only; the silica Kerr fit uses f_R = 0.18 +- 0.03.

• Status: open (ED-4).

TC-598 liu_1978 (Liu, Smith, Lotem, Bechtel, Bloembergen & Adhav, PRB 17, 4620 (1978)) (2026-09-27)

• Transcribed: Tables I (355 nm) and II (266 nm): beta (cm/MW) per row, 39 datasets (26 primary, 9 check: other polarization, sample length, F-centre sample, the silica and quartz 266-nm limits; 4 excluded upper bounds), relative % per row + systematic 0.43 (“the sum”, level not stated); band gaps (16, kind not stated), P_cr (9, check, W with scale 1e3), n (27 files per material and ray, check), m*/m (14, carrier reduced, check). Formula keldysh_gamma_n. 30-ps pulses, reflection losses removed (Eq. 5, 9-10).

• Checked: images of both tables; footnotes of Table I from the rendered page (pdf p. 6). Eq. (4) reproduces the 266-nm beta from Table II’s E_g, m*/m, n to 0.2-0.7 % for nine materials only with (8 pi/(n0 c))^N (the printed (8 pi/n0)^N lacks 1/c^N: a factor c^2); KDP +6 %, ADP +8 %, NaBr -41 %, fused silica -35 %. P_cr of KI scales as lambda^2 between the tables. Relative ratios RbBr/KI, RbI/KI.

• Doubt / findings: (1) The missing c in Eq. (4) (as printed also in liu_1979). (2) NaBr and silica fits not reproduced with the printed inputs. (3) Fused silica and quartz at 266 nm (4.5e-5 cm/MW, no +-) are the detection limit (liu_1979). (4) “A2O3” label misprint (sapphire). (5) Axis assignments of the KDP isomorphs (“45° z cut”, E “z axis” -> e; “⊥z” -> o) and of c-axis sapphire/quartz (o) are the reading made at extraction.

• Status: open (Eq. 4’s c; NaBr, silica).

TC-599 liu_1979 (Liu, Yen & Bloembergen, Appl. Opt. 18, 1015 (1979)) (2026-09-27)

• Transcribed: Table I (tbl_14fb6f23a7e6): beta at 355/266 nm: fused silica 266 nm 1.7e-5 +- 20 % (+ 43 % systematic; primary), CdF2 4.17e-5 +- 15 % and 1.60e-3 +- 5 % (primary), 7 upper bounds (MgF2, SrF2, BaF2 at both, LiYF4 at 266; excluded); band gaps of MgF2 11.8, BaF2 9.06 (reproduced from Strehlow & Cook 1973), CdF2 ~6, LiYF4 ~11, SiO2 7.8 (SrF2 “?” not recorded).

• Checked: image; the extraction drops the superscript of 10^-6 (read as “10-6”).

• Doubt: the fused-silica value supersedes liu_1978’s 4.5e-5 (the paper says so).

• Status: verified (2026-09-27).

TC-600 du_1994 (Du, Liu, Korn, Squier & Mourou, APL 64, 3071 (1994)) (2026-09-27)

• Transcribed: no datasets (thresholds are Fig. 2 only; the text gives only the rms threshold field ~5e7 V/cm at 1 ps, no quantity). Formula thornber_alpha (Eq. 3; E_i 30, E_p 3.2, E_kT 0.01 MV/cm; v_drift 2e7 cm/s; the factor 1.7). Notes: breakdown criterion eta tau_p = 18 / 30, n_th, tunnelling-rate estimates, collision time < 0.4 fs (Fischetti), Corning 7940, 780 nm, 150 fs - 7 ns, 1-on-1, bulk.

• Findings: ln(1.6e21/1e10) = 25.8, not “~30”; the critical density at 780 nm is 1.83e21 cm^-3, not 1.6e21; E_kT l_kT = 0.5 meV, not kT (kT with 5 A gives 0.52 MV/cm): the printed E_kT does not follow from the stated rule; U_i = E_i l_i = 9 eV and E_p l_p = 0.16 eV do.

• Status: open (E_kT).

TC-601 lenzner_1998 (Lenzner et al., PRL 80, 4076 (1998)) (2026-09-27)

• Transcribed: inline: avalanche coefficient alpha (4 +- 0.6 cm^2/J fused silica; 1.2 +- 0.4 cm^2/J Corning 7059, primary), sigma_6 = 6 x 10^(8 +- 0.9) and sigma_3 = 7 x 10^(17 +- 0.5) cm^-3 ps^-1 (cm^2/TW)^k (multiphoton_ionization_cross_section, per volume, primary; exponent uncertainty in notes), band gaps ~9 and ~4 eV (check), the Keldysh masses 0.5 m (Fischetti) and m (assumed). Formula rate_equation (Eq. 1). Corning 7059 registered.

• Checked: solving Eq. (1) (Gaussian, peak fluence, n_th 1e21) gives F_th(FS) = 1.58 J/cm^2 at 10 fs (text: ~1.5 J/cm^2 for tau <= 10 fs); the printed photoionised fractions are reproduced to within a factor 3-4 (FS) and ~20 % (BBS) (pulse shape not stated).

• Doubt: F_th ~ 1.5 J/cm^2 not recorded as a dataset (it spans 5-10 fs).

• Status: verified (2026-09-27).

TC-602 liu_2005 (Liu, Jiang, Sun, Wu, Yang & Gong, J. Opt. A 7, 198 (2005)) (2026-09-27)

• Transcribed: threshold energy 0.18 +- 0.01 uJ at 400 fs, effective NA 0.255, bulk, single shot, plasma luminescence (damage_threshold_energy, primary); model inputs (check, assumed): n2 3.54e-16 cm^2/W, E_g 9 eV, sigma_6 9.8e-70 s^-1 cm^12/W^6, tau_c 2.33e-14 s (Sudrie et al. 2002), rho_at (Ward & Berge 2003). Formula rate_equation.

• Erratum: rho_at printed 2.1 x 10^21 cm^-3 -> 2.1 x 10^22 (the paper’s own ratio rho_at/rho_c ~ 12 with rho_c = 1.742e21 cm^-3 at 800 nm; couairon_2005 prints 2.1e22); on the dataset and as a formula correction.

• Findings: sigma = 1.55e-18 cm^2 is not reproduced by its formula with tau_c = 2.33e-14 s (1.19e-18 with n0 = 1.45); the paper prints “effective NA = 0.225” once (p. 202), 0.255 elsewhere (the origin of hamam_2018’s 0.225); hamam_2018’s Table 2 intensities are not in this paper (figure of energies only).

• Status: corrected (2026-09-27; rho_at); open (sigma).

TC-603 mero_2005 (Mero, Liu, Rudolph, Ristau & Starke, PRB 71, 115109 (2005)) (2026-09-27)

• Transcribed: Table I (n0 at 800 nm: check; E_g: primary; D in notes), Table II (alpha, beta_m as multiphoton_ionization_cross_section in cm^(2m-3) fs^(m-1)/J^m, T as electron_trapping_time, all primary; m_r/m0 as effective_mass, check) for the IBS films TiO2 (registered TiO2_amorphous), Ta2O5, HfO2, Al2O3 (Al2O3_amorphous), SiO2 (form film). Table III kappa in notes. Formulas scaling_law (Eq. 3) and keldysh_mpa (Eq. 2).

• Structural fix: Table II’s beta_m cells are extracted as “1.531023” (x read as 3, superscript lost): parsed in the script, checked against the image.

• Checked: Eq. (2) inverted reproduces Table II’s m_r (26.9, 1.96, 1.56, 5.47, 2.24 vs 27.0, 1.9, 1.6, 5.4, 2.2); beta_3/beta_6 = 1.5e42 (J/cm^2 s)^3 (text ~1e42, TiO2 over SiO2); alpha = 30/E_g + 5 from 14.1 to 8.6.

• Doubt: beta_m is a carrier-generation coefficient per volume (the paper calls it “MPA coefficient”): recorded as multiphoton_ionization_cross_section, not multiphoton_absorption_coefficient. Thresholds are figures only.

• Status: verified (2026-09-27).

TC-604 blow_1989 (Blow & Wood, IEEE JQE 25, 2665 (1989)) (2026-09-27)

• Transcribed: raman_fraction 1 - alpha = 0.3 (printed alpha = 0.7, the instantaneous weight), raman_response_time tau1 = 0.0122 ps, tau2 = 0.032 ps; formula response (Eqs. 5, 8).

• Checked: int g_R = 1; gain peak 13.08 THz (the paper’s Stokes band ~13 THz); Re response varies 24 % (Eq. 5) / 18 % (Eq. 8) over 0-13 THz (“about 20 percent”).

• Findings: this is the origin of 12.2 fs / 32 fs, but the numbers are chosen (“give a Raman gain consistent with” Stolen & Lin 1978, Spirit & Williams 1988, Gordon 1986), not fitted to a named spectrum. The Raman fraction is 0.3 in the field-squared response and 0.222 in the envelope equation (factor 2/3, Eq. 8); neither is lin_2006’s “about 0.2” or stolen_1989’s 0.18.

• Status: verified (2026-09-27).

TC-605 Re-points of the records that reprint the papers of TC-594 (2026-09-27)

• milam_1998/milam_weber_1976 -> milam_1976 (2.73 +- 0.27, agrees).

• white_1984/previous_1064_SiO2 -> weber_1978, milam_1976: DISAGREES in the uncertainty (printed 2.7 +- 0.5; the original 2.73 +- 0.27).

• adair_1989/n2_tri_SiO2 -> milam_1976 (0.95, agrees); technique cites adair_1987.

• boling_1978 n2_measured_table3_{BK7, ED-2, FR-5, SiO2, FK-5, FK-51} -> milam_1976 (all agree); EV-1, LHG-5, LHG-6 equal weber_1978’s reference-e values (Milam & Weber IEEE 1976; EV-1 confirms the existing 0.9 -> 0.09 erratum); EY-1 is Bliss et al.’s value (weber_1978 reference d), not Milam and Weber’s; the “fluoro-phosphate” row (n_d 1.492) equals A86-82 (0.712 +- 0.142): identity for review.

• ensley_2019 lit_BK7_l -> milam_1976 (3.43, agrees), lit_BK7_m -> adair_1987 (3.6 = 1.30e-13 esu converted, agrees).

• taylor_1988 liu_266_*: SiO2, BaF2, SrF2, MgF2 -> liu_1979; CaF2, LiF -> liu_1978 (all agree); its band gaps match Liu’s except SrF2 9.6.

• brimacombe_1989: liu_1979_266 -> liu_1979 (1.7 +- 0.3, the +-20 % rounded); liu_1978 -> liu_1978 (the 355-nm bound printed 1.3 against Liu’s 1.25; the 266-nm “<” added); band_gap_liu_1978 -> liu_1978.

• dragomir_2002: liu_1979_SiO2 -> liu_1979; liu_1978_1979_SiO2 and _SiO2_quartz -> liu_1978 (the “<4.5” is liu_1978’s 4.5e-5, printed there without “<”); liu_1978_Al2O3 -> liu_1978.

• couairon_2005: sigma6_lenzner -> lenzner_1998: DISAGREES by 1.0e7 (Lenzner’s per-volume 6e-52 cm^-3 s^-1 (cm^2/W)^6 is 2.9e-74 per atom with rho_at = 2.1e22; Couairon prints 3e-67); band_gap_78 -> liu_1978, liu_1979; model_band_gap’s Lenzner citation -> lenzner_1998.

• jing_2012 sigma6_lenzner and schaffer_2001 sigma6_lenzner_SiO2 -> lenzner_1998 (agree); jing_2012 lidt_typical’s Lenzner citation -> lenzner_1998 (Lenzner prints no 2.8 J/cm^2).

• hollenbeck_2002 and lin_2006 blow_wood_times -> blow_1989 (agree); lin_2006 f_R_literature -> stolen_1989, blow_1989 (Blow prints alpha = 0.7).

• dubietis_2019 damage_scaling (formula) notes -> mero_2005 (same coefficients).

• No re-pointed dataset is named in a fit configuration; all were already reproduced (or excluded), so no use changed.

• Status: decided (2026-09-27).

TC-606 Gases: the new data as validators of the fits; the DOSD sums against the fits (2026-09-27)

• Where: data/gas/fits/{H2,CH4,Xe,SF6,CO2,Ar}.toml, their stored fits and robustness records (refitted; the models are unchanged, only the validation is new); olney_1997 (an erratum); hohm_1993, hohm_1994b, hohm_2013, kumar_1985b, sakamoto_2010 (re-points made in review), after two extractions’ reviews (their entries follow and precede).

• Validators added (compared with the fit, not fitted):

  Gas	Dataset	Against the fit
  H2	may_2009/recommended_H2, static dielectric A_eps at 273 K (1σ 84 ppm)	−18 ppm
  CH4	thomas_1977/moments, S(−2) and S(−4) of Thomas & Meath’s DOSD	+0.07 %, −0.32 %
  Xe	hohm_1994c/alpha_294.26_Xe, 325-633 nm at 294 K	+0.15 %
  SF6	hosticka_1974/A_eps_SF6, static dielectric, 323-374 K	+0.60 %
  CO2	bose_1970/A_eps_CO2, static dielectric, 303-323 K	+0.13 %
  Ar	bose_1970/A_eps_Ar, static dielectric, 323 K	−0.02 %

  • May et al.’s value confirms the H2 fit’s static limit (on Raj et al.’s ab initio polarizability) to 18 ppm, within their 84 ppm.

  • Hohm & Trümper’s xenon lies 0.15 % above the fit, and Hohm’s other 1994 xenon (hohm_1994b, fitted with its level free) 0.47 % above: the two measurements, from one laboratory and year, differ by 0.31 %, eleven times the stated uncertainty. The fit’s level rests on the other xenon data and is not changed.

• The DOSD sums against the fits (electronic S(−2), the static electronic polarizability): CH4 (Thomas & Meath) +0.07 %, CO (Jhanwar & Meath) +0.05 %, CO2 (Jhanwar & Meath, ultraviolet) −0.10 %, SF6 (Kumar, Fairley & Meath, ultraviolet) −0.07 %, Xe (Hohm & Trümper) +0.17 %. Five independent constrained-DOSD evaluations agree with the fits’ static limits within 0.2 %.

  • The higher sums (S(−4) and above) test the fits’ effective-oscillator shape rather than the data. They agree within a few per cent for CH4, CO and CO2. SF6 is the exception: Kumar et al.’s S(−4) is 70 % above the fit’s. The DOSD’s dispersion is 5.7 % above the fit at 300 nm, and the authors themselves find it 1 % high at 436 nm. The fit follows the measured dispersion (Vuković, Burns, Swift), so the difference is the DOSD’s.

  • Only S(−2) and S(−4) of CH4 enter as validators; the other DOSD sums are recorded here, not as validators, because their mean deviation would be dominated by the orders the effective oscillators do not represent.

• Not used:

  • Hohm & Kerl’s α(0, T) and α(λ, 0 K) (hohm_1990b), extrapolations of their own fits.

  • Hohm & Kerl’s CH4 α(633 nm, T) (hohm_1991), a temperature series (the fits are at room temperature). Its 296 K value is 0.15 % above hohm_1993 and hohm_1990.

  • The CO fit’s validator zhao_2026/kumar_meath_1994_moments_CO is kept: it is digit-identical to kumar_1994/moments, now its reproduced_from.

• Olney et al.’s S(−6) for CH4: an erratum in olney_1997 corrects the reprint’s 289.3 to Thomas & Meath’s 298.3 (transposed digits; p. 121 of the original).

• Re-points applied in review: hohm_1993 (2 datasets) and hohm_1994b (1) → thomas_1977; hohm_1994b (1) and hohm_2013 (dosd_CO, dosd_CO2) → jhanwar_1982; hohm_2013/dosd_CH4 → thomas_1977; hohm_2013/dosd_SF6 → kumar_1985b; kumar_1985b/total_polarizability_hosticka → hosticka_1974 (44.27 au = 6.560e-24 cm³); sakamoto_2010/discrete_N2 → chan_1993_n2 (Berkowitz rescales Chan et al.’s per-state values by 1.034). Values equal.

• Findings recorded, not acted on: Olney et al.’s S(−2) of the published spectra, recomputed from the curated tables, is 4.7 % high for N2O (19.32 against 20.23) and 3.2 % low for CH4 (17.06 against 16.52); CO, N2 and CO2 agree to 1 %. topfer_2023 quotes Olney’s 20.23 for N2O.

• Status: decided (2026-09-27).

TC-607 chan_1992_h2 (Chan, Cooper & Brion, Chem. Phys. 168, 375 (1992)): H2 Lyman and Werner bands (2026-09-27)

• Transcribed: Table 1 (tbl_aae134e5c906, Lyman B-X v’ = 0-22; six columns: present 23 values, Geiger & Schmoranzer 20, Fabian & Lewis 11, Hesser et al. 6, Haddad et al. 4, Allison & Dalgarno 23), Table 2 (tbl_254f5e9a82b9, Werner C-X v’ = 0-6; present 7, Geiger & Schmoranzer 7, Fabian & Lewis 6, Allison & Dalgarno 7), Table 3 (tbl_5acc9741b87e, band totals, 15 sources, 1-2 values each) as oscillator_strength with a label abscissa (v’; lyman/werner for the totals). Text: B’ v’ = 0 at 13.702 eV, 0.00384 (present) and 0.00292 (Chan’s conversion of Glass-Maujean’s A); the total below the IP, 0.836 (check).

• Uncertainty: “+-5% for fully resolved peaks, and +-7-15% for the partially resolved peaks” (p. 6); which peaks are partial is not said; 5 % stored, level not stated.

• Structural: “(0.0101)^a”, “(0.00308)^a” (interpolated, v’ = 14, 20) are stripped of parentheses and mark and excluded (excluded_rows); “0.0544a)” (Werner v’ = 3, Lyman v’ = 14 subtracted) stripped.

• Checked: every cell against the images. Present Lyman sum 0.30117 (printed 0.301); Werner 0.3218 (text 0.322) + Allison-Dalgarno’s v’ = 7-13 0.019 = 0.341 (so the Werner total is partly theory). Eqs. (6), (7) (|R_e(r)| straight lines) reproduce Table 4’s present D_e(r_0) = 0.94 and 1.08 (0.9403, 1.0837) with Eq. (8), r_0 = 0.741 A.

• Not extracted: Table 4 (dipole strengths D_e(r_0) in au; no quantity; values in notes); Figs. 1-6 (the 11-20 eV df/dE spectrum and the transition moments).

• Finding: sakamoto_2010 lyman_H2 (and presumably werner_H2) from Berkowitz’s book Table 4.1 are Allison & Dalgarno’s (1970) theoretical band strengths (0.001689, 0.005790, 0.01156 … identical to Chan’s Allison-Dalgarno column), not a measurement.

• Doubt: none on the transcription; the 5 % stored under-states the partially resolved peaks.

• Status: verified (2026-09-27).

TC-608 chan_1993_co (Chan, Cooper & Brion, Chem. Phys. 170, 123 (1993)): CO 7-200 eV (2026-09-27)

• Transcribed: Table 1 (tbl_ca93596af562): low-resolution df/dE (1e-2/eV), 7-200 eV, 184 points (primary). Table 2 (tbl_889679627bd2): A-X v’ = 0-12, present (13, primary) and eight literature columns (Lassettre & Skerbele 13, Eidelsberg et al. 13, Lee & Guest 1, Rich 2, Field et al. via Kirby & Cooper 11, Hesser 6, Chantranupong et al. 8, Kirby & Cooper 11). Table 3 (tbl_05bec4dbd2ec): A-state totals, 12 sources. Table 4 (tbl_0aedd197bfd4): B, C, E v’ = 0, 1: present (6, primary), 5 literature rows, and 5 theory rows whose values are state sums (*_sum, rows B, C, E). Table 5 (tbl_d446b685ddb3): integrated strengths over 28 energy intervals 12.13-16.98 eV (interval_oscillator_strength; present primary 28, Stark et al. 7, Letzelter et al. 11). Text p. 11: 12-14 eV, present 0.640 (check), Berkowitz from Huffman 0.7921 and from Cook 0.8165 (reproduced).

• Uncertainty: discrete, “about 5% for resolved peaks and about 10% for unresolved” (p. 7), 5 % stored; no uncertainty stated for Table 1 or Table 5.

• Structural: Table 4’s Nielsen, Padial, Wood, Coughran, Rose values are printed centred between v’ = 0 and 1 (image): state sums, own datasets. Table 3’s “Lasscttce and Skcrbcle” is an extraction garble (image: Lassettre and Skerbele).

• Errata (3 values, 4 entries): Table 2 Field et al. v’ = 4 printed 0.0358 -> 0.0258 (column then sums to Table 3’s 0.187; smooth envelope). Table 5 “12.237-13.364” -> 13.237 (contiguous intervals; in the three interval datasets). Table 5 “15.085-15.296” -> 15.269 (next row starts 15.269; f/dE per eV 0.244, 0.247 against 0.213, 0.293 otherwise).

• Checked: column sums of Table 2 against Table 3: present 0.18074 (0.1807), Lassettre 0.19445 (0.1945), Eidelsberg 0.19406 (0.1941), Chantranupong 0.2250, Field 0.187 after the erratum; Kirby & Cooper sums to 0.1668 against their 0.1636 (unexplained, kept). Sums from Table 1 (trapezoid + the paper’s A E^-B tail, B = 2.243): S(0) = 9.610 (7-200 eV), 10.352 total (paper: 10.3 with 6.7 % above 200 eV); S(-1) 9.246, S(-2) 12.662 au (Olney et al. 1997 quote 12.64 au for “the originally published CO spectrum”), S(-3) 22.06, S(-4) 45.05, S(-6) 259.7. The paper prints no S(k).

• Not recorded as formulas: Eq. (2) (Field et al.’s |R_e| = 7.48(1 - 0.683 r)) and Eq. (3) (De Leon’s, 1.5741(1 - 1.17722 r + 0.35013 r^2)): other authors’ functions with no value here to check; at r = 1.128 A they give 1.72 and 0.185, so Eq. (3) as printed is in other units or misprinted. In notes.

• Doubt: Table 1 points 41.0 eV (11.69) and 43.0 eV (10.33) stand off their neighbours; kept. Olney et al. found the LR energy scale about 0.25 eV too high.

• Status: verified (2026-09-27).

TC-609 chan_1993_o2 (Chan, Cooper & Brion, Chem. Phys. 170, 99 (1993)): O2 5-30 eV (2026-09-27)

• Transcribed: no df/dE table (Figs. 1-3 only). Table 1 (tbl_64a7a5d7efc8, unlabelled, 9.75-12.07 eV): present (13), Huebner et al. (13), Ogawa & Ogawa (8) as interval_oscillator_strength over the printed ranges; Lewis et al. (2, isotopic O2), Buenker et al. (6), Yoshimine et al. (3), Li et al. (3) as band oscillator_strength (label rows E0-E2, Pi0-Pi2). Table 2 (tbl_41c9c9856c23, 12.070-18.287 eV): present (39), Huebner et al. (16). Text (pp. 3-9): Schumann-Runge continuum 6.56-9.46 eV, present 0.169 (primary, the only present value below 9.75 eV) and Lassettre 0.179; 9.46-10.7 eV 0.0185 / 0.020; to the IP 0.198; 12.10-14.04 eV 0.151 / Huebner 0.181; 12.07-16.53 eV 0.578 / Berkowitz 0.724 / Chan’s re-integrations of Matsunaga & Watanabe 0.587 (figures) and 0.685 (table) / Huffman 0.685; below 18 eV 1.13 (HR) / 1.12 (Brion 1979 LR).

• Uncertainty: +-5 % (p. 3), level not stated.

• Checked: images; Table 2 present 12.070-14.056 sums to 0.1511 (text 0.151), Huebner 0.1804 (0.181); to 16.481/16.581 eV 0.569/0.586 (text 0.578 at 16.53); 0.169 + Table 1 (0.0281) = 0.197 (text 0.198 to the IP).

• Not extracted: Huebner et al.’s SR continuum 0.161 and total 0.198 (ranges not given).

• Relation: kumar_2011_supplement O2 intervals j = 4, 7-11, 15-17 come from this paper (integrated by Kumar & Thakkar; not reprinted values): chan_1993_o2 may be cited there.

• Status: verified (2026-09-27).

TC-610 chan_1993_n2 (Chan, Cooper, Sodhi & Brion, Chem. Phys. 170, 81 (1993)): N2 11-200 eV (2026-09-27)

• Transcribed: Table 1 (tbl_0c46ead68b63): LR df/dE 11-200 eV, 177 points (primary). Table 2 (tbl_cffab8566e21): 45 present discrete strengths by energy 12.500-14.839 eV (primary; four braced blends joined structurally: 13.345, 13.760+ (13.760 and 13.785), 14.230, 14.720). Tables 3-7 (per state b, b’, c’, c, o): present (check; repeat Table 2) and literature columns (James, Zipf & McLaughlin, Carter, Lawrence, Ajello): 20 datasets. Table 8 (tbl_c43a8a42aa78): state totals, present (check) and 11 sources. Table 9 (tbl_21883bc6ed1a): 16 intervals 14.92-16.91 eV (primary). Text: below 15.56 eV 1.173 (present) / 1.153 (Berkowitz from Lassettre); 15.56-16.76 eV 0.319 / 0.3299 (Berkowitz from Carter).

• Uncertainty: Table 2 “about 5-10%” (strong peaks 12.40-13.27 eV) and “about 10-20%” (others): upper ends stored (0.10 by row, 0.20 otherwise). None stated for Tables 1, 9.

• Checked: images; S(0) from Table 1 = 9.721 (11-200 eV), 10.332 with the A E^-B tail (B = 2.283; paper 10.3 with 5.6 % above 200 eV); S(-2) = 11.654 au against Olney’s 11.54 for “the originally published spectrum” (1 %); S(-1) 9.208, S(-3) 17.69, S(-4) 29.82, S(-6) 100.4. Tables 3-7 present sums = Table 8 (0.2435/0.243, 0.2777/0.278, 0.1451/0.145, 0.2792/0.279, 0.0802/0.080).

• Doubts (no errata): (1) Table 2 vs Table 4 for b’ v’ = 23, 24: 0.0102, 0.00455 (Table 2) against 0.00897, 0.00363 (Table 4); Table 8’s 0.278 follows Table 4; Table 2’s 0.00455 repeats its v’ = 22 value. Both kept as printed. (2) Zipf & McLaughlin’s b column sums to 0.2601 against their Table 8 0.283; Ajello et al.’s b’ column to 0.3426 against 0.321 (their v’ = 7, 8 values look out of line).

• Status: verified (2026-09-27).

TC-611 chan_1993_co2 (Chan, Cooper & Brion, Chem. Phys. 178, 401 (1993)): CO2 6-203 eV (2026-09-27)

• Transcribed: Table 1 (tbl_b45cfc94562b): LR df/dE 8.53-203.00 eV, 162 points (primary). Table 2 (tbl_914f5351589b; the extraction labels it “Table 3” and detaches its caption into the footnotes: structural): 1Delta_u and 1Pi_g bands below 10 eV, present (primary, label rows) and Rabalais, Meyer & Lassettre, Inn et al. (= inn_1953), Wilkinson & Johnston. Table 3 (tbl_ae9d1bb0325b): 1Sigma_u+ and 1Pi_u; present as intervals 10.30-11.28, 11.28-11.49 eV (merged with Table 4’s 16 intervals 11.49-13.78 eV into intervals_present, 18 points, primary); others (Padial, McCurdy, Klump, Rabalais, Meyer, Inn) as band labels. Text: 14.83-20.66 eV present 1.674 (check), Nakata 1.372, Berkowitz 2.031.

• Formula: tail_fit, A E^-2 + B E^-3 + C E^-4 (A = 2.616, B = 95.24, C = 246.9, “(x10^4)”): reproduces the printed 8.51 % above 203 eV (8.511 %) only with the factor on all three coefficients and df/dE in 10^-2 eV^-1; 0.750 at 203 eV against the table’s 0.788, 3.549 at 100.54 eV against 3.58.

• Uncertainty: none stated in the paper.

• Checked: images; S(0) = 15.020 (8.53-203 eV) + tail = 16.425 (normalised to 16.51); S(-2) = 16.876 au (Olney 16.92), S(-1) 13.384, S(-3) 26.63, S(-4) 47.73, S(-6) 187.9. Present intervals 10.30-13.78 sum to 1.197; with the two bands, 1.210 below the IP. Inn et al.’s values equal inn_1953 continuum_f (0.0043, 0.0053, 0.12).

• Doubt: the peak energies of Table 2 (about 8.38, 9.30 eV) differ from the text’s (about 8.35, 9.40 eV).

• Status: verified (2026-09-27).

TC-612 chan_1994 (Chan, Cooper & Brion, Chem. Phys. 180, 77 (1994)): N2O 5.5-203 eV (2026-09-27)

• Transcribed: Table 1 (tbl_b536b17df805): LR df/dE 7.40-203.00 eV, 164 points (primary, +-5 %). Table 2 (tbl_c3cbc336c3cb): B, C, D continuum bands (present as intervals 5.70-7.70, 7.70-8.97, 8.97-10.23 eV, merged with Table 3; Lee & Suto as intervals (Chan’s integration of their digitised figure); Chutjian & Segal, Huebner, Rabalais, Zelikoff (= zelikoff_1953) as band labels). Table 3 (tbl_989c4d1b6636): 35 intervals 10.23-16.40 eV present, 21 Huebner et al. intervals_present has 38 points.

• Structural: Table 2’s theory values sit on the “theory” row, the reference on the next.

• Errata (2): Table 1 energies 129.28 -> 129.23 and 131.23 -> 131.28 (2.05 eV grid; the CO2 paper’s identical grid).

• Formula: tail_fit (A = 2.005, B = 150.9, C = -652.3, “(x10^4)”): 7.08 % above 203 eV (printed 7.1 %); 0.663 at 203 eV (table 0.686), 3.404 at 100.54 eV (3.44).

• Checked: S(0) = 15.341 + tail = 16.509 (16.51); S(-2) = 19.319 au, but Olney et al. quote 20.23 au for the originally published spectrum (4.7 % higher; CO, N2, CO2 agree to 1 %): a finding for review (it bears on topfer_2023’s 20.23 and on the N2O dipole sums). S(-1) 14.254, S(-3) 34.02, S(-4) 70.57, S(-6) 401.9. Zelikoff values equal zelikoff_1953 continuum_f.

• Status: verified (2026-09-27); open: Olney et al.’s S(-2) of N2O (TC-606).

TC-613 au_1993 (Au, Cooper, Burton, Olney & Brion, Chem. Phys. 173, 209 (1993)): CH4 (and the alkanes) (2026-09-27)

• Transcribed (CH4 only): Table 7 (tbl_f5a4c303b9e9, unlabelled): LR df/dE 7.5-220 eV, 176 points (primary, +-5 %). Table 1 (tbl_8bb88b5f26fe): CH4 vertical IPs quoted from Kimura et al.’s handbook (13.6, 14.4, 15.0 eV, 1t2 Jahn-Teller components) and Potts & Streets (22.91 eV, 2a1) as reproduced ionization_energy (kind vertical); the same values as bieri_1977 (Heilbronner et al.), 22.9 there.

• Formula: tail_fit_CH4, Eq. (1) with Table 2’s CH4 row (A = 1.4128e2, B = -2.8212e4, C = 2.0379e6): the tail above 220 eV is 0.4145 = 4.98 % of 8.33 (printed 5.0 %); the curve gives 0.114, 0.146, 0.265 (1e-2/eV) at 220, 180, 130 eV against the table’s 0.12, 0.15, 0.26.

• Checked: S(0) = 7.915 (7.5-220 eV) + tail = 8.330 (normalisation 8.33); S(-1) 10.533, S(-2) 17.063 au (Thomas & Meath’s DOSD: 17.27; hohm_1993’s CH4 is the refractivity value), S(-3) 31.45, S(-4) 63.56, S(-6) 316.6 (Thomas & Meath 298.3). The paper prints no S(k).

• Not extracted: Table 3 (CH4 feature energies, term values, Rydberg assignments; no quantity); all other alkanes (C2H6 … C8H18; Tables 4-6, 8-14; notes).

• Status: verified (2026-09-27).

TC-614 thomas_1977 (Thomas & Meath, Mol. Phys. 34, 113 (1977)): CH4 DOSD (2026-09-27)

• Transcribed: Table 1 (tbl_df5a5473a0a4): recommended DOSD over 17 regions, 145.86-0.00 nm, as interval_oscillator_strength in nm (check; sums to 9.9995; threshold to 49.59 nm 4.982, text 4.98). Table 2 (tbl_010d4e4faeeb): S(-1), S(-2), S(-4) of the DOSD (10.86, 17.27, 62.41; check) and of Platzman, Santar & Bednář (DOSDs) and of Thomas & Meath’s own Cauchy fits to Watson & Ramaswamy (watson_1936), Cuthbertson (cuthbertson_1920), Friberg, Frivold et al. (reproduced). Text p. 121: S(-3/2), S(-3), S(-6) … S(-16) (inline, check). p. 123: the infrared (vibrational) polarizability bounds 3.304e-32 and 4.467e-32 m^3 (polarizability_correction, part vibrational, check), the “experimental” 3.17e-32 m^3 (reproduced, alpha_T - alpha_e), alpha_e = 2.5590e-30 m^3 (W&R) and alpha_T = 2.5907e-30 m^3 (Watson, Rao & Ramaswamy 1934, dielectric).

• Formula: Eq. (8), the eight-term Cauchy R(lambda): each coefficient equals (4 pi/3) N_A a0^3 S(-2l) (hc/Eh)^(2(l-1)) to 3.3e-4 (1973 vs 2018 constants); R(0.5462 um) = 6.622e-6 m^3/mol against 6.620e-6 from W&R’s 405.90e-6 (25 C, ideal gas).

• Uncertainty: S(k) about 1 % to k = -8; 1.5 % at -10 rising to 4 % at -16 (stored 4 % for -12, -14); “only valid if the refractivity data … is reliable to a few tenths of a per cent”.

• Finding: S(-6) = 2.983(2) = 298.3 (p. 121) confirms that Olney et al.’s 289.3 for this DOSD is Olney’s misprint (olney_1997 finding (1)); Hohm 1993 and Spackman print 298.3.

• Not extracted: L(k), mean excitation energies, C6 (Table 3 and the combination rule values): no quantity (notes).

• Status: verified (2026-09-27); Olney’s S(-6) corrected by an erratum (TC-606).

TC-615 jhanwar_1982 (Jhanwar & Meath, Chem. Phys. 67, 185 (1982)): CO and CO2 DOSDs (2026-09-27)

• Transcribed: Table 1 (tbl_025ed8b378b2; caption detached into the text, structural): CO DOSD, 24 regions (check; sums to 14.002). Table 2 (tbl_abfee4bd8e42): CO2 UV (21 regions, 22.0015) and total (21 regions + the IR row 0.000155, 22.0017) (checks). Table 3 (tbl_61308cacb9a8): CO S_k, k = 2 … -10 (check) and the literature (Mulder & Meath SCF, Parker & Pack Cauchy, Watson & Ramaswamy = watson_1936, Liebmann & Moskowitz, Mulder et al. Unsold / Kirkwood). Table 4 (tbl_b9eb3fd4a103): CO2 UV and total S_k (check) and literature (Mulder & Meath, Pack UV and total, W&R UV and total (dielectric), Morrison & Hay, Mulder et al.).

• Formulas: pseudospectrum_CO, pseudospectrum_CO2 (form oscillator; Table 5): S(k) reproduce Tables 3-4 to the printed digits (e.g. CO S_-2 13.084 / 13.08, S_-6 296.50 / 29.65(1); CO2 S_-2 17.505 / 17.51, S_-8 1029.6 / 10.30(2)); range_nm lower bound 1.1 x the lowest pole’s wavelength (170.8, 178.1 nm; extractor’s choice, TC-119). pseudospectrum_CO2_total (footnote, no form): with one correction (f11 printed “524045(1)” -> 0.524045(1), 300-dpi page image) it reproduces Table 4’s total S_k.

• Structural: Table 2’s last lower edge illegible (“10^2” extracted) read as 10^4 (contiguity); Table 4’s “S_{-5}” row is S_-8; the extraction joins Table 4’s two lines per cell (recommended split by two-decimal mantissas; literature by entry count per line); the “X and Y” pairs of footnote e read as Unsold then Kirkwood (the text says the Kirkwood CO value, 13.10, agrees with 13.08) - a doubt.

• Values for review: CO electronic S_-2 = 13.08 au; CO2 electronic 17.51, total 19.79 (so the CO2 vibrational polarizability in this DOSD is 2.28 au; W&R dielectric 19.68); the IR bands’ summed f = 0.000155.

• Not extracted: C6 (Tables 6-7), Berkowitz comparisons (notes).

• Status: verified (2026-09-27).

TC-616 kumar_1985b (Kumar, Fairley & Meath, J. Chem. Phys. 83, 70 (1985)): SF6 DOSD (2026-09-27)

• Transcribed: Table I (tbl_e5a10522c2c9): adopted UV DOSD, 27 regions 5.0 eV-inf (check; sums to 69.996). Table II (tbl_bfe8065fdca1): UV and total S_k, k = 2, 1, -1/2, -1, -3/2, -2, -5/2, -3, -4 (checks; UV S_-2 = 30.04, total 44.21 = constraint). Text/caption: IR strengths (adjusted 1.331e-5, 2.317e-4 at 0.0027999, 0.0043190 hartree; Pack’s initial 1.327e-5, 2.264e-4), S_-6 = 982.1 (UV), Pack’s Cauchy S_-2 30.38 +- 0.02, S_-4 32.6 +- 4.9, S_-6 680 +- 310, Tipton 44.21 +- 0.05, Hosticka & Bose 44.27 +- 0.07, Lazzeretti CHF 22.76, W&R R(6440 A) = 11.4057 and R(4360 A) = 11.5212 cm^3/mol, DOSD R(4359.6) = 11.6474 and the alternative DOSD’s R(6440) = 11.2843.

• Formulas: pseudospectrum_SF6 (oscillator; range from 263.9 nm, TC-119 convention) and pseudospectrum_SF6_total (no form): integer-k sums reproduce Table II; S_-1/2 from the pseudo-DOSDs is 40.43 / 40.46 against Table II’s 40.34 / 40.37 (half-integer k not constrained; kept, doubt).

• Doubt: Pack’s S_-2 “+- .02”: read as absolute au (0.02), as the S_-4 “+- 4.9” must be.

• Finding for review: the adopted DOSD (constrained at 6440 A) is 1 % above W&R at 4359.6 A; the authors: the dipole properties are “probably slightly high” (up to 2.2 % for S_-6). alpha(632.8 nm) from the UV pseudo-DOSD = 30.53 au (electronic): 0.8 % above fit/SF6 at 632.8 nm and 5.7 % above at 300 nm (its 5.0-10.1 eV strength, 0.117, puts poles at 5.2-6.4 eV). By contrast the CO and CO2 pseudo-DOSDs of jhanwar_1982 agree with fit/CO and fit/CO2 to 0.1 % at 250-633 nm, and margoliash_1978’s CH4 (fitted to thomas_1977) is 0.06 % above fit/CH4 at 632.8 nm.

• Re-point for hosticka_1974 (another extraction’s record): this record cites Hosticka & Bose’s 44.27 +- 0.07 (dataset total_polarizability_hosticka) by citation; once hosticka_1974 exists, its reproduced_from can be set to it (compare the value).

• Status: verified (2026-09-27).

TC-617 kumar_1994 (Kumar & Meath, Chem. Phys. 189, 467 (1994)): CO anisotropic DOSD (2026-09-27)

• Transcribed: Table 1 (tbl_a5187b988bd4): isotropic S_k (12 k; check) and Ref. [22] (= jhanwar_1982, reproduced; agrees with jhanwar_1982’s Table 3 to the digits). Table 3 (tbl_77c53d70381b): alpha(lambda) and gamma(lambda) at 24 wavelengths (this work, check; SOPPA Oddershede & Svendsen and Jorgensen et al., reproduced; experiment = watson_1936 at infinity and smith_1976 in the UV, reproduced). Table 4 (tbl_d2eb2911fa57): 100 rho_v^T (scale 1e-2, depolarization_ratio, kind rayleigh, linear) and Q_Ray (1e-27 cm^2), 18 wavelengths (checks). Text: Bogaard et al.’s gamma (3.797, 3.772, 3.590 at 4880, 5145, 6328 A), Amos’s gamma(0) = 3.65 +- 0.06, and the depolarization ratios of Bridge & Buckingham (0.4800 +- 0.005), Baas & Van den Hout, Bogaard et al., Rodwell et al. (reproduced).

• Excluded row: Q_Ray at 1854.6 A printed 2.159(2) = 215.9 (below 794.0 at 1862.7 A; Eq. (10) gives about 815): unrecoverable misprint, excluded. Eq. (10) reproduces 6328 A (3.233 / 3.234) and 2754 A (109.0 / 1.090(2)).

• Formulas: perpendicular and parallel pseudo-DOSDs (Table 9; no form, components): reproduce Table 1’s component sums and the 6328 A constraints (12.145 / 12.15, 15.737 / 15.74).

• Format need: the S_k^perp, S_k^par (Table 1), alpha^perp, alpha^par and L_k, I_k have no quantity (components listed in the record notes). The Verdet V_N (Table 5) is not extracted: its density is not stated.

• Values for review: CO gamma(0) = 3.567 a0^3 (DOSD, constrained to Bridge & Buckingham at 6328 A); gamma(6328) = 3.592 vs Bogaard’s 3.590; alpha(0) = 13.08.

• Status: verified (2026-09-27).

TC-618 Re-points of olney_1997, spackman_1991, zhao_2026, margoliash_1978 and others (2026-09-27)

• olney_1997: kumar_1994_CO -> kumar_1994 (all 7 sums equal); jhanwar_1982_CO2 -> jhanwar_1982 (all 7 equal the UV sums); thomas_1977_CH4 -> thomas_1977 (equal except S(-6): Olney 289.3, original 2.983(2) = 298.3 (p. 121): Olney’s transposition, kept as printed, no erratum added - a decision made in review). Notes: the Expt rows’ and Table 1’s spectra named (chan_1993_n2, chan_1993_o2, chan_1993_co, chan_1993_co2, chan_1994, au_1993); finding (4): Table 1’s S(-2) of the published spectra recomputed from the curated tables: CO 12.66 (12.64), N2 11.65 (11.54), CO2 16.88 (16.92), N2O 19.32 (20.23, +4.7 %), CH4 17.06 (16.52, -3.2 %). None of these datasets is in a fit.

• spackman_1991: meath_CH4 -> thomas_1977 (17.27, 62.41, 298.3 equal); meath_CO -> jhanwar_1982 (13.08, 48.27, 296.5 equal; not kumar_1994’s 48.26, 292.9); meath_CO2 -> jhanwar_1982 (equal); meath_SF6 -> kumar_1985b (30.04, 88.59, 982.1 equal). Not in fits.

• zhao_2026: kumar_meath_1994_moments_CO -> kumar_1994 (48.26, 292.9, 2308 equal; this dataset is in the CO fit (fits/CO.toml): use left as is (reproduced); the original kumar_1994/moments exists now (use check): still to be decided); kumar_meath_1994_dosd_CO -> kumar_1994: S(-2) = 13.08 gives 4.889 cm^3/mol, so the record’s “4.8953 misprint” reading of 4.89(53) is not supported (notes updated).

• margoliash_1978: CH4 pseudospectrum notes: Thomas & Meath curated; the pseudospectrum reproduces thomas_1977’s S(-1) … S(-16) within 3e-4; E0 = 145.86 nm (8.500 eV), so the stated accuracy holds above 153.6 nm; still no form (a model decision still to be made).

For another extraction’s records (not edited):

• hohm_1993/moments_thomas_1977_CH4 -> thomas_1977 (17.27, 62.41, 298.3, 1714 equal).

• hohm_1993/thomas_1977_CH4 and hohm_1994b/thomas_1977_CH4 -> thomas_1977 (Hohm’s alpha from the Cauchy series of the sums: 17.6016 at 632.99 nm reproduced from thomas_1977’s S(-2) … S(-10)).

• hohm_1994b/jhanwar_1982_CO2 -> jhanwar_1982 (17.7800 at 632.99 nm reproduced from jhanwar_1982’s UV S(-2) … S(-10)).

• hohm_2013/dosd_CO (13.08) and dosd_CO2 (17.51) -> jhanwar_1982; dosd_CH4 (17.27) -> thomas_1977; dosd_SF6 (30.04) -> kumar_1985b (values equal; the +- are Hohm’s).

• None of these is in a fit.

Other records (not assigned to an extraction; for review):

• sakamoto_2010/discrete_N2 (Berkowitz Table 4.7, “W. F. Chan et al., Chem. Phys. 170, 81 (1993)”) equals chan_1993_n2’s per-state present values times 1.034 (b v’ = 0 0.00254 -> 0.0026264; c’ v’ = 0 0.195 -> 0.20163; b’ v’ = 23, 24 0.00897, 0.00363 -> 0.009275, 0.0037534: Berkowitz used Tables 3-7, not Table 2, and rescaled by 3.4 %): chan_1993_n2 can be named in its reproduced_from.

• sakamoto_2010/lyman_H2 (and presumably werner_H2) = Allison & Dalgarno’s theory (chan_1992_h2’s lyman_allison_1970), not Chan et al.’s measurement.

• sakamoto_2010 notes cite Chan et al. for CO (12.130-14.013 eV, chan_1993_co’s Table 5), CO2 (chan_1993_co2) and N2O (chan_1994) intervals.

• kumar_2011_supplement O2 intervals j = 4, 7-11, 15-17 “Chan et al. (Chem. Phys. 170, 99 (1993))” = chan_1993_o2 (integrated by Kumar and Thakkar).

• brion_1984’s O2 table reprints Brion et al. 1979, the absolute scale of chan_1993_o2.

• The hohm_1994b rows c (kumar_1985) are unaffected.

• Status: decided (2026-09-27); the re-points in other extractions’ records applied in review (TC-606).

TC-619 The metals: silver, gold, copper and aluminium as table models (2026-09-27)

• Where: data/solid/tables/{Ag,Au,Cu,Al}.toml, data/solid/defaults.toml, docs/metals.md, tests/solid/test_metals_page.py; after the extraction of babar_2015, werner_2009, ordal_1988, mcpeak_2015, hagemann_1975 and stahrenberg_2001 (their entries follow).

• Decisions:

  • Ag, Au, Cu: Werner et al.’s REELS permittivity from 17.6 to 206 nm (6.0-70.5 eV) and Babar & Weaver’s from 207 nm to 12.4 µm (0.10-6.00 eV), joined at 6.0 eV.

    • REELS is the only measured source above 6 eV in the library. Werner et al. put it at about 10 % above 5 eV and warn that it is unreliable below.

    • Their DFT columns are a calculation with a universal 0.1 eV broadening. They differ from REELS by up to 20 % between 6 and 10 eV, and they are not used.

    • Babar & Weaver’s Kramers-Kronig analysis of single crystals is the optical reference below 6 eV. There, REELS ε₂ is several times the optical one (silver at 3 eV: −5.16 + 2.42i against −5.25 + 0.23i).

  • The join: at 6.0 eV, where both tabulate, the sources differ by 6-15 % in n and 12-30 % in k (silver 1.08 + 1.25i against 0.95 + 1.55i). Nothing in the library bridges them. The table joins them without averaging, and the page states the step.

  • Al: Ordal et al.’s n and k from 667 nm to 200 µm (with the 51 errata of their Table I), the only aluminium data in the library. The ultraviolet and visible are missing: McPeak et al.’s data files, Hagemann et al.’s DESY report SR-74/7 (and Rakić 1995) are requested.

• solprop: its silver and aluminium are refractiveindex.info’s copies of these papers. Where the sources are the same they agree to 1 % in n and 0.2 % in k:

  • silver from 17.6 to 124 nm (the REELS columns) and from 207 nm to 5 µm (Babar);

  • aluminium from 2.5 to 200 µm (Ordal).

  They differ in three places:

  • silver at 128-207 nm, where solprop has Stahrenberg et al.’s ellipsometry (up to 16 % in n);

  • aluminium below 1.7 µm, where solprop has McPeak et al.’s films (20 % in n at 1.2 µm);

  • between Babar’s widely spaced infrared points. Near 10 µm the points are 4 µm apart, and solprop’s cubic spline and optmat’s monotone interpolant differ by 17 % in n and 0.4 % in k: the uncertainty of any interpolation there.

• Status: decided (2026-09-27); open: the missing ultraviolet and visible aluminium data and silver’s 128-207 nm.

TC-620 babar_2015 (Babar & Weaver, Appl. Opt. 54, 477 (2015)) (2026-09-27)

• Transcribed: Table 1 and its continuation (tbl_8cb2a14ef702, p. 479, 0.10-2.00 eV; tbl_76629faf19ce, p. 480, 2.10-6.00 eV) by tools/extract/babar_2015.py: epsilon_1 (permittivity_real) and epsilon_2 (permittivity_imaginary) of Cu, Ag and Au, 69 rows each: 6 datasets, 414 points, use = primary, form = bulk. R (no quantity) kept in printed.

• Checked: both parts cell by cell against the images; the printed R agrees with |(sqrt(eps) - 1)/(sqrt(eps) + 1)|^2 from the same row to at most 0.0013 (Ag, 3.4 eV, where epsilon_2 = 0.25 has two decimals).

• Findings:

  • The samples are mechanically polished single crystals, chemically cleaned (p. 477), not evaporated films as first supposed: no thickness or substrate.

  • “JHW” is J. H. Weaver (Fig. 1 caption), not Johnson; JC is Johnson & Christy. Kramers-Kronig of Weaver’s absorptivity A = 1 - R; Ag extended to 30 eV with Leveque, Olson & Lynch; Cu joined to JC and then HGK to 30 eV; R = R_o E^-3.5 to 1000 eV. The Au reflectance is that of Weaver et al.’s 1981 ZAED volume (Fig. 3 caption).

  • No uncertainty, temperature or Drude parameters are given.

  • The supplement (original/source_02, 17 pp.) is figures only (to 6 and 30 eV).

  • JC comparison (text): IR epsilon_2 differs by a factor 2-4 for Cu, much better agreement for Ag, intermediate for Au; figures otherwise.

• Status: verified (2026-09-27).

TC-621 werner_2009 (Werner, Glantschnig & Ambrosch-Draxl, J. Phys. Chem. Ref. Data 38, 1013 (2009)) (2026-09-27)

• Transcribed: by tools/extract/werner_2009.py from the JSON cells (no CSV): Table 16 Cu (tbl_bbde835d361c, tbl_77acafd389e3, tbl_d3f670af9b86, pp. 1059-1061), Table 20 Ag (tbl_a521b89d0a14, tbl_ba923cb150a2, tbl_d7484476dcbe, pp. 1071-1073), Table 24 Au (tbl_991d52c88cc2, tbl_f4fe6ec8cdaa, tbl_4c92ff38fd6e, pp. 1083-1085). epsilon_1 and epsilon_2 per metal and method (parameters.technique “DFT” or “REELS”), 0.50-70.5 eV, 150 rows: 12 datasets, 1,800 points. REELS use = primary (10 % bound; epsilon_1 below 10 eV at 100 %, a floor as the paper says “may exceed”); DFT use = check (a calculation with a universal 0.1 eV broadening; this may be decided otherwise in review). ELF, w_b, w_s in printed.

• Page order: each part is one page with the metal’s name and “DFT | REELS” header; the energies continue from part to part (0.50-21.5, 22.0-47.5, 48.0-70.5 eV) on consecutive PDF pages (47-49, 59-61, 71-73). The script checks the order and that the DFT and REELS energy columns agree.

• Checked: the first parts (to 6 eV) and Au’s last part against the images cell by cell; every row of all nine parts satisfies ELF = epsilon_2 / (epsilon_1^2 + epsilon_2^2) to the printed rounding (<= 0.0015), for DFT and REELS.

• Formulas: drude_lorentz_Cu, _Ag, _Au (Eq. 25-26 with Tables 6, 8, 9; no form; coefficients from the images; Table 6’s last Cu row is merged in the library’s cells). With q = 0 and f_i = A_i the formula reproduces the REELS tables to three digits at 40 and 70 eV (e.g. Cu 70 eV 0.804 + 0.257i exactly), to ~0.01 at 10 eV, and worse below 5 eV (Cu 1 eV: -78.8 + 86.7i vs -73.064 + 86.333i; Ag 5 eV: -2.28 + 8.59i vs -1.599 + 9.249i) from the printed rounding of the parameters.

• Findings:

  • Al is not among the 17 metals (Ti, V, Fe, Co, Ni, Cu, Zn, Mo, Pd, Ag, Ta, W, Pt, Au, Pb, Bi, Te). Te has no numerical table (Tables 11-26 are the other 16).

  • The REELS epsilon are the fitted Drude-Lorentz model’s values, not a point-by-point inversion (Summary, p. 1038). Low-energy REELS rows are erratic (Cu epsilon_2 49.3, 86.3, 41.4 at 0.75-1.25 eV), consistent with the paper’s statement that REELS is unreliable below ~5 eV.

  • Table 2 sum rules (Cu, Ag, Au) in the record’s notes.

• Status: verified (2026-09-27).

TC-622 ordal_1988 (Ordal et al., Appl. Opt. 27, 1203 (1988)) (2026-09-27)

• Transcribed: Table I (tbl_131e600939fe, p. 1204) by tools/extract/ordal_1988.py: Al n and k (primary), -epsilon_1 (as printed, scale = -1, so the dataset holds epsilon_1) and epsilon_2 (check, since they repeat n and k), 50-15000 cm-1, 51 rows each: 4 datasets, 204 points. R in printed.

• Which table is Al: from the page image, Table I sits under its caption in the Al section on p. 1204, shows Al’s interband dip (R = 0.868 at 12000 cm-1) and the Drude wing omega_p ~ 9.5e4 cm-1; Tables II-VI (Fe, Ti, Ta, W, Mo) each match their own Drude wings. Other metals not transcribed (not registered).

• Errata (51): in Table I every |epsilon| >= 1000 is printed ten times too small (the decimal point one place left): -epsilon_1 at 50-3000 cm-1 (28 rows), epsilon_2 at 50-1750 cm-1 (23 rows); e.g. 50 cm-1: printed 4445.8912 and 42405.361, where the row’s n, k give 44458.912 and 424053.61. Evidence: every corrected value equals k^2 - n^2 or 2nk from the same row to all eight digits; the uncorrected rows need nothing; Fig. 2 shows -epsilon_1 ~ 4e4 and epsilon_2 ~ 4e5 at 50 cm-1. n, k and R are mutually consistent to 1e-6. The other five tables have no such misprint.

• Formulas: drude_wing_Al (omega_tau 408, omega_p 92,700 cm-1, the KK wing), drude_cavity_Al (424, 95,400, fit to the cavity data), drude_ordal_1985_Al (660, 119,000, quoted from Ref. 3, not in the library). No Drude formula is printed; the assumed form epsilon = 1 - omega_p^2/(omega^2 + i omega omega_tau) reproduces the table’s epsilon_2 at 50 cm-1 to 0.15 % (cavity fit) and 2 % (wing); epsilon_1 is 12-14 % off there (KK result, not a Drude curve). Other metals’ parameters in notes.

• Doubt: only 30-300 cm-1 is measured; 320 cm-1 and above rest on Shiles et al. (Weaver’s compilation, not in the library).

• Status: corrected (2026-09-27).

TC-623 mcpeak_2015 (McPeak et al., ACS Photonics 2, 326 (2015)) (2026-09-27)

• Transcribed: nothing. The optical constants are in figures only (Figs. 4, 5, S1, S2, S5-S7); the “digital files containing the actual data points” of the Supporting Information are not in the library (the SI PDF has methods and figures only). Table 1 (figures of merit, image checked; the library merges the metals’ cells) in notes. Recipes (300 nm template-stripped films; Ag 50 A/s, Cu 35 A/s, Au 10 A/s at 3e-8 Torr; Al ~150 A/s), roughness, ellipsometers and ranges (Al VUV-VASE 150-1700 nm; Cu, Au, Ag V-VASE 400-1750 nm) in notes.

• Status: open: the data files are missing.

TC-624 hagemann_1975 (Hagemann, Gudat & Kunz, JOSA 65, 742 (1975)) (2026-09-27)

• Transcribed: nothing. Table I (sum rules, image checked) and the method (film transmittance 13-150 eV at DESY; three Kramers-Kronig procedures; Au and Ag by transmission phase) in notes; figures (mu against energy) described. The numerical tables and the sources of each range are in DESY report SR-74/7, not in the library.

• Status: open: the report is missing.

TC-625 stahrenberg_2001 (Stahrenberg et al., Phys. Rev. B 64, 115111 (2001)) (2026-09-27)

• Transcribed: read the pages (no tables). Figures only for Cu and Ag epsilon (Figs. 2, 5). One check dataset: Ag epsilon_1 = 0 at 3.79 and 7.95 eV (text, p. 115111-6), 2 points, use = check. Method (UHV ellipsometry, single crystals Cu(110), Ag(110), 67.5 deg, BESSY; roughness correction from AFM 0.41/0.42 nm), text values (roughness corrections, differences from Palik and JC, dε2/dE features, scissors shifts) in notes.

• Status: open: the numerical data (provided privately to refractiveindex.info) are missing.

TC-626 ordal_1983 (Ordal et al., Appl. Opt. 22, 1099 (1983)) (2026-09-28)

• What the paper is: a compilation, not a measurement (“Infrared optical constants collected from the literature are tabulated”). Tables 1-12 are runs of blocks, one per original source, each under its own caption and reference line; columns omega (cm-1), lambda (um), -epsilon_1, epsilon_2, n, k to three figures. Ordal et al. converted the originals’ n, k to epsilon (Sec. III, p. 1116).

• Transcribed: by tools/extract/ordal_1983.py, the 18 blocks of Tables 1 (Al: Shiles 26 rows, Bennett 25, Schulz 12), 2 (Cu: Schulz 11, Lenham & Treherne 10, Robusto & Braunstein 7, Hagemann 10, Dold & Mecke 11), 3 (Au: Bennett 18, Schulz 7, Motulevich & Shubin 11, Padalka & Shklyarevskii 11, Bolotin 12, Brandli & Sievers 14, Weaver 21) and 5 (Ag: Bennett 19, Schulz 12, Hagemann 8): 245 rows, 72 datasets (n, k, eps1, eps2 per block), 980 points. n and k use = "reproduced", eps1 (scale -1, the “-epsilon_1” column) and eps2 use = "check"; all with reproduced_from: shiles_1980 + weaver_1981 (Shiles block), hagemann_1975 + hagemann_1974 (Hagemann blocks), weaver_1981 (Weaver Au block), otherwise the block’s reference line as printed. lambda in printed. Not “n and k primary” as first requested: every value is another author’s, so the data rules make them reproductions (a reproduction whose original is not in the library may still be fitted, docs/data.md).

• Page order and block identity (structural): read from the page images (PDF pp. 5-11), where each caption and reference line sits directly above its block. The library’s captions are unreliable: tbl_6418218be243, labelled “TABLE 3. Au, GOLD”, is copper after Dold & Mecke; gold starts with the unlabelled tbl_d345d262b8b8 (Bennett); Padalka’s reference is attached to the Motulevich block; seven blocks have no caption. The script checks each block’s first wavenumber and row count. The epsilon header cells are misread (“-€ 1”, “-61”, “-<1”): columns taken by position.

• Checked (2026-09-28): every row of all 39 blocks (not only these 18) satisfies epsilon_1 = n^2 - k^2, epsilon_2 = 2nk and lambda = 1e4/omega to the printed rounding (half a unit in each cell’s last digit). Worst row per table: Al, Shiles 6.45E+03, -eps1 252 vs 253.9 (0.91 of the bound); Cu, Lenham 5.00E+02, 13500 vs 13401 (0.57); Au, Weaver 1.21E+03, 3070 vs 3077.6 (0.72); Ag, Bennett 8.33E+02, eps2 1280 vs 1283 (0.47). No factor-of-ten misprint of the kind ordal_1988 has; no errata.

• Formulas: Table 13 (p. 1118) for Al, Cu, Au, Ag as drude_<metal> (Eq. 2, no form, epsilon_inf = 1; coefficients as printed “6.47x10^2”). Checks: (omega_p/omega_tau)^2 against the printed -epsilon_1(0) (Al 33,829 vs 3.37e4; Cu 52,669 vs 5.27e4; Au 112,660 vs 1.13e5; Ag 250,000 exactly); Cu at its forced omega_f = 2000 cm-1 reproduces Lenham & Treherne to 0.3/0.9 %; Ag at omega_f = 1000 reproduces Bennett to 0.1/0.3 %; Au reproduces Bennett to < 1.5 %; Al reproduces Bennett to 2-5 % but is 15-40 % off Shiles. Pb and W parameters in notes.

• Findings:

  • Bennett & Bennett’s blocks (Al, Au, Ag) are a Drude curve, not measured points: every row gives the same omega_tau and omega_p by Eqs. (12)-(13) to the printed rounding (Ag 144.8-146.1 / 72,360-72,710; Au 214-217 / 72,500-73,000; Al 657-669 / 118,200-119,100 cm-1), matching Ref. 5’s estimates (145, 216, 663).

  • The Shiles block is Weaver et al.’s tabulation (Physics Data 18-2, p. 79) rounded: 0.040-0.062 eV checked against the scan (e.g. 0.040 eV: 98.595 + 203.701i there, 98.6

    • 204i here).

  • The Hagemann blocks are the DESY report’s rows (not the JOSA paper’s figures), n, k rounded and epsilon recomputed. Against the library’s reading of the report (Hagemann_1974_OpticalConstantsFar, tbl_52ae5a332285 Cu, tbl_5954ad9a5d51 Ag): agreement to the rounding except Cu 0.1 eV (n, k 29.7, 71.6 here; the report prints 2.91E 01, 7.11E 01 — image checked — while its own epsilon, -4.24E3 and 4.25E3, equal this row’s and fit 29.7, 71.6), Cu 0.5 eV n (1.71 vs 1.692), Cu 1.0 eV (0.44, 8.48, 7.46 vs 0.433, 8.46, 7.39), Ag 0.1 eV n (9.91 vs 9.936). For hagemann_1974: the report’s n and k at Cu 0.1 eV do not satisfy its own epsilon (2nk = 4138 vs 4250).

  • The Weaver Au block equals the book’s gold table (Au.pdf p. 64) at all 21 energies (n to its two decimals, k rounded), and the Babar-Weaver xlsx sheet JHW-Au-ZAED at every 0.1-eV energy; epsilon here is recomputed from the rounded n, k (1.0 eV eps2 2.09 vs the sheet’s 2.03). For weaver_1981: a second copy of the book’s gold table.

  • The blocks disagree with one another by tens of percent (gold at 10 um: 7.62 + 71.5i Bennett, 11.5 + 67.5i Motulevich, 7.41 + 53.4i Padalka, 10.9 + 50.6i Bolotin at 9.5 um).

• Doubts:

  • Ag, Schulz block, 2.22E+04 cm-1 (450 nm): n printed 5.50E-01 (image checked), ten times its neighbours (0.050, 0.075) and Babar’s ~0.05; eps2 = 2.66 (neighbours 0.29) and -eps1 = 5.55 are computed from it. Probably 0.055 (giving 0.266 and 5.85), but Schulz 1954 is not in the library: kept as printed, flagged in the dataset notes. The row may be excluded (excluded_rows), or Schulz requested.

  • Brandli & Sievers’s gold (31-150 cm-1): they published R(omega)/Z_0; Ordal et al. do not say how n and k were derived from it.

  • Nothing is said about any original’s samples (film or bulk) or methods.

• Other metals (notes only): Pb, Co, Fe, Ni, Pd, Pt, Ti, W blocks listed with ranges. Ti: Bolotin et al.’s block repeats Kirillova & Charikov 1964’s from 1180 to 4000 cm-1 (identical but one digit at 2220). Pd’s Bolotin block is not among the library’s tables; the library merges Weaver & Benbow with Johnson & Christy into one 12-column table without a CSV. PDF page 22 belongs to another article.

• Status: verified (2026-09-28).

TC-627 ordal_1985 (Ordal et al., Appl. Opt. 24, 4493 (1985)) (2026-09-28)

• Transcribed: Table II (tbl_08c9b2542049, p. 4495) by tools/extract/ordal_1985.py: copper n, k (primary), -epsilon_1 (scale -1) and epsilon_2 (check), 180-19400 cm-1, 56 rows each: 4 datasets, 224 points. The cells’ spaced exponents (“1.80E + 2”) are stored without spaces (“1.80E+2”), printed kept. The authors’ own measurement: reflectance against a corrected Al mirror (Perkin-Elmer 580, 180-4000 cm-1; a second spectrophotometer, model 2300, 4000-50,000 cm-1), Kramers-Kronig to n, k, epsilon from n, k. Wings: Drude to 1 cm-1 then constant; above 20,000 cm-1 Weaver et al.’s data, then E^-4. Sample and temperature not stated; no uncertainty (the wing choice moves 180 cm-1 values by <= 4 %, 500 cm-1 by < 1 %).

• Checked: every row consistent (worst eps2 at 1900 cm-1, 239 vs 238.05, 0.80 of the bound); first, last and several middle rows against the image.

• Formulas: Table I (p. 4494) for Al, Cu, Au, Ag as drude_<metal> (coefficients as printed under “10^-2 omega_tau” and “10^-4 omega_p”, e.g. Al “6.60”, “11.9”). Checks: rho_opt = 60 omega_tau / omega_p^2 reproduces the printed column (Al 2.796 vs 2.80; Cu 1.236 vs 1.24; Au 2.434 vs 2.43; Ag 1.646 vs 1.65). Cu reproduces Table II at 180 cm-1 (0.1 %) but eps2 falls 45-91 % below from 500 cm-1 up. Au and Ag reproduce ordal_1983’s Bennett curves to < 1 %; Al follows Bennett’s curve (1-2 %) and is 15-40 % off Shiles. The other ten metals in notes.

• Findings: Tables III (Ni, not extracted by the library), IV (Fe; last row misprinted: n 5.36, k 13.0 with -eps1 2.08, eps2 3.11), V (Mo; 5970 cm-1 -eps1 69.7 vs 67.9) and VI (V; lambda at 1.05E+4 printed 0.984) in notes. The text calls Tables III and IV Fe and Ni; the captions are Ni and Fe. Fig. 9 cites Ref. 4 for Johnson & Christy (Ref. 3).

• Status: verified (2026-09-28).

TC-628 ordal_1988 re-pointed (2026-09-28)

• Edited: drude_ordal_1985_Al: reproduced_from = ["ordal_1985"], the check now states that ordal_1985’s Table I prints the same values (6.60 x 10^2, 11.9 x 10^4 cm-1), the notes say the fit follows Bennett & Bennett’s Drude curve rather than Shiles’s data. The three formulas’ variable now names the form as Refs. 3 and 9’s Eq. (2) with epsilon_inf = 1 (it was “assumed”); the record’s notes say Refs. 3 and 9 are ordal_1985 and ordal_1983 and that the Ref. 3 values quoted for Al, Fe, Ti and Mo equal ordal_1985’s Table I (Fe 147/33,000, Ti 382/20,300, Mo 412/60,200: all agree). No value changed.

• Finding: ordal_1988 says Ref. 3 “fit the above data [Shiles et al.’s]”; the fitted curve (660, 119,000) is 15-40 % from Shiles’s epsilon at 1000-5000 cm-1 and within 1-2 % of Bennett & Bennett’s Drude curve (their omega_tau 663). drude_ordal_1985_Al should not be treated as a fit to Shiles.

• Status: decided (2026-09-28).

TC-629 ordal_1983 and ordal_1985 against the tables (2026-09-28)

table/Ag, table/Au, table/Cu are Babar & Weaver to 12.4 um (and REELS above 6 eV); table/Al is ordal_1988 (0.667-200 um). Differences are (Ordal - table)/table where both tabulate (the table model clamps outside its range, so only in-range points count).

• Al, 620-667 nm and below: the Shiles block adds one point at 621 nm (1.30 + 7.48i); at 0.83-31 um it equals table/Al to <= 3 % in n and <= 1 % in k (the same Shiles lineage). Schulz’s Al (1954), 400-950 nm, is the only new Al below 667 nm here: n 0.40-1.24, k 3.92-6.60 at 400-650 nm; against table/Al at 752-952 nm, n -28 % to +6 %, k -18 % to -4.5 %. 1954 data whose samples Ordal does not describe; Shiles/Rakic/Hagemann (in other records) are better candidates. Bennett’s Al block is a Drude curve, 21-36 % above table/Al in n.

• Beyond 12.4 um (Ag, Au, Cu):

  • Cu: ordal_1985 Table II is the only measured copper beyond 12.4 um in these records (to 55.6 um). At the join it is close to table/Cu (12.5 um: n +2 %, k -10.5 %); over 5.5-10.5 um k is 9-10 % below Babar and n 10-50 % above; 1.1-2.2 um k 4-6 % below. Lenham & Treherne (4-20 um): k 12-16 % below Babar at 4-12 um. Dold & Mecke: 23-30 % below. The 1985 Drude fit (73.2, 59,600) is not a usable extrapolation: 14-17 % below Babar in k at 2-12 um and 70 % in n.

  • Ag: no measured data beyond 12.4 um here, only Bennett & Bennett’s Drude curve to 32 um and the Drude fits. The 1985 fit (145, 72,700) matches table/Ag at 2-8 um to 1.2 % in k (n -3 to +9 %) and at 12.3 um k +2.9 %, n +55 %: a candidate extrapolation (with the caveat that Babar’s n at 12.4 um is 5.05, the Drude 7.8).

  • Au: Brandli & Sievers (67-318 um, far infrared, the one measured far-IR gold set) and Bennett’s Drude curve (to 32 um). The 1985 Drude fit (215, 72,800) is 5-7 % above table/Au in k at 2-12 um and 13-32 % in n; it is +30 %/+23 % (-eps1/eps2) off Brandli & Sievers at 31 cm-1. The Weaver Au block equals table/Au’s lineage (n within 9 %, k 1-1.5 % below at 1.2-12.4 um).

• Ag at 0.6-12.4 um: Hagemann’s Ag agrees with Babar in k to 1 % at 0.6-6 um (4 % at 12.4 um) but n is 1.5-5.6 times Babar’s; Schulz’s Ag k 2-10 % below Babar.

• Status: open (for review: which, if any, extends table/Ag, /Au, /Cu beyond 12.4 um and table/Al below 667 nm).

TC-630 johnson_1972 (Johnson & Christy, Phys. Rev. B 6, 4370 (1972)) (2026-09-28)

• Transcribed: by tools/extract/johnson_1972.py. Table I (tbl_c125cb44d750, p. 4374; JSON only, merged header): n and k of Cu, Ag and Au against photon energy (eV as printed; no wavelength column exists), 0.64-6.60 eV, 49 rows: 6 datasets (n_Cu, k_Cu, n_Ag, k_Ag, n_Au, k_Au), primary, form = film, 294 points. The printed errors Delta n and Delta k (one pair of columns common to the three metals, printed “±0.18”) are each point’s sigma (the “±” dropped by the script); level “not stated”: estimates from the instrumental accuracy (±0.5 % of full scale of R and T; Delta n 0.18 falling to 0.02, Delta k 0.65 falling to 0.007). Table II (tbl_d5e8fa5d3264, p. 4376): m_0 as effective_mass (carrier electron, unit m_e) and tau as electron_collision_time (unit s, scale 1e-15, the printed column factor), with the printed errors as sigma: 6 datasets, 1 point each.

• Checked: Table I cell by cell against the image (all 441 cells agree). No redundant columns (no epsilon, R or wavelength). Table II against its image. Table II against Table I (scratch): Drude slopes of Table I at 0.64-1.26 eV give tau = 6.7e-15 (Cu), 2.7e-14 (Ag), 7.9e-15 s (Au) against (6.9 ± 0.7), (31 ± 12), (9.3 ± 0.9) e-15; hbar omega_p = 8.73, 9.10, 9.07 eV, i.e. N = 8.24e28, 5.77e28, 5.90e28 m^-3 with Table II’s m_0 (N is not printed; the paper assumes one conduction electron per atom). Silver’s epsilon_1 from Table I crosses zero at 3.81 eV (interpolated); the paper’s p-transmission minimum is 3.78 ± 0.02 eV (notes only).

• Films (notes): 99.99 % metals at ~60 A/s, < 4e-6 Torr, oil-pumped bell jar, onto fused quartz at room temperature; Cu 297 and 305 A (486 A check), Ag 304 and 375 A, Au 343 and 456 A (186 A rejected); some Au annealed at 150 C.

• Doubt: the error columns are “approximate” and apply to all three metals alike; the paper says silver’s infrared n is uncertain by ~40 %, more than the table’s Delta n there. Whether effective_mass (a Drude optical mass) is the right home for m_0: it is “the effective mass of a solid’s carriers”; the notes say it is a Drude parameter.

• Status: verified (2026-09-28).

TC-631 leveque_1983 (Leveque, Olson & Lynch, Phys. Rev. B 27, 4654 (1983)) (2026-09-28)

• Transcribed: no tables as data: Table I (R of four Ag samples at 5, 9.5, 15, 23 eV) and Table II (structure energies, 8-30 eV) have no quantity: in notes, images checked. One text value as a check: eps2_max_Ag, epsilon_2 = 3.77 at “the 4.5-eV maximum” (p. 4656), use = check, inline.

• Checked: Table I’s “estimated ideal value” = clean crystal x (film on glass)/(film on crystal) reproduces 0.294, 0.068, 0.113, 0.106 to rounding.

• Findings: the dielectric function is in figures only (Figs. 2-4, to 30 eV; single crystal and film). The Kramers-Kronig analysis used J. H. Weaver’s unpublished absorptance at 0.16-2.8 eV, “taken at low temperature” (p. 4657), Haensel et al. to 105 eV and Hagemann et al. (DESY SR-74/7) above. Babar & Weaver “used the results of Leveque, Olson, and Lynch up to 30 eV” without saying which reflectance (film, crystal, ideal); the paper publishes R only in Fig. 1 and Table I’s four energies, so their numbers came from elsewhere. Circularity: Leveque’s analysis rests on Weaver’s data below 2.8 eV, Babar & Weaver’s Ag above 6 eV on Leveque’s.

• Doubts: the summary’s 25.5 eV structure is 25.0 in Table II’s R column (image checked). The text says the film data were analysed and presented, but Figs. 2-3 show both samples. Fig. 4’s caption refers to “Figs. 5 and 6”. p. 4655 names two crystal faces, p. 4658 “all three faces”. Ref. 18 (Johnson and Christy) is printed as Phys. Rev. B 11, 1315 (1975), whereas the silver data on quartz are Phys. Rev. B 6, 4370 (1972).

• Status: verified (2026-09-28).

TC-632 rakic_1995 (Rakic, Appl. Opt. 34, 4755 (1995)) (2026-09-28)

• Transcribed: by tools/extract/rakic_1995.py. Table 2 (four library tables, pp. 4762-4765: tbl_a8fb03d43d0c, tbl_956d16c6a12e, tbl_7415e4ccca18, tbl_784e13d5a0b4): n and k of Al against hbar omega (eV, as printed), 6.1993E-03 eV to 1.0000E+04 eV, 206 rows: 2 datasets (n_Al, k_Al), primary, form = film, 412 points. R and lambda in printed. Row id = position in the table (the energy column is not unique as printed).

• Structural fix: the library’s cells encode the exponent signs as digits (the PDF’s font: “6.1993E203” for the printed “6.1993E-03”, “E102” for “E+02”; header “”v 1eV2”); the script decodes “E2” to “E-” and “E1” to “E+” and keeps the page’s strings. Checked on all four images. Two energies print one-digit exponents (“2.1697E-2”, “4.0000E-2”) on the page too.

• Checked (redundant columns): every cell against the images. R from n and k: to 4.4e-4 relative in every row to 66 eV (worst 62 eV, R = 2.3042E-05); above 68 eV (R < 4e-4) within the rounding of n and k except 700 eV (just outside), 6 keV (4 %), 10 keV (2 %). E x lambda = 1.23984 eV um to 5e-5 except the misprints below.

• Errata (9): energies misprinted on the page (confirmed on the images): row 74 “1.0000E+00” for 10 eV (lambda 0.12399 um); rows 177, 179, 187 “1.4500E-03”, “1.5200E-03”, “1.5620E-03” for 1450, 1520, 1562 eV (lambda confirms): 8 errata (x of n_Al and k_Al). n at 1.1 keV printed “9.9961E-05” for 9.9961E-01 (R confirms): 1 erratum. Not an erratum: the wavelength at 1.9 eV printed 6.5225E-01 for 0.65255 um (lambda is not stored; noted).

• Formulas (4, no form): semiquantum_model_Al (Eqs. 1-4, Table 1): the trial model; against Table 2 at 0.1-10 eV epsilon_1 is 4-9 % and epsilon_2 1-12 % smaller, and at 6.2 meV far off (-24,682 + 301,350i against -54,224 + 410,139i): it is the initial approximation, as the paper says. drude_damping_Al (Table 3 row 1, Gamma_0 = Gamma + omega^2 tau, tau/hbar assumed for the units): 6.2 meV epsilon_2 -2 %, epsilon_1 -14 %; 0.1 eV -9,452 + 6,152i against -9,134 + 6,790i. drude_constant_Al (row 2): epsilon_0 Omega_p^2/Gamma = 3.442e7 1/(Ohm m) reproduces the text’s sum-rule sigma_0 = 3.44e7 (2.90 uOhm cm) to three digits. asymptotic_eps2_Al (Eqs. 13-14): does NOT reproduce Table 2’s 2nk in its fitted range 4-10 keV (+25 % at 4 keV, -14 % at 10 keV; the table falls as omega^-3.7, the formula as omega^-4.0); no single correction explains it.

• Findings: the input data by range (technique): Ordal 1988 (6.2-37.8 meV), Bennett et al., Hass & Waylonis, Endriz & Spicer, Ditchburn & Freeman, Hunter (reflectance to 24.8 eV); the model at 11.7-15 eV; Shiles et al.’s k (from Palik’s Handbook) from 14.94 eV to 10 keV. Mathewson & Myers are a comparison only, not input. Against Weaver’s reprint of Shiles (scans, read by eye): agreement within the reprint’s three decimals from ~35 to 100 eV; k 10-28 % lower at 15-30 eV. Against ordal_1988: n -3 to -10 % at 50-1000 cm-1 and +0 to +10 % at 0.15-1.9 eV; k -0.3 to -5 % throughout. k is non-monotonic at 8-10 keV (consistent with R: as printed).

• Atom density (added in review): atom_density_Al, inline, 6.028 x 10^28 at/m^3 (value 6.028, scale 1e28, unit m-3, counts atoms, assumed, use check; p. 4759), with 13 electrons/atom (N = 13 n_at not printed as a number); omega_p,t = 32.86 eV (checked 32.87). Johnson & Christy, Leveque and Shiles print no atom, electron or mass density (Shiles: N symbolic only; JC: N symbolic, one electron per atom assumed).

• Status: corrected (2026-09-28).

TC-633 shiles_1980 (Shiles, Sasaki, Inokuti & Smith, Phys. Rev. B 22, 1612 (1980)) (2026-09-28)

• Transcribed: nothing (notes-only record). Tables I (plasmon energy and width), II (n_eff per shell) and III (mean excitation energy I) in notes, images checked; the vocabulary has none of these quantities.

• Ref. 12 is printed “E. Shiles and D. Y. Smith (unpublished)”. The tabulation is in Weaver et al.’s Physics Data 18-2, pp. 79-86 (confirmed on J. C. Travers’s scans: “publication by E. Shiles, T. Sasaki, M. Inokuti, and D.Y. Smith in Phys. Rev. B 22, 1612 (1980) based on the following tabulation”; Energy, epsilon_1, epsilon_2, n, k, Im(-1/epsilon), R; 0.040-1551 eV; three decimals), and per Rakic’s Ref. 27 in Smith, Shiles & Inokuti, Palik’s Handbook (1985), pp. 369-408.

• Notes: data sources per range; the 14 % reduction of kappa from the L edge to 300 eV, tapering linearly to zero at 500 eV (f sums 14.08 -> 13 e/atom); electron counts (13 e/atom; n_eff,c = 3.1(1), epsilon_b = 1.04 then 1.03(5); N not printed); sum rules (zeta ~ -0.002; sigma_0 = 3.21e17 s^-1, 2.80 uOhm cm); HGK comparison (HGK’s n smaller by a factor 2/3 at 0.08-1.5 eV; f sums 13.4-13.6).

• Status: verified (2026-09-28).

TC-634 babar_2015: the website data (0.1-30 eV) (2026-09-28)

• Transcribed: optical-constantsCuAgAu.xlsx, sheet This work, by tools/extract/babar_2015.py (the Table 1 part unchanged): per metal, n and k (refractive_index, extinction_coefficient, primary) and e1, e2 (permittivity_real, permittivity_imaginary, check), ids web_n_<M>, web_k_<M>, web_eps1_<M>, web_eps2_<M>. Cu 0.10-29.92 eV (169 rows), Ag 0.10-30.42 eV (170), Au 0.10-30.01 eV (168); each metal has its own E column (0.05 eV steps to 6.10 eV, then 0.5 eV: Cu and Ag 6.42, 6.92 …; Au 6.51, 7.01 …). R in printed. Values are the cells’ stored doubles in shortest exact form (the workbook displays 0.00/0.000; the stored values have five significant figures).

• Checked: every row, every metal: epsilon = N^2 within the bound set by the five printed figures (worst Cu 10.92 eV at 0.96 of the bound; Au 5.75 eV e1 = -0.00012672 with n = k = 1.2272); R = |(N-1)/(N+1)|^2 to 2.3e-5 (Ag 5.95 eV).

• Against Table 1 (every row 0.10-6.00 eV): the sheet’s R, e1, e2 round to Table 1’s printed R (three decimals) and epsilon (two decimals) in all 69 rows of all three metals: no difference. Table 1 is this sheet rounded; below 6 eV the web datasets duplicate Table 1 (both primary: only one should be used; data/solid/tables/*.toml use Table 1 now).

• Above 6 eV (the paper, p. 477): Ag from Leveque, Olson & Lynch’s reflectance to 30 eV; Cu, the JHW reflectance joined to Johnson & Christy’s, then HGK’s, to 30 eV; Au the 1981 compilation’s reflectance (Weaver 0.2-4 eV, Olson & Lynch ~4-30 eV); R = R_o E^-3.5 above 30 eV. So 6-30 eV is Babar & Weaver’s Kramers-Kronig analysis of other authors’ reflectance (Cu’s partly film data).

• Not extracted: sheets JC (Cu, Ag, Au, 0.64-6.6 eV, 49 rows, E R n k e1 e2), HGK (0.1-30 eV) and Palik (0.125-30 eV): other authors’ values. Their comparison with johnson_1972 and hagemann_1974 (other extractions) is left to review after the merge.

• Status: verified (2026-09-28).

TC-635 weaver_1981: Weaver, Krafka, Lynch & Koch, Physics Data 18-2 (1981); the gold table (2026-09-28)

• Record: the book’s citation (the library’s asserted BibTeX; no DOI; ISSN 0344-8401), identity = "ASSERTED", kind = "compilation". The library now has the front matter (source_01), Ag (source_02, supplement_01), Al (source_03, supplement_02), Au (source_04, supplement_03) and the bibliography (source_05, supplement_04, text only); Cu.pdf is not in it. The introduction’s statements in notes with pdf pages (+-10 % “in most cases”, p. 22; exp(-i omega t); bulk samples; oxide above 6 eV on electropolished surfaces; “room temperature or liquid helium temperature data only”).

• Gold, as preferred in review: the book’s printed table is now the primary data: n_Au, k_Au (primary, relative 0.10, level “not stated”), eps1_Au, eps2_Au (check), from supplement_03’s six tables (pp. 64-69, page order = pdf order), 284 printed rows (283 used), 0.10-30.00 eV, two decimals, loss and R in printed. The workbook’s copy is kept as sheet_n_Au, sheet_k_Au, sheet_eps1_Au, sheet_eps2_Au (check, 217 rows, five figures).

• Checked: the library’s cells against my independent transcription of the images (made in the first pass from the scans): identical except four library misreadings, fixed in the script against the images: 2.20 eV R “.980” for “.880”; 2.50 eV epsilon_1 “-1.96” for “-1.86”; 19.40 eV k “0.76” for “0.78”; 28.80 eV epsilon_2 “0.65” for “0.85”. Then epsilon = N^2 within the printed rounding in every row (worst 0.93 of the bound, 15.50 eV) and the loss function within its (worst 0.97, 1.90 eV). The printed R is not |(N-1)/(N+1)|^2 of the printed n, k (differences -0.0049 to +0.0064; worst 24.20 eV .119 against 0.125): R is presumably the measured reflectance (not stated).

• Errata (8): the energy after 6.50 eV printed “6.50” (p. 66; the digit is a 5 on the image; row id “6.50 (repeat)”) -> 6.60, and “26.50” (p. 68) -> 26.60, in each of the four datasets; evidence: the 0.1 and 0.2 eV sequences and the workbook’s 6.6 and 26.6 rows with the same values. Excluded: the 8.40 eV row printed twice, identically (p. 66; “8.40 (repeat)”).

• The four sheet-against-book differences, settled: all four are the workbook’s copying errors, the book (library cells and images agree) is right: 12.2 eV e2 sheet 2.02, book 2.03; 17.6 eV e1 sheet 0.86 (copying 17.8 eV), book 0.85; 21.4 eV e1 sheet 0.23, book 0.27 (consistent with the book’s n, k 1.03, 0.88); 11.4 eV R sheet 0.11, book .111. No book erratum follows. Otherwise the sheet’s n, k round to the book’s except 27 rows (at most 0.0071), and the sheet agrees with the book at every energy they share.

• Against ordal_1983’s copy (Table 3’s Weaver block, 21 rows): the same to its three figures.

• Temperature (doubt): the survey table (p. 57) lists “We Unpl, 0.26-4.2 eV, Refl, 4.2 K, X-tal, EP, A, absorptivity measured by calorimetry”; bibliography p. 255 “We Unpub: J.H. Weaver, Unpublished”. The table’s heading gives no temperature; temperature_k is not set; stated in the record’s notes and every Au dataset’s notes. “OL Unpub” (Olson & Lynch, ~4-30 eV) has no survey or bibliography entry.

• Bibliography used for the abbreviations cited in notes (SS80, HGK74, HGK75, HGK76, JC72, JC75, TH70, AKB80, BG68, BoL70, BL75, HKL77, MM71, GMS60, GB70, HKS68, DFR70, WG74, Bio56, SeS70, We Unpub, Th Pvt); not found in the library’s text of the bibliography: EPS63, RSK69, Hun Unpl, Ben Unpl, OL Unpub.

• Copper: still only J. C. Travers’s scan (not in the library): described in notes; its table is Hagemann et al.’s (0.10-61 eV, cut off).

• Status: verified (2026-09-28) for the gold table and its errata; open for the temperature of the 0.2-4 eV part.

TC-636 mcpeak_2015: the Supporting Information data files (closes TC-623’s missing item) (2026-09-28)

• Transcribed: ph5004237_si_002.txt (Ag, Au, Cu: 300-1700 nm, 10 nm, 141 rows) and ph5004237_si_003.txt (Al: 200-1700 nm, 5 nm, 287 rows; 1360-1425 nm absent in the file) by tools/extract/mcpeak_2015.py: eps1_, eps2_, primary, form = "film", technique “spectroscopic ellipsometry (V-VASE / VUV-VASE), two-phase model”. The recipe (rate, pressure, roughness) in each dataset’s notes; no grade (the files do not name the recipe, but they are Fig. 4’s data: its curves start at 300 nm for Cu, Au, Ag and 200 nm for Al, as the files do).

• Against the stated measured range (SI p. 2): V-VASE 400-1750 nm for Cu, Au, Ag, so the ten rows 300-390 nm of each lie outside it (kept; Fig. 4 plots them); 1710-1750 nm measured but not in the file. Al (VUV-VASE 150-1700 nm): every row inside; 150-195 nm measured but not in the file.

• Doubt: smoothing not stated for the files (the figures’ film data “were smoothed with a five-point moving average”); no uncertainty; vacuum wavelength presumed.

• refractiveindex.info / solprop: solprop’s aluminium 0.15-1.7 um (the Al/McPeak page) equals this Al file at all 287 wavelengths (4e-9 relative); its ten rows at 150-195 nm are not in the SI file (source unknown).

• Status: verified (2026-09-28); TC-623’s missing data files are no longer missing.

TC-637 stahrenberg_2001: the numbers through refractiveindex.info (2026-09-28)

• Transcribed: main/Ag/nk/Stahrenberg.yml (0.12782-0.49594 um, 361 rows) and main/Cu/nk/Stahrenberg.yml (0.13776-0.49594 um, 326 rows) by tools/extract/stahrenberg_2001.py: n_Ag, k_Ag, n_Cu, k_Cu, primary, abscissa um, no reproduced_from, provenance in notes (“Numerical data kindly provided by Prof. Dr. Norbert Esser”; J. C. Travers’s choice, 2026-09-28). The existing check dataset eps1_zero_Ag kept.

• Checked: Ag epsilon_1 = n^2 - k^2 crosses zero (- to +) at 3.788 and 7.948 eV: the text’s 3.79 and 7.95 eV (and + to - at 4.462 eV). d epsilon_2/dE maxima: Cu 4.30 and 4.70 eV (text 4.3, 4.7); Ag 4.04 eV (text 4.03). epsilon_2 at 4.49 eV exceeds Johnson & Christy’s (the workbook’s JC sheet) by 1.0 (Cu) and 0.4 (Ag), the text’s “1.0-1.5” and “0.5”. The files span the paper’s measured ranges (Ag 2.5-9.7 eV, Cu 2.5-9.0 eV, 0.02 eV steps).

• Roughness-corrected? Not established. Read off the pixels of Figs. 2 and 5 (a check, not data): at the epsilon_2 maxima the corrected curves are ~6.41 (Cu, 4.86 eV) and ~4.17 (Ag, 4.48 eV), the measured ones ~6.18 and ~4.09; the numbers give 6.25 and 4.12, between the two, nearer the measured curve for Cu. The database does not say.

• solprop: its silver table’s 185 rows at 0.12782-0.20595 um equal the file’s.

• Status: open (whether the numbers are the roughness-corrected function).

TC-638 weaver_1981: Shiles, Sasaki, Inokuti & Smith’s aluminium (pp. 79-86) (2026-09-28)

• Transcribed: supplement_02’s eight tables (pp. 79-86; tbl_41f659cbf54e, tbl_41f03578c473, tbl_550bc2056f85, tbl_6b7f728e7af0, tbl_5937497d4313, tbl_7ae05093ee33, tbl_b1243e5e0609, tbl_bd839bc39e50; all with CSV), page order = pdf order (each page continues the last), 447 rows, 0.040-1551.000 eV, energies as printed (1049.999 …). n_Al, k_Al (primary, relative 0.10 “not stated”), eps1_Al, eps2_Al (check); loss and R in printed. No reproduced_from: the book is where the tabulation was first printed (shiles_1980’s Ref. 12: “E. Shiles and D. Y. Smith (unpublished)”); the notes cite shiles_1980 as the analysis.

• Checked: every page against its image; every row with the redundant columns to the printed rounding: epsilon = N^2 (worst 0.97 of the bound, 0.650 eV), the loss function from epsilon (worst 0.99, 1.280 eV), R from N (within 0.0016, inside the bound). The cells that failed, read on the images: structural fixes (library misreadings) 1.700 eV R “.8977” for “.8972”; 27.000 eV epsilon_1 “0.700” for “0.706”; 134.000 eV Im(-1/epsilon) “0.036” for “0.038”. Erratum: 17.500 eV k printed 0.036 -> 0.038 (epsilon 0.269 + 0.040i gives k = 0.0385; 2nk = 0.0374 against epsilon_2 0.040; the loss 0.537 agrees with epsilon).

• k = 0.000: all 47 rows from 500 eV to 1551 eV print k = 0.000 (and epsilon_2 and the loss function 0.000 from 600 eV); kept as printed, with notes that they carry no absorption information (the range is to be cut in review). n is 0.996-1.000 above ~350 eV.

• Comparisons: ordal_1983’s Shiles block (26 points, 0.040-2.0 eV): n within 0.85 %, k within 0.41 %, its three figures (a faithful copy). ordal_1988 (40 points, 0.043-1.86 eV): n +2.1 % (median; to +3.0 %), k +1.1 % (to +1.35 %); e.g. 1.0 eV 1.233

  • 12.61i against 1.212 + 12.46i. rakic_1995: 0.05 eV 68.5 + 164.8i against 75.0 + 172.2i (n -9 %, k -4 %); 1.0 eV 1.316 + 12.24i against 1.212 + 12.46i; 5-10 eV k within 1-2 %; plasma edge (15 eV) n 0.151 against 0.125, k 0.110 against 0.153; from ~35 eV the same to three decimals (Rakic used Shiles et al.’s k above 14.9 eV, via Palik). mcpeak_2015’s film: |epsilon| 21-31 % below this table at 200-1700 nm (31 % at 200 nm, 21-22 % at 800-1700 nm).

• Re-point for the extraction of shiles_1980 (merged): its notes say the tabulation is “not yet in the library”; it now is (weaver_1981/n_Al, k_Al, pp. 79-86). Report only; I did not edit it.

• Status: corrected (2026-09-28).

TC-639 weaver_1981: the silver table (pp. 52-53), not extracted (2026-09-28)

• The book’s silver table (supplement_01, tbl_495baf394146 and tbl_2489ab9aa2d9) is headed “Silver: publication by H.J. Hagemann, W. Gudat, and C. Kunz in J. Opt. Soc. Am. 65, 742 (1975) based on the following tabulation”: 93 rows, 0.10-100.00 eV, two decimals. A reprint of a subset of the DESY report’s Table 4 (hagemann_1974: three figures, 5 meV-50 keV, with the loss function and reflectance): it adds nothing, so notes only.

• Compared with the workbook’s HGK sheet (Hagemann et al.’s silver, 61 common energies, 0.1-30 eV): the same to the book’s rounding except 11.00 eV (epsilon_1 2.00 against 2.08, n 1.52 against 1.543), 13.00 eV (epsilon_1 2.33 against 2.392) and 21.50 eV (epsilon_1 1.23 against 1.28). The comparison with hagemann_1974 itself is left to that record’s extraction.

• Library misreadings in this table (for whoever extracts it): 0.20 eV epsilon_2 “200.00” for 260.00; 3.50 eV epsilon_2 “0.00” for 0.60; 4.00 eV n “1.01” for 1.61; 10.00 eV k “0.50” for 0.56 (images checked).

• Status: verified (2026-09-28).

TC-640 hagemann_1974 (Hagemann, Gudat & Kunz, DESY SR-74/7, May 1974) (2026-09-28)

• Transcribed (tools/extract/hagemann_1974.py, from the library’s JSON cells; pages and order from the images and the margin labels “Table N, page M”):

  • Table 2 Al (PDF pp. 40-42; tbl_5eadb4abaadf, tbl_e9bd35b2f535, tbl_7ad069048df5): 148 rows, 1.00E-03 to 1.20E+05 eV;

  • Table 3 Cu (pp. 43-45; tbl_52ae5a332285, tbl_163d5f56d649, tbl_a4df553b9b72): 150 rows, 2.00E-03 to 5.00E+04 eV;

  • Table 4 Ag (pp. 46-48; tbl_5954ad9a5d51, tbl_a9377026a90a, tbl_44c1d033263c): 148 rows, 5.00E-03 to 5.00E+05 eV;

  • Table 5 Au (pp. 49-51; tbl_e95227627cb4, tbl_62a5fb0c7bc4, tbl_a46c4afa9069): 150 rows, 1.00E-03 to 1.50E+05 eV;

  • Table 6 Au “FROM REFLECTIVITY-DATA FITTED TO CANFIELD ET AL (10)” (pp. 52-54; tbl_376d0c04b097, tbl_28efb140cb95, tbl_5ab449433de5): 124 rows, 1.50-350 eV;

  • Table 9 Al2O3, evaporated amorphous (pp. 60-61; tbl_7cb0a953178f, tbl_73348bbbe4f6): 100 rows, 6.00 eV to 1.60E+03 eV.

  Per table five datasets: n_* (refractive_index), k_* (extinction_coefficient), eps1_*, eps2_* (permittivity_real/imaginary), mu_* (absorption_coefficient, cm-1, base e). Point counts: Al 100/148/100/148/148; Cu 99/150/99/150/150; Ag 100/148/100/148/148; Au (Table 5) 99/150/99/150/150; Au (Table 6) 100/124/100/124/124; Al2O3 100 each. use: n, k primary (Tables 2-5, 9); Table 6 all check; eps, mu check (computed from n and k). R, the loss function and N-EFF in printed (no quantity).

• Columns and units (from the images; the unit of ABSCOEFF confirmed by mu = 2 E k / (hbar c) in cm-1 to the printed rounding): ENERGY (eV), EPSILON1, EPSILON2, N, K, ABSCOEFF (cm-1), REFLECT% (percent), ENERGYLOSS (-Im 1/eps), N-EFF (Eq. 6). The last page of each metal’s table prints “1.-EPSL1” and “1.-N” (three decimals) instead of EPSILON1 and N: from 122 eV (Al), 65 eV (Cu), 90 eV (Ag), 84.5 eV (Au Table 5), 91 eV (Table 6). These have no quantity; they stay in printed and the n and eps1 datasets end there. Format question for review: a quantity for 1 - n (the x-ray decrement delta) or an offset key would let these rows in; they are the only printed n above those energies (three decimals).

• Structural fixes (in the script, all stated in its docstring): (1) the zeros the library reads as C, O, Q, D, U (and “,” for “.”, “F” for “E”) are read as printed; (2) 395 further cells corrected, each as (library cell, cell on the page) and checked on the 300-dpi render: by page 40: 20, 41: 9, 42: 16, 43: 14, 44: 13, 45: 27, 46: 26, 47: 27, 48: 75, 49: 23, 50: 16, 51: 19, 52: 21, 53: 23, 54: 7, 60: 35, 61: 24; by column: energy 48, eps1 30, eps2 115, n 29, k 8, mu 18, R 33, loss 45, N-EFF 69. Every cell of the 17 pages was compared with the image. On PDF p. 48 (Table 4 page 3, faint print) a few N-EFF digits, one R and one loss cell cannot be read and are written “?” in printed (no dataset value affected).

• Checked (in the script, on every row): eps1 = n^2 - k^2, eps2 = 2nk, R = |(N-1)/(N+1)|^2, loss = eps2/|eps|^2, mu = 2 E k/(hbar c), by interval arithmetic over the printed rounding, with 3 % allowed beyond it; energies increasing; N-EFF non-decreasing. 25 rows fail on the page itself and are listed (INCONSISTENT, the script insists the list is exact); all were read again on the image. Worst row per table (relative excess beyond the rounding):

  • Table 2 Al: mu and loss 13 % / 11 % at 72.9 eV (the ABSCOEFF and ENERGYLOSS cells of 72.9-80 eV are pasted in, another typeface; mu 4-13 % below 2Ek/hbar c, k and eps2 consistent); eps2 3.4 % at 3.00 eV (printed 5.68, 2nk = 5.48); eps1 1.2 % (3.00 eV).

  • Table 3 Cu: mu 13 % at 2 meV (eps1 and n blank there); eps2 2.3 % (0.1 eV).

  • Table 4 Ag: R 7.4 % at 3.80 eV; eps2 3.7 % at 25 meV; mu 3.9 % at 1.5 keV.

  • Table 5 Au: at 5 meV eps1 10 %, eps2 5 %, loss 20 %, mu 8 %; 0.1 eV loss 6 %.

  • Table 6 Au: loss 1.8 % (2.2 eV); nothing beyond 3 %.

  • Table 9 Al2O3: at 6 eV loss 28 %, mu 17 %, eps2 9 % (k = 2.2E-03 at the edge); 77.5 eV loss 11 %; 250-500 eV mu 3-8 % below. No erratum: none of these is a clear misprint of one cell (they are the report’s columns computed on the analysis grid and printed at the table energies, or the pasted amendments).

• Errata sheet (PDF p. 2, image checked), recorded in notes as the report states: (1) Table 10 missing, printed on the back (PDF p. 3; tbl_7ffa99e81efc, checked); (2) Table 8 page 1, carbon: the first 13 energies should have a negative exponent (carbon not extracted: no erratum entry).

• Table 10 (sum rules): in notes; identical value for value to hagemann_1975 Table I.

• Densities (added in review): B = m A/(2 pi^2 e^2 rho L) (Eqs. 6-8) but no atomic, mass or electron density of Al, Cu, Ag, Au or Al2O3 is printed anywhere (text, section 5, table headers, Table 10 searched): no atom_density dataset. The only density is carbon’s mass density, 1.5 g cm-3 (report p. 20, PDF p. 24), in notes. Electron counts Z of Table 10 in notes (Mg 12, Al 13, Cu 29, Ag 47, Au 79, Bi 83, C 6, Al2O3 50). Last printed N-EFF: Al 13.495, Cu 27.505, Ag 47.506, Au 78.465 (Table 5), Au 18.584 at 350 eV (Table 6), Al2O3 45.09 at 1.6 keV.

• Method per range (section 4) in notes with the references as printed. Summary:

  • Al: DrP (Bennett & Bennett) to 0.155 eV, interpolation to 0.8, Mathewson & Myers ellipsometry to 2.0, DrP estimate to 13.5, Ditchburn & Freeman to 36, own UHV films to 74, Hagemann’s Diplomarbeit to 150, Gahwiller & Brown / Haensel et al. shape fitted to Fomichev & Lukirskii to 300, Hubbell above;

  • Cu: Johnson & Christy (DrP to 0.5, k to 6.5), Ehrenreich & Philipp / Canfield & Hass interpolation to 13, own to 150 (mu - 0.8e5), Sonntag to 450, Hubbell;

  • Ag: Johnson & Christy (DrP to 0.5, k to 3.5), Irani et al. to 11, interpolation to 16, own to 110 (Eqs. 4-5, mu - 0.7e5), Haensel et al. to 300, Hubbell;

  • Au: Johnson & Christy (DrP to 0.6, k to 2.4), Irani et al. to 10.5, fitted segment with Canfield, Hass & Hunter’s shape to 20, own to 117 (mu - 1.4e5), Haensel et al. (1969) to 300, interpolation to 500. Table 5 fitted to the transmission (79 electrons); Table 6 from the measured reflectance extrapolated (closer to energy loss; R at 22.5 eV 16.0 % against Table 5’s 26.1 %);

  • Al2O3: Hass, Hunter & Tousey to 10, Hunter to 20, own to 150, Fomichev & Parobets to 500, Al + O from Hubbell above.

• Doubts:

  • Table 9 stops at 1.6 keV (N-EFF 45.1) though Table 10 integrates to 50.2-50.6: either the printout was cut or a page is missing from this copy (PDF p. 62 is a figure).

  • p. 45 (Cu) at 78 eV, 1-eps1: settled as 0.048 (TC-641).

  • The noble metals’ n below ~3.5 eV (Ag), 2.4 eV (Au) is 2-5x Babar & Weaver’s; the report warns that Johnson & Christy’s n is not KK-consistent with its absorption, but its own n there is not reliable either (k is fine). The primary flag on n below those energies is still to be decided.

  • The Table 6 / Table 5 choice for gold (use = check for Table 6 as recorded).

• Comparisons (report only):

  • Weaver et al.’s reprint of Table 4 (Physics Data 18-2, pp. 52-53, J. C. Travers’s scan, PDF pp. 10-11): eps to two decimals, n, k, loss, R recomputed from them; 0.1-100 eV, some rows omitted. Agrees to the last digit except 11 eV eps1 (2.00 vs 2.080), 36 eV eps2 (0.78 vs 0.732), 70 eV eps1 (0.65 vs 0.698), each the reprint’s slip; one unit at 22.5 and 100 eV. It confirms many script corrections independently (3.50 eV eps2 0.60, 3.60 eV -1.22, 3.90 eV, 4.00 eV eps2 1.94, 7.0 eV 2.49, 17 eV 1.02, 25 eV 1.57, 28 eV 1.06, 48 eV 0.55, 76 eV 0.27, 85 eV 0.19). Weaver’s reprint is reproduced from this report (through the Letter).

  • babar_2015 (0.1-6 eV): k within 1-7 % (0.5-6 eV); n 2-5x larger below ~3.5 eV (Ag 1 eV: 0.278+9.02i vs 0.098+8.98i). At 6 eV: Cu 1.036+1.590i vs 1.020+1.597i; Ag 1.339+1.280i vs 1.079+1.247i; Au T5 1.618+1.300i, T6 1.412+1.330i vs 1.243+1.151i. Below 0.5 eV the Drude extrapolations differ (Cu 0.1 eV eps2 4250 vs 1911).

  • werner_2009 REELS (20-70 eV): rms eps differences 0.10 (Cu), 0.28/0.49 (Ag eps1/eps2), 0.40/0.80 (Au T5), 0.26/0.32 (Au T6); worst at 20-25 eV (Au 20 eV eps1 1.374 vs 0.240). Table 6 is closer to REELS.

  • ordal_1988 (Al, 0.006-1.86 eV): k within 1-8 %; n 20-40 % lower at 0.2-1.3 eV (1 eV: 0.949+12.2i vs 1.233+12.61i), +26 % at 0.05 eV.

• Status: verified (2026-09-28).

TC-641 hagemann_1974: the “1.-N” columns as delta (after the merge of 5660a92) (2026-09-28)

• Transcribed: with the new quantity refractive_index_decrement (delta = 1 - n; commit ea7d69e, merged into data/metals-D), the “1.-N” column of each metal table’s last page is now a dataset, same row ids, printed string kept, use as the table’s n:

  • delta_Al (Table 2, PDF p. 42): 48 points, 1.22E+02 to 1.20E+05 eV, primary;

  • delta_Cu (Table 3, p. 45): 50 points, 6.50E+01 to 5.00E+04 eV, primary;

  • delta_Ag (Table 4, p. 48): 48 points, 9.00E+01 to 5.00E+05 eV, primary;

  • delta_Au (Table 5, p. 51): 50 points, 8.45E+01 to 1.50E+05 eV, primary;

  • delta_Au_table6 (Table 6, p. 54): 24 points, 9.10E+01 to 3.50E+02 eV, check.

  220 points; the record now has 35 datasets, 3,876 points. Each continues its n dataset without a gap (n ends at 120, 64, 85, 84 and 89 eV). “1.-EPSL1” stays in printed. Table 9 has no “1.-N” page, hence no delta.

• Checked: as before, on every row (n = 1 - delta and epsilon_1 = 1 - printed value against k, epsilon_2, R and the loss where they allow; mu against k); no new failure.

• Doubt, for review: three decimals are coarse at x-ray energies: above 1 keV delta is printed -0.003 to +0.002, and 33 printed values are negative (Al above 3 keV, Cu 8-9 keV, Ag 350-370 eV and above 2 keV, Au 5-83 keV; the worst Ag -0.007 at 370 eV). Read them as the printout’s resolution (the report could not evaluate its sum rule on n - 1 for the same reason, p. 23), not as n > 1.

• The p. 45 cell settled: Cu 78 eV “1.-EPSL1”, read “0.043” at 300 dpi, is 0.048: at 600 dpi the row’s glyphs have faded left halves (its leading 0 reads as a 3) and the last digit is an 8 missing its left half; 0.048 is what 1 - n = 0.020 and k give. Now the script’s 396th correction (the k, eps2 and mu files of Cu change only in that row’s printed).

• The decision recorded in the notes: the noble metals’ n below 3.5 eV (Ag) and 2.4 eV (Au) stays primary in the record (it is what the report prints); it will not be used.

• Status: verified (2026-09-28).

TC-642 hagemann_1975 (re-pointed) (2026-09-28)

• Notes only (no datasets): the “DESY report missing” paragraph now points to hagemann_1974 (the tables, the method per range); Table I stated to reproduce the report’s Table 10 value for value (compared 2026-09-28). No dataset to re-point.

• Status: verified (2026-09-28).

TC-643 The metals’ further sources and external data (2026-09-28)

• The request: J. C. Travers supplied the sources TC-619 to TC-625 found missing: the DESY report SR-74/7 and Weaver et al.’s Physics Data 18-2 chapters (Ag, Al, Au, the bibliography) in the library, with Johnson & Christy 1972, Leveque et al. 1983, Ordal et al. 1983 and 1985, Rakic 1995 and Shiles et al. 1980; McPeak et al.’s two data files. Four parallel extractions curated them (TC-626 to TC-642).

• External data (src/optmat/data/external/, each with its PROVENANCE.md):

  • henke/{al,ag,au,cu}.nff, CXRO, fetched 2026-09-28;

  • refractiveindex_info/main/{Ag,Cu}/nk/Stahrenberg.yml at the database’s commit c5c2f18: J. C. Travers’s decision (2026-09-28) to take Stahrenberg et al.’s numbers, which exist only as a private communication to the database (“kindly provided by Prof. Dr. Norbert Esser”), as that paper’s data (TC-637);

  • weaver/optical-constantsCuAgAu.xlsx, from J. H. Weaver’s website (the paper’s Ref. 4): Babar & Weaver’s analysis to 30 eV (TC-634);

  • mcpeak_2015/ph5004237_si_00{2,3}.txt, supplied by J. C. Travers (TC-636).

• Status: decided (2026-09-28).

TC-644 A quantity for 1 - n (2026-09-28)

• The DESY report prints 1 - n (and 1 - epsilon_1) instead of n above 65-122 eV (TC-640, TC-641). refractive_index_decrement (delta = 1 - n, family refractive, unit 1, abscissa wavelength) takes those columns; 1 - epsilon_1 stays in printed.

• Three decimals make the printed decrement coarse above a few hundred eV: 33 printed values are negative, the printout’s resolution and not n > 1 (TC-641).

• Status: decided (2026-09-28).

TC-645 Table models: pairing by shared wavelength, the decrement, Henke segments (2026-09-28)

• Pairing. A segment’s two datasets are paired at the wavelengths they share, not required to have identical abscissae: the DESY report prints n to 64-120 eV and 1 - n above, and k throughout (tests/solid/test_tabulated.py).

• Decrement. A refractive_index_decrement dataset pairs with k: n + ik = 1 - delta + ik.

• Henke segments. henke = "<element>" with an atom_density dataset (counts = atoms) gives n + ik = 1 - r_e lambda^2 N (f1 - i f2)/(2 pi) (Henke et al. 1993, Eq. 3). With Rakic’s aluminium density (6.028e28 m^-3, TC-632) it gives k within 2 % of Rakic’s at 1 keV (tested) and 1-7 % at 300-1000 eV, but 27-48 % below it at 25-72 eV and 4-25 % above at the L edge: the independent-atom limit fails near the plasma and L edges, as it must. No table uses it: the measured tables reach 0.8-4 nm, and neither the DESY report nor Weaver et al. print the noble metals’ densities (TC-640).

• Status: decided (2026-09-28).

TC-646 The tables of silver, gold and copper (2026-09-28)

• Silver: DESY Table 4 (1 - n, 90-300 eV, then n, 50-85 eV; 4.13-24.9 nm), Werner et al.’s REELS (25-70 nm), Babar & Weaver’s website analysis (70.5 nm-12.4 um). Gold: DESY Table 6 (1 - n, 91-350 eV, then n; 3.54-24.9 nm), REELS (25-70 nm), Babar & Weaver (70.5 nm-12.4 um). Copper: DESY Table 3 (1 - n, 65-400 eV, then n; 3.1-41.35 nm), Babar & Weaver (41.4 nm-12.4 um), Ordal et al. 1985 (12.5-55.6 um).

• Babar & Weaver’s website data, not Table 1: the same analysis (Table 1 is it rounded, TC-634), with five figures and to 30 eV. Below 6 eV the table’s values are unchanged at the tabulated points; between them the finer grid (0.05 eV) changes the interpolant (copper at 10 um: 7.30 + 73.2i against 7.39 + 70.1i).

• The vacuum ultraviolet. From 40 to 200 nm the sources for silver and gold spread by 20-50 % in k (docs/metals.md): Babar & Weaver (Kramers-Kronig of reflectance), REELS, the DESY films (Kramers-Kronig of transmission), Stahrenberg et al.’s ellipsometry (to 128 nm, 13-27 % above Babar & Weaver in silver’s k) and Johnson & Christy (to 188 nm). Decision: keep Babar & Weaver’s single analysis down to 70 nm, then REELS, then the DESY report, because (1) Babar & Weaver and REELS, independent methods, agree to 3-16 % at 41-70 nm (4 % at 70 nm) while the DESY films’ k is 25-100 % above both at 40-50 nm (an oxide on the films is possible; Shiles et al. suspected one for aluminium); (2) Babar & Weaver’s k is likely least reliable at the top of their range, where they extrapolate the reflectance beyond 30 eV; (3) REELS and the DESY tables meet at 25 nm to 1.5-6 % in n and 2-8 % in k. The joins’ steps: silver 25 nm (-1.5 % n, -7 % k), 70 nm (+3 %, +1 %); gold 25 nm (+6 %, +2 %), 70 nm (+3.5 %, +2.7 %); copper 41 nm (+1.8 %, +5 %).

• Gold, Table 6 over Table 5: Table 6 (joined to Canfield et al.’s measured reflectance) meets REELS at 25 nm; Table 5 (fitted to the transmission, 79 electrons) is 30-40 % higher in k at 17-30 nm. The report says Table 6 is closer to the energy-loss data (TC-640).

• The X-ray ends are where the printed 1 - n is still >= 0.004 (silver 300 eV, copper 400 eV) or the table ends (gold, Table 6, 350 eV).

• Beyond 12.4 um: copper takes Ordal et al.’s 1985 measurement, 11 % below Babar & Weaver in k at the join (9-10 % below where both tabulate). Silver and gold have only Drude curves beyond 12.4 um (Bennett & Bennett’s in ordal_1983; the Drude fits of ordal_1983 and ordal_1985): the tables hold their end values, with a warning.

• Not used: the DESY report’s noble-metal n below 3.5 eV (Ag) and 2.4 eV (Au), built on Johnson & Christy’s k and Drude parameters, 2-5 times Babar & Weaver’s (TC-640); the films (Johnson & Christy, McPeak et al.) and Stahrenberg et al., kept as datasets and compared on docs/metals.md.

• Status: decided (2026-09-28).

TC-647 The table of aluminium (2026-09-28)

• Rakic’s Table 2 (40 eV-1.56 keV; 0.79-31.0 nm), Shiles et al.’s tabulation in Weaver et al. 1981 (0.040-39 eV; 31.8 nm-31 um), Ordal et al. 1988 (33-200 um). Replaces TC-619’s Ordal-only table (667 nm-200 um).

• Why Shiles et al.: one self-consistent Kramers-Kronig analysis of bulk aluminium from the far infrared to the soft x-ray, tested by sum rules, the dc conductivity and the stopping power (TC-633, TC-638); Ordal 1988 rests on it above 320 cm-1 and lies 1-3 % above it. The alternatives differ more: Rakic (films; n -9 to +9 %, k -2 to -4 % below 2 eV, the plasma edge shifted), the DESY report (n 20-40 % lower at 0.4-1.6 eV), McPeak et al.’s film (|epsilon| 21-31 % smaller).

• Why Rakic above 40 eV: there its k is Shiles et al.’s (through Palik’s handbook) and its n within 0.3 % of theirs, with five figures where the tabulation’s three leave k at 0.00x (0.000 from 500 eV); it samples the L edge every 0.05-0.1 eV. Join at 31 nm: 0.942 + 0.0078i against 0.935 + 0.008i.

• Status: decided (2026-09-28).

TC-648 The metals: what stays open (2026-09-28)

• Weaver’s gold below 4 eV may be at 4.2 K (the survey table; TC-635): it enters table/Au through Babar & Weaver’s analysis. Unresolved.

• Whether Stahrenberg et al.’s numbers are roughness-corrected (TC-637).

• ordal_1983’s copy of Schulz’s silver at 450 nm (n printed 0.55, ten times its neighbours; TC-626): not used by any table; Schulz 1954 would settle it.

• Measured far-infrared silver and gold (Ordal et al., Appl. Opt. 26, 744 (1987) for gold); the DESY report’s Table 9 above 1.6 keV; the metals’ densities (for Henke).

• Parity with solprop (tests/solid/test_metals_page.py) now holds where the sources are the same: silver 25-70 nm and 207 nm-5 um, aluminium 33-200 um. solprop’s silver at 70-207 nm (REELS, Stahrenberg) and aluminium at 0.15-1.7 um (McPeak’s film) differ by 12-18 % in k (docs/metals.md).

• Status: open (2026-09-28).

TC-649 schott_2023 (SCHOTT’s N-BK7 data sheet, as of 01-Dec-2023, with TIE-29) (2026-09-28)

• The source: not a paper; J. C. Travers supplied the data sheet and SCHOTT’s Technical Information TIE-29 (“Refractive Index and Dispersion”, August 2023) and asked that they be used directly, not added to the paper library. The data sheet’s text layer (the PDF is made from a spreadsheet) is kept as data/external/schott/n-bk7-datasheet.txt with a PROVENANCE.md (the PDFs’ SHA-256; the PDFs stay in J. C. Travers’s private copy), checked against the page image cell by cell, and extracted by tools/extract/schott_2023.py.

• Transcribed: the 20 printed indices (312.6-2325.4 nm; use = check, catalogue values for a nominal melt), the internal transmittance of 10 mm (26 values, 290-2500 nm) and 25 mm (25 values, 300-2500 nm) as the new quantity internal_transmittance (parameters.thickness_mm), and dn_rel/dT and dn_abs/dT at 1060.0 nm, e and g for three temperature intervals (6 datasets of 3). Formulas: the Sellmeier (form n2_sellmeier) and TIE-29’s dn/dT formula (Eq. 11, no form).

• Conventions (TIE-29): indices relative to air (‘measured relative to the refractive index measured in air’, p. 1) at 20 C (‘Reference temperature (20 C)’) and ‘normal air pressure (0.10133 x 10^6 Pa)’ (section 5); exact to five decimals (+-2e-5 beyond 2 um). The formula’s wavelengths are those of TIE-29’s Table 1, the lines’ standard-air wavelengths (C 656.2725 nm): recorded as standard air, an inference.

• Checked: the Sellmeier formula reproduces all 20 indices to their five decimals at TIE-29’s line wavelengths (four come out one unit off at the data sheet’s 0.1 nm rounded wavelengths); the dn/dT formula, averaged over each interval, reproduces all nine printed dn_abs/dT to their one decimal. The coefficients are solprop’s (the Zemax catalogue of 2017-01-20).

• Status: verified (2026-09-28).

TC-650 weber_2003 (Weber, Handbook of Optical Materials, CRC 2003): sapphire’s two rays (2026-09-28)

• The source: J. C. Travers supplied the handbook’s section PDFs (a private copy), not for the paper library. Section 1.3.4, ‘Dispersion Formulas for Refractive Indices’ of crystals ‘at room temperature’, p. 76: sapphire’s ordinary and extraordinary Sellmeier formulas, 0.22-5.0 um, Ref. 13 = Malitson & Dodge, J. Opt. Soc. Am. 62, 1405 (1972), a talk abstract (p. 89). Transcribed from the text layer and checked against the page image digit by digit; reproduced_from names the abstract.

• What it is: the formulas solprop uses (refractiveindex.info’s Malitson-o and -e, which cite Dodge’s 1986 handbook at 20 C), the ordinary ray’s first coefficient with one digit more (1.43134936). No index is printed with them.

• Conditions: room temperature, read as 20 C; relative to room air on air wavelengths, inferred from the NBS method as for malitson_1962 (TC-546).

• Checked: against malitson_1962/sellmeier_o at the same argument, 9.4e-5 lower at 0.3 um, 5-8e-5 at 0.4-2 um, 0.9e-5 at 4 um, 6.5e-5 higher at 5 um (4 K of temperature accounts for about 5e-5); the extraordinary ray gives 1.74754 at 1.01398 um against malitson_1962’s single measured 1.74794 (another sample, presumably). Birefringence 0.0091 at 0.3 um to 0.0056 at 5 um.

• The book’s other rows (CaF2, MgF2, BaF2 and many more crystals) are not curated.

• Status: verified (2026-09-28).

TC-651 Sapphire’s two rays and N-BK7 recommended (2026-09-28)

• N-BK7: schott_2023/sellmeier, relative to air at 20 C and 101 330 Pa, made absolute with Edlen’s air (the formula models’ index_medium = "air", TC-398). solprop uses the same coefficients as absolute indices: 4.1e-4 low at 1 um. A catalogue value for a nominal melt; a given melt departs by up to its tolerance grade (+-5e-4 at Step 3; TIE-29 Table 3). The model is lossless; the transmittance and dn/dT are curated for later.

• Sapphire: both rays from weber_2003 (Malitson & Dodge 1972), replacing TC-546’s malitson_1962/sellmeier_o for the ordinary ray. Reasons: one determination for both rays keeps the birefringence consistent (mixing Malitson’s 1962 ordinary ray with the 1972 extraordinary one would shift it by 5-9e-5, about 1 %); the pair reaches 220 nm where the 1962 formula starts at 265 nm; it is solprop’s formula. Against it: the 1972 work was published only as an abstract and in handbooks, with no indices. Malitson’s 1962 formula, fitted to 46 measured indices, stays by name and is the check (5-8e-5 above at 0.4-2 um, the temperature difference).

• solprop: every solid it models now has a recommended optmat model (docs/crystals.md, docs/metals.md; tests/solid/test_crystals_page.py covers N-BK7’s parity).

• Status: decided (2026-09-28).

TC-652 The ionisation rates of the noble gases enter optmat (2026-09-28)

• Where: optmat.gas.ionisation_rates, optmat.gas.ionisation_validation, data/gas/ionisation_rates.toml, the manual page Ionisation rates.

• Decision: optmat gives the strong-field ionisation rates of He, Ne, Ar, Kr and Xe, and not only their parameters. This supersedes the boundary of TC-439 (“solprop keeps the response kernels and the rate formulas”) for the rates of the atoms; the response kernels and the molecules’ rates are unchanged.

• Reason: the parameters and the formula are valid only together. Tong and Lin’s and Zhang et al.’s constants were fitted relative to a tunnelling rate with Tong et al.’s coefficient and m = 0 for one electron; applied to the Hartree coefficient of the propagation codes they are off by 0.57 (Ne) to 2.0 (Xe) (TC-657). A rate can be validated against rates and yields only where the formula is.

• What optmat gives: the rate as a function of the field, per atom, in SI, with its sources, its stated range and its uncertainty; the named models of ionisation_rates.toml. What it does not: tables for interpolation, clipping, or the plasma response, which are the propagation code’s.

• Status: decided (2026-09-28).

TC-653 The Coulomb factor of the rate of Perelomov, Popov and Terent’ev (2026-09-28)

• Where: optmat.gas.ionisation_rates.coulomb_factor; Perelomov_1966_IonizationAtomsAlternating, Ilkov_1992_IonizationAtomsTunnelling, Larochelle_1998_CoulombEffectMultiphoton, Berge_2007_UltrashortFilamentsLight, Popruzhenko_2008_StrongFieldIonization (the Letter) and Popruzhenko_2008_CoulombCorrectionIonization in the library.

• Finding: three Coulomb factors multiply the short-range rate (Perelomov et al. 1966, eq. 54) in the literature, and the first two are not distinguished:

  • static, (2F_0/F)^(2n*): Perelomov and Popov 1967 (not in the library), as Larochelle et al. 1998, eqs. (9)-(10), and as Popruzhenko et al. (2008) describe Becker et al. 2001;

  • Ilkov, (2F_0/F)^(2n*) (1 + gamma^2)^(-n*): Ilkov et al. 1992, eq. (8), and Bergé et al. 2007, eq. (B14), in which the power 2n* stands under the same bracket as the short-range rate’s |m| + 3/2. No paper read derives it. Ilkov et al.’s own footnote (p. 4007) says that for linear polarisation the Coulomb function is 1 for gamma << 1;

  • Popruzhenko, (2F_0/F)^(2n*) (1 + 2 gamma/e)^(-2n*): Popruzhenko et al. 2008, eq. (5), derived for any gamma and checked by its authors on hydrogen at 400 nm and Xe17+ at 13 nm; the recent literature’s choice (Zhao et al. 2016, eq. 7).

• Checked: each factor in the same model (one electron, m = 0, Tong et al.’s coefficient, Tong and Lin’s correction, so that the static limits are equal), model over reference:

  • One electron, 800 nm, 6 fs (travers_2026_trecx, the population beyond 20 bohr; the cycle-averaged rate on the envelope). Argon, from 1.7e13 to 8.4e14 W/cm2 (gamma 2.8 to 0.4): static 0.94 to 1.21; Ilkov 0.13 at 1.7e13, 0.76 at 9.6e13, 1.4 to 1.6 at 2.3e14 to 3.5e14 (its missing static correction); Popruzhenko 0.15, 0.63, 1.1 to 1.4. Helium, from 2.4e14 to 2.1e15 W/cm2: static 1.00 to 1.15.

  • Helium, all electrons (parker_2007, eq. 5), with the default’s effective number of electrons: at 780 nm and 1e14, 2e14, 4e14, 1.4e15 W/cm2 (gamma 1.47, 1.04, 0.74, 0.39), static 1.00, 0.95, 1.01, 1.17; Ilkov’s factor 0.42, 0.55, 0.73, 1.06; Popruzhenko’s 0.34, 0.41, 0.53, 0.80. At 390 nm and 1e14 to 1.4e15 W/cm2 (gamma 2.9 to 0.8): static 1.27 to 1.42; Ilkov’s 0.24 to 0.91; Popruzhenko’s 0.24 to 0.66.

  • Measured (wallace_2016, TC-660): the static factor matches the yields of Ar, Kr and Xe with the intensities scaled by 0.98, 1.00 and 1.00; the forms of the literature need 1.16, 1.09, 1.05 (Ilkov) and 1.18, 1.08, 0.98 (Popruzhenko).

• Doubt:

  • Popruzhenko et al.’s Phys. Lett. A paper (eq. 20) gives, for gamma >> 1, a factor larger than the static one by (2 gamma)^(2n*), which contradicts the Letter’s by (4 gamma^2/e)^(2n*). The Letter says of an earlier derivation that it was “orders of magnitude off because of the erroneous omission of a seemingly higher-order term” (its ref. 20); the Phys. Lett. A result is taken to be superseded.

  • The static factor has not been tested on hydrogen, on which Popruzhenko et al. and Zhao et al. validated theirs, or at wavelengths other than 390, 780 and 800 nm.

  • In the vacuum ultraviolet no such rate holds: for argon at 140 nm and 5e12 to 1e14 W/cm2 J. C. Travers’s one-electron calculations (not curated) give yields 6 to 13 times below the Ilkov form, and the static form is higher still. The models warn below 350 nm.

• Decision: the static factor is the default’s. The other two are kept (coulomb = "ilkov", "popruzhenko"; the models ppt_ilkov, ppt_popruzhenko) to reproduce rates computed with them.

• Status: decided (2026-09-28); open: hydrogen, 1030 nm and beyond. The static factor at first hand, and its range of validity: TC-670. Against the one-electron calculations’ ionised fraction the margin is narrower: TC-812.

TC-654 The sum over channels of the rate, and its integral (2026-09-28)

• Where: optmat.gas.ionisation_rates.channel_factor.

• Decision: by default the sum of Perelomov et al.’s eq. (55) over the numbers of photons above the threshold nu is replaced by its integral, sqrt(pi) |m|! beta^|m| sqrt(beta/alpha) / (2 (alpha + beta)^(|m| + 1)). The sum has a step wherever nu passes an integer, which leaves kinks in the rate as a function of the field; the integral is smooth, as an interpolation table and a quadrature over a beam need.

• Checked: the closed form against quadrature for m = 0 and 1 at gamma = 0.3, 1 and 3 (1e-6, tests/test_ionisation_rates.py); it tends to 1 with A_m for gamma -> 0. For argon at 800 nm the rate with the sum over the rate with the integral is 1.33 at 2e13 W/cm2 (gamma 2.6), 0.69 at 5e13 (1.6), 0.77 at 1e14 (1.15), 1.06 at 2e14 (0.81) and 1.03 at 4e14 (0.57): within 10 % below gamma = 1 and 30 to 50 % above it, oscillating with the channel closings.

• Decision: channel_sum = "sum" gives the sum.

• Status: decided (2026-09-28).

TC-655 The static correction of the tunnelling rate (2026-09-28)

• Where: optmat.gas.ionisation_rates.tong_lin_factor, zhang_factor; tong_2005, zhang_2014.

• Finding: the tunnelling rate (Perelomov et al. 1966, eq. 4; Tong et al. 2002, eq. 7) is too high at every field at which an atom ionises. For argon (zhang_2014 Table IX, the exact rate of one electron in the GSZ potential) with Tong et al.’s coefficient it is 2.2 times too high at 0.053 au, 0.64 of the barrier-suppression field, and 3.8 times at 0.094 au (TC-542’s numbers). “Barrier suppression” is a misnomer for the correction, which is the term of first order in the field of the tunnelling rate: in the weak-field asymptotic theory (trinh_2013, Ar: B = -7.7) it is 0.6 at 0.053 au.

• Checked: the one-electron static rate of the model (one_electron) over Zhang et al.’s exact rates, up to 0.164 au (1.95 of the barrier-suppression field): 0.94 to 1.01 in Tong and Lin’s potential, 1.10 to 1.20 in the GSZ and 1.09 to 1.19 in Muller’s. Tong and Lin’s and Zhang et al.’s factors agree within 10 % between 0.64 and 1.7 of that field for argon.

• Decision:

  • Tong and Lin’s factor for every gas: it is smooth and tends to 1 at low field. Zhang et al.’s polynomial is positive at low field for every gas but neon (for argon up to 0.22 of the barrier-suppression field), where it is held at 1, which leaves a corner in the rate; it is fitted from 0.5 to 4.5 of that field only.

  • Krypton and xenon: Tong and Lin fitted no alpha. Their suggestion, 9.0 “for ionization from the higher partial waves”, with which the rates agree with the calculated ones “within 50%” (p. 2596), is taken. Zhang et al.’s factors for Kr and Xe correspond to alpha = 9.7 and 8.3 at the barrier-suppression field, and to 10.2 and 4.8 at half of it.

  • The models warn above twice the barrier-suppression field (Tong and Lin), where Zhang et al. find the factor to fail.

• Doubt: for krypton and xenon no exact static rate is tabulated (Zhang et al. give fits only), and the coefficient to which their constants are relative is not stated.

• Status: decided (2026-09-28).

TC-656 Ilkov et al. 1992, eq. (8), and the equation of Bergé et al. 2007 (2026-09-28)

• Where: Ilkov_1992_IonizationAtomsTunnelling eqs. (2) and (8) (p. 4007 and after), Larochelle_1998_CoulombEffectMultiphoton eq. (10), Perelomov_1966_IonizationAtomsAlternating eqs. (54)-(55), Berge_2007_UltrashortFilamentsLight eq. (B14), each read on the page image; optmat.gas.ionisation_rates.short_range_rate_au.

• Finding:

  • Ilkov et al.’s eq. (8) is printed with the prefactor (3/2 pi)^(1/2), which is half of the (6/pi)^(1/2) of Perelomov et al.’s eq. (54) and of Larochelle et al.’s eq. (10). With A_m -> 1 for gamma -> 0 (their definition, which is Perelomov et al.’s eq. 55), eq. (8) tends to (3/2 pi)^(1/2) (2F_0/F)^(2n - |m| - 3/2) …, and eq. (2) is (3F/pi F_0)^(1/2) (2F_0/F)^(1/2) = (6/pi)^(1/2) times the same: the statement that eq. (8) “transforms to” eq. (2) does not hold as printed. A misprint of eq. (8).

  • Bergé et al.’s rate is eq. (B14) of their Appendix B; Appendix A is the list of abbreviations. Its prefactor, 4 sqrt(2)/pi, is (6/pi)^(1/2) times the 4/sqrt(3 pi) of A_m, and it agrees with Perelomov et al. It is a rate per (l, m), without a sum over m or a number of electrons.

• Checked: tests/test_ionisation_rates.py writes out eq. (B14) independently and compares the model ppt_ilkov with it (1e-10), and compares the tunnelling limit of eq. (54) with the cycle average of the static rate (1e-5 at gamma = 1e-3).

• Decision: the rates here follow Perelomov et al.’s eq. (54). ilkov_1992 has no formula recorded, so there is no formula correction to enter; the misprint is noted here and on the manual page.

• Status: verified (2026-09-28).

TC-657 The asymptotic coefficient of the ionising orbital (2026-09-28)

• Where: data/gas/ionisation_rates.toml (structure); tong_2002, ammosov_1986; Gao_2020_DeterminationStructureParameters, Tolstikhin_2014_WeakFieldAsymptotic in the library (not curated).

• Finding: the sources differ. In Tong et al.’s normalisation (F_l -> C_l r^(n* - 1) e^(-kappa r)), C_l of He, Ne, Ar, Kr, Xe:

  Source	He	Ne	Ar	Kr	Xe
  tong_2002 Table II (self-interaction-free density functional)	3.13	2.10	2.44	2.49	2.57
  ammosov_1986 Table II, “from handbook”, times kappa^(n* + 1/2)	2.88	1.76	2.11	2.22	2.08
  Gao et al. 2020, Table 2 (read, not curated)	2.42	1.47	1.85	2.17	4.39
  Hartree, Ammosov et al. eq. (19), l* = n* - 1, times kappa^(n* + 1/2)	2.98	2.78	2.25	2.05	1.80

  The numerical sources span 25 to 50 % in C_l^2 for He to Kr and a factor of 3 for Xe. For helium the exact value follows from the correlated wave function: Tolstikhin et al.’s (2014, Table I) g = 2.932 in the parabolic normalisation (the rate is g^2 W, both electrons counted) is C_l = 2.85 per electron (C_l^2 = g^2 kappa 2^(2n* - 1)/2; the same conversion gives hydrogen’s 2).

• Decision: Tong et al.’s coefficients, because Tong and Lin’s constants were fitted relative to the rate with them (“derived from the ground-state wavefunction calculated from the model potential, see table II of (Tong et al 2002)”, tong_2005) and Zhang et al.’s reproduce their own Table IX with them (TC-509). With the Hartree coefficient of the propagation codes the rate is 0.91 (He), 1.75 (Ne), 0.85 (Ar), 0.68 (Kr) and 0.49 (Xe) of the rate with Tong et al.’s.

• Consequence: the coefficient and the effective number of electrons (TC-658) are not separable. Only their product, the all-electron rate, is determined by the references.

• Status: decided (2026-09-28); open: Gao et al.’s table is not curated; xenon.

TC-658 The effective number of electrons (2026-09-28)

• Where: data/gas/ionisation_rates.toml (electrons); parker_2009, scrinzi_1999, majety_2015; Majety_2015_StaticFieldIonization Fig. 1, Jagau_2016_InvestigatingTunnelAbove Figs. 6 and 7, Tolstikhin_2014_WeakFieldAsymptotic, Trinh_2015_WeakFieldAsymptotic, Lotstedt_2020_StaticFieldIonization in the library.

• Finding:

  • The weak-field limit is 2 per doubly occupied orbital. Tolstikhin et al. (2014, section II G): for unrelaxed Hartree-Fock orbitals “the SAEA result for the ionization rate must be multiplied by 2, due to the summation over M_S’”. The orbitals with m = +-1 are separate channels, smaller by F/(4 kappa^2). Perelomov et al.’s eq. (61) and Larochelle et al.’s eq. (4) average over m instead, which is the rate of one electron of unknown m.

  • At working fields the atom’s rate is not twice the one-electron rate. For helium (Trinh et al. 2015, Table 1: g = 2.932, A = 0.235, B = -2.60, of which -kappa (alpha_0 - alpha_+) = -1.48) the exact static rate (parker_2009) is 0.60, 0.74, 0.68, 0.55 and 0.43 of the leading order g^2 W at 0.05, 0.08, 0.10, 0.15 and 0.20 au. Lötstedt et al. (2020) find the one-electron rate times 2 “larger than the MCTDHF rate by around 30%”.

• Checked (the all-electron static rate over the one_electron model’s):

  • He (parker_2009 Table 1, tabulated): 1.12 to 1.17 at 0.045 to 0.05 au, 1.32 to 1.40 at 0.055 to 0.06, 1.48 to 1.59 from 0.067 to 0.14, 1.27 to 1.46 from 0.15 to 0.25, 1.25 to 1.34 to 0.38 au. Geometric mean from 0.07 to 0.25 au: 1.474.

  • Ne (read from the vector figures of the two papers; not data, and not curated): Majety and Scrinzi’s haCC(4) 0.97 to 1.07 from 0.05 to 0.16 au; Jagau’s coupled-cluster 1.03 to 1.20 from 0.14 to 0.24 au (1.4 to 1.7 at 0.10 to 0.12).

  • Ar (the same): haCC(4) 1.72 at 0.04 au, 1.50 at 0.05, 1.32 at 0.06, 1.05 at 0.08, 0.79 to 0.88 from 0.10 to 0.16; Jagau 1.57 at 0.06, 0.84 to 1.00 from 0.08 to 0.16, 1.2 to 1.5 at 0.18 to 0.20. The two calculations agree with each other within 10 to 20 %. Majety and Scrinzi: Tong and Lin’s formula times 2 “still over-estimates by at least a factor 2”.

  • Measured (wallace_2016, TC-660): with 1.0 for Ar, Kr and Xe the measured yields are matched with the intensities scaled by 0.98, 1.00 and 1.00.

• Decision: He 1.47; Ne, Ar, Kr, Xe 1.0. Krypton’s and xenon’s are argon’s: no all-electron rate exists for them. The constants are optmat’s own, labelled as model constants, as Tong and Lin’s alpha is. This replaces the statement of TC-444 that the occupancy of helium is 1, which compared the uncorrected tunnelling rate.

• Doubt: argon’s ratio rises to 1.3 to 1.7 below 0.07 au (1.7e14 W/cm2), where a constant of 1.0 is low; the calculations’ rates there are below 1e-4 au and the formula’s correction is least tested. The values for Ne and Ar rest on figures.

• Status: decided (2026-09-28); open: Kr and Xe. The tables of Jagau’s supplement are curated (TC-668) and the values of Ne and Ar restated on them (TC-669).

TC-659 The fine structure of the ion (2026-09-28)

• Where: optmat.gas.ionisation_rates (Channel), data/gas/ionisation_rates.toml (fine_structure_level), nist_asd_2026 (TC-663).

• Decision: a p shell ionises to the ion’s 2P3/2 level with the weight 2/3 and to 2P1/2 with 1/3, each with its own ionisation energy (the atom’s, plus the level’s energy). The weights are those of the m = 0 orbital with either spin in the states of the hole: |l = 1, m = 0; s = 1/2> = sqrt(2/3) |J = 3/2, 1/2> - sqrt(1/3) |J = 1/2, 1/2>. The same coefficient C_l is used for both levels.

• Size: the rate over that with all the weight on 2P3/2, in the tunnelling limit, at 5e13, 1e14, 2e14 and 4e14 W/cm2: Ne 0.93 to 0.97, Ar 0.89 to 0.96, Kr 0.75 to 0.87, Xe 0.69 to 0.81.

• Doubt: the estimate is optmat’s; no paper read gives the rate to the two levels of a noble-gas ion in a linearly polarised field. The calculations of the references are non-relativistic (Wallace et al.: “the fine-structure splitting was ignored”; Muller neglects it).

• Status: decided (2026-09-28).

TC-660 The ionisation rates against their references, and their stated uncertainty (2026-09-28)

• Where: optmat.gas.ionisation_validation, tools/ionisation_rate_tables.py, the tables of docs/ionisation_rates.md (checked by tests/test_ionisation_rates_page.py), tests/test_ionisation_validation.py.

• Checked (the default model over the reference):

  • He, static (parker_2009): 0.92 to 0.99 from 0.07 to 0.15 au, 1.10 at 0.20, 1.17 at 0.30. scrinzi_1999 0.97 to 1.19 from 0.09 au; majety_2015 0.94 to 1.10.

  • He, 780 and 390 nm (parker_2007 eq. 5): 0.95 to 1.17 and 1.27 to 1.42.

  • One electron, 800 nm, 6 fs (travers_2026_trecx; the model one_electron, the instantaneous rate on the calculation’s field): Ar 0.93 to 1.20 and He 1.00 to 1.16 of the population beyond 20 bohr, of which the photoelectron spectrum’s integral is 0.64 to 0.93.

  • Wallace et al. 2016 (5.5 fs, 800 nm, 1e14 to 5e14 W/cm2, the scale of the yield free): the factor on the intensities at which the focal-averaged yield of the model has the measured dependence on intensity is 0.98 (Ar, calibration 1.3 %), 1.00 (Kr, 1.5 %) and 1.00 (Xe, 2.5 %). One per cent is about 5 % in the rate. Without the effective number of electrons and the fine structure (one_electron): 0.97, 0.95, 0.92.

  • Wahlstrand et al. 2018 (42 fs, 800 nm, absolute): the model is 1.7 to 3.9 times above the fits for Ar (45 to 135 TW/cm2) and Kr (35 to 105), and 4.2 to 7.8 times for Xe (18 to 78). The intensity’s 13 % is a factor of 1.9 in the yield.

• Finding: the two measurements disagree, by a factor of about 3 in the rate for argon where their ranges meet (1e14 to 1.35e14 W/cm2). The calculations, for one electron and for the helium atom, side with Wallace et al.’s. Every form of the rate, the literature’s included, is above Wahlstrand et al.’s yields at their higher intensities (2.7 to 3.7 times for ppt_ilkov at 94 and 135 TW/cm2 in argon), and steeper: the measured exponent is 5.1 and the models’ 6 to 7. optmat’s own n2 of argon at 800 nm (1.045e-19 cm2/W at 1 atm and 20 C) is 8 % above the (9.7 +- 1.2)e-20 with which the intensity was calibrated, which would lower the measured intensities and widen the gap.

• Doubt:

  • The shape of Wallace et al.’s published curve (alpha, gamma) was fitted to the authors’ own one-electron calculation, and only I_c to the measurement. The 37 measured Kr yields of their supplement are not in the library.

  • The carrier-envelope phase of the measurement is random; the model’s yield is the mean of two phases (0 and pi/2).

  • The one-electron calculations retain no convergence runs (TC-666).

  • What might reconcile the measurements: the intensity scale of the longer-pulse measurement; a dependence of the rate on the pulse’s duration at gamma above 1; the atoms left in Rydberg states, which the calculations’ upper bracket counts and a plasma’s index does not.

• Decision (the uncertainty stated by the models, a factor on the rate): He 1.3; Ne 1.5; Ar 1.5; Kr 2; Xe 2. A judgement from the comparisons above, not a statistical interval.

• Status: decided (2026-09-28); open: the disagreement of the two measurements; a one-electron calculation for the 42 fs pulse; 400 nm and 1030 nm. The 42 fs calculation: TC-702. In the meantime the default follows Wallace et al.: TC-814.

TC-661 No Stark shift and no factor for the polarisation of the ion (2026-09-28)

• Where: optmat.gas.ionisation_rates; Trinh_2015_WeakFieldAsymptotic, Brabec_2005_TheoryTunnelIonization, Pfeiffer_2011_AttoclockRevealsNatural, Zhao_2014_DynamicalCorePolarization, Majety_2015_StaticFieldIonization, Ilkov_1992_IonizationAtomsTunnelling in the library.

• Finding:

  • Stark shift (I_p + (alpha_0 - alpha_+) F^2/2, as in Luna and solprop): to first order it multiplies the rate by exp(-kappa (alpha_0 - alpha_+) F), which is the first term of the coefficient B of the first-order weak-field asymptotic theory (Trinh et al. 2015, eq. 3b), with alpha_0 - alpha_+ of the atom. For helium it is -1.48 of B = -2.60; the distortion of the orbital (-0.54) and the rest (-0.58) are of the same size. The exact rates to which Tong and Lin’s constant was fitted contain the terms of the one electron (trinh_2013: for argon -1.42 of B = -7.7), and the all-electron rates behind the effective number of electrons those of the atom.

  • exp(-2 alpha_+ F) (“dipole correction”): in none of the 35 papers read for this work, Ilkov et al. (1992), to which solprop attributes it, included: that paper contains no polarizability. Brabec et al. (2005, eq. 4) raise the barrier by 2 beta E/z^2 - beta/z^4 inside a WKB integral, for C60 ions. Pfeiffer et al. (2012) use -alpha_+ F.r/r^3 for the tunnel exit and the trajectories, and state that their result is “insensitive to the exact form of the rate”. Zhao and Yuan (2014, eq. 9) derive, for calcium, exp[-(2 beta_+ E/kappa)(1/z_0 - 1/z_1)], z_0 the radius of the core and z_1 the tunnel exit, which is exp(-2 alpha_+ F) only for z_0 = 1/kappa and z_1 -> infinity. For argon at 0.1 au the factor of Luna and solprop is 0.26 (alpha_+ = 6.83 au); Zhao and Yuan’s prescription, with z_0 = alpha_+^(1/3), gives about 0.6.

  • Majety and Scrinzi (2015): the first excited channel of the ion changes the static rates of neon and argon “by less than 2%”.

• Decision: neither is in the models. In the form exp(-c F) they do what the static correction and the effective number of electrons do, with constants that rest on references.

• Status: decided (2026-09-28).

TC-662 The instantaneous rate and the cycle-averaged rate (2026-09-28)

• Where: optmat.gas.ionisation_rates.cycle_average, power_law_average, IonisationRateModel.instantaneous_rate, cycle_averaged_rate.

• Finding: the theory gives the rate averaged over a cycle. Propagation codes that resolve the carrier divide it by (3F/pi F_0)^(1/2), the factor of the cycle average in the tunnelling limit (Perelomov et al. 1966, eq. 7, stated for omega << omega_t), and evaluate the result at the instantaneous field. The average of that rate over a cycle is not the cycle-averaged rate it was made from: for argon at 800 nm and 2e13, 5e13, 1e14, 2e14 and 4e14 W/cm2 (gamma 2.6 to 0.57) it is 1.41, 1.21, 1.11, 1.04 and 1.00 times it with the form of Ilkov et al. and Bergé et al. (ppt_ilkov) and 1.48, 1.26, 1.16, 1.08 and 1.03 with Larochelle et al.’s; at 400 nm (gamma 5.1 to 1.15) 1.85 to 1.07 and 2.04 to 1.17. The yield of a pulse is too high by the same factor.

• Decision: with L = ln W as a function of ln F, its slope s and its curvature q, the average over a cycle of W(F |cos|) is W(F) c(s) [1 + (q/2) c’’(s)/c(s)], c(s) = Gamma((s + 1)/2) / (sqrt(pi) Gamma(s/2 + 1)), exact for a power law and, to the order kept, for any steep rate; in the tunnelling limit c -> (3F/pi F_0)^(1/2). In the default model:

  • the static rate is exact in the limit gamma -> 0 (the instantaneous rate at a static field is the tunnelling rate with its correction);

  • the cycle-averaged rate is the average of that static rate, times the enhancement of the theory’s cycle-averaged rate over its own tunnelling limit;

  • the instantaneous rate is the cycle-averaged rate over the average factor of its own slope and curvature. The models of the literature’s forms keep the factor of the tunnelling limit (averaging = "tunnelling"), so that they are what the codes compute.

• Checked: the average of the instantaneous rate over a cycle, by quadrature, over the cycle-averaged rate: within 3 % from 0.32 to 1.0 of the barrier-suppression field for Ar at 800 and 400 nm, He at 800 nm, Xe at 1030 nm and He in a static field (tests/test_ionisation_rates.py). The yields of a 42 fs pulse from the two rates agree within 3 % (tests/test_ionisation_validation.py).

• Doubt: the convention fixes the yield, not the timing of the ionisation within the cycle, which at gamma above 1 is less confined to the crests than any function of the instantaneous field alone gives (Yudin and Ivanov 2001).

• Status: decided (2026-09-28).

TC-663 A quantity for level energies; nist_asd_2026, the 2P*<1/2> levels of Ne+, Ar+, Kr+ and Xe+ (2026-09-28)

• Where: optmat.vocabulary (level_energy), the quantities table of docs/data.md, data/external/nist_asd/<Ne, Ar, Kr, Xe>_II_levels.tsv (as returned, with the query and the sha256 of each in PROVENANCE.md), the record nist_asd_2026 (datasets level_Ne+_2P12, level_Ar+_2P12, level_Kr+_2P12, level_Xe+_2P12), tests/test_nist_asd.py.

• Decision: a new quantity, level_energy, family ionisation: the energy of a level of an atom or ion above its ground level, in cm-1 or eV, abscissa label or none, with the required parameters configuration, term and j. An ionization_energy is a threshold of the species below (its final_state names the level of the ion left); the fine-structure splitting of the ion is a property of the ion and is not an ionisation energy, so the existing quantity was not bent to hold it (data rule 7). The atom’s second threshold (to the ion’s 2P*<1/2> level) is the sum of the atom’s ionization_energy and the ion’s level_energy.

• Transcribed: the second row of each file, the np5 2P*<1/2> level of the ion’s ground term, as inline points holding NIST’s strings (cm-1), material the ion:

  Ion	Configuration	Level (cm-1)	Uncertainty (cm-1)	NIST key
  Ne+	2s2.2p5	780.4240	0.002	L9088
  Ar+	3s2.3p5	1431.5831	0.0008	L15349
  Kr+	4s2.4p5	5370.10	none given	none given (ground level: L12196)
  Xe+	5s2.5p5	10537.01	none given	L6925

  use = "primary". The files were queried on 2026-09-28 with the levels form (tab-delimited, cm-1); they hold every level of the four spectra (386, 420, 164 and 165 lines), of which only these four are curated.

• Checked: tests/test_nist_asd.py compares each dataset’s value, uncertainty, configuration, term and J with the second row of its file, checks that the first row is the 2P*<3/2> ground level at zero with the same configuration, that NIST’s Prefix and Suffix cells (which would mark a bracketed or uncertain value) are empty, and that a level without a NIST uncertainty has none recorded. The test of the ionisation energies is unchanged in substance (it now selects the ten ionization_energy datasets).

• Doubt:

  • Kr+ and Xe+: NIST gives no uncertainty, and for Kr+ no reference, for the level. None is recorded (the sigma cell is empty, the standard uncertainty NaN); the number of digits printed (0.01 cm-1) is not an uncertainty.

  • Level: the confidence level of NIST’s uncertainties is not stated (TC-443).

  • Version: the returned files do not name the database version. The record’s citation says 5.12, checked on 2026-09-26 (TC-443); it was not checked again on 2026-09-28.

• Status: verified (2026-09-28).

TC-664 wallace_2016 (Wallace et al., Phys. Rev. Lett. 117, 053001 (2016)) (2026-09-28)

• Where: the record wallace_2016, tools/extract/wallace_2016.py, six data files data/values/ionisation/<Ar, Kr, Xe>/wallace_2016__tableI_{shape,Ic}_<gas>.csv.

• Transcribed: Table I (p. 4, tbl_03b3d0db2cd3): the parameters of the phenomenological yield curve Eq. (4), S = exp[-alpha (I/I_c)^(-1/2)] / [1 + (I/I_c)^gamma], per gas, as ionization_model_parameter (model wallace_2016_yield_fit), use = "check":

  Gas	alpha	gamma	I_c (1e14 W/cm2)
  Ar	2.84	-3.03	3.86 ± 0.05
  Kr	4.24	-2.49	2.06 ± 0.03
  Xe	3.71	-2.69	1.18 ± 0.03

  Two datasets per gas, so that each has one unit: tableI_shape_<gas> (rows alpha, gamma; unit 1; no uncertainty given) and tableI_Ic_<gas> (row I_c; unit W/cm2, scale 1e14; the uncertainty in the sigma column, level “1 sigma”: “we have here stated the 1σ standard deviation for I_c, i.e., the 68% confidence interval”, ref. 27). The material is the neutral gas; the table’s headers name the ion produced. Eqs. (3)-(4) are the formula eq4_yield. Technique, accuracy statements and the theories compared are quoted in the record with their pages.

• Checked:

  • The table image: the I_c cells are “3.86 ± 0.05”, “2.06 ± 0.03”, “1.18 ± 0.03”. The library’s text layer has “3.86 - 0.05” (the plus-minus sign lost) and “Arþ” for Ar+ (the superscript plus lost). Both are structural faults of the extraction and are handled in the script, which stops on any other form; no printed value is corrected. Eq. (4) was read on the equation image.

  • 0.05/3.86, 0.03/2.06 and 0.03/1.18 are 1.3, 1.5 and 2.5 %, the calibration accuracies the text gives for Ar, Kr and Xe (p. 4).

  • Kr against the supplement’s Table I (37 measured Kr+ yields; the supplement is not in the library, read from J. C. Travers’s copy): with Kr’s alpha, gamma and I_c, the tabulated I_0 and only the scale A fitted (A = 190.0), the curve is within -16.6 to +9.7 % of the yields, rms 4.4 %, seven points beyond 5 %; the point at 3.49e14 W/cm2 (Y = 6.9126) lies 17 % above the curve and is an outlier of the data. chi^2 is 369 for 37 points with the printed errors, so the curve does not fit within them. This is the scatter of Fig. 2(e)’s “Phenomenological” residuals. The supplement restates Kr’s three parameters (its p. 6), with the plus-minus sign.

  • The supplement’s I_0/I_est is 0.639-0.643: I_0 = eta_1 I_est with eta_1 = 0.641 (the hydrogen calibration), not the eta_2 = 0.638 its own fit returns.

• Doubt:

  • What the curve is. alpha and gamma were fitted to the authors’ single-active- electron TDSE, focal-volume averaged in two dimensions, and only I_c (and the free scale A) to the data (p. 4). The curve is a yield in arbitrary units for this pulse (800 nm, 5.5 fs FWHM of intensity, carrier-envelope phase not stabilised) and this geometry. It is not a rate or a single-atom probability, and the authors warn: “We emphasize that Eq. (4) is not associated with any model of the ionization physics. Hence, we do not expect it to be valid outside the range of intensities studied here”, (1-5)e14 W/cm2.

  • The measured yields of Ar+, Kr+ and Xe+ are in Fig. 2 only. The 37 Kr+ yields of the supplement are not curated, because the supplement is not in the library (the record describes the table and says where the file is).

  • The Letter prints “the p-orbital (l = 0)” for the ADK comparison; a slip, noted.

• Status: verified (2026-09-28); open: the supplement’s Table I, to be extracted when the supplement is in the library.

TC-665 wahlstrand_2018: the fits of the measured ionisation yields (Supplemental Material, Table 1) (2026-09-28)

• Where: the record wahlstrand_2018 (notes “THE IONISATION YIELDS”, the formula yield_fit, ten new datasets), tools/extract/wahlstrand_2018.py, ten data files data/values/ionisation/<gas>/wahlstrand_2018__yield_fit_{c1,m}_<gas>.csv.

• Transcribed: Table 1 of the Supplemental Material (its p. 11; library supplement_01, tbl_668d3655bf2e), the fit Y = c_1 I_0^m, Eq. (S1), to the measured yield of Fig. 3, as ionization_model_parameter (model wahlstrand_2018_yield_fit), use = "check":

  Gas	c_1 ((cm2/TW)^m)	m_fit	m_MPI (not curated)
  Ar	2.05e-13	5.14	11
  Kr	5.17e-11	4.43	9
  Xe	5.47e-10	4.36	7
  N2	5.7e-16	6.28	11
  O2	9.6e-11	4.09	7

  Two datasets per gas: yield_fit_c1_<gas> (row c1, unit (cm2/TW)^m as printed, which depends on the gas’s m) and yield_fit_m_<gas> (row m, unit 1). I_0 is the temporal peak intensity in TW/cm2 of the 42 fs (FWHM of intensity), 800 nm pump, Y = N_e/N_0 the ionisation fraction after the pulse. How Y was obtained (the plasma index -N_e/2N_cr with N_cr = 3.1e21 cm-3 at the 600 nm probe, L_eff ~ 450 µm, the thin target) is quoted in the record with the pages.

• Checked:

  • Every cell of the columns Gas, c_1, m_fit and m_MPI against the table image and against the page rendered from the PDF (150 dpi). The values are the ones expected.

  • The supplement is in the library: it was attached on 2026-09-28 as supplement_01 (original/source_02), and is the same file as J. C. Travers’s copy ionization_SOM_accepted_final.pdf (sha256 4cd891d0…66ef940). The values therefore go through an extraction script, not inline points.

  • The unit of c_1: the image has “(cm²/TW)^m”; the library’s text layer has “-m”. With I_0 in TW/cm2 the fits give Ar 3.9e-3 at 100, Kr 1.05e-2 at 75, Xe 1.4e-2 at 50, N2 2.1e-3 at 100 and O2 4.5e-3 at 75 TW/cm2, which agree with the dashed lines and points of Fig. 3 as far as it can be read (about 30 %).

• Doubt:

  • No uncertainty of c_1 or m is given. “The accuracy of the ionization yield measurement is set by the vertical scatter of the points, while the intensity accuracy is ∼13%” (Fig. 3’s caption). With m about 5, 13 % in intensity is a factor 1.8 in yield. L_eff, N_0 and N_cr carry no stated uncertainty.

  • The fitted range is not stated. The points of Fig. 3 span about 45-133 (Ar), 35-105 (Kr), 18-78 (Xe), 75-125 (N2) and 40-105 TW/cm2 (O2), read on the figure. The power law has no saturation and is not to be extrapolated; the authors say it is not a model of ionisation.

  • Fig. 3’s PPT curve is not specified (no form of the rate, Coulomb correction, m sum, electron number, constants or pulse integration is given), so it cannot be reproduced and is not a reference.

  • The gas is cold and its pressure is not given: the rotational fits of N2 and O2 needed 200 K (SM p. 8). Y is a ratio to the measured N_0, so this does not enter the yield directly.

• Decision: validators (use = "check"); nothing is fitted to them. The measured points are in the figure only and are not digitised.

• Status: verified (2026-09-28); open: the two n2 columns of the same table (effective n2 over the full intensity range, new values of this work: Ar (12.2 ± 1.6)e-20, Kr (2.7 ± 0.4)e-19, Xe (7.1 ± 0.9)e-19, N2 (7.4 ± 1.0)e-20, O2 (5.8 ± 0.8)e-20 cm2/W) are in the record’s notes and are not yet curated as third-order data.

TC-666 travers_2026_trecx: J. C. Travers’s tRecX yields of Ar and He (tier 3) (2026-09-28)

• Where: data/external/trecx/ (the result tables ar_results.csv, he_results.csv and all_runs.csv, the three scripts that made them, the 51 inputs as run, the two READMEs of the runs, PROVENANCE.md with the sha256 of each), the record travers_2026_trecx, tools/extract/travers_2026_trecx.py, nine data files.

• Transcribed: ionization_yield against peak intensity (W/cm2), unit 1, use = "check", the numbers as the tables’ strings (four significant digits), rows labelled by the index of the intensity (0-9, the suffix of the run):

  Dataset	Target	Pulse	Yield	Rows	Excluded
  chi_gauss_Ar_m0, norm_gauss_Ar_m0	Ar 3p, m = 0	Gaussian	chi-loss, norm-loss	10	none
  isurff_cos8_Ar_m0	Ar 3p, m = 0	cos8	iSurff	7	none
  chi_gauss_Ar_m1, norm_gauss_Ar_m1	Ar 3p, m = 1	Gaussian	chi-loss, norm-loss	10	0
  isurff_cos8_Ar_m1	Ar 3p, m = 1	cos8	iSurff	7	none
  chi_gauss_He, norm_gauss_He	He 1s	Gaussian	chi-loss, norm-loss	10	0, 1, 8, 9
  isurff_cos8_He	He 1s	cos8	iSurff	7	none

  Ar: 1.6881e13 to 8.4407e14 W/cm2; He: 1.0000e14 to 5.0000e15 W/cm2. 800 nm, 6.0 fs FWHM of the intensity envelope, linear polarisation, one carrier-envelope phase. One active electron in Tong and Lin’s potential (tong_2005), velocity gauge, exterior complex scaling. The model’s ionisation energies are 0.579689 au (Ar 3p) and 0.903801 au (He 1s).

• Checked (against the run directories, 2026-09-28):

  • Every yield of the two tables was recomputed by an independent script from the runs’ expectation-value files (last row) and spec_total (trapezoid integral) and agrees to the digits written, for all 51 runs but he_scan_03, whose expectation-value file holds one row only; its yields are the last row of its outf, read by eye.

  • Every archived input equals the copy tRecX wrote into its run directory, and its intensity is the table’s.

  • The pulse, from the field each run wrote: A(t) = (E0/ω) g(t) sin(ωt) to 1e-6 of the peak, E0 = sqrt(I/3.50945e16 W/cm2) au, g a Gaussian or cos^8 whose square has a FWHM of 6.0 fs. The envelope is on the vector potential; the field’s largest maximum is at the peak of the envelope.

  • The potentials in the inputs are Tong and Lin’s Table 1 as curated (tong_2005, and zhang_2014 Table I).

  • Only he_scan_08 and he_scan_09 carry the warning “norm>1, possible instability” (1973 and 2902 times; largest norm 3.16 and 3.41).

• Convergence evidence: none is retained. Every run has one discretisation (30 angular functions; radial elements of orders 14 and 12; cutEnergy 60). The READMEs state that iSurff changes by less than 1 % from 30 to 40 angular functions and 150 to 250 radial points, and that He at 5e15 W/cm2 gives 96.5 % with BOX = 160 and 96.2 % with 180; the runs behind these statements are not on disk. What the retained runs show:

  • Pulse shape: the chi-loss of the cos8 and the Gaussian runs agree to 1.6 % for yields above 1e-7 and to 7 % at 1e-8.

  • The three measures: iSurff is 0.68-0.92 (Ar m = 0), 0.64-0.96 (Ar m = 1, rows 1-6) and 0.77-0.88 (He, rows 2-6) of the chi-loss of the same run; the norm-loss is 0.71-0.99, 0.81-1.00 and 0.94-0.98 of the chi-loss of the Gaussian runs. The chi-loss counts bound excited population beyond 20 bohr; the norm-loss misses what has not reached the absorber; the runs end with the pulse.

  • Noise floor: the loss before the pulse is 1.2e-10 (Ar) and 4.2e-8 to 8e-10 (He, falling with the time step).

• Decision:

  • Excluded rows (kept in the files, with the reasons in the record): He rows 0 and 1 and Ar m = 1 row 0 of the chi- and norm-loss, at the noise floor (He: 3.1e-7 and 4.8e-7 against iSurff’s 1.2e-9 and 8.7e-8; Ar m = 1: 7.9e-10 against 1.1e-10); He rows 8 and 9, the unstable runs.

  • No uncertainty is recorded. A user of these validators should take the spread of the three measures as the least uncertainty: 10-40 % below a yield of 1e-3, a few percent near saturation.

  • Tier 3: validators only, below published calculations and measurements; nothing is fitted to them.

• Doubt:

  • The code’s version. The executable was built from J. C. Travers’s local commit 05f9cdea (two ahead of upstream master fd6da402) with uncommitted changes of pulse.cpp, pulse.h and run_trecx.cpp (the build’s GIT_DIFF), ten minutes before they were presumably committed as 96bc605d. That the built and the committed sources are the same was not checked. The changes concern fields read from files; the analytic pulses used here were checked on the fields written.

  • One electron, one m. The yields are of one electron in one orbital. The yield of the atom needs a rule for the other electrons (two in He 1s; two m = 0 and four |m| = 1 in Ar 3p), which is a model. The tables’ shell_* and mavg_* columns are such combinations and are not curated.

  • One carrier-envelope phase of a 2.25-cycle pulse; no average.

  • The smallest iSurff yields (He 1.2e-9 and 8.7e-8; Ar m = 1 1.1e-10) have nothing to check them against, and the spectra of ar_isurff_00 and _01 are cut where the integrand is still 2.7 % of its maximum.

  • The intensity is that of a continuous wave with the peak field’s amplitude; with the envelope on the vector potential the field is not E0 g(t) cos(ωt) (up to 7 % of E0 apart in the wings).

• Status: decided (2026-09-28); open: convergence runs (a second angular and radial discretisation, and a field-free propagation after the pulse) for a stated uncertainty. The iSurff yields are biased low: TC-703. Superseded as the 6 fs yield by the ionised fraction of the repeated runs, with convergence runs: TC-812.

TC-667 Findings of the curation of 2026-09-28 that correct earlier assumptions (2026-09-28)

• Where: TC-664, TC-665 and TC-666.

• Checked:

  • Wahlstrand’s supplement is in the library (since 2026-09-28), contrary to what was assumed; its Table 1 is extracted by a script (TC-665).

  • The helium inputs differ in more than the intensity and the box: also in the number of radial elements (14 to 37 in [20, BOX]) and the time step (0.0283 to 0.0129 au). All 51 inputs are archived instead of one per family.

  • “l_max = 29” holds for m = 0. The inputs ask for 30 associated Legendre functions per m; for m = 1 these begin at l = 1. The record says “30 associated Legendre functions (l up to 29 for m = 0)”.

  • The complex-scaling angle is 0.3 for Ar and 0.15 for He.

  • The README’s “cos8 == gauss to <0.1 %” at 8.8e14 W/cm2 is 0.2 % in the tables; its “1e15 point reproduces the independent reference” compares with a run of another pulse (10 fs cos8) and is not evidence of convergence.

• Status: verified (2026-09-28).

TC-668 jagau_2016 (Jagau, J. Chem. Phys. 145, 204115 (2016)): all-electron static rates of He, Ne and Ar (2026-09-28)

• Where: data/sources/jagau_2016.toml, tools/extract/jagau_2016.py; Jagau_2016_InvestigatingTunnelAbove/supplement_01 in the library, Tables S3 (tbl_835beff31b7f), S4 (tbl_bdfc58139762) and S5 (tbl_e8cea2aae6b7).

• Transcribed: the ionisation rate Gamma (au) against the static field F (au) of the ground states of He (0.10 to 0.50 au, 21 fields), Ne (0.08 to 0.24 au, 11) and Ar (0.05 to 0.20 au, 11), at three levels of theory each: complex-scaled Hartree-Fock, MP2, and full configuration interaction (He) or coupled cluster with singles and doubles and all electrons correlated (Ne, Ar). Nine datasets, tableS<n>_<level>_<gas>; the correlated level is primary, the other two check. Gamma is the width of the N-electron resonance, E_res = E - i Gamma/2 (the paper’s Eq. 4): the rate of the atom. Cells printed as a dash (four) are skipped. The Stark shifts of the same tables are kept in the printed cells only.

• Checked: every cell of the three tables against the table images: they agree. The tables have merged header cells and are read from the library’s cells, not from a CSV; the script checks the header. Table S2 (four basis sets for He) against its image, for the values quoted in the record.

• Doubt:

  • No uncertainty is stated for any tabulated value. The paper finds its method “impractical” for rates “below ca. 10^-6 a.u.” (p. 13) and the rates “more sensitive towards the basis set than Stark shifts” (p. 6).

  • Helium at low field depends on the basis. Table S2: at 0.10 au the basis of Table S3 gives 0.00000232 and the one with six diffuse functions per angular momentum 0.00000348, against 0.00000288 (Scrinzi et al. 1999) and 0.00000294 (Parker et al. 2009). At 0.14 au and from 0.20 to 0.50 au the basis of Table S3 is within 2.5 % of Scrinzi et al.; at 0.16 and 0.18 au it is 8 % and 6 % above them.

  • Neon below 0.14 au is not smooth in the field: the rate rises by 3.77 from 0.10 to 0.11 au and by 2.12 from 0.11 to 0.12 au, where optmat’s default model gives 3.0 and 2.5.

  • Argon at 0.05 au, 0.00004270, is 3.7 times Majety and Scrinzi’s haCC(4) rate read from their Fig. 1 (1.16e-5; not data). At 0.06 au the two differ by 1.2.

  • No comparison of basis sets is given for Ne or Ar.

  • The calculation is non-relativistic: the ion has one threshold.

• Decision: the values are as printed; nothing is corrected or excluded. The comparisons give the low-field values no weight (TC-669). Tables S1 and S2 (the basis-set study), S6 to S8 (Li, Be, C) and S9 to S14 (moments) are not taken.

• Status: verified (2026-09-28).

TC-669 The effective number of electrons of neon and argon on tabulated rates (2026-09-28)

• Where: data/gas/ionisation_rates.toml (the reasons of electrons and uncertainty_factor of Ne and Ar); optmat.gas.ionisation_validation (STATIC_REFERENCES); docs/ionisation_rates.md; jagau_2016 (TC-668).

• Finding: TC-658 set the effective number of electrons of Ne and Ar on values read from figures. Jagau’s are now tabulated. The all-electron rate over the rate of the one_electron model (one electron, m = 0, Tong et al.’s coefficient, Tong and Lin’s correction, no fine structure), and the default model over the all-electron rate:

  F (au)	Ne: atom / one electron	default / atom	Ar: atom / one electron	default / atom
  0.05			5.48	0.17
  0.06			1.57	0.59
  0.07			1.21	0.78
  0.08	2.63	0.37	0.96	0.99
  0.09	1.38	0.70	0.86	1.11
  0.10	1.36	0.71	0.83	1.15
  0.11	1.71	0.57
  0.12	1.47	0.66	0.84	1.16
  0.14	1.20	0.82	0.88	1.11
  0.16	1.05	0.93	1.00	0.98
  0.18	1.03	0.96	1.20	0.82
  0.20	1.04	0.94	1.50	0.66
  0.22	1.06	0.93
  0.24	1.10	0.90

  • The values read from Jagau’s figures for TC-658 agree with these to 1 %.

  • Neon: 1.03 to 1.10 from 0.16 to 0.24 au (1.0 to 1.5 barrier-suppression fields), 1.20 at 0.14 au.

  • Argon: 0.83 to 1.00 from 0.08 to 0.16 au (0.95 to 1.9 barrier-suppression fields), 1.21 at 0.07 au, 1.57 at 0.06 au. Beyond 0.168 au (twice the barrier-suppression field) Tong and Lin’s correction is out of its range, and the comparison stops there.

  • Helium (the same comparison, default over Jagau’s full configuration interaction): 0.96 to 1.20 from 0.10 to 0.40 au; 1.20 is at 0.10 au, where Jagau’s rate is 19 % below Scrinzi et al.’s (TC-668).

• Decision: 1.0 stands for Ne and Ar, now on tabulated values. The stated uncertainty factors (1.5) stand. The comparisons of the manual and the tests hold the default within 19 % for Ne from 0.14 au and within 23 % for Ar from 0.07 to 0.16 au, and give the lower fields no bound but the sign.

• Doubt:

  • The number rises toward low field, as its weak-field limit of 2 requires (TC-658). For argon below 0.07 au (1.7e14 W/cm2) a constant of 1.0 is low by 1.2 to 1.6 on these rates, and by 1.3 to 1.5 on Majety and Scrinzi’s figure. This is the range of Wahlstrand et al.’s measured yields, which lie 1.7 to 3.9 times below the model (TC-660). The static rates and that measurement ask for changes of opposite sign; no field-dependent number is introduced.

  • For neon the rise begins at 0.14 au (6.9e14 W/cm2), if the rates below are right (TC-668).

• Status: decided (2026-09-28); open: the low-field rates of Ne and Ar.

TC-670 perelomov_1967, perelomov_1968: the static Coulomb factor at first hand, and its range (2026-09-28)

• Where: data/sources/perelomov_1967.toml, data/sources/perelomov_1968.toml (formulas; no data); optmat.gas.ionisation_rates.coulomb_factor; Perelomov_1967_IonizationAtomsAlternating_af59d3 (paper III of the series) and Perelomov_1968_AllowanceCoulombInteraction in the library. Adds to TC-653, which had the factor through Larochelle et al. (1998).

• Checked (page images):

  • Perelomov and Popov 1967, eq. (42), p. 341: exp{-2 Im delta S} = (2F_0/F)^(2 lambda), lambda = Z/kappa, for linear polarisation. “The dependence of delta S on the frequency has dropped out, i.e., the Coulomb correction in the ionization probability w(F, omega) has the same form as for a static field”.

  • Their eq. (45), for elliptical polarisation: [2F_0 C(gamma, epsilon)/F]^(2 lambda). C(gamma, 0), evaluated from eqs. (46) to (48), is 1.0000 at gamma = 0.5 to 30 (computed): for linear polarisation the factor has no dependence on gamma. Ilkov et al.’s footnote (p. 4007), “C = 1 for gamma << 1”, understates it.

  • Perelomov, Popov and Kuznetsov 1968, p. 452: “the main Coulomb correction to the penetrability is given by formula (1) and does not depend on gamma at all”.

• Finding:

  • The factor (1 + gamma^2)^(-n) is in neither paper.* Ilkov et al. (eq. 8) and Bergé et al. (eq. B14) cite Perelomov and Popov for the Coulomb correction and print it under the bracket of the short-range rate, which carries sqrt(1 + gamma^2). This confirms TC-653 from the source.

  • The range of validity (1968, eq. 20 and footnote 3): gamma << gamma_k = 2I/(lambda omega), and exactly s = lambda omega/2I below s_cr(gamma), the value at which the Coulomb force changes the sub-barrier trajectory qualitatively. Table I (read on the image; not extracted): s_cr = 0.0400, 0.0368, 0.0342, 0.0315, 0.0273, 0.0248 at gamma = 3, 5, 7, 10, 15, 20; nothing is tabulated below gamma = 3, and Fig. 4 shows s_cr rising toward small gamma.

  • At 800 nm s = 0.0234 (He), 0.0285 (Ne), 0.0457 (Ar), 0.0546 (Kr), 0.0677 (Xe): helium is inside the range to gamma = 20 and neon to gamma = 10; argon, krypton and xenon are outside it at gamma = 3 and enter it at some gamma below 3 that the table does not give. At 400 nm s is twice as large, and every gas is outside it at gamma = 3 (helium: 0.047 against 0.040).

• Doubt: the agreement of the static factor with the one-electron calculations of argon up to gamma = 2.8 (TC-653) is at or beyond the edge of the derivation. It is an empirical finding. Popruzhenko et al.’s (2008) factor is the published treatment beyond that edge, and is lower than those calculations by 1.6 at gamma = 1.2 and by 7 at gamma = 2.8.

• Decision: the static factor stays the default’s. The module and the manual cite these two papers for it, and the manual states the range.

• Status: verified (2026-09-28).

TC-671 zhang_2014, Table II: the GSZ parameters printed for neon do not give the paper’s neon (2026-09-28)

• Where: zhang_2014/tableII_Ne (H = 2.219, d = 0.751, as printed and as the image shows); the paper’s Table V; Garvey_1975_IndependentParticleModel, trinh_2013/potential_Ne for comparison.

• Checked: the 2p level of V(r) = -[(Z - Z_c)/(H (e^(r/d) - 1) + 1) + Z_c]/r (the paper’s Eq. 6), by finite differences on a logarithmic grid, converged to five figures between 4000 and 16000 points, and exact for hydrogen’s 2p (-0.12500) (computed 2026-09-28):

  Gas	Parameters	E(np) computed (hartree)	Printed by the paper that gives them
  Ne	Zhang et al., H = 2.219, d = 0.751	-0.95137	-0.79466 (Table V)
  Ne	Trinh et al. 2013	-0.79337	-0.793
  Ne	Garvey et al. 1975, Table I	-0.81111
  Ar	Zhang et al., H = 3.469, d = 0.997	-0.57931	-0.57830 (Table VI)
  Ar	Trinh et al. 2013	-0.57907	-0.579

• Finding: with the printed parameters neon’s 2p is bound by 0.951 hartree, 20 % more than the 0.795 the paper prints for the same potential; argon’s parameters reproduce the paper’s level to 0.2 %. One of H and d of neon is probably misprinted. Which, and what was meant, cannot be told from the paper.

• Decision: no erratum: the intended value is unknown. The dataset stays as printed and check. It is used by nothing in optmat, which takes Zhang et al.’s rates of argon and their constants a_1 to a_3, fitted in Tong and Lin’s potential for neon (the paper’s p. 5), and not their potentials. A calculation for neon in “Zhang et al.’s GSZ potential” must not use the printed numbers.

• Doubt: Garvey, Jackman and Green’s own parameters (1975, Table I) miss the measured ionisation energies of Ne, Ar, Kr and Xe by 2 to 11 % (computed: 0.811, 0.606, 0.459, 0.486 hartree) and put krypton below xenon; Trinh et al., Zhang et al. and Batishchev et al. each use parameters adjusted to the measured energy. “The GSZ potential” of a gas is therefore not one potential.

• Status: open (the intended parameters of neon).

TC-672 wallace_2016: the measured Kr+ yields of the supplement’s Table I (2026-09-28)

• Where: wallace_2016/supplement_tableI_yield_Kr, tools/extract/wallace_2016.py; Wallace_2016_PreciseAccurateMeasurements/supplement_01, tbl_2cab2b41f725 (SM p. 7), in the library since 2026-09-28; optmat.gas.ionisation_validation. measured_points_test. Completes TC-664, which left the table for the day the supplement was in the library.

• Transcribed: 37 rows: the yield of Kr+ (arbitrary units) and its absolute error against the calibrated peak intensity I_0 (printed in 10^14 W/cm^2, written 1.31e14), with the estimated intensity I_est as an extra column. 800 nm, 5.5 fs, carrier-envelope phase not stabilised, averaged over the two transverse dimensions of the focus. check.

• Checked: every cell against the table image: they agree. I_0/I_est is 0.639 to 0.643.

• Doubt:

  • The confidence level of the printed errors is not stated.

  • The point at 3.49e14 W/cm2 (row 27, 6.9126) is 15 to 17 % above any smooth curve through its neighbours. Kept as printed.

  • The printed errors (0.9 to 2.7 %) are below the scatter of the points: the authors’ fit function has chi^2 = 369 for the 37 points (TC-664).

• Finding (the models fitted to the points, amplitude free, weights 1/sigma^2):

  Model	Scale of least chi^2	chi^2	chi^2 at a scale of 1	rms of model/measured - 1
  default	1.01	282	286	3.8 %
  one_electron	0.96	279	442	3.8 %
  ppt_ilkov	1.01	616	630	7.3 %
  ppt_popruzhenko	1.01	561	577	6.8 %

  • The default fits the points at the measurement’s own intensities (1.007, inside the calibration of 1.5 %), and better than the authors’ fit function does.

  • Without the fine structure of the ion the model needs 4 % in intensity: the points support the fine-structure channels (TC-659), as the fit function did (scales 1.00 and 0.95, TC-660).

  • The forms of the literature fit at the same scale with twice the chi^2. Against the fit function they needed 8 to 9 % (TC-660). With the amplitude free the two tests weigh the shape and the position of the curve differently; neither form fits both.

• Status: verified (2026-09-28).

TC-673 The molecules’ ionisation rates in the forms of the literature (2026-09-28)

• Where: optmat.gas.molecular_ionisation_rates, optmat.gas.molecular_ionisation_validation, data/gas/molecular_ionisation_rates.toml, docs/molecular_ionisation_rates.md; tests/data/solprop_molecular_rates.json (solprop at b871f18, written by tools/solprop_molecular_rates.py). Follows TC-652, which brought the atoms’ rates into optmat and left the molecules’.

• Decision: the three rates that solprop computes for molecules are given as named models, each of ONE electron and as its source gives it, so that results computed with them can be reproduced:

  • moadk_zhao_2010, moadk_tong_2002: Tong, Zhao and Lin’s (2002) molecular tunnelling rate, eqs. (8)-(9), averaged over the orientations of the molecule, <B^2(m’)> = sum_l C_l^2 Q(l, m’)^2 / (2l + 1), with the structure coefficients of Zhao et al. (2010, Table III) or of Tong et al. (Table I). H2, D2, N2, O2; CO2 with Zhao et al.’s.

  • ppt_talebpour: the rate of Perelomov, Popov and Terent’ev for l = m = 0 with Talebpour et al.’s effective charge (N2 0.9, O2 0.53, D2 0.72), the Hartree coefficient with l* = n* - 1 and the static Coulomb factor: the rate the charges were determined within (talebpour_1999 Appendix A, talebpour_1998 eq. 2, which are Larochelle et al.’s eq. 10).

  • ppt_talebpour_ilkov: the same charges with Ilkov et al.’s Coulomb factor: solprop’s PPT for N2 and O2.

  • moadk_zhao_2017: the molecular tunnelling rate with the coefficients of zhao_2017 (TC-675); the only form of its kind for N2O.

  • adk_hydrogenic: the tunnelling rate of a hydrogen-like s electron (Z = 1, l* = 0, no angular factor) on the ionisation energy alone; every molecule.

  • No default model. None of the forms is validated as the rate of a molecule.

  • The static forms’ cycle-averaged rate, and the ppt form’s instantaneous rate, use the factor of the tunnelling limit, (3F/pi F_0)^(1/2), as the codes do; the consistent average of TC-662 is for the validated rate to come.

  • The ionisation energy is the adiabatic one of ionisation.toml.

• Checked:

  • Parity with solprop. Evaluated with solprop’s ionisation energies and occupancies, the models reproduce solprop’s IsotropicMOADK (H2, D2, N2, O2, both tabulations) and ADK (H2, D2, CH4, SF6, N2O; instantaneous and cycle averaged) to 1e-10, and ppt_talebpour_ilkov its PPT (N2, O2; 800 and 400 nm; both rates) to 1e-8, at ten fields from 8e9 to 6e10 V/m. solprop’s zero below its threshold field and its ceiling of one per atomic unit of time are not part of the formulas and are left to it.

  • What optmat’s energies change. optmat’s energy less solprop’s, and the rate with the former over that with the latter at 2e10 V/m: H2 -0.3 meV, 1.001; D2 -0.5, 1.001; N2 -0.5, 1.001; O2 -0.1, 1.000; CH4 -5.2, 1.010; N2O -12.2, 1.024; SF6 +30.0, 0.938 (solprop has 15.32 eV; optmat’s 15.35 eV is Frost et al.’s first threshold).

  • Against all-electron static rates (majety_2015, fixed nuclei), averaged over orientations (seven angles for N2; for H2 the two orientations, taken as w_perp + (w_par - w_perp) cos^2 theta). Model over reference:

    Molecule	Model	0.03 au	0.04	0.06	0.08	0.10	0.12	0.14
    N2	moadk_zhao_2010	0.90	1.10	1.78	2.78	4.04	5.37	6.64
    N2	moadk_tong_2002	0.50	0.61	0.99	1.55	2.25	2.99	3.69
    N2	adk_hydrogenic	0.50	0.60	0.97	1.51	2.17	2.86	3.51
    H2	moadk_zhao_2010			2.05	1.87	1.98	2.19
    H2	moadk_tong_2002			4.06	3.71	3.92	4.33

    The reference’s rate along the axis over its average is 2.57 at 0.03 au and 1.21 at 0.14 au for N2, and 1.19 to 1.13 for H2.

• Finding:

  • solprop uses Talebpour et al.’s effective charges in a rate they were not fitted within. The papers’ rate has the static Coulomb factor; solprop’s PPT has Ilkov et al.’s, lower by (1 + gamma^2)^(n*): for N2 (n* = 0.841) 1.8 at a Keldysh parameter of 1 and 3.4 at 1.8 (800 nm, 4e13 W/cm2). With its occupancy of 2, solprop’s rate is 1.1 of the papers’ one-electron rate at gamma = 1 and 0.6 at 1.8.

  • The forms lack a correction at finite field and rise against the reference as the uncorrected tunnelling rate of an atom does (TC-655): for N2 by a factor of 7 from 0.03 to 0.14 au.

  • The moadk form for H2 is twice the all-electron rate at fixed nuclei with Zhao et al.’s coefficients and four times with Tong et al.’s, with one electron counted.

  • For O2 the hydrogen-like form is 5 to 19 times the forms that know the orbital or were fitted to yields (800 nm, 5e13 to 2e14 W/cm2).

  • solprop has no rate for CO2; optmat has Zhao et al.’s coefficients for it.

• Doubt: the tabulations of the structure coefficients were made with vertical energies (15.58 eV for N2, 12.03 eV for O2, 15.47 eV for H2 in Zhao et al.’s Table II) and the models take the adiabatic ones; for O2 the curated vertical energy is 12.31 eV. The choice is part of TC-676.

• Status: decided (2026-09-28); open: the validated rate, and TC-676.

TC-674 The “molecular PPT” rates of the literature are three different formulas (2026-09-28)

• Where: Benis_2004_IonizationSuppressionCl2, Zhao_2014_MultiphotonTunnelingIonization (with its corrigendum), Sapkota_2026_LaserFilamentationMolecular, Ionin_2009_TunnelingIonizationAir in the library; docs/molecular_ionisation_rates.md. No data are taken from them: none tabulates a rate, a yield or a ratio.

• Checked (equations read on the page images):

  • Benis et al., Phys. Rev. A 70, 025401 (2004), eq. (2): w = [B^2(m)/(2^|m| |m|!)] [A_m(omega, gamma)/kappa^(2Z_c/kappa - 1)] exp[-(2 kappa^3/3F) g(gamma)] (2 kappa^3/(F sqrt(1 + gamma^2)))^(2Z_c/kappa - |m| - 1). One m; no average over a cycle is printed; A_m and g are referred to Perelomov et al. 1966 and Talebpour et al. 1998 and not written out. “We will refer to the PPT model as the molecular PPT, or MO-PPT model” (p. 3).

  • Zhao, Liu and Zhou, Opt. Commun. 313, 74 (2014), eq. (13): the same with (2 kappa^3/(F (1 + gamma^2)))^(…), without the square root. The corrigendum (Opt. Commun. 355, 615 (2015)): “There is a printing error in Eq. (13)”, and the corrected formula is Benis et al.’s. “We assume that the molecular axis is aligned along the external field direction” (p. 2).

  • The same paper’s atomic rate, eq. (8), has (2F_0/F)^(2n* - |m| - 1) (1 + gamma^2)^(|m|/2 + 3/4): the static Coulomb factor. Its molecular rate, eq. (13), does not reduce to it for one partial wave: the two differ by (1 + gamma^2)^(-n* - 1/4).

  • Sapkota et al., Phys. Rev. A 114, 023518 (2026), eq. (5), attributed to Zhao et al. 2016: (3E/pi kappa^3)^(1/2) sum_m’ [B^2(m’) A_m’/(2^|m’| |m’|! kappa^(2Z_c/kappa - 1))] (1 + gamma^2)^(|m’|/2 + 3/4) (2 kappa^3/E)^(2Z_c/kappa - |m’| - 1) (1 + 2 gamma/e)^(-2Z_c/kappa) exp[-(2 kappa^3/3E) g(gamma)]: the static factor times Popruzhenko et al.’s. It is evaluated at one angle, that of the ensemble’s mean cos^2 theta.

  • Ionin et al., JETP Lett. 90, 181 (2009): a hydrogen-like tunnelling rate with I_p = 13.6 eV for air, against an optoacoustic signal in arbitrary units at 5e14 to 2e16 W/cm2. No test of a molecular rate.

• Finding:

  • The first form carries the factor (1 + gamma^2)^(-n*) of Ilkov et al. (TC-653, TC-670) into the molecular rate; the third carries Popruzhenko et al.’s. Against the references of the atoms both are too low by 2 at gamma = 1.

  • None is averaged over the orientations of an unaligned gas, none has a correction at finite field or a count of electrons, and none says which ionisation energy is meant.

  • Their comparisons with measurements are of yields normalised to the measurement or to a calculation at one intensity: they test the dependence on intensity, not the magnitude.

• Decision: none of the three is a model in optmat. The rate to be validated for molecules is that of TC-652 with the molecular structure factors.

• Doubt: the library’s text of these papers has “CO:Ar” for “CO:Kr” and “g -> 0” for “gamma -> 0” (Benis et al.), “PM/cm2” for “PW/cm2” (Ionin et al.), and the first row of Sapkota et al.’s Table I merged with its header; none touches optmat’s data.

• Status: verified (2026-09-28).

TC-675 zhao_2017 (Zhao, Li, Wang, Li & Zhou, Commun. Theor. Phys. 67, 289 (2017)) (2026-09-28)

• Where: src/optmat/data/sources/zhao_2017.toml, tools/extract/zhao_2017.py; library Zhao_2017_AccurateStructureParameters. Journal pp. 289-300 = PDF pp. 2-13; identity checked on the article’s first page. data/gas/ionisation.toml: the tabulation zhao_2017 of H2, D2, N2, O2, CO2 and N2O.

• Transcribed (35 datasets; H2+, H2, N2, O2, CO, CO2, N2O of the paper’s 123 molecules): Table 1 (pp. 292-293; tbl_3e9e6c6c77bf, tbl_8aa77f541a54, tbl_eeca443820ae; cells): the LB-alpha HOMO energy (7, check, kind not stated) and the “experimental vertical” I_p (7, check, no reference given), eV. Table 2 (pp. 294-297; tbl_5cfe79479e68, tbl_a21cdf242a86, tbl_3ac1855eb657; cells): C_lm of the HOMO, this work (7, check: H2+ 3 points, H2 2, N2 3, O2 2, CO 5, CO2 3, N2O 6) and the reprinted rows (14, reproduced): [30] = tong_2002 (H2+, H2, N2, O2, CO), [33] Kjeldsen & Madsen 2005 (H2, N2, O2, CO), [53] Abu-samha & Madsen 2010 (N2, O2, CO2), [34] Zhao et al. 2009 (CO2), [60] Le et al. 2007 (CO2). R from Table 1 as the column internuclear_distance of every C_lm file (N2O: internuclear_distance_nn, internuclear_distance_no); alpha of the LB-alpha potential in the printed cells and the notes. Table 3 (z coordinates, pp. 297-299) has no quantity: CO and N2O quoted in the notes.

• Checked: every row written, cell by cell against the table images (and the page image of p. 294), 2026-09-28: they agree. The reprinted tong_2002 rows agree with tong_2002, except that H2’s C_4 = 0.00 is not reprinted and CO gains a C_4 = 0.00. Table 3’s coordinates reproduce Table 1’s R and put the centre of nuclear charge at z = 0 (computed). The other reprinted rows were not checked against their papers (not in the library).

• Structural fixes: (1) O2’s rows run over the page break 294/295; the two unlabelled rows at the top of the second fragment are O2’s [53] and [33]. (2) Two fragments merge C_5m … C_9m and the reference mark into one cell; the rows taken print nothing beyond C_4m and the script raises otherwise. (3) In the 11-column fragments the reference mark is in the cell under C_9m. (4) N2O’s two distances are on two rows of Table 1.

• Doubt 1 (no validation of the change): against zhao_2010 (exchange-only LDA + LB) the sum of C_l^2 changes by -7 % (H2), +60 % (N2), +52 % (O2), +61 % (CO), -22 % (CO2); H2+ is unchanged. The paper does not reprint zhao_2010’s Table III, does not discuss the change, and computes no rate with the new coefficients; the validation it cites (p. 297) is that of the earlier parameters. Against the orientation average of the all-electron static rates of N2 (TC-673) the molecular tunnelling rate with the new coefficients is 1.44 at 0.03 au, where that with zhao_2010’s is 0.90.

• Doubt 2 (CO): the even and odd partial waves of the CO row have opposite signs (-2.78, 2.17, -1.22, 0.28, -0.09), against all-positive rows in tong_2002 and zhao_2010; Table 3 puts O on +z. Wang et al. (Mol. Phys. 112, 1102 (2014), p. 1110) call the new signs “correct”, without a derivation, and find that with them the tunnelling rate “fails to fit the experimental data” of the orientation dependence. The on-axis sum, sum_l C_l sqrt((2l+1)/2), is -0.90 towards O and -7.27 towards C, against 5.35 and 0.74 for zhao_2010’s row. CO is not among the molecules of the rate models.

• Doubt 3 (misprints): Table 2’s F2 and S2 rows are identical (1.26, 0.20), not curated species; the reprinted CO2 row [34] (1.27, 0.188, 0.014) has three decimals and was not checked against Zhao et al. 2009.

• Doubt 4 (I_p): “experimental vertical” per the caption, without references; H2’s 15.47 and O2’s 12.03 eV are tong_2002’s Table I values, which tong_2002 says are not the vertical energies. N2 15.60, CO2 13.80 and H2+ 30.00 differ in the last digit from zhao_2010’s 15.58, 13.78 and 29.99. The LB-alpha energies are fitted (alpha) to these I_p.

• Not stated in the paper: the fit range of r, which I_p enters kappa, any uncertainty of the C_lm, m (taken as 0 for sigma, 1 for pi), the method and basis of the GAUSSIAN orbitals, l_max except for CO (40). Neither this paper nor Wang et al. treats a molecule that is not linear: CH4 and SF6 remain without coefficients.

• Not curated: Wang, Zhao, Zhang, Li & Zhou, Mol. Phys. 112, 1102 (2014) (Wang_2013_DeterminationStructureParameters in the library), whose rows of N2O and CO are those reprinted here as this paper’s own, and which adds the inner orbitals of N2O. Its extraction is prepared and awaits J. C. Travers.

• Decision: all datasets are check or reproduced; no default is switched to them. N2O, which had no coefficients, gets this tabulation and no default.

• Status: open.

TC-676 What the ionisation rate of a molecule is to mean: orientation, energy, nuclei (2026-09-28)

• Where: docs/molecular_ionisation_rates.md; the evidence is set out for J. C. Travers in a private note (not in the repository). A propagation code holds one rate W(|E|) per species; three choices fix what it is for an unaligned gas at room temperature.

• Checked (computed from the curated tables; model over or against the reference):

  • Orientation. The all-electron static rate of N2 (majety_2015, seven angles) along the axis is 2.57 times its average over orientations at 0.03 au, 1.83 at 0.08 au and 1.21 at 0.14 au; that of H2 1.19 to 1.13. The molecular tunnelling rate has one anisotropy at all fields (3.2 to 3.3 for N2).

  • Energy, H2. The molecular tunnelling rate (zhao_2010, along the axis) over majety_2015’s fixed-nuclei rate is 2.2, 2.1, 2.2, 2.5 at 0.06, 0.08, 0.10, 0.12 au with the adiabatic energy, and 0.87, 1.00, 1.23, 1.52 with 16.06 eV, the full-CI vertical energy at 1.4 bohr of awasthi_2008 (Table I).

  • Nuclei, H2. saenz_2002 Table I, v = 0: the rate averaged over the vibrational ground state over the fixed-nuclei rate (majety_2015, its own and Saenz’s column) is 1.56 at 0.06 au, 1.32 to 1.36 at 0.08, 1.16 to 1.19 at 0.10, 1.12 to 1.16 at 0.12 au. The ADK rate with the adiabatic energy (its row d) is 2.0 to 2.4 times the averaged ab initio rate (row a) from 0.053 to 0.08 au.

• Finding:

  • The tabulations of the structure coefficients (tong_2002, zhao_2010, zhao_2017) are captioned or used with “vertical” energies, but print 15.47 eV for H2 and 12.03 eV for O2, which are the adiabatic energies to 0.04 eV. Tong et al. (2002, pp. 6-7) evaluate their rates with energies 0.88 eV (D2) and 0.33 eV (O2) higher.

  • Talebpour et al.’s charge of O2 belongs with 12.55 eV (TC-542).

  • The averages in the literature are of ionised fractions over orientations (Tong et al. 2002, eqs. 15-17; Zhao et al. 2016, eqs. 13-14), not of rates.

• Decision: none yet. The forms of TC-673 take the average of the rate over orientations, the adiabatic energy and no nuclear motion, as solprop does.

• Status: decided (2026-09-28) by J. C. Travers: the average of the rate over orientations; the vertical energy in the rate; the rate at the neutral’s geometry times a vibrational factor where a reference gives one (H2; D2 by H2’s, as an assumption); O2’s vertical energy the band maximum, 12.307 eV; the energy of the plasma loss for solprop’s SEP-3; a statement for the alignment left behind a pulse. Implemented in TC-677 to TC-680.

TC-677 The molecules’ rate: the model default (2026-09-28)

• Where: optmat.gas.molecular_ionisation_rates (the form molecular), data/gas/molecular_ionisation_rates.toml (models.default), optmat.gas.ionisation_rates._log_short_range_strength, docs/molecular_ionisation_rates.md. The decisions of TC-676.

• Decision (the rate): W = N_eff V sum_m’ K_m’ w_sr,m’(F, omega) Q(F) S(F), with K_m’ = <B^2(m’)> kappa^(1 - 2n*) / (2^|m’| |m’|! I_p):

  • <B^2(m’)> the structure factor of Tong, Zhao and Lin (2002, eqs. 8-9) averaged over orientations, sum_l C_l^2 Q(l, m’)^2/(2l + 1), which for a molecule that is not linear needs only sum_m |C_lm|^2 per l (the orthogonality of the rotation matrices over both indices);

  • w_sr,m’ the rate of Perelomov, Popov and Terent’ev in a short-range potential (eq. 54) for the projection m’, with K_m’ in the place of an atom’s |C_kappa l|^2 f(l, m): the static tunnelling term of Tong et al. for the projection m’ is I_p K_m’ (2F_0/F)^(2n* - |m’| - 1) e^(-2F_0/3F), the atom’s with that substitution, so that the short-range rate’s tunnelling limit is the molecular static rate term by term;

  • Q the static Coulomb factor (TC-653, TC-670); S Tong and Lin’s form of the correction (TC-678); N_eff the shell’s electrons (TC-678); V the vibrational factor (TC-679);

  • the cycle-averaged and the instantaneous rate related as for the atoms (TC-662).

• Checked: with one s wave and helium’s constants the form gives the atoms’ rate of helium to 1e-9 at 800 nm, 400 nm and in a static field, both rates (a test). In a static field it is N_eff V S times the orientation-averaged tunnelling rate to 1e-12. At 30 um (gamma < 0.04) the cycle-averaged rate is the average over a cycle of the static rate to 0.5 %. The yields of a 42 fs pulse from the two rates agree to 1.2 % for N2, O2, H2, CH4 and CO2 at 0.6 of the barrier-suppression field.

• Doubt: the rate depends on the energy through its exponent and its prefactor; the vibrational factor follows the exponent only (TC-679). No calculation of a molecule tests the dependence on the frequency (TC-680).

• Status: decided (2026-09-28).

TC-678 The molecules’ electron count and correction at finite field (2026-09-28)

• Where: data/gas/molecular_ionisation_rates.toml (electrons, tong_lin_alpha); optmat.gas.molecular_ionisation_validation.fitted_constants; majety_2015 Tables A1 (N2, seven angles) and 2, 3 (H2, along and across the axis).

• Decision:

  • N_eff is the number of electrons in the ionising shell, each orbital of a degenerate shell counted: H2, D2, N2 and O2 2; CO2 and N2O 4; CH4 6. The weak-field limit of the many-electron theory (Tolstikhin, Madsen and Morishita 2014, section II G; TC-658), and the count of Kjeldsen et al. (2005): “the rates … must be multiplied by the number of electrons which occupy the active orbital, i.e., four for the degenerate HOMO of benzene and two for the nondegenerate closed shell orbitals” (TC-682).

  • alpha is fitted with that count, by least squares in the logarithm, to the average over orientations of the all-electron static rates at fixed nuclei, the model evaluated with the vertical energy (TC-679) and Zhao et al.’s coefficients of 2010: H2 6.02 (0.06 to 0.12 au; residuals within 3.3 %), N2 14.02 (0.03 to 0.14 au, to 1.7 times its barrier-suppression field; residuals -19 % to +13 %, rms 10 %). Curated as 6.0 and 14.0. Tong and Lin’s own alpha for H2+ is 6 (tong_2005).

  • O2, CO2, N2O and CH4 take N2’s 14.0, an assumption: no all-electron static rate of them is published.

• Checked:

  • With the count left free as well, the references ask for 2.12 (H2) and 1.76 (N2) electrons and alpha 6.49 and 13.12: the weak-field count within 12 %.

  • With other coefficients the free counts are 2.27 and 1.10 (zhao_2017), 1.07 and 3.16 (tong_2002): only the product of count and C_l^2 is determined, and zhao_2010’s coefficients are the ones that make the count the theory’s. This is the reason the default takes them for H2, D2, N2, O2 and CO2.

  • fitted_constants recomputes the fit; a test holds the curated constants to it.

• Doubt:

  • The N2 residuals are not flat: the reference’s ratio to the model falls faster than a linear exponent above 0.12 au. One constant per molecule is enough to 13 % to 0.12 au, and 19 % at 0.14 au.

  • The all-electron rates are at fixed nuclei with a stated accuracy of 10 % (TC-658); for N2 Majety and Scrinzi’s is the one calculation.

• Status: decided (2026-09-28).

TC-679 The molecules’ ionisation energy and vibrational factor (2026-09-28)

• Where: data/gas/molecular_ionisation_rates.toml (ionization_energy, vibrational_constant); optmat.gas.molecular_ionisation_rates (the vibrational factor, _VIBRATIONAL_TAIL); saenz_2002 Table I row (a); majety_2015 Table 2 column [18]; awasthi_2008 Table I.

• Decision (energies of the rate, vertical): H2 16.06 eV (awasthi_2008/ip_ci, the configuration-interaction vertical energy at 1.4 bohr, the geometry of the references); D2 the same (at fixed nuclei the electronic energy does not depend on the isotope); N2 15.58 eV (Svensson et al. as majety_2015 reprints them, 0.7 meV below the adiabatic energy); O2 12.307 eV (Baltzer et al.’s band maximum, as mahla_2025 reprints it); CO2 13.79 and N2O 12.89 eV (Turner et al.’s band maxima as potts_1974 reprints them); CH4 13.6 eV (the first maximum of the 1t2 band, heilbronner_1977). The adiabatic energy of ionisation.toml is kept as adiabatic_ionization_energy.

• Decision (vibrational factor): V is the average of the rate over the vibrational ground state over the rate at the neutral’s bond length. The rate depends on the energy chiefly through its exponent (2F_0/3F) g(gamma), whose derivative is -(2 kappa/F) h(gamma), h = g + gamma g’/3. For a Gaussian spread of the energy over the ground state the average is exactly exp(c h^2/F^2): h = 1 in a static field, h ~ ln(2 gamma)/gamma in the multiphoton limit. The average is dominated by the bond length x = sqrt(2c) h/F standard deviations out; beyond two, ln V is continued as 2x - 2 (continuous, with a continuous slope).

  • c = 0.00165 au (H2), by least squares in ln V against Saenz’s rates averaged over the ground state (v = 0) over his rates at 1.4 bohr, the field along the axis, 0.06 to 0.12 au: ratios 1.562, 1.320, 1.158, 1.157, fitted within 3.1 % (rms 2.2 %). A form ln V = b/F fits them to 5.7 % rms.

  • D2 takes H2’s c, an assumption: in the harmonic estimate c scales as the square of the ground state’s width, 1/sqrt(2) of H2’s.

  • N2, O2, CO2, N2O, CH4: V = 1. For N2 Kornev and Zon’s (2015) sum over the ion’s vibrational levels is the fixed-nuclei rate at the Franck-Condon mean energy to 2

• Finding (why the tail): with ln V = c/F^2 followed to zero field the factor grows faster than the tunnelling rate falls: the rate of H2 in a static field turns up below 2c/(2 kappa^3/3) = 0.004 au, and at 800 nm, where the exponent grows only as ln(1/F), at still higher fields if the factor ignores the frequency; a pulse’s wings then ionise it completely (the first implementation had both faults: at 800 nm and 1e-3 au it gave 1e30 s^-1). A test now holds the rate monotonic from 1e-4 to 0.1 au, static and at 800 nm, both rates.

• Checked: the factor against Saenz’s ratios: 1.013, 0.981, 1.019, 0.969 (model over reference). At 0.05 au it is 1.94, and at 0.03 au 6.3 in a static field; a Morse model with constants from memory (not curated) gives 2.0 and 4.7 there.

• Doubt:

  • Saenz’s rates are for the field along the axis; V is applied to the average over orientations.

  • Below 0.06 au V is an extrapolation of the fit; the switch to the tail is at 0.029 au in a static field.

  • The vertical energies are band maxima or calculated values: O2’s choice among 12.31 to 12.55 eV is a factor of 1.3 to 2 at 1e14 W/cm2, CH4’s among 13.6 to 15.0 eV a factor of 3 or more.

• Status: decided (2026-09-28).

TC-680 The molecules’ rate against its references, and its stated uncertainty (2026-09-28)

• Where: optmat.gas.molecular_ionisation_validation (orientation_averaged_rates, vibrational_factors), optmat.gas.ionisation_validation.measured_yields (now with N2 and O2), tests/test_molecular_ionisation_rates.py, docs/molecular_ionisation_rates.md.

• Checked:

  • Static, fixed nuclei, averaged over orientations (the references the constants were fitted to): H2 0.97 to 1.03 (0.06 to 0.12 au); N2 0.99 to 1.13 to 0.12 au and 0.81 at 0.14 au.

  • Measured (wahlstrand_2018, 42 fs, 800 nm; the model’s yield over the fit): N2 8.8 at 75 TW/cm2 falling to 5.1 at 125; O2 2.2 to 2.9 from 40 to 105 TW/cm2. The same measurement is 1.7 to 3.9 times below the atoms’ default (TC-660). Divided by the atom of the same experiment at the same intensity, which removes the intensity scale to first order: N2 over Ar 2.7 falling to 1.3, O2 over Xe 0.34 rising to 0.90. Part of N2’s excess over Ar is argon’s rate being low at these fields: argon’s all-electron static rates are 1.2 to 1.6 times its model’s below 1.7e14 W/cm2 (TC-669).

• Finding: the literature’s forms are nearer Wahlstrand et al.’s absolute yields for N2 (ppt_talebpour_ilkov 1.2 to 1.3, moadk_zhao_2010 0.9 to 2.1); none of them reproduces the all-electron static rates (TC-673). The measurement’s conflict with the calculations is the atoms’ (TC-660).

• Decision (uncertainty factors): H2 1.5 and N2 1.5 (the static references and, for H2, the vibrational factor; the dependence on the frequency rests on the atoms’); D2 2 (its vibrational factor assumed); O2, CO2 and N2O 3 (alpha by analogy; O2’s energy); CH4 5 (alpha by analogy; the vertical energy of a Jahn-Teller band; one tabulation, fitted with an energy 1 eV below the rate’s).

• Doubt: no calculation of a molecule tests the dependence on the frequency; a time-dependent calculation of N2 or H2 at 800 nm would.

• Status: open (the frequency dependence of the molecules; Wahlstrand et al.’s conflict).

TC-681 zhao_2011 (Zhao, Xu, Jin, Le & Lin, J. Phys. B 44, 035601 (2011)): CH4’s structure coefficients (2026-09-28)

• Where: src/optmat/data/sources/zhao_2011.toml, tools/extract/zhao_2011.py; library Zhao_2011_EffectOrbitalSymmetry, Table 1 (p. 7; tbl_6768a1c91416), the CH4 block; Table 2 (p. 9) for the frame, quoted in the record. optmat.gas.ionisation.combined_structure_coefficients; ionisation.toml (CH4.structure.zhao_2011).

• Transcribed: CH4’s “experimental vertical” ionisation energy (12.60 eV) and the C_lm of the three degenerate 1t2 HOMOs (HF/AUG-cc-pVQZ orbitals from GAUSSIAN 03, fitted at r = 5 to 10 au for small molecules): 11 datasets, one per orbital and signed m (HOMO1, HOMO2: m = +-1, l = 1 to 4, and m = +-3, l = 3, 4; HOMO3: m = 0, l = 1, 3, and m = +-2, l = 2, 4), the value the real part and the column imaginary the imaginary part; 20 printed cells. All check. SF6 and the other molecules are not taken.

• Checked: every CH4 cell against the table image, the page at 400 and 800 dpi and the PDF’s text layer. The library misreads two paired signs as ‘+-’ where the page prints ‘-+’: HOMO1 C_{3+-1} (-+0.13) and HOMO3 C_{4+-2} (-+0.11i), restored by the script as a structural fix. The library’s orbital label ‘1b_2’ is 1t_2 on the page. Sum over m of |C_lm|^2: 11.34 (HOMO1, HOMO2) and 11.38 (HOMO3), equal per l to the rounding (l = 2: 1.28 in all three).

• Decision: the average over orientations takes the mean over the three orbitals of sum_m |C_lm|^2 per l, and the count 6 (TC-678). No default tabulation is named in ionisation.toml: the one tabulation.

• Doubt:

  1. The paper does not state how C_{l+-m} = -+a is read; the upper sign for +m is assumed. With Condon-Shortley Y_lm it puts each orbital’s l = 2 admixture in phase with the l = 1 part at all four hydrogens of Table 2, as a C-H bonding orbital requires. The average over orientations does not depend on it.

  2. 12.60 eV is labelled vertical but is the adiabatic threshold (berkowitz_1987: 12.61 eV), about 1 eV below the 1t2 band maxima (13.6, 14.4, 15.0 eV; heilbronner_1977); the coefficients were fitted with an energy of that order and the rate takes 13.6 eV (TC-679).

  3. How the degenerate orbitals combine in a rate, the orbital normalisation, Z_c and the kappa of the fit are not stated; the paper says the C_lm “may not be highly accurate” (p. 6).

  4. SF6 cannot be taken from the library’s cells of the table’s continuation (tbl_4df3e935bc02), which mix CCl4’s coefficients into SF6’s rows, lose its I_p (15.69 eV on the page) and six of its columns, and print every paired sign as ‘+-’. The page itself (p. 8) prints SF6’s coefficients; they await a re-extraction of the table in the library.

• Status: open (the sign reading is an assumption; SF6 not curated).

TC-682 Kornev & Zon 2015 and Kjeldsen et al. 2005: read, not curated (2026-09-28)

• Where: Kornev_2015_TunnelingIonizationVibrationally (Phys. Rev. A 92, 033420 (2015)) and Kjeldsen_2005_InfluenceMolecularSymmetry (Phys. Rev. A 71, 013418 (2005)) in the library. Read on the page images; no dataset is taken.

• Finding (Kornev and Zon):

  • Their rate, eq. (16), is the molecular tunnelling rate with Franck-Condon factors over the ion’s vibrational levels, an overlap of electronic states and a differential dynamic Stark shift; the average over orientations, eq. (19), is the one of TC-677.

  • Their sum over the ion’s levels is the fixed-nuclei rate at the Franck-Condon mean energy (15.60 eV from their Table III) to 1.7 % at 3.5e13 W/cm2 and 0.6 % at 1e14 W/cm2 and above (computed from their constants by a reader of the paper): the vibrational factor of N2 is 1 with the vertical energy (TC-679). Their “20-40 %” reduction by vibration is mostly their electronic overlap (0.96) and Stark shift, not the Franck-Condon factors.

  • Their Table VII is not reproduced by their printed eq. (16): the reader reproduced it to 0.4-1.2 % only with the factor sqrt((2l + 1)/2) of B(m’) dropped, which makes their dependence on the angle flatter (0 over 90 degrees 2.5) than Majety and Scrinzi’s all-electron rates (5.4 to 3.6). Their absolute rates are 6 to 8 times the orientation average of the latter. They are not used to validate.

  • The HOMO-1 (1pi_u) adds 0.5 to 4 % to the average over orientations of N2’s rate at 0.5e14 to 5e14 W/cm2 on their numbers; Majety and Scrinzi’s rate contains all channels.

  • Their x2DHF coefficients of 3sigma_g, in Tong et al.’s normalisation, are about 1.35 times zhao_2017’s.

• Finding (Kjeldsen et al.): C_lm for ethylene and benzenes (not optmat’s molecules); the rates “must be multiplied by the number of electrons which occupy the active orbital” (p. 7; TC-678); their tunnelling rates, normalised to measured ion signals at high intensity, agree poorly with them, which they ascribe to the intensities not being in the tunnelling regime.

• Status: verified (2026-09-28).

TC-683 The molecules’ rate: its range, CO as a test of N2’s constant, Guo et al.’s ratios (2026-09-28)

• Where: optmat.gas.molecular_ionisation_rates (_MAXIMUM_FIELD, MolecularRateModel.maximum_field), molecular_ionisation_rates.toml (CO in default and the moadk and adk forms), ionisation.toml ([CO]), optmat.gas.molecular_ionisation_validation (CO’s thirteen angles; the average over 0 to 180 degrees for a polar molecule), tests/test_molecular_ionisation_rates.py, docs/molecular_ionisation_rates.md and the gallery (plot_molecular_ionisation, _default, _measured). Steps 7 and 8 of the port (TC-673): validation, and the manual’s figures.

• Finding (the range): drawing the default to twice the barrier-suppression field, the range the atoms’ rate is given in, showed that with N2’s alpha of 14 the rate of every molecule that takes it (N2, CO, O2, CO2, N2O, CH4) stops rising at 1.70 to 1.82 times that field, static and at 800 and 1800 nm, instantaneous and cycle averaged: the correction outruns the tunnelling exponent. H2 and D2 (alpha 6) and the five atoms rise to twice it. N2’s references reach 0.14 au (1.71 times), where the model is already 19 % low.

• Decision (the range): the default is given without a warning up to 1.5 times the barrier-suppression field, the range where it holds N2’s all-electron rates within 13 % (0.12 au is 1.46 times); a test holds every molecule’s rate rising to there. The forms keep the barrier-suppression field.

• Decision (CO): CO enters the default with N2’s alpha, not fitted (isoelectronic with N2), 2 electrons (5 sigma), Zhao et al.’s coefficients of 2010, and the vertical 14.01 eV (potts_1974/hei_CO#3sigma), which also stands for the adiabatic energy: none is curated. Uncertainty factor 1.5. It enters the moadk forms and adk_hydrogenic too. solprop has no rate for CO.

• Checked (CO): against the average over the thirteen angles of majety_2015’s haCC(6) rates (Table A2, 0 to 180 degrees; the rate differs by up to 2.1 between the two directions along the axis): the default is 1.26 to 1.32 times the reference from 0.03 to 0.09 au (0.45 to 1.36 times CO’s barrier-suppression field), flat: the dependence on the field of N2’s correction carries to CO, the magnitude is 30 % high. At 0.025 au every model, with or without a correction, jumps by 1.6 to 1.8 against the reference, whose anisotropy jumps from 1.4 to 2.7 between neighbouring fields: taken as the reference’s. Fitted to CO with the count at 2, alpha would be about 16, absorbing the offset as a slope. The average over 0 to 180 degrees interpolates the logarithm in cos(theta) and is checked on 2 + cos and 1 + cos^2.

• Checked (Guo et al. 1998): their yields are in figures only (not digitised), but the text states N2 behaves like Ar and “the O2+ LP ion yield is roughly ten times below Xe+ in the unsaturated range”. The default’s yields of a 30 fs pulse at 800 nm: N2/Ar 1.41 to 0.84 from 2e13 to 1.5e14 W/cm2, as stated; O2/Xe 0.022 to 0.024 from 2e13 to 7e13 W/cm2, flat, so that the intensity scale (ADK’s argon) does not move it: 4.5 times below the statement. Wahlstrand et al.’s O2 against Xe points the same way by 1.1 to 3 (TC-680). Talebpour et al. (1998, 1999) print no number for their molecule-to-atom comparisons.

• Doubt:

  1. Two measurements put the default’s O2 low relative to xenon. A ratio does not say which: against Wahlstrand et al.’s absolute yields Xe’s model is 4 to 8 times high and O2’s 2.2 to 2.9. O2’s factor of 3 is kept.

  2. CO’s 30 % offset is in the coefficients, the count or the permanent dipole’s Stark shift, which the average over orientations of a rate without it does not hold; which is not decided.

• Status: open (O2 against xenon).

TC-684 zhao_2011: SF6’s structure coefficients read on the page, by exception; SF6’s rate (2026-09-28)

• Where: tools/extract/zhao_2011.py (SF6_PAGE, CORROBORATED, the checks), src/optmat/data/sources/zhao_2011.toml (21 datasets, the notes), data/values/ionisation/SF6/zhao_2011__*.csv, ionisation.toml (SF6.structure.zhao_2011), molecular_ionisation_rates.toml (SF6 in default), the manual page and its figure.

• Decision (J. C. Travers, 2026-09-28): an exception to “extracted, not typed”. The library’s cells of Table 1’s continuation (tbl_4df3e935bc02, p. 8) are not a rendering of the page, which prints the table rotated by 90 degrees (the extraction backend, MinerU, run without the Docling check, read it as 12 rows by 6 columns): SF6’s energy and six of its columns are lost, CCl4’s coefficients stand on its rows, and every paired sign is ‘+-’. No structural fix recovers the table, and a re-extraction with the same backend would repeat it. SF6’s energy and 24 cells were read on the table image turned upright and are written in the extraction script as the page prints them; the files are written by the script from them.

• Evidence, checked by the script:

  1. the library’s table is still the reading the exception was made for: a re-extraction fails the script, and SF6 is then taken from the new cells;

  2. 11 of the 24 cells are also among the library’s cells with the same header and magnitude;

  3. the three degenerate 1t1g orbitals, rotations of one another, have the same sum of |C_lm|^2 over m per l to the table’s rounding: l = 4 145.5 in all three; l = 6 3.24, 3.24, 3.28; l = 8 0.356, 0.356, 0.354 (l = 10 printed for HOMO3 only).

• Decision (the rate): SF6 enters the default with 6 electrons (1t1g), N2’s alpha (an assumption), the first band maximum 15.69 eV (potts_1970, which assigns it to 3t1u; Zhao et al. print the same energy for their 1t1g HOMO) and uncertainty factor 10.

• Finding: the l = 4 wave dominates (the fluorine lone pairs lie 3 bohr from the centre, and a one-centre expansion of them has large high partial waves): the orientation-averaged structure factor at m’ = 0 is 75 per orbital (N2 4.2, CH4 5.7), and SF6’s default is 83 times N2’s rate at 2e14 W/cm2 for nearly the same ionisation energy, and 100 to 2300 times the hydrogen-like form solprop uses (5e13 to 2e14 W/cm2). The decomposition is m’ = 0 of l = 4, not a numerical artefact.

• Doubt: nothing tests it. The library holds no calculation or measurement of SF6’s strong-field rate; the authors call their orbitals’ asymptotic tails “not accurate” (p. 6); the MO-ADK expansion about one centre is the less reliable the farther the orbital’s density lies from it. A measured SF6+ yield beside an atom’s or N2’s would decide. Factor 10 is a judgement, not a measured spread.

• Status: open (SF6’s rate untested).

TC-685 The Raman response in optmat: the boundary, the convention and the tensor form (2026-09-28)

• Where: optmat.gas.raman_response (new), optmat.solid.raman_response (new), docs/raman_response.md; optmat.gas.raman (band_lines, BandLines; the bands’ transition_anisotropy and depolarization).

• Decision (J. C. Travers, 2026-09-28): the boundary moves. optmat gives the Raman response function itself, not only its lines (TC-439), as it now gives the ionisation rates (TC-652): the response of a gas or mixture as a function of the delay, of the frequency and of the density, and fused silica’s normalised response with its size. The propagation code keeps the sampling: its grid, taper, padding, FFTs and any tabulation or grouping for speed. solprop is not changed; its SEP 3 is to be rewritten to use these responses.

• Decision (the convention): TC-442’s, P_x = eps0 N E_x ∫ h(tau) E_x²(t - tau) dtau with h = sum A sin(Omega tau) exp(-Gamma tau), Gamma = pi FWHM; a mixture’s lines carry their constituent’s mole fraction, so N is the mixture’s density. The transform H(omega) = ∫ h exp(+i omega tau) dtau is given analytically; its imaginary part is positive at a Stokes shift and gives the gain omega_s N Im H / (c² eps0), which equals stokes_gain for an isolated line (tested to 1e-15).

• Decision (the tensor form): Hellwarth’s, R_ijkl = a delta_ij delta_kl + (b/2) (delta_ik delta_jl + delta_il delta_jk), h = a + b for one linear polarisation. A line’s isotropic share enters a only; its anisotropic share h2 enters as a = -h2/2, b = 3h2/2, because the induced anisotropic polarizability follows the traceless part of E E. A weak probe across the pump sees a: -1/2 of the rotational response (the known ratio of the rotational birefringence), all of an isotropic vibrational one.

• Checked:

  • the analytic H against the trapezoidal transform of h for N2, H2 and dry air at three frequencies, within the quadrature’s 1e-2;

  • a + b = h to 1e-15, a/h = -1/2 for every rotational line;

  • the Placzek-Teller coefficients by Gauss-Legendre quadrature of the M-averaged squared element of cos² - 1/3: (4/45) b_JJ for the Q lines, (4/45) b_{J+2,J} for the S lines (which gives TC-442’s (2/15)(J+1)(J+2)/(2J+3) n_J), and their sum 4/45, for J = 1-11;

  • the response vanishes before the impulse and is finite at every density.

• Status: decided (2026-09-28).

TC-686 The anisotropic share of the Q lines, and the O and S branches left out (2026-09-28)

• Where: optmat.gas.raman_response (_anisotropic_share, placzek_teller_q), optmat.gas.raman (VibrationalBand.transition_anisotropy, VibrationalBand.depolarization), data/gas/raman.toml (N2’s and O2’s depolarization).

• Decision: a Q(J) line’s anisotropic share is (4/45) b_JJ gamma’² P_J/(hbar eps0), b_JJ = J(J+1)/[(2J-1)(2J+3)], beside the isotropic share a’² P_J/(hbar eps0) of TC-442:

  • H2 and D2: gamma’_J = <0J|alpha_par - alpha_perp|1J> per J from Hunt et al. 1984’s components, the same tables as the mean element (the share per line is 0 for Q(0), 2.4 % for H2’s Q(1), 1.6 % above J = 3);

  • N2 and O2: from Danichkin et al.’s recommended Q-branch depolarisation ratio at 488 nm (linear polarisation, 90 degrees), rho = 0.021 and 0.047, through rho = 3 b gamma’² / (45 a’² + 4 b gamma’²): the branch’s share is 4 rho/(3 - 4 rho), 2.9 % and 6.7 %, shared between the lines as b_JJ over its population average;

  • CO2: the two dyad members’ curated rho (0.027, 0.044), which also reduced their cross sections (4.7 % together);

  • CH4 and SF6: none: a totally symmetric mode of a spherical top has an isotropic polarizability derivative (the curated rho are 0);

  • N2O: none: rho is taken as 0 where no ratio is curated (TC-542’s stopgap).

  • The dispersion factor of the mean element (TC-542) is applied to the anisotropy too, and the anisotropic lines take the isotropic lines’ widths, although reorientation also relaxes them (an approximation, stated).

• Left out: the vibrational O and S branches (Delta J = -+2), anisotropic only. With the Q lines’ gamma’ they would carry (1 - b_JJ)/b_JJ times the anisotropic Q share: 8.3 % of N2’s Q branch, 19.1 % of O2’s, 14 % of CO2’s and 3.3 % of H2’s and D2’s, spread over some 100 cm⁻¹ (H2: its S1(J) and O1(J) lines) about the band.

• Checked: the share of N2’s branch equals 4 rho/(3 - 4 rho) to 1e-12; H2’s per line equals (4/45) b_JJ (gamma’/a’)² to 1e-13.

• Status: decided (2026-09-28); open: the O and S branches, the anisotropic lines’ widths.

TC-687 The widths of the response’s lines: three coefficients, damping groups, the partners (2026-09-28)

• Where: optmat.gas.raman_response (_width_coefficients, GasRamanResponse.fwhm, decay_rates, damping_group).

• Decision (the density dependence): every width law of optmat.gas.linewidths is, at a fixed temperature and composition, c + d/n + beta n (n in amagat; the exponential-gap law is proportional to n). The response finds each line’s c, d and beta from the law at 1, 2 and 4 amagat (a 3 x 3 system of condition number 20), requires them to reproduce the law at 8 amagat to 1e-9, and sets a coefficient the law does not have (below 1e-12 of the widths) to zero. The widths are then a cheap, vectorised function of the density, the part a propagation code evaluates along a density gradient.

• Checked: the response’s widths equal raman_lines’ to 1e-12 at three densities within each gas’s range, for all eight gases.

• Decision (damping groups): lines of one species and band whose c, d, beta, cap and shift are identical share a group; they can be summed before the damping with no approximation. N2: 106 lines, 43 groups (the S lines beyond Herring et al.’s S(2)-S(14) and the Q lines beyond Rosasco et al.’s J hold the end values); H2: 20 lines, 3 groups (one law for every Q(J)); dry air: 170 lines, 82 groups.

• Decision (the partners): a constituent’s widths in a mixture use the mixture’s mole fractions as its partners (self for itself), through raman.toml’s substitutes (Ar as O2 for N2’s S lines, as air for O2’s), not the total density with the gas’s own coefficient: solprop’s shortcut (TC-368, SEP 3 G7). A partner with neither a coefficient nor a substitute is refused (H2 in He).

• Status: decided (2026-09-28).

TC-688 The response’s ranges, the Doppler cap and the line shifts (2026-09-28)

• Where: optmat.gas.raman_response (_band_limits, _fwhm, _shift), data/gas/raman_response.toml; herring_1986 (formula eq3_cutoff, added).

• Transcribed: Herring, Dyer & Bischel 1986, Eq. (3), p. 5 (journal p. 1948): rho_c = 3.33 A/Delta nu_D, the density at which the diffusion (Dicke) law of the width is 10 % above the hard-collision line shape (from Bischel & Dyer). It reproduces their Table IV’s rho_c (0.095, 0.087, 0.068, 0.134 amagat; the table prints 0.088 for 80 K S(1)).

• Decision (the densities): the lines are independent collisional Lorentzians between two densities, found for each band’s strongest line (the response’s range is the narrowest of its bands’):

  • below: for a line with a Dicke term, Herring et al.’s rho_c with Delta nu_D their Eq. (4) for forward scattering (the propagation geometry; the curated Dicke terms are all for forward scattering: herring_1986, bischel_1986, smyth_1987); for H2 0.943 amagat (Bischel & Dyer print 0.92 for Q(1) at 298 K, Table III, which Owyoung’s A = 302 rather than their own 309 reproduces), D2 0.616. For a line without one, the density at which its collisional width falls to Delta nu_D: N2 0.054 (its Q branch), O2 0.035, CO2 0.011, N2O 0.021 amagat;

  • above: the width of the strongest line reaches the spacing to its nearest neighbour: N2 2.09 amagat (the Q branch; Koszykowski et al. 1987 find its lines “essentially isolated” at 1 atm and collapsed by 10 atm, Herring et al. require mixing “at densities of 1 amagat or larger”), O2 4.2, CO2 13.1, D2 1020, H2 3290 amagat (their S lines);

  • outside them ModelRangeWarning. The measured density ranges of the width data (Herring 0.01-2 amagat, Rosasco 0.2-2 atm, Hölzer 1 bar, Millot 0.2-2 atm, Bischel 1-25 amagat, Smyth 0.3-20, Keijser 65-90 amagat) are recorded in the reasons; the impact widths are extrapolated linearly between them and these limits.

• Decision (the Doppler cap): below rho_c the Dicke term d/n is capped at the Doppler width of the band’s strongest line (the line the band’s Dicke coefficient is measured for: Q(1), S(1)), a Lorentzian stand-in for the Doppler limit that keeps the response finite as n -> 0. The masses in Eq. (4) are nominal mass numbers (Herring et al. use m = 2 amu for H2): the width is only a cap and a range criterion.

• Decision (the shifts): H2’s Q lines shift by Bischel & Dyer’s Eq. (4), C = -96.1 + 0.777 (T - 298) - 8.82e-4 (T - 298)² MHz/amagat, used for every Q(J) as their width law is (their Q(0) shift is -64 MHz/amagat at 298 K; Q(0) holds 13 % of the molecules): at 298 K the shift is 1.85 times the collisional width’s coefficient and moves the line by 2.9 GHz at 30 amagat. Not used: H2’s S shifts (+6 MHz/amagat, Herring et al. Table VI, 5 % of the widths’ coefficients), O2’s Q shifts (Millot et al., -2.3 to -3.5e-3 cm⁻¹/atm, 3-5 %), N2’s (below 0.001 cm⁻¹/atm, Rosasco et al., under 1 %); D2’s Murray & Javan shifts are doubtful (TC-586).

• Decision (the temperatures): each band’s width measurements, widened by 5 K at a measured end; room temperature stated without a number is 290-300 K (raman_response.toml). N2’s rotational widths reach 295 K (Herring et al.’s power laws), so N2 and air warn above 300 K; its Q widths reach 1500 K.

• Checked: the cap’s value against Eq. (4) (H2 Q(1) at 295 K); the warnings; N2’s upper limit between 1 and 3 amagat.

• Status: decided (2026-09-28); open: the line shapes below rho_c, Q-branch mixing.

TC-689 The Raman response of dry air (2026-09-28)

• Where: data/gas/raman_response.toml ([mixtures."dry air"]), optmat.gas.raman_response (_composition).

• Decision: the CIPM-2007 composition (TC-548) with N2, O2 and Ar kept, 99.957 % of the molecules, renormalised; Ar has no Raman lines and takes part as a collision partner. CO2 (400 ppm) is left out: it has no broadening coefficients by N2 and O2, and its long-pulse rotational index, ten times N2’s, would add 0.3 % to air’s. The trace constituents add less.

• Checked: air’s lines are the constituents’ times their renormalised mole fractions (to 1e-14); N2’s widths in air differ from pure N2’s; air’s long-pulse rotational index at 1 amagat and 295 K is 3.22e-23 m²/W.

• Status: decided (2026-09-28).

TC-690 The gases’ responses against measurements and against solprop (2026-09-28)

• Where: optmat.gas.raman_response_validation, tools/raman_response_tables.py, tools/solprop_raman_response.py, tests/data/solprop_raman_response.json (solprop 2dc84d0, read only, at 295 K), docs/raman_response.md.

• Checked (gains): from Im H at the (shifted) line with every other line’s tail and the anisotropic share: H2 Q(1) +30 % (Ottusch & Rockwell, 532 nm, 60 amagat), +36 %, +14 %, +23 % (Bischel & Black 1986, 532, 477, 308 nm); D2 Q(2) +41 %; CH4 0 %: TC-542’s gains, 2-3 % higher by the anisotropic share. The excess of H2 and D2 stays TC-542’s.

• Checked (the rotational revivals, independent): Chen et al. 2007’s decay time of O2’s revivals at 5.1 atm, 23.2 ps from an exponential fit to the revival peaks up to 1.25 periods, against the same fit to the response’s revivals: 23.5 ps (+1 %), with Hölzer et al.’s per-N widths (the amplitude-weighted mean width would give 27 ps).

• Checked (against solprop): per part at 1 amagat, the least-squares scale over the first 100 fs: rotation of N2 and O2 1.000; H2 1.10 and D2 0.98 (solprop’s fitted anisotropies against Bishop & Pipin’s per J and Carusotto’s); the vibrational parts 1.033 (N2), 1.081 (O2), 0.897 (H2), 0.772 (D2), 1.116 (CH4), 1.124 (SF6), which are the ratios of the strengths (TC-542: N2 0.996, O2 1.015, H2 0.884, D2 0.760, CH4 1.116, SF6 1.124, optmat’s |<0|a|1>|²/(hbar eps0) over solprop’s (4 pi eps0 da/dq)²/(2 mu Omega eps0)) times one plus the anisotropic share (N2 2.9 %, O2 6.7 %, H2 and D2 about 2 %): no factor of the convention differs between the two. Near 20 ps the responses differ by the widths: N2’s vibrational part is 5.5 times solprop’s, whose single 6 ps line (the branch’s envelope, TC-491) has decayed.

• Checked (performance, for SEP 3): the family of kernels over a density range is of low rank: on a 2^15-point window (131 ps at 4 fs; H2 and D2 66 ps at 2 fs) and 64 densities, the largest error of the best rank-r sum on the spectrum falls below 1e-3, 1e-4 and 1e-6 of the kernel’s largest value at r = 3, 4, 5 (N2, 0.5-2 amagat), 5, 6, 9 (N2, 0.1-10), 5, 6, 8 (O2 and air), 4, 5, 6 (H2, 1-30) and 4, 4, 5 (D2). A rebuild per line and sample costs about 7 ms for N2 at N = 2^14 (one numpy core) against 0.2 ms per convolution; a rank-r rebuild needs no exponentials.

• Status: decided (2026-09-28); the H2 and D2 gain excess remains open (TC-542).

TC-691 hollenbeck_2002: TC-382 resolved; the analytic normalisation (2026-09-28)

• Where: optmat.solid.raman_response (_hollenbeck_parameters, _hollenbeck_integral, spectrum), optmat.solid.kerr (raman_response, _response_spectrum), data/solid/raman/SiO2.toml.

• Checked (TC-382, doubt 1): on the table image (tbl_3554e41bb9a2) and the text: the model is Eq. (9) with Table 1’s footnote a, Gamma = pi c x “Gaussian FWHM”, gamma = pi c x “Lorentzian FWHM”, omega = 2 pi c x position, and the “Peak Intensity” column is A_i = A_i’/omega_v,i, the coefficient of Eq. (9) as it stands. With these the column headed “Gaussian FWHM” is in effect a full width at 1/e of the Gaussian (TC-382); the footnote, not the heading, defines the model, and optmat follows it (as solprop and Luna do). Nothing in the data changes.

• Checked (TC-382, doubt 2): mode 2’s Lorentzian width is printed 38.81 (image checked); the text’s ratio of 3 would make it 36.81. The response and the gain differ by at most 0.2 % of their peaks between the two: kept as printed, no erratum.

• Decision (the normalisation): analytic, through the Faddeeva function, ∫ exp(-gamma t - Gamma² t²/4) sin(omega t) dt = (sqrt(pi)/Gamma) Im w[(omega + i gamma)/Gamma], and the transform likewise. The numerical normalisation of TC-393 (trapezoid on 0.1 fs to 4 ps) was 4e-6 low; the Kerr fit’s eta now uses the analytic transform on the same frequency grid, so that eta = 1 for a long pulse exactly. The stored Kerr fit reproduces to 1e-6 (tests/solid/test_kerr.py).

• Checked: the gain peaks at 439 cm⁻¹ (measured about 440); the first maximum of h_R at 16.3 fs; the analytic transform against the sampled one to 4e-6.

• Status: corrected (2026-09-28), TC-382’s doubts resolved.

TC-692 Fused silica’s Raman models and their pairing with the Kerr fit (2026-09-28)

• Where: optmat.solid.raman_response, data/solid/raman/SiO2.toml.

• Decision (J. C. Travers, 2026-09-28): the default is Hollenbeck & Cantrell’s shape with the Kerr fit’s f_R (0.151, TC-393, TC-594), the one found with this shape, so that (1 - f_R) n2 and the Raman part add up to the fitted n2. lin_2006 (f_R = 0.245) and blow_1989 are the literature’s forms with their own f_R, marked not paired: with the Kerr fit’s electronic part, Lin & Agrawal’s would total 1.09 n2.

• Decision (the size in a real-field model): f_R is a share of the long-pulse n2 (Stolen et al.’s alpha, Lin & Agrawal’s f_R, the Kerr fit’s). A kernel slower than the optical cycle follows only the slowly varying half of E², while an instantaneous term also has its 3 omega part, so P = eps0 chi_e E³ + eps0 K E ∫ h_R E² with chi_e = (4/3) n0² eps0 c (1 - f_R) n2 and K = 2 n0² eps0 c f_R n2; K h_R is the counterpart of a gas’s N h. Luna’s fibre model and solprop’s GNLSE use the same K with n0 = 1 (2 f_R n2 eps0 c). The gain is g = 2 omega_s n2 f_R Im H_R/c.

• Decision (Blow & Wood): their alpha = 0.7 acts on E² (Eq. (2)); their envelope equation carries (2/3)(1 - alpha) (Eq. (8)), so their Raman share of n2 is (2/3)(0.3)/(0.7 + 0.2) = 0.222 (TC-594).

• Checked:

  • 3 chi_e/(4 n0² eps0 c) + K/(2 n0² eps0 c) = n2 to 1e-14;

  • Lin & Agrawal’s model with their n2 = 2.6e-20 m²/W and f_R = 0.245 gives peak gains of 1.163e-11 cm/W at 795.5 nm and 1.780e-11 cm/W at 526 nm (at 434 cm⁻¹). They print 1.2e-11 and 1.81e-11: their gamma = n2 omega0/c takes the pump frequency, and with it the model gives 1.204e-11 and 1.821e-11 (+0.3 %, +0.6 %);

  • their f_a = 0.75 isotropic, f_b + f_c = 0.25 anisotropic, a + b = h;

  • every shape integrates to one and H(0) = 1.

• Status: decided (2026-09-28).

TC-693 stolen_1973: the measured Raman gain of fused quartz (2026-09-28)

• Where: src/optmat/data/sources/stolen_1973.toml (R. H. Stolen and E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973)). Values in the text only (inline points); no table, no script.

• Transcribed: raman_gain of SiO2 in cm/W (scale 1e-11), the pump 526.0 nm as the abscissa (its medium not stated) and as pump_nm:

  • gain_amplifier: 1.5, primary: the small-signal amplifier measurement in a 590 cm single-mode fibre with a fused-quartz core, at the 330 cm⁻¹ shift (526.0 -> 535.3 nm; shift_cm1), relative uncertainty 0.10 (“of the order of 10%”, level not stated);

  • gain_cross_section: 1.49, check: from the polarised spontaneous cross section relative to benzene, Eq. (4), where sigma = 0.80 sigma_p;

  • gain_band_1060, gain_band_1190: 0.10 and 0.07, the peaks of the 1060 and 1190 cm⁻¹ bands by Eq. (4), no uncertainty;

  • in the notes: Eqs. (1)-(3), the fibre (effective area 1.34e-7 cm², effective length 308 cm, core 3.8 um), the cross sections and the uncertainty budget.

• Checked: every number on the page images (not only the text rendering):

  • p. 277 prints “the calculated gain at 535.5 for a pump at 526.0 nm”; everywhere else (twice on p. 276, twice on p. 277) the signal is 535.3 nm, and 526.0 -> 535.3 nm is 330.3 cm⁻¹ (535.5 would be 337): a slip in the text, not a value; no erratum;

  • ln(2.2) x 1.34e-7 / (22 W x 308 cm) = 1.56e-11 cm/W reproduces the printed 1.5;

  • Eq. (4) with n = 1.4607 and 295 K gives 1.44e-11, 3.5 % below the printed 1.49 (the paper states neither n nor T);

  • the peak gain 1.49/0.80 = 1.86e-11 cm/W is computed, not printed; Fig. 2’s curve peaks at about 1.87e-11 near 400-440 cm⁻¹ (by eye, not digitised).

• Doubt: the pump wavelength’s medium; Fig. 2’s error bar (about 1.31-1.71) combines both determinations; Hellwarth et al. 1975 find gains about 20 % higher from their own cross sections, within these errors.

• Status: verified (2026-09-28).

TC-694 hellwarth_1975: the nonlinear parameters of five glasses, and silica’s nuclear share (2026-09-28)

• Where: src/optmat/data/sources/hellwarth_1975.toml (R. Hellwarth, J. Cherlow and T.-T. Yang, Phys. Rev. B 11, 964 (1975)), tools/extract/hellwarth_1975.py, data/values/third_order/{SiO2,LSO,ED-4,SF-7,LaSF-7}/hellwarth_1975__*.csv, data/values/raman/{...}/hellwarth_1975__nuclear_fraction_*.csv.

• Transcribed: Table I (tbl_aa2b556d00dc, p. 967), all five glasses, the +- as sigma (level not stated):

  • sigma_*: 10^15 sigma, nonlinear_susceptibility (esu, hellwarth_sigma, process kerr, part electronic), at the IIPC’s 694 nm, primary;

  • iipc_*: 10^15 (sigma + 2 B0), Owyoung’s IIPC at 694 nm (part electronic_vibrational), reproduced;

  • n2_*: 10^14 n2 by Eq. (9), nonlinear_index_field (n = n0 + n2 <E²>, linear polarisation, part electronic_vibrational), a long-wavelength prediction, primary;

  • n2_measured_SiO2 (18 +- 3, footnote c) and n2_measured_ED-4 (26 +- 3, 15 +- 2, 15 +- 3; c, d, e), reproduced, part unknown;

  • nuclear_fraction_*: the complement 1 - f_e of the column f_e (%), a raman_fraction (the nuclear share of the long-pulse n2 of Eq. (9), linear polarisation): the script subtracts the printed whole percent from 100, the +- kept. Fused quartz 0.21 +- 0.03 (f_e 79 +- 3, image checked); LSO 0.19, ED-4 0.15, SF-7 0.21, LASF-7 0.29. A decision made in review, as blow_1989 records the complement of its printed alpha; B0 and A0 + B0 stay in printed.

• Checked: every cell against the table image (pdf p. 4). The derived columns are reproduced for all five rows: sigma = (sigma + 2 B0) - 2 B0 (28.2, 40.4, 51.8, 160, 176); Eq. (9), n2 = pi(3 sigma/2 + 2 A0 + 2 B0)/n (11.49, 15.29, 18.45, 57.69, 60.55); f_e = [1 + 4(A0 + B0)/(3 sigma)]^-1 (78.65, 81.08, 85.15, 79.21, 70.97 %). boling_1978’s “29, 21, 15, 19, and 21 percent” nuclear are the complements. For fused quartz the nuclear term 2 pi (A0 + B0)/n = 2.45e-14 esu of 11.49e-14 is 0.2135: it is stolen_1989’s alpha = N2R/N20 in kind, and the source of its 0.18 with stolen_1973.

• Doubt:

  1. The header prints “10^14 n2 [Eq. (4)]” where the caption and the text mean Eq. (9): a header slip.

  2. The footnote numbers of the measured n2 do not match the reference list (d is Stolen & Ippen’s gain letter, e Kato & Takuma’s benzene paper); the letters are recorded as printed.

  3. The paper warns that A0 and B0 may be 10-20 % above their long-wavelength values: scaled down by 10 or 20 %, the nuclear share of fused quartz is 0.19 or 0.17.

  4. The reference to Stolen & Ippen is printed as p. 275; the letter begins on p. 276.

• Status: decided (2026-09-28); open: the footnote numbering of the measured n2.

TC-695 Fused silica’s Raman fraction against its absolute gain (2026-09-28)

• Where: optmat.solid.raman_response_validation, docs/raman_response.md, docs/silica.md; the Kerr fit kerr/SiO2 (TC-393, TC-594).

• Finding: each silica model with its own f_R and optmat’s long-pulse n2 at 526 nm (2.67e-20 m²/W), against Stolen & Ippen’s gain of fused quartz at 330 cm⁻¹, 1.5e-11 cm/W +- 10 % (TC-693):

  • the default (Hollenbeck & Cantrell, the Kerr fit’s f_R = 0.151): 0.91e-11, 40 % below; its peak (1.28e-11 at 440 cm⁻¹) is 31 % below the peak Stolen & Ippen’s cross section implies (1.86e-11);

  • Lin & Agrawal (f_R = 0.245): 1.34e-11, 11 % below; Blow & Wood (0.222): 1.42e-11, 6 % below.

  • Matching the gain at 330 cm⁻¹ with Hollenbeck & Cantrell’s shape asks for f_R = 0.25; matching the implied peak, 0.22. Hellwarth et al.’s nuclear share of the long-pulse n2 is 0.21 +- 0.03 (TC-694), Weber et al.’s 0.26 (TC-594). The Kerr fit’s 0.15 +- 0.03 is its prior (0.18 +- 0.03, Stolen et al. 1989) pulled down by the measured n2: the absolute gain and the spontaneous spectra disagree with it by about two sigma.

• Finding (the shape below 25 cm⁻¹): against Stolen et al. 1989’s Eq. (10) (the gain over its peak, a Omega + b Omega³), Hollenbeck & Cantrell’s shape is 2.4, 2.2 and 1.6 times it at 5, 10 and 20 cm⁻¹, Lin & Agrawal’s 1.3 times; Blow & Wood’s 1.3, 1.2 and 0.8. The low-frequency gain acts on picosecond pulses (the soliton self-frequency shift of long solitons).

• Doubt: the gain was measured in a fibre whose core is fused quartz; Hollenbeck & Cantrell’s shape is fitted to Stolen et al.’s fibre spectra, normalised; TC-383’s unit question of Eq. (10) stands (it is read here as normalised, as its text says).

• Proposal (for J. C. Travers): the Kerr fit takes Stolen & Ippen’s gain (with Hollenbeck & Cantrell’s shape) as a constraint on f_R n2, in place of or beside the prior; f_R would move to about 0.2 and the electronic n2 down by about 6 %. Not done: it changes a stored fit (TC-393) and the default’s pairing.

• Status: decided (2026-09-29): J. C. Travers accepted the proposal; see TC-696.

TC-696 The silica Kerr fit takes the measured Raman gain; the prior on f_R is dropped (2026-09-29)

• Where: optmat.solid.kerr (GainOptions, GainPoints, gain_points, the fit’s residuals; KerrConfig.raman_fraction now optional), data/solid/kerr/SiO2.toml ([[raman_gains]]) and .json, docs/silica.md, docs/raman_response.md, data/solid/raman/SiO2.toml.

• Decision (J. C. Travers, 2026-09-29, on TC-695): Stolen & Ippen’s gain of fused quartz, stolen_1973/gain_amplifier (1.5e-11 cm/W +- 10 %, 526.0 nm pump, 330 cm⁻¹), is fitted, predicted as g = 2 omega_s n2(526 nm) f_R Im H_R(330 cm⁻¹)/c with Hollenbeck & Cantrell’s normalised response (TC-692). It fixes f_R n2 at the pump, and so pairs f_R with that shape.

• Decision (the prior): the prior 0.18 +- 0.03 (TC-393) is dropped: Stolen et al. 1989’s alpha was derived from Hellwarth et al. 1975’s spectra and from this gain (TC-694), so keeping it would count the gain twice (data rule 5). With both, f_R would be 0.204 +- 0.021. Hellwarth et al.’s nuclear share (0.21 +- 0.03) stays a validator: its cross sections and Stolen & Ippen’s are separate measurements that agree within their errors, but the gain’s is the measurement of the quantity the response is used for.

• Result: f_R = 0.219 +- 0.026 (was 0.151 +- 0.030), N = 2.432e-20 m²/W +- 4.5 % (was 2.379e-20), a = 0.0267 +- 0.0079 eV⁻² (was 0.0245); chi-squared 42.6 for 35 degrees of freedom (was 37.5; the gain contributes 0.95, the n2 data 4.1 more). n2 is 3.05, 2.78, 2.59, 2.53, 2.47 and 2.46e-20 m²/W at 400, 532, 800, 1030, 1550 and 2000 nm, 2.7 % above the previous fit at 800 nm; its electronic part 2.02e-20 at 800 nm, 5.4 % below. The calibration scales move by 0-5 %: Santran et al.’s (who isolate the electronic part) to 1.374 (was 1.31); Milam’s recommended values are 7.5-11 % above the fit (were 11-16 %), Couairon’s critical-power n2 1.37 times it.

• Checked: the default response now gives 1.35e-11 cm/W at 330 cm⁻¹ (10 % below the measurement, where the n2 data pull), a peak of 1.91e-11 cm/W at 440 cm⁻¹ for a 526 nm pump (the peak Stolen & Ippen’s cross section implies is 1.86e-11), and f_R 4 % above Hellwarth et al.’s share. The Kerr fit’s prediction of the gain equals SilicaRamanResponse.gain of the stored fit to 1e-12 (tests/solid/test_kerr.py). Lin & Agrawal’s form with the Kerr fit’s electronic part now totals 1.03 n2 (was 1.09, TC-692).

• Doubt: one gain measurement, of one fibre with a fused-quartz core, sets f_R; the shape of Hollenbeck & Cantrell’s response at 330 cm⁻¹ relative to its peak (0.71) is below Stolen & Ippen’s (0.80), so matching their implied peak instead would give about 0.21.

• Status: decided (2026-09-29).

TC-697 Luna.jl’s master compared: the page Coming from Luna (2026-09-29)

• Where: docs/luna.md, docs/corrections.md, tools/luna_reference.jl, tools/luna_tables.py, tests/data/luna_master.json, tests/test_luna_page.py, the gallery’s Luna’s material parameters against optmat’s and docs/gallery/_helpers.py.

• What was evaluated: Luna.jl’s master branch at commit 32a6701 (2026-08-15), run in its own environment, for He, Ne, Ar, Kr, Xe, H2 and D2 at 1 bar and 20 °C:

  • ref_index and dispersion(2, ...) from 200 to 2500 nm, and n - 1 at 800 nm at 1, 10 and 100 bar;

  • density, γ3_gas and ionisation_potential;

  • the rate prop_capillary uses with the plasma on at 800 nm: IonRatePPT with its defaults (occupancy 2, the sum over m, the Stark shift and dipole factor for He, Ne and Ar) for the noble gases, and IonRateADK for H2 and D2 (Interface.jl’s makeplasma!). Both were taken at the peak field and averaged over a cycle, from 3e12 to 3e15 W/cm². Each rate of one electron without Luna’s factors was also evaluated (PPT at m = 0, no Stark shift or dipole factor; ADK without the threshold);

  • raman_parameters of H2 and D2.

• Same as the earlier comparisons: master’s PhysData.jl is identical to that of de9db7c, the commit of TC-395 and TC-396. Its Ionisation.jl differs only in code that computes no material parameter (device evaluation, the cache key), with the literal channel sum (sum_integral = false) as the default on master.

• Checked (the parity tests of tests/test_luna_page.py):

  • Read at Luna’s reference state, luna_physdata/jct_He, luna_physdata/kingston_fit_Ar and peck_1977/eq7 give Luna’s n - 1 within 2e-5 (relative) from 200 to 2500 nm. Börzsönyi’s formulas are the exception: Luna refers them to the real-gas density at 0 °C and 1 bar, and optmat to the ideal one (0.05-0.7 %).

  • Luna’s densities are optmat’s real-gas densities within 6e-6.

  • Luna’s γ3 of every gas equals solprop’s fixture within 2e-8.

  • Its H2 and D2 Raman parameters equal solprop’s, except D2’s rotational width per amagat: 1.20e8 Hz in Luna, 1.32e8 in solprop.

  • Luna’s PPT rate of one electron equals ppt_ilkov within 5 % where the Keldysh parameter is below 0.5; above it, Luna’s sum over the channels and optmat’s integral part (TC-654). Its ADK rate equals adk_hydrogenic within 0.5 %.

• Findings, against optmat’s recommended models at 800 nm (the page’s tables):

  • GVD: He −12.5 % (TC-397), D2 +2.9 %, the others within 1.3 %.

  • Kerr γ: Ne −29 %, Ar −19 % (TC-313); THG γ 21-34 % low for every gas but He.

  • Density scaling: Luna’s χ is linear in the number density. Against Lorentz–Lorenz with the virial, its n - 1 at 800 nm falls 1.9 % (Ar), 3.6 % (Kr) and 16 % (Xe, a dense supercritical fluid at 20 °C) below optmat’s at 100 bar, against +0.1 %, 0.0 % and +0.2 % at 1 bar; from 1 to 10 bar the ratio moves by 0.5 % at most. New.

  • Ionisation rate: over the intensities where optmat’s cycle-averaged rate is 1e9 to 1e13 per second, Luna’s cycle-averaged rate is 0.93-1.3 (He), 2.4-3.9 (Ne), 0.50-0.87 (Ar), 0.56-2.4 (Kr) and 0.14-1.5 (Xe) times optmat’s, and 0.03-2.1 times it for H2 and D2. The table splits this into the form of the rate and Luna’s factors:

    • the hydrogenic ADK rate has no multiphoton regime, and is 70 times below optmat’s molecular rate at 4e13 W/cm²;

    • Ilkov et al.’s form with the Hartree coefficient is 1.4-3 times optmat’s default for neon;

    • Luna’s factors are 2.0-2.1 for Kr, Xe, H2 and D2, 1.3-1.8 for He and Ne, and 0.69-1.3 for argon, whose ion’s polarizability makes the dipole factor largest. New.

  • Shared with solprop (Luna carries the same values): the Hartree–Fock polarizabilities of He, Ne and Ar and their ions (TC-441); krypton’s ionisation energy (TC-443); the occupancy of 2 (TC-444); N2’s 6 ps dephasing (TC-485); Talebpour et al.’s charge for O2 with 12.07 eV (TC-508); the H2 and D2 Raman constants (TC-492); Murphy et al.’s CH4 and SF6 derivatives (TC-518); N2’s D (TC-466). docs/corrections.md now names Luna for each.

• The documentation’s GVD helper: _helpers.group_velocity_dispersion took the second difference of omega n / c. Its vacuum part is linear in omega and only adds round-off: about 1e-4 of β2 at 800 nm for helium and neon, and a few 1e-3 beyond 1.5 µm. It now differences omega (n - 1) / c, which is stable to 1e-6 across steps from 3e-4 to 3e-3. The accuracy table’s solprop column moves from -13.66 % to -13.65 % (He) and from -0.44 % to -0.45 % (Ne); no other entry changes.

• Not verified: Luna’s cached PPT rate (IonRatePPTCached, the one prop_capillary builds) was not evaluated. It is a log-spline of the direct rate (2^16 points) and stops at twice the barrier-suppression field. Nothing is changed in Luna.

• Status: verified (2026-09-29).

• Note (2026-10-16): the Luna comparison page, its corrections page, its table script and its test named here (docs/luna.md, docs/corrections.md, tools/luna_tables.py, tests/test_luna_page.py) are kept with the maintainer’s development material, not in the repository; the comparison data are tests/data/luna_master.json and tests/test_luna_reference.py.

TC-698 jagau_2018 (Jagau, J. Chem. Phys. 148, 204102 (2018)): coupled-cluster static rates of molecules; O2’s and CH4’s constants (2026-09-29)

• Where: src/optmat/data/sources/jagau_2018.toml, tools/extract/jagau_2018.py, data/values/ionisation/{H2,CO,CH4,O2}/jagau_2018__*.csv (54 files); optmat.gas.molecular_ionisation_validation (JAGAU_2018, FITTED_REFERENCES, the reference of orientation_averaged_rates, CH4’s average); molecular_ionisation_rates.toml (O2, CH4); the manual page and its tables.

• Transcribed: the supplement’s Tables S3 (H2, full CI and HF, parallel and perpendicular, the standard basis), S6 (CO, HF and CCSD, 13 angles, F = 0.06 and 0.09), S8 (CH4, HF and CCSD, orientations A, B, C), S9 (O2, parallel and perpendicular, F = 0.04 to 0.16) and S10 (O2, 7 angles between, F = 0.06 and 0.10): the rates Gamma (au) of the molecule, all electrons, fixed nuclei. Every rate cell checked against the table images. Excluded rows, by the paper’s own statement of the method’s low-field limit (Gamma of at least ~1e-5 au, p. 4): O2’s CCSD rate at 0.04 au (7e-6), and CH4 at 0.04 au in all orientations (the rate rises to 0.06 au by 7 to 14, where a tunnelling rate rises by some 400). Not taken: He (the method’s calibration), H2 against the bond length, H2O (not an optmat gas), the moments.

• Orientation averages: O2 over its nine angles at 0.06 and 0.10 au (the fields of Table S10); CO over its thirteen (0 deg is the field from C to O, the reverse of majety_2015’s; the average does not depend on it); H2 as (par + 2 perp)/3; CH4 as 0.3 A + 0.3 B + 0.4 C, Lebedev’s 14-point rule on the sphere (weight 1/15 on each of the six face normals, the C directions, and 3/40 on each of the eight cube corners, the A and B directions), exact to spherical harmonics of degree 5.

• Checked (cross-checks of majety_2015): H2: the default within 4 % of Jagau’s full CI from 0.08 to 0.14 au (1.30 at 0.06 au, where the rate is 2e-5 au, at the method’s floor), as of Majety’s. CO: Majety’s average 18 % above Jagau’s at 0.06 au and 13 % at 0.09 au, as Jagau’s text reports (its ‘4-8.10-4 a.u.’ is read as a misprint of 10-5, the record); the default 1.54 and 1.14 times Jagau’s.

• Finding (O2): with N2’s alpha of 14 the default was 0.32 of Jagau’s CCSD average at 0.06 au and 0.12 at 0.10 au: the correction, exp(-alpha F/(I_p kappa^3)), is a factor 0.03 at 0.10 au for O2’s small I_p kappa^3. Jagau places O2’s barrier suppression at about 0.12 au, not the atomic formula’s 0.05.

• Finding (CH4): with the first maximum of the 1t2 band, 13.6 eV, the default was 2 to 4.8 times Jagau’s average, and no alpha reproduces the reference’s dependence on the field (the best, 19.7, leaves 2.4 falling to 0.5). With the middle maximum, 14.4 eV, it does (below). Jagau’s EOM-IP-CCSD puts CH4’s vertical energy at 14.43 eV: at fixed nuclei the tunnelling electron sees the degenerate state at the neutral’s geometry, the centre of the Jahn-Teller-split band, not its first peak.

• Decision: O2’s alpha 6.1 (the least-squares value with 2 electrons, 6.10; both fields within 10 %); CH4’s energy 14.4 eV (heilbronner_1977/vertical_CH4#1t2_2) and alpha 18.0 (17.99; 0.06 to 0.12 au within 27 %). Uncertainty factors: O2 2 (was 3), CH4 2 (was 5). CO2, N2O and SF6 keep N2’s 14.

• Consequence (measured yields): O2’s rate at 800 nm rises (2.8 times at 1e14 W/cm2). Against Wahlstrand et al. O2 is now 5.0 to 6.5 times above (was 2.2 to 2.9), as N2’s 5 to 9; relative to xenon 0.65 to 2.4 (was 0.34 to 0.90), which brackets the measurement. Against Guo et al.’s text O2/Xe is 0.035 to 0.055 (was 0.022), 2 to 3 times below ‘roughly ten times below Xe+’ (was 4.5): TC-683’s conflict is reduced, not closed.

• Doubt:

  1. One method for O2 and CH4: CCSD without triples ((T) raises CO’s rate by about 20 % at 0.06 au, Jagau p. 6) and complex basis functions (5 % above explicit complex scaling for He, more below 0.14 au).

  2. alpha is not one constant: H2 6.0, O2 6.1, N2 14.0, CH4 18.0, and CO would ask for 16.3. Whether CO2’s and N2O’s pi orbitals follow O2’s (6) or N2’s (14) is not known; at 1e14 W/cm2 the difference is a factor of about 2 in CO2’s rate, within its factor 3.

  3. O2’s fit rests on two fields; beyond 0.10 au the reference keeps rising where the model’s range (1.5 times the barrier-suppression field, 0.077 au for O2) has ended.

• Status: decided (2026-09-29).

TC-699 Values read from figures: the rule (2026-09-29)

• Where: AGENTS.md (data rule 8), docs/data.md (digitised, table), optmat.datasets.Dataset (digitised, _check_digitised), tests/test_datasets.py, pyproject.toml (pypdfium2, a development dependency of the extraction scripts), tools/extract/_figure.py.

• Decision (J. C. Travers, 2026-09-29, without an OEP): a value a source gives only in a figure may be taken from it, when no table, text, supplement or data repository gives it. Before, figures were never digitised and such values were read qualitatively only (TC-508, TC-510 to TC-512, TC-683).

• Why: most figures of the last two decades are vector drawings in the PDF, whose markers and lines are stored as coordinates. Read from the drawing, with the axes calibrated from the drawing’s own tick marks, they reproduce the numbers a paper also prints to about 1 % (van der Hart 2007, TC-700). An embedded image can be read too, less precisely.

• The rule:

  1. Vector figures are read from the PDF by the source’s extraction script; raster figures from the image, with the calibration and the picked pixels written in the script.

  2. digitised = "vector" or "raster"; table names the library figure (fig_...); the uncertainty is stated and includes the digitising uncertainty. The loader rejects a figure dataset without either.

  3. Every extraction is checked against every number the source prints for the same quantity and against an overlay on the rendered figure, both recorded here.

  4. Figure values are use = "check". Values read from an image are never fitted (the loader rejects it); values read from a vector drawing may be primary only with J. C. Travers’s approval, recorded here.

• Status: decided (2026-09-29).

TC-700 vanderhart_2007 (van der Hart, Phys. Rev. A 76, 043405 (2007)): time-dependent R-matrix rates of Ar at 390 nm; the first vector figure (2026-09-29)

• Where: src/optmat/data/sources/vanderhart_2007.toml, tools/extract/vanderhart_2007.py, tools/extract/_figure.py, data/values/ionisation/Ar/vanderhart_2007__*.csv; optmat.gas.ionisation_validation.rmatrix_rates, docs/ionisation_rates.md.

• Transcribed: Table I (the rates of Ar at 0.48, 0.75 and 1.50e14 W/cm2 with one and with two Ar+ target states; the library’s cells print the times sign as a backspace and run the exponent into the 10, read by the script’s check of that shape, every cell checked against the image). Fig. 4, a vector drawing, read from the PDF by data rule 8 (TC-699): the nine circles at intensities Table I does not print (the time-dependent rates), and the 1221 vertices of the R-matrix Floquet curve within the frame (van der Hart 2006’s, reproduced). The axes are calibrated from the drawing’s ticks (x at 0.25e14 steps, y 1e8 to 1e14 in two-decade steps; every tick within 0.001 pt).

• Checked: the figure’s circles at Table I’s intensities are 1.013, 1.056 and 1.003 times the table’s one-state rates; the script fails if one strays beyond 6 %. The intensities come out at round values (0.250, 0.480, 0.650 …). The overlay of the extracted circles and vertices on the rendered figure matches every marker and the line through its resonances (inspected 2026-09-29). Uncertainty: 6 % (the table check), 10 % at 2.5e14 W/cm2 (the paper’s).

• Doubt: the calculation’s ionisation energy of Ar is not stated; the polarisation is not stated in words (recorded as linear, from the paper’s ‘m = 0’ counting).

• Status: verified (2026-09-29).

TC-701 vanderhart_2006 (van der Hart, Phys. Rev. A 73, 023417 (2006)): R-matrix Floquet rates of He, Ne, Ar at 390 nm, read from an image; the default against them (2026-09-29)

• Where: src/optmat/data/sources/vanderhart_2006.toml, tools/extract/vanderhart_2006.py, data/values/ionisation/{He,Ne,Ar}/vanderhart_2006__*.csv; rmatrix_rates, tests/test_ionisation_validation.py, docs/ionisation_rates.md, docs/gallery/plot_ionisation_rmatrix.py.

• Transcribed: Fig. 6, an image embedded in the PDF (900 x 635 pixels, 300 dpi), read from its native pixels by data rule 8: the frame and inward ticks found in the image and checked against the calibration written in the script (every tick within 0.3 pixel); each curve traced column by column from its crossing of the 1.30e14 W/cm2 column (Ar above Ne above He there) and sampled every 0.05e14 W/cm2 on its smooth part: He 1.05-2.45 (29), Ne 0.90-2.10 (23), Ar 0.65-1.90 (25), without the peaks of Ne’s resonances at 1.01 and 1.45e14 and Ar’s 3d at 0.90e14, where the curve changes by some 40 % within a pixel. A sample in a gap of the dashes is interpolated between the nearest traced columns within 10 pixels; each value’s pixel is in its printed cell. One pixel is 3.4 % in the rate.

• Checked: the Ar samples are 0.97 to 1.04 times TC-700’s vector copy of the same curve (median 1.004; 1.37 on the 3d peak, left out); the script and a test fail beyond 5 % and 4 %. The overlay of the samples on the image was inspected. Hence 5 %.

• Finding (helium): Parker et al.’s two-electron rate is 0.96 to 1.25 times the Floquet rate away from the resonance at 1.5e14 W/cm2 (0.8 on geometric average, with the resonances): two all-electron methods agree, and the Floquet rates are not low. The default is 1.13 times them on average (its 1.47 electrons).

• Finding (argon): the default is 1.6 to 2.9 times the Floquet and the time-dependent R-matrix rates from 1.25e14 to 3e14 W/cm2 (Keldysh parameter 2.1 to 1.4) and 7 to 12 times at 0.25 to 0.75e14 W/cm2 (4.7 to 2.7), where the rate is multiphoton and resonant; the one_electron model likewise. Its one-electron form matches tRecX’s one-electron calculation of argon at 800 nm to a Keldysh parameter of 2.8 (TC-653): the gap is between one active electron and the atom. It points the way Wahlstrand et al.’s measurement does (TC-660), and against argon’s all-electron static rates, which lie above the model at low field (TC-669). Neon: 1.4 to 3 times above.

• Doubt: one ionic state in both calculations; their ionisation energies are not stated (at 390 nm the rate is a 5- to 6-photon process and depends steeply on it). No change to the model follows from one method at one wavelength.

• Status: open (argon’s rate against the atom’s).

TC-702 travers_2026_trecx: argon’s one-electron ionised fraction in a 42 fs pulse (2026-09-29)

• Where: src/optmat/data/external/trecx/ar_42fs/ (results.csv, manifest.csv), PROVENANCE.md there (its section on the 42 fs runs), src/optmat/data/sources/travers_2026_trecx.toml (ionised_gauss42_Ar_m0), tools/extract/travers_2026_trecx.py, optmat.gas.ionisation_validation.long_pulse_yield, docs/ionisation_rates.md, docs/gallery/ionisation/plot_ionisation_measured.py.

• Transcribed: the ionised fraction, 1 - (ground + bound states up to n = 10) at the end of the pulse, of one electron (Ar 3p, m = 0, Tong and Lin’s potential) in Wahlstrand et al.’s pulse (800 nm, a Gaussian of 42 fs full width at half maximum of the intensity) at 17 peak intensities from 4.0e13 to 1.35e14 W/cm2: J. C. Travers’s tRecX runs of 28-29 September 2026, with a build that adds the bi-orthogonal populations of the field-free states (tRecX’s own Occupation is not a population under complex scaling). Tier 3 (use = "check"), as the 6 fs runs.

• Checked (against the archived table, 2026-09-29): the initial energy in every run (spread 8e-12); the pulse as run (FWHM 41.99977 fs, peak field to 4e-7); the norm never above 1; the drift without a field (4.8e-9, below every yield by 900 or more); the bound populations constant after the pulse; the convergence runs at 4.0e13, 7.8e13 and 1.35e14 W/cm2 (angular functions, radial elements and order, box, step, ECS angle, cutEnergy, operator threshold): the largest change, 2.6 %, 1.3 % and 0.1 %, is the stated uncertainty. The cutEnergy part is one-sided: the yields are low by about 3 % at 4.0e13 and 1.5 % at 7.8e13. The three BOX 120 runs warn of an eigenproblem of H0 satisfied to 1e-7 and agree with BOX 80 to 0.03 %.

• Finding: the one_electron model is 0.99 to 1.8 times the calculation (1.24 on geometric average), the most just past each channel closing: the calculated yield has a resonance structure (local slope 2.4 to 10.7) that no rate has. The calculation, one electron, is 1.3 to 4.1 times Wahlstrand et al.’s measured yield of the atom; excited states hold 1 to 30 % of it. So the disagreement of TC-660 is not in the rate’s dependence on frequency or pulse length, nor in Rydberg atoms counted as ionised: it is between one active electron and the measurement. With the all-electron R-matrix rates of argon at 390 nm below the one-electron model (TC-701), two references point to the atom ionising less than one active electron; argon’s all-electron static rates (TC-669) point the other way.

• Not curated: the chi-loss, norm-loss and iSurff (biased low, TC-703) of these runs (PROVENANCE.md), the populations by shell, the convergence rows. The inputs, the scripts and the runs’ report are kept with the runs, recorded by sha256.

• Doubt: the model’s ionisation energy is 0.579689 au (15.774 eV), 14 meV above argon’s; the models are evaluated at argon’s, about 2 % higher in the yield at 1e14 W/cm2. One orbital: how the atom’s electrons combine is the open question.

• Status: verified (2026-09-29); the finding is open with TC-660.

TC-703 travers_2026_trecx: iSurff is biased low with the untruncated potential (2026-09-29)

• Where: src/optmat/data/external/trecx/PROVENANCE.md (the 42 fs section, Not curated); src/optmat/data/sources/travers_2026_trecx.toml (the record’s notes, and isurff_cos8_Ar_m0, isurff_cos8_Ar_m1, isurff_cos8_He); docs/ionisation_rates.md.

• Checked:

  • In the 42 fs argon runs (TC-702), iSurff is 1.4 to 23 % below the ionised fraction. The shortfall is least at 4.0e13 W/cm2 and largest at 5.0e13, just above a channel closing.

  • The shortfall shrinks as the surface moves out: at 1.35e14 it is 10.8 % at BOX = 80 and 6.6 % at 120.

  • It is not the infinite-time part of iSurff, which is at most 0.3 % of the total.

  • J. C. Travers’s runs with the same pulse and the potential switched off between 60 and 80 bohr, at 4.0e13, 5.0e13, 7.8e13 and 1.35e14 W/cm2: the truncated potential has 41 bound states, all projected, so its 1 - bound is complete. iSurff equals it to 0.04 to 0.15 % below 1.35e14, and to 1.7 % at 1.35e14, where summing the spectrum on every second momentum point changes iSurff by 0.8 %. The norm-loss equals it to 0.5 % or better.

  • So the shortfall comes from the Coulomb tail at the tSurff surface. tSurff maps the flux through the surface onto free-electron (Volkov) waves, which assumes no potential there.

  • The table and script of the check are recorded by sha256 in PROVENANCE.md.

• Decision:

  • The 6 fs iSurff yields (TC-666) are lower bounds, not one side of a spread: their inputs (inputs/*isurff*.inp) keep the full potential at an 80 bohr surface. Their notes now say so; the values are unchanged.

  • No correction is derived. Truncation changes the model: it removes the Rydberg states above n of about 6, moves the resonances, and changes the ionised fraction by -11 to +5 %. The size of the bias at 6 fs was not measured.

  • The 42 fs ionised fraction (TC-702), a projection on the bound states, is not affected. The check confirms it: projection, flux and absorption agree when the flux is exact.

• Doubt: the 6 fs spectra were computed on 150 momentum points. At 42 fs that grid was too coarse, wrong by up to 15 %; at 6 fs the peaks are broader, but it was not checked.

• Status: decided (2026-09-29); open with TC-666: the 6 fs yields as a projection on the bound states. Done: TC-812.

TC-704 puchalski_2020 (Puchalski, Szalewicz, Lesiuk & Jeziorski, Phys. Rev. A 101, 022505 (2020)): the alpha^3 QED static polarizability of 4He (2026-09-29)

• Where: src/optmat/data/sources/puchalski_2020.toml, tools/extract/puchalski_2020.py, data/values/refractive/He/puchalski_2020__*.csv (3 files).

• Transcribed (by script, Table VIII, p. 11; image checked):

  • “Total” 1.38376078(14) a0^3: static electric polarizability of 4He, all corrections (check).

  • Molar polarizability 0.51725408(5) cm^3/mol (check).

  • “Experiment, Ref. [58]” 0.5172544(10) (reproduced from gaiser_2018).

  • The component rows are in the notes: nonrelativistic 1.3838099864, alpha^2 -80.3599e-6, alpha^2/M -0.0935(1)e-6, alpha^3 QED 30.4738e-6 + 0.1822e-6, alpha^3/M 0.01112(1)e-6, alpha^4 0.56(14)e-6, finite size 0.0217(1)e-6.

  • Also in the notes, from the text: the field derivative of the Bethe logarithm, 0.0485572(14) (p. 5).

  • Uncertainties are convergence estimates; the total’s (14) is the alpha^4 allowance. Level not stated.

• Checked:

  • The components add to 1.38376078182, matching the printed total.

  • 30.4738 + 0.1822 (+ 0.01112) gives the printed 30.6560 and 30.6671.

  • The total times the package’s (4 pi/3) N_A a0^3 gives 0.517254083 cm^3/mol, matching the printed 0.51725408(5).

• Finding:

  • Against puchalski_2016’s static total 1.38376077(14): the change is +0.0104e-6 a0^3 (+7.5 ppb, 0.07 sigma). It comes from the field-derivative term (0.1822, where 2016 used a preliminary 0.183(1)) and from the QED recoil +0.01112, which 2016 left out.

  • The paper gives no dynamic polarizability and does not revise alpha_2, alpha_4, ….

  • fit/He’s electric S(-2) = 1.38376077 is 5 ppb (0.04 sigma) below this total.

  • Theory is 0.3 sigma below Gaiser and Fellmuth’s 0.5172544(10).

• Doubt: the alpha^4 QED term is incomplete (one-loop only, 25 % allowance). It dominates the uncertainty.

• Decision: both datasets are checks. They carry the same theory as puchalski_2016/cauchy_total row -2, which fit/He fits, so fitting them beside it would count it twice.

• Status: verified (2026-09-29).

TC-705 pachucki_2019 (Pachucki & Puchalski, Phys. Rev. A 99, 041803(R) (2019)): the retardation correction to helium’s refractive index (2026-09-29)

• Where: src/optmat/data/sources/pachucki_2019.toml (formula retardation; no datasets); yang_2025.toml (puchalski_He: reproduced_from now uses the ids).

• Transcribed: Table I (p. 3; read on the image, because the extracted cells merge the last two rows into one garbled cell): alpha_0(0) = 2.0747883, alpha_1(0) = 4.0751385, alpha_2(0) = 9.3176426, alpha_3(0) = -4.4176694 and kappa = -0.5069525, in atomic units, for infinite-mass nonrelativistic He. These are the coefficients of the formula retardation, [alpha + chi]_ret = alpha_nrel (a0 k)^2 kappa (Eqs. 29-30). Also taken from the text: -1.40e-7 of n - 1 at 633 nm (Eq. 30) and -1.98e-7 at 532 nm (p. 4). No uncertainty is stated.

• Checked:

  • kappa recomputed from the printed alpha_i: -0.50695245 (printed -0.5069525).

  • (2/3) alpha_0(0) = 1.3831922, the infinite-mass static value (liu_1997: 1.38319194).

  • Eq. (30) with a0 = 0.529e-10 m gives -1.3978e-7 at 633 nm and -1.9789e-7 at 532 nm, matching both printed values.

  • The paper compares with a relativistic omega^2 term of -1.24e-7 (n - 1). That term equals puchalski_2016’s (alpha_2^(20) + alpha_2^(21)) omega^2 / alpha: -1.236e-7.

• Finding:

  • The correction is a pure omega^2 term of the refractive polarizability, kappa alpha_nrel alpha_em^2 omega^2 = -3.7341e-5 omega^2 a.u. (omega in hartree). This is -24.2 ppm of S(-4).

  • fit/He does not contain it: fit/He’s S(-4) = 1.5432396, the uncorrected puchalski_2016 value.

  • Against fit/He, adding the term changes n - 1 by -0.087 ppm at 800 nm and -0.139 ppm at 633 nm. The fit’s stated sigma is 0.102 and 0.103 ppm, so these are 0.9 and 1.35 sigma.

  • It changes the group-velocity dispersion by -23.9 ppm at 800 nm and -23.6 ppm at 633 nm, and the third-order dispersion by about -23 ppm. The fit’s GVD sigma is 3.96 and 3.93 ppm, so the GVD shift is 6 sigma.

  • Measurement agrees with the correction:

    • yang_2025’s measured A_2 = 1.332468(6)e-4 cm^3/mol (formula he_A2) is 4.8 of its sigma below fit/He’s A_2 (1.332497e-4). With the correction the gap is 0.6 sigma (1.332465e-4, Yang’s theory row).

    • rourke_2021/A_R_He (0.52025565(5) cm^3/mol at 632.9908 nm, retardation included) is +0.14 ppm (1.4 sigma) from fit/He, and 0.0 with the correction.

• Doubt:

  1. kappa has no stated uncertainty.

  2. The derivation is first order in density, with static alpha_i(0). The omega^4 terms are not given, so extending the term beyond the visible (it reaches -2.2 ppm of n - 1 at 150 nm) extrapolates the paper.

  3. The package has no quantity or correction part for the term.

• Decision: recorded as a formula, not data. The fit change is recommended (see Implications) but not made.

• Status: open (whether fit/He takes the term, and in what form); decided (2026-09-29) by TC-728.

TC-706 lesiuk_2023b (Lesiuk and Jeziorski, arXiv:2311.11357 (2023)): relativistic chi_0 of Ne and Ar; three misprints in Table X (2026-09-29)

• Where: src/optmat/data/sources/lesiuk_2023b.toml, tools/extract/lesiuk_2023b.py, data/values/refractive/{Ne,Ar}/lesiuk_2023b__*.csv.

• Transcribed:

  • Table IX, the total row only: chi0_Ne -8.4786(7) and chi0_Ar -22.9545(32), both x 10^-5 a.u. These are static values for 20Ne and 40Ar, primary, and the paper states no confidence level.

  • Table X, as reproduced: Havens (Ne -8.574(9)e-5, Ar -2.15(2)e-4), Mann (-7.56(20)e-5, -2.19(2)e-4) and Barter et al. (Ne -7.80(16), erratum below; Ar -2.16(2)e-4, the first line of the cell).

  • Table X, the authors’ earlier values, as reproduced from lesiuk_2020 and lesiuk_2023: -8.484(19)e-5 and -2.30(2)e-4.

  • Each Table X cell prints its own power of ten. The script takes that power as the dataset’s scale and checks it.

• Checked:

  • The Table IX rows sum exactly to the totals, and their quadrature gives the printed uncertainties: 0.00065 and 0.00317 (printed (7) and (32)).

  • Eq. (3) with Eq. (23)’s <r^2>_HF reproduces chi_0^HF: -8.31772 and -23.10612.

  • The table images were checked. The library cell for Barter et al.’s argon value interleaves its two printed lines; the script asserts the garbled string and takes the first line.

• Findings (misprints):

  • (i) Barter et al.’s neon value is printed x 10^-4 and corrected to x 10^-5 by a scale erratum. The printed value is ten times every other neon entry. The text describes a discrepancy of ordinary size. nie_2025 takes the same Barter value as A_mu = -29.2(6)e-6 cm^3/mol, which is -7.81(16)e-5 a.u.

  • (ii) The revised argon uncertainty line (Rourke 2021) is printed -2.16(15) x 10^-5; it should read x 10^-4, since rourke_2021’s -8.09(57)e-5 cm^3/mol is -2.164e-4 a.u. This line is not extracted.

  • (iii) Table X’s “this work” argon value, -2.29548(32)e-4, disagrees with the abstract, the text and Table IX, which give -22.9545(32)e-5. The Table IX rows reproduce the latter. Not extracted.

• Comparison:

  • The new values are 0.064 % (Ne) and 0.20 % (Ar) smaller in magnitude than the values the fits now use (TC-71). Argon’s change comes mainly from the mass-velocity correction to the wavefunction, +0.0529e-5.

  • The effect on n - 1 at 632.99 nm is +0.020 ppm for Ne and +0.041 ppm for Ar, against the fits’ 12.6 and 3.5 ppm.

  • Barter et al.’s argon value is not an independent measurement (p. 9). It is 6.3 % below theory in magnitude, and its neon value 8.0 %. Yet it is the value behind rourke_2021’s and nie_2025’s A_mu.

• Doubt:

  • The published version (Phys. Rev. A 109, 012820 (2024)) is not in the library, so the numbers are the preprint’s.

  • Erratum (i) is not stated by the authors. The original Barter et al. 1960 paper is not in the library.

  • chi_0 is static. The authors estimate its frequency dependence at order alpha^5, which is negligible.

• Decision: the new chi_0 supersedes lesiuk_2020’s and lesiuk_2023’s for the magnetic term. The fit change is made separately (see below).

• Status: verified (2026-09-29), against the preprint.

TC-707 egan_2023 (Egan and Yang, Int. J. Thermophys. 44, 181 (2023)): A_R of Ar and N2 at 632.99 nm on a piston-gauge scale; N2’s temperature coefficient (2026-09-29)

• Where: src/optmat/data/sources/egan_2023.toml.

• Transcribed (text, inline points; standard uncertainties, p. 8):

  • A_R_Ar: 4.195735(13) cm^3/mol at 632.9908 nm (vacuum), from the 303 K isotherm with T* = 302.9184 K (p. 11); primary.

  • A_R_N2: A_303 = 4.446175(14) cm^3/mol at 632.9908 nm, 303 K (p. 17); primary.

  • Formula n2_temperature: Eq. (8), with A_theta = 1.18(4)e-6 K^-1.

  • A_R is the electric plus the magnetic term, i.e. the refractive polarizability (p. 5).

• Checked:

  • Eq. (8) at 293.1529 K is 3.7e-6 above egan_2019’s N2 value; the paper says “3.7e-6”.

  • Eq. (8) at 302.919 K is 8.0e-6 above Egan et al. 2016’s value; the paper says “8.0e-6”.

  • Argon is 11.9e-6 above egan_2019 (the paper: 11.8e-6).

  • Argon against Lesiuk & Jeziorski’s recommendation, computed with S(-8) and chi_0 = −2.3004e-4: −5.0e-6. The paper says 5.3e-6; the 0.3e-6 difference is not resolved. Without S(-8) the difference is −0.3e-6.

• Comparison with the stored fits (633 nm):

  • fit/Ar gives alpha_refr = 11.224482 a.u. (sigma 3.5 ppm). Egan 2023 is −2.7 ppm from it (0.6 sigma combined); egan_2019, which the fit uses, is −14.6 ppm (1.0 sigma).

  • fit/N2 gives 4.446143 cm^3/mol (sigma 15 ppm). Egan 2023 is +7.2 ppm at 303 K and −4.4 ppm when carried to 293.15 K with A_theta.

• Dispersion finding (Ar):

  • Inputs: Egan’s A_R, gaiser_2018’s static alpha_0 11.077183(27), lesiuk_2023’s S(-6) and S(-8), and lesiuk_2023b’s chi_0.

  • Result: S(-4) = 27.965(9), 0.031 %. That is −0.039 % from lesiuk_2023’s 27.976(15) (−0.6 sigma) and +0.059 % above yang_2025’s 27.9486 (+1.9 sigma).

  • Omitting S(-8) gives 27.975(9), which equals lesiuk_2023 and is 3.1 sigma above yang_2025.

• No double counting:

  • Independent of egan_2019: different apparatus (Fabry–Perot cavity rather than the MIRE cells) and a different pressure scale (a piston gauge rather than helium-calibrated transducers). The paper presents the N2 values as a closure test between three pressure scales, and it does not supersede egan_2019.

  • Not reproduced in yang_2025 or egan_2026. yang_2025 uses the same cavity and this paper’s B_rho for Ar and N2, so it is correlated but not a copy.

• Doubt:

  • The correction (doi 10.1007/s10765-024-03473-6) is not in the library.

  • A_R(Ar) is tied to the gallium point’s consensus T − T90. A_303 and A_theta of N2 depend on the T − T90 function used (Fischer 2011); the authors give no number for that dependence of A_303.

  • The helium theory enters through kappa (at about 0.5 ppm).

• Status: open (the correction is not checked; the fit decision is pending).

TC-708 lang_2026 (Lang et al., arXiv:2607.21261 (2026)): ab initio polarizability, Cauchy moments and magnetic susceptibility of N2 at 303 K; N2’s first magnetic term (2026-09-29)

• Where: src/optmat/data/sources/lang_2026.toml.

• Transcribed:

  • Eq. (53), p. 14, at 303 K: alpha_0 = 11.717(13), alpha_2 = 29.928(80), alpha_4 = 100.62(82), alpha_6 = 383(38) a.u. These are stored as S(-2) to S(-8) (cauchy_303K, k = 2; alpha_6 carries a flat 10 %). Also chi_0 = -1.75(9)e-4 a.u. (chi0_303K, a flat 5 %, level not stated).

  • p. 15, the semi-empirical values: alpha_0(303 K) = 11.735962 (“no worse than 10ppm”) and alpha_2(303 K) = 30.086359 (semi_empirical_303K), and alpha_0(273.16 K) = 11.735585 (semi_empirical_273K).

  • p. 15, Egan & Yang’s measured molar polarizabilities at 303 K: 11.762120(37) at 1542.383 nm and 11.894428(37) at 632.9908 nm (egan_yang_303K, reproduced).

  • p. 15, four historical chi_0 values as the paper converts them (reproduced; originals not in the library): Hector 1924 -1.34e-4 (2 %), Vaidyanathan 1928 -1.45e-4 (303 K, 5 % bound), Bitter 1930 -1.66e-4 (298 K), Havens 1933 -1.338(2)e-4.

  • Formulas:

    • cauchy_theory_303K, the alpha_series of Eq. (53), 455.6 nm to static.

    • alpha_n_of_R, Eq. (50) with Table III.

    • chi0_of_R, Eq. (51) with the text’s parameters.

  • Electric polarizability throughout; the magnetic term is separate.

• Checked:

  • Eq. (53) and the p. 15 numbers against the pdf text; Table III against its image.

  • Eq. (55) reproduces the paper’s theoretical 11.743(13) and 11.875(13) (computed 11.743019 and 11.874645).

  • The semi-empirical alpha_0 and alpha_2, with the theoretical alpha_4, alpha_6 and chi_0, reproduce the measured 11.762120 and 11.894428 to 1e-6.

  • Eq. (50) reproduces Table I’s totals at R = 1.75, 2.07 and 2.60 bohr within their uncertainties. Eq. (51) reproduces Table II’s aug-cc-pV5Z diamagnetic + paramagnetic sums.

  • The 633 nm “experimental” value is Egan & Yang 2023’s A_303 = 4.446175(14) cm^3/mol (in the library, not curated).

• Doubt:

  • The paper is a preprint.

  • The ab initio values sit below the measurements: alpha_0 by 1600 ppm (2.9 sigma of k = 2 / 2) and alpha_2 by 0.53 % (4 sigma).

  • chi_0 is 5-31 % larger in magnitude than every measurement, and the authors cannot explain why. Havens’ neon agrees with theory to 1.1 % and his argon is 6.3 % low (lesiuk_2023b). Scaled by argon’s 6.3 %, his N2 is still 18 % below this theory.

  • Papers I and II are cited only as “Paper I/II” and are absent from the reference list. Neither is in the library.

  • The supplement (alpha_n(T), chi_0(T), Eq. (52) parameters) is not in the library. The 1542.383 nm value’s original is not in the library either; yang_2025’s laser corresponds to 1542.3912 nm.

  • The conclusions speak of “the single experimental result”, but p. 15 quotes four.

• Decision:

  • The polarizability and Cauchy moments are check, not fitted: a preprint, 100 times less precise than the metrology, and 3-4 sigma low.

  • The semi-empirical values are check: they rest on Egan & Yang’s measurements.

  • Egan & Yang’s two values are reproduced, the best copy in the library.

  • chi0_303K is primary, as the value to adopt for fit/N2’s chi0_au. It is the only calculation of N2’s susceptibility in the library.

  • fit/N2 is not changed here.

• Status: open (fit/N2’s chi0_au and temperature reference to be decided; the supplement and Egan & Yang 2023/2024 to be curated).

TC-709 garberoglio_2023 (Garberoglio et al., J. Phys. Chem. Ref. Data 52, 031502 (2023)): the metrology review; helium’s relativistic A_mu (2026-09-29)

• Where: src/optmat/data/sources/garberoglio_2023.toml.

• Transcribed: p. 30, helium’s molar magnetic term A_mu = -7.92128(13)e-6 cm^3/mol (16 ppm, level not stated). This is the reviewers’ conversion of Puchalski, Lesiuk & Jeziorski’s relativistic susceptibility (Ref. 80, “in preparation”, published as Phys. Rev. A 108, 042812 (2023)). The original is not in the library, so this copy is reproduced and is the best one available. Nothing else is transcribed. Every other optical number is another paper’s, and each is already curated from its original or is not a number:

  • Table I = puchalski_2020;

  • the p. 25 molar polarizabilities = gaiser_2018 and puchalski_2020;

  • the p. 30 uncertainties of lesiuk_2020 and lesiuk_2023.

• Checked:

  • The A_mu value and the p. 9, 14, 25, 30 and 40 statements against the pdf text.

  • Table I’s contributions sum to its total, 1.38376078(14). That total is 7 ppb above puchalski_2016’s static 1.38376077(14): the Bethe-logarithm derivative term changed from 0.000000183 to 0.0000001822, and an alpha^3/m recoil term of 0.00000001112 was added.

  • A_mu/(0.3738031 cm^3/mol per a.u.) gives chi_0 = -2.119105e-5 a.u. That is 1.4e-4 of itself below fit/He’s Bruch & Weinhold value (-2.1194(1)e-5, about 3 of its sigma) and a change of 2.1e-9 in helium’s refractive polarizability.

  • The p. 9 ratio A_mu/A_eps ≈ -1.53e-5 agrees with fit/He (-1.532e-5).

• Doubt: the library copy is in a preprint-like layout (“Dated: 21 July 2023”), and its pages are the pdf’s, not the journal’s. Identity is VALIDATED_WITH_WARNINGS.

• Decision:

  • A_mu_He is reproduced: fit/He’s chi0_au could move to -2.119105e-5 (2 ppb; optional).

  • The record is otherwise a citation for the review’s statements.

  • In Table IV, He A_eps and all three A_mu agree with optmat’s backbones, and experiment beats theory for Ne and Ar A_eps (the gaiser_2018 anchor).

  • The review’s B_R sources (Garberoglio & Harvey 2020; Hellmann et al. 2021) are not in the library.

  • The review has nothing for Kr, Xe or molecular susceptibilities, and no molecular refractivity virial.

• Status: verified (2026-09-29).

TC-710 chan_1993_erratum (Chan et al., Phys. Rev. A 48, 858 (1993)): erratum to chan_1992’s Tables V, VII, IX (2026-09-29)

• Where: src/optmat/data/sources/chan_1993_erratum.toml (no datasets); src/optmat/data/sources/chan_1992.toml ([[errata]], excluded_rows, notes); data/gas/euv/Ar.toml (unchanged; its result changes).

• Transcribed: nothing is taken as a dataset. The erratum’s whole text is that some values in Tables V, VII and IX “were incorrectly positioned”, and it reprints the three tables in full (library tables tbl_73d8dcfe47d0, tbl_70b698d2df73, tbl_3ba04aab3432, tbl_2389d67b360e, tbl_60dfca332c57). Each was compared cell by cell with chan_1992’s tbl_699514709b3b, tbl_0dd5fa4f52b5 and tbl_1dbc4809ef5a, images checked. Three rows change, and all three are blends. The 1992 tables printed one value under every line of an unresolved group; the reprint prints it once, under a brace spanning the group.

  • Present work, Ar V(b): 0.0426 for 7s (15.186 eV) plus 5d-underlined (15.190 eV). The uncertainty is printed “0.0063” where 1992 had (0.0043) under each line.

  • Geiger [82], Kr VII(b): 0.187 for 5d-underlined (13.099) plus 7s (13.114); 0.054 for 6d-underlined (13.423) plus 8s (13.437).

  • Delage & Carette [81], Xe IX(b): 0.251 for 9s (11.583) plus 5d’ (11.607); 0.171 for 8d (11.683), 8d-underlined (11.740) and 10s (11.752).

• Applied to chan_1992: each group’s value is kept once, at the row of its strongest line in the present work. For the unresolved Ar pair, Natali et al.’s resolved values (0.0139 and 0.0234) decide it. The kept rows are Ar 15.190, Kr 13.114 and 13.423, and Xe 11.607 and 11.740. The repeats are excluded_rows, with the erratum as the reason. One [[errata]] entry was added: present_Ar 15.190 sigma, printed 0.0043, corrected 0.0063.

• Checked: the (a) sub-tables and every other row are reprinted unchanged.

  • Total to ionization, Ar: the reprint gives 0.859 (0.043). This confirms the existing erratum of the printed (0.0043), which rested on the table’s own evidence (TC-68).

  • Wiese, Smith & Miles 3d’ (14.304 eV) is reprinted 0.0106. The existing correction to 0.106 is therefore still ours alone (TC-68).

  • The present-work Ar lines now sum to 0.7233 (0.7659 with the repeat). With the 0.859 total, the unlisted-members pseudo-line of euv/Ar grows from 0.0931 to 0.1357 at 15.70 eV.

• Doubt:

  • The Ar blend’s new uncertainty, 0.0063, is 15 % where every other non-resonance line carries 10 %. It is printed without parentheses. Taken as printed.

  • Choosing the kept row by the strongest line is a convention. The kept energies differ from the other members of each group by 4-57 meV.

  • The erratum’s name typos (“Greiger”, “Delgage”, “Mielczarek and Mielczarek”) touch no value.

• Finding (euv/Ar): removing the repeat moves 0.0426 of oscillator strength from 15.19 eV into the pseudo-line at 15.70 eV. Numbers are before and after the erratum.

  Quantity	Before	After	Against
  Constraint scale	0.98020	0.98135
  S(0)	18.491	18.506	TRK 18
  S(-4)	27.974	27.933	Lesiuk 27.976(15): -0.1 sigma becomes -2.9 sigma
  S(-6)	95.53	95.31	Lesiuk 95.02(11): +4.6 sigma becomes +2.6 sigma
  Re alpha vs fit/Ar, 0.5-2 um	+29 to +34 ppm	+3 to +27 ppm
  Re alpha vs fit/Ar, 200 nm	+408 ppm	+185 ppm
  Re alpha vs fit/Ar, 150 nm	+0.214 %	+0.169 %
  Re alpha vs fit/Ar, 120 nm	+0.91 %	+0.83 %
  Im alpha, 60-70 nm		+0.12 %

  Kr and Xe do not change: their EUV models use only the present-work lines, which the erratum does not touch.

• Status: corrected (2026-09-29).

TC-711 thalman_2014 (Thalman et al., JQSRT 147, 171 (2014); erratum 189, 281 (2017)): Rayleigh cross sections of N2, Ar, O2 at 370-660 nm (2026-09-29)

• Where: src/optmat/data/sources/thalman_2014.toml, tools/extract/thalman_2014.py, data/values/refractive/{N2,Ar,O2}/thalman_2014__*.csv.

• Transcribed: Table 2 (tbl_576e4a7df80e, CSV, image checked, cells agree) at 370.0, 405.8, 532.2 and 660.0 nm, in 10^-27 cm^2. The caption prints “cm^-3”; the erratum gives cm^2.

  • CRDS N2 at 405.8 and 532.2 nm: 16.1(1) and 5.32(2), absolute. The parenthesis is “the range” of repeat runs; taken as bound.

  • BBCES Ar at all four wavelengths: 20.2(3), 14.0(2), 4.57(6), 1.91(2); one sigma.

  • BBCES O2 at 370, 405.8 and 660 nm: 21.4(3), 14.4(2), 1.96(3); one sigma.

  • The BBCES values are relative to the n-based N2 cross section, not independent absolutes.

  • N2 and O2 are one dataset per wavelength, because king_factor is per dataset. Their King factors are Bates’s formulas at vacuum nu: N2 1.03593 and 1.03512; O2 1.11384, 1.10975 and 1.09994.

  • The “Theory” columns are check datasets.

  • Air (Theory and BBCES 23.0(3), 15.7(2), 2.15(3)) is not a registered material; its values are in the record’s notes.

• Errata: from the authors’ erratum, JQSRT 189, 281 (2017). Its reprinted Table 2 is tbl_c363d0a7b75b.

  • Named in its text: N2 Theory at 660 nm, 2.988 corrected to 2.210; O2 Theory at 532.2 nm, 4.740 corrected to 4.660.

  • Changed in the reprint but not named in the text: N2 Theory 23.698 to 23.709, 16.146 to 16.145 and 5.302 to 5.300; O2 Theory at 660 nm, 1.935 to 1.938.

  • Table 1, recorded in notes only (the formulas are sneep_2005’s):

    • N2 B is 307.43305e12, not 307.4335e13;

    • N2 F_k is 1.034 + 3.17e-12 nu^2, not “… nu”;

    • O2 F_k’s constant is 1.096, not 1.09 (unstated in the erratum’s text);

    • the O2 low-wavenumber branch A = 21351.1, B = 2.18567e13 is added (Bates).

  • The Exp columns are unchanged.

• Checked: the corrected Theory columns are reproduced from the corrected Table 1 with Eq. (1), to the printed digits:

  • N2 23.7092, 16.1455, 5.2998, 2.2099;

  • Ar 20.3614, 13.8807, 4.5633, 1.9038;

  • O2 21.2685, 14.3728, 4.6600, 1.9378.

  This needs vacuum wavenumbers (standard-air wavelengths give values 0.1 % lower), so the wavelengths are recorded as vacuum. The printed 2014 values 23.698 and 4.740 are not reproduced by any reading of the formulas.

• Against the fits (alpha measured / alpha model - 1; scattering is electric, so no chi_0):

  • fit/N2: CRDS 405.8 nm -0.06 % (-0.4 sigma); 532.2 nm +0.25 % (+2.3 sigma on the bound reading, +1.3 sigma if the parenthesis is one sigma). Sneep’s 532.2 nm is -1.8 %.

  • fit/Ar: BBCES -0.29, +0.54, +0.18 and +0.27 % at the four wavelengths (chi-squared 1.1 for 4 points).

  • fit/O2: +0.25, +0.08 and +0.93 % (+1.2 sigma at 660 nm).

  • The n-based N2 scale behind the BBCES values is itself 0.06-0.10 % above fit/N2 in alpha, which raises the BBCES values by that much.

  • Air, computed from fit/N2, fit/O2, fit/Ar and fit/CO2 with the CIPM-2007 composition and Bates’s King factors: 23.148, 15.744, 5.154, 2.146 (x 1e-27 cm^2). The BBCES air values are 0.64 %, 0.28 % and -0.17 % below this in cross section, within 1 sigma.

• Doubt:

  • The CRDS “range”: whether it is a half-width or the full span. Taken as a bound, the larger reading.

  • The O2 King factor constant: 1.09 as printed in 2014, 1.096 as reprinted. It shifts alpha by 0.27 %; 1.096 is the value that reproduces the corrected Theory column.

  • The BBCES O2 values come from a single density between O4 bands, so any residual O4 absorption is not separated.

• Status: verified (2026-09-29).

TC-712 wilmouth_2019 (Wilmouth & Sayres, JQSRT 234, 32 (2019)): BBCES Rayleigh cross sections at 333-363 nm; methane resolved (2026-09-29)

• Where: src/optmat/data/sources/wilmouth_2019.toml.

• Transcribed:

  • No printed cross sections: they are in Figs. 2-4 only (218 wavelengths, raster).

  • Text: the mean ratio of measured to n-based cross sections over 333-363 nm (p. 37): Ar 0.998, CO2 0.990, SF6 0.978, CH4 0.778. Mean 1-sigma uncertainty (p. 35): 2.5, 1.9, 1.6 and 1.6 %, including 1.3 % from the path length (the N2 reference), 0.3 % temperature and 0.1 % pressure. SF6 was raised by 0.1 % for purity.

  • Table 1 (image checked): identical to wilmouth_2020’s Table 1 (Sneep & Ubachs’s formulas; N = 2.5469e19 cm^-3). F_k = 1 except CO2 (1.1364 + 2.53e-11 nu^2).

  • Eq. (4), image checked: CH4 (n - 1) x 10^8 = 40161.8 + 4.75e-6 nu^2, at 288.15 K and 101325 Pa (ideal), from the measured cross sections with F_k = 1. Recorded as formula CH4_eq4.

• Reconstructed (not printed): band_{Ar,CO2,SF6,CH4} are cross sections at 348.0 nm, each the printed ratio times Table 1’s n-based value there.

  • Ar 2.625e-26, CO2 7.761e-26 (F_k 1.1573), SF6 1.945e-25, CH4 6.756e-26 cm^2.

  • Each carries the printed mean relative 1-sigma. use = "check".

  • This is the same kind of reconstruction as zhao_2026’s A_R_1566.

  • It assumes a flat ratio over the band. For CH4, Eq. (4) against Table 1 runs 0.781-0.775 (mean 0.7780, reproducing the printed 0.778). Eq. (4) at 348.0 nm gives 6.7552e-26 against the reconstruction’s 6.7556e-26.

• Checked:

  • Eq. (4) reproduces the printed CH4 mean ratio.

  • Against wilmouth_2020’s Eq. (5), cross sections differ by -0.6 to +0.4 %; against its Eq. (7), by -1.1 to -0.4 % over 333-363 nm.

• Against the fits (alpha measured / alpha model - 1; electric; the fits’ own statistical uncertainties are 0.005-0.03 %, negligible):

  Gas	This paper, 348 nm	wilmouth_2020 reconstructed, 280.5 nm
  Ar	+0.01 % (0.0 sigma)	+0.49 % (+0.3 sigma)
  CO2	+0.34 % (+0.4 sigma)	+0.38 % (+0.4 sigma)
  SF6	+1.82 % (+2.3 sigma)	+2.01 % (+2.1 sigma)
  CH4	+0.88 % (+1.1 sigma)	+0.32 % (+0.3 sigma)

  The n-based formulas the papers compare with differ from the fits by: Ar +0.10 %, CO2 +0.85 %, SF6 +3.0 % (+4.2 % at 280 nm), and CH4 +14.4 %.

• Finding (CH4, TC-150): these data resolve the discrepancy in favour of the refractive level.

  • Sneep & Ubachs’s CH4 formula (sneep_2005 ch4_eq18, from Hohm’s polarizabilities) sits a flat +14.3 % above fit/CH4 in alpha (n - 1) at 325-633 nm. That is a level error of the formula, not dispersion.

  • The “22 % disagreement” the authors report is this error. Their measured cross sections are +0.9 +- 0.8 % (333-363 nm) and +0.3 +- 1.0 % (264-297 nm) from the refractive fit.

  • The CH4 outliers of TC-150 remain outliers against BBCES: Sneep’s 532 nm CRDS (+5.4 %, 5.8 sigma) and Ityaksov’s 198-270 nm CRDS (+12 to +20 %). Eq. (4) extrapolated gives -0.5 % at 532 nm.

  • The index-based predictions quoted in TC-150 (Sneep +14 %, Ityaksov +10-14 %) are ch4_eq18’s level error, not evidence against refraction.

• Finding (SF6): both BBCES papers lie about 2 % above fit/SF6 in alpha (2.1-2.3 sigma each; correlated through the shared 1.3 % path length, 0.65 % in alpha). Below 458 nm, fit/SF6 has no data (Burns 458-633 nm, Swift 458-1315 nm), so there it is an extrapolation. Ityaksov’s +5 % at 250-270 nm has the same sign. This is the only evidence on SF6’s UV dispersion.

• Doubt:

  • The reconstruction assumes the ratio is flat and that wavelengths are vacuum. The spectrometer was calibrated on Hg lines; the medium is not stated, and it matters 0.06 % in alpha.

  • F_k = 1 for CH4 is assumed.

  • The ratios are 3-digit means (+-0.05 % in alpha from rounding).

• Status: open, pending J. C. Travers’s acceptance of reconstructed check datasets.

TC-713 kramer_1985 (Kramer, Payne & Chen, JOSA B 2, 1284 (1985)): xenon’s refractivity per atom at 115-117 nm, beyond the first resonance, read from a scanned figure (2026-09-29)

• Where: src/optmat/data/sources/kramer_1985.toml, tools/extract/kramer_1985.py, data/values/refractive/Xe/kramer_1985__fig3_Xe.csv.

• Transcribed: Fig. 3 (p. 3), the 26 measured points of n_3(Xe) = (n - 1)/N (cm^3, all negative, -9.8e-24 at 115.23 nm to -1.7e-21 at 117.03 nm, vacuum wavelengths), the only place the paper gives its result. The page is an embedded scan (400 dpi, one bit), read by data rule 8 (TC-699) as digitised = "raster", use = "check", beyond_resonance: the axes are bilinear maps of (column, row), fitted to the ticks of opposite sides (the scan is skewed and keystoned by up to 11 pixels across the plot), every tick within 1.5 pixels; each open circle’s centre is the centroid of the white region it encloses (two overlapping circles at 117.02-117.03 nm split by k-means). One pixel is 0.0022 nm and 1.3 % in n_3. The sigma column is the paper’s uncertainty: alpha = -9.0(+-0.9)e-19 cm^2 through Eq. (1), 0.1 |n_3 - lambda_3 beta| (41 % at 115.23 nm, 10 % near 117 nm), with 2 % for the reading. State nominal (1 atm, 0 degrees C), as for mahon_1979 and ferrell_1987; the reduction then adds a Lorentz-Lorenz factor of at most 0.8 % (at 117.03 nm) that the paper’s dilute definition does not have.

• Checked: against every number the text prints for the quantity: the pairs R = 4.00 at 115.41 nm and R = 40.0 at 116.94 nm, with the printed alpha (interpolated between -9.9e-19 at 115.24, -9.0e-19 at 116.23 and -8.4e-19 at 117.02 nm) and beta = 2.6e-18 cm^2, give -1.498e-23 and -3.654e-22 cm^3, 2.4 % and 0.8 % from the reading (the script fails beyond 6 %). The upper ends of the error bars drawn at 115.23, 115.41 and 115.81 nm are 1.09, 0.99 and 1.07 times the sigma above. The overlay of the 26 centres on the page image matches every marker (inspected 2026-09-29). The package’s own fit/Ar and fit/Xe give alpha = -1.019e-18, -9.32e-19, -8.72e-19 cm^2 at 115.24, 116.23, 117.02 nm (3-4 % beyond the printed values, inside their 10 %) and beta = 2.564e-18 (1.4 % below).

• Doubt:

  1. The text’s third pair, R = 9.11 at ‘106.23 +- 0.01 nm’ (page image checked), lies outside the tuning range; read as 116.23 nm (the centre, where alpha and beta are quoted), it gives -6.51e-23, 23 % (1.5 sigma) more negative than the figure’s point at 116.229 nm. Fig. 2’s tuning curve for 60 Torr Xe and 550 Torr Ar (R = 9.17) peaks near 116.49 nm by eye, which is consistent with Fig. 3 there. The pair is not used.

  2. The uncertainty is mostly common to all points (argon’s VUV index in alpha), not independent; the wavelength’s +-7 cm-1 (+-0.0094 nm) is not in the sigma and moves n_3 by 20 % or more within 0.03 nm of the 117.04 nm line.

  3. The phase-matching pairs (R, lambda_3) are the primary measurement; the package has no quantity for the density ratio that phase-matches a sum-frequency process 2 omega_1 + omega_2 (phase_match_density_ratio is for harmonics).

• Finding: fit/Xe (range 148 nm to the static limit) evaluated here fails, as expected: its effective oscillator at 119.77 nm (f = 0.775) stands for the 119.20 nm, 125.02 nm and higher lines and it has no 117.04 nm (7s) line, so it is 4.3 times too negative at 115.23 nm, crosses the data at 116.3-116.5 nm and is 0.05 of the data at 117.03 nm (chi^2 = 886 for 26 points). euv/Xe (Chan et al.’s lines, including 7s at 10.593 eV, f = 0.0859, and continuum) has the right shape: 0.79-0.94 of the data from 115.9 to 117.02 nm (median 0.83), 0.45-0.60 at 115.2-115.4 nm where the discrete and continuum parts nearly cancel, and 1.34 at 117.03 nm next to the line (chi^2 = 54 for 26, about 1.4 sigma per point, the sigma being mostly common). With NIST’s line energies instead of Chan’s 1-meV-rounded ones euv/Xe moves by 1-3 % below 116.9 nm and by 5-10 % at 116.99-117.02 nm (median 0.85). Re-reducing the points with the package’s alpha and beta instead of the paper’s makes them 4-14 % more negative (14 % at 115.2 nm, 6 % at 116.2 nm, 4 % near 117 nm), and euv/Xe is then 0.74-0.87 of them (about 20 %).

• Decision: a check dataset; not proposed as a fit/Xe validator (outside its range, it would only record that the effective oscillators are not physical below 129.6 nm). The natural test is of euv/Xe between its lines.

• Status: verified (2026-09-29) for the transcription; open for the R = 9.11 pair and the euv/Xe offset.

TC-714 laporte_1975 (Laporte, Damany & Damany, Phys. Rev. A 12, 1944 (1975)): density shift of the Kr and Xe resonance lines to 80 amagat; Table I’s oscillator strengths (2026-09-29)

• Where: src/optmat/data/sources/laporte_1975.toml, tools/extract/laporte_1975.py, data/values/absorption/{Kr,Xe}/laporte_1975__*.csv.

• Transcribed: Table I, the oscillator strengths of Kr 123.58 nm and Xe 146.96, 129.56, 125.02 and 119.22 nm (header wavelengths, nm, vacuum), from 14 references (Refs. 32-42 experimental, 43-45 theoretical). There are four datasets, experimental and theoretical per gas, all reproduced with the originals’ citations (none is in the library). Rows name the reference. Refs. 43 and 45 print two values per line under a brace, which become rows a and b. There are no uncertainties. The cells were checked against the table image. The header’s 119.22 nm is the line the text calls 119.20 nm (NIST 119.204).

• Not transcribed: the measured shifts (Figs. 2-6, images only). The package has no quantity for the density shift of an absorption line. Read by eye only: Kr 123.58 nm about 0.13 nm at 80 amagat; Xe 146.96 nm about 0.05 nm at 20 amagat and 0.12 nm at 41 amagat. Stated accuracy is +-0.01 to 0.02 nm. Selective reflection can only lower the shift, by at most 0.007 nm.

• Checked: Eq. (3)’s constant, q_e^2/(24 pi^2 m_e eps0 c^2) = 1.4950e-16 m, matches the printed 1.494e-16 (truncated). Eq. (2), the Lorentz shift with the background factor (n_0^2 + 2)/3, is the pole of the Lorentz-Lorenz susceptibility 3y/(1 - y) for a line on a background: the package’s density-dependent index carries the shift already. With fit/Xe’s f (0.2678) and background, the shift of Xe 146.96 nm is 0.0034 nm per amagat (0.070 nm at 20 amagat, 0.142 at 40; the background factor 1.016 and 1.033). With fit/Kr’s f (0.2050), Kr 123.58 nm shifts 0.0016 nm per amagat (0.131 nm at 80). By eye, the measured Kr shift follows this. The Xe 146.96 nm shift is about 70 % of it at 20 amagat, closer to the paper’s f = 0.214 curve. The paper expects a lower shift of the absorption maximum (kappa_max) than of n kappa at high density, depending on the damping it did not determine. Amagat here is the real gas’s 0 degrees C, 1 atm density (Xe 27.067e18 cm^-3, Kr 26.953e18).

• Finding: Table I’s f values scatter widely. For Xe 146.96 nm: 0.214-0.28 (mean 0.257; NIST 0.265, fit/Xe 0.2678). For Xe 129.56 nm: 0.180-0.27 (0.213; NIST 0.191, fit 0.1910). For Kr 123.58 nm: 0.158-0.266 (0.195; NIST 0.205, fit 0.2050). For Xe 119.22 nm: 0.395, 0.381 (chan_1992 0.379). For Xe 125.02 nm: 0.0095, 0.012 (chan_1992 0.0105). The fits’ NIST priors (2 %) lie inside the historical spread.

• Doubt: Ref. 37 (Vaughan 1968) is given Kr 0.204. Gerardo & Johnson 1974 give 0.204 to Lewis 1967. Which one measured it is not resolved; both are outside the library.

• Status: verified (2026-09-29).

TC-715 laporte_1981 (Laporte, Subtil, Bon & Damany, Appl. Opt. 20, 2133 (1981)): VUV reflectance spectrophotometer; a misprinted Lorentz-Lorenz formula (2026-09-29)

• Where: src/optmat/data/sources/laporte_1981.toml.

• Transcribed: nothing. The paper describes an instrument (105-200 nm reflectance and transmittance of gases, liquids and solids, -200 to +100 degrees C, 0-150 bar) and is recorded for method only. Figs. 4-5 (liquid and solid Xe-MgF2 reflectance, excitons) are condensed phases, outside the package.

• Checked: the stray-light test (p. 5). With n_0(Xe, 190 nm, 0 degrees C, 760 Torr) = 1.000995, quoted from Chashchina & Shreider 1969 or Abjean et al. 1971 (which one is not said), and n’(MgF2) = 1.430, the paper finds n = n’ at N/N_0 = 389 and observes a reflectance minimum of 0.05 % at 383. Its formula is printed L = (n^2 - 1)/(n^2 + 1) x N_0/N (page image checked). The 389 follows only from (n^2 - 1)/(n^2 + 2) (389.5); the printed form gives 345. So the formula is misprinted and the calculation is right. fit/Xe gives n - 1 = 996.9e-6 at 190 nm (real gas, 0 degrees C, 1 atm), 0.19 % above the quoted value; abjean_1971’s measurements interpolate to about 998e-6. With fit/Xe’s A_R = 14.790 cm^3/mol and Burns et al.’s B_R = 25.5 cm^6/mol^2 (the package’s choice, 633 nm), n = 1.430 is reached at 377.7 amagat (Xe amagat 4.4927e-5 mol/cm^3), and at 388.8 amagat without B_R. The observation, 383, lies between.

• Doubt: the test does not measure B_R. 0.001 in MgF2’s index (source and axis not stated) moves the crossing by 0.5 %, the temperature and the density scale are not given, and residual Xe absorption raises the minimum.

• Status: verified (2026-09-29).

TC-716 gerardo_1974 (Gerardo & Johnson, Phys. Rev. A 10, 1204 (1974)): photoattenuation of dense Xe and Kr in the red wings of the first resonance lines; Table II’s oscillator strengths (2026-09-29)

• Where: src/optmat/data/sources/gerardo_1974.toml, tools/extract/gerardo_1974.py, data/values/absorption/{Xe,Kr}/gerardo_1974__table2_*.csv.

• Transcribed: Table II, the oscillator strengths of the 3P1 and 1P1 resonance lines, each from two references. Xe 1470 A: 0.26 (Wilkinson 1966), 0.256 (Anderson 1965). Xe 1296 A: 0.27, 0.238. Kr 1236 A: 0.204 (Lewis 1967), 0.158 (Wilkinson). Kr 1165 A: 0.184, 0.135. Wavelengths are as printed, rounded to 1 A. reproduced, originals not in the library, no uncertainties. The cells were checked against the image.

• Not transcribed: Figs. 3-5, k_s (cm^2, the attenuation per atom linear in N) and k_a (cm^5, the N^2 part) against nu_0 - nu = 2000-20000 cm-1 at 273-373 K. They are images only. k_s is an attenuation cross section (Rayleigh scattering plus other processes, temperature-dependent), not the vocabulary’s rayleigh_cross_section, and k_a has no quantity. Also not transcribed: Figs. 7-9 (derived Xe2*, Kr2* potentials and A coefficients) and Table I (Beattie-Bridgeman constants; not optical).

• Checked: Eq. (7a), k_s = 330 lambda^-4 N^-2 (n - 1)^2 (cgs), is the dilute Rayleigh cross section (32 pi^3/3 = 330.7). By eye, the 300 K xenon k_s is about 1e-23 cm^2 at 7000 cm-1, 5e-24 at 12000 and 2e-24 at 20000. That matches fit/Xe’s Rayleigh cross section per atom, (8 pi/3) k^4 (alpha/4 pi eps0)^2 = 1.09e-23, 5.26e-24 and 2.01e-24 cm^2 at 163.8, 178.4 and 208.1 nm, to about the reading (10-20 %). The 373 K k_s is higher, which the paper attributes to other scattering. Since sigma goes as alpha^2, this tests alpha only to 5-10 %.

• Doubt: Laporte et al. 1975 (Table I) give Kr 123.58 nm 0.204 to Vaughan 1968, not Lewis 1967.

• Status: verified (2026-09-29).

TC-717 garrett_1986 (Garrett, Ferrell, Payne & Miller, Phys. Rev. A 34, 1165 (1986)) (2026-09-29)

• Where: src/optmat/data/sources/garrett_1986.toml.

• Transcribed: from the text on p. 1175, krypton’s [n(3 omega) - 1]/N = 2.61e-23 at 146.4 nm (refractivity_per_density, check). The printed unit, “cm^-3”, is wrong: it should be cm^3, the same misprint as in ferrell_1987. It comes from the Xe-Kr phase matching of Fig. 9, 1.64 nm to the blue of Xe 6s. No uncertainty is stated. The state is nominal (per atom).

• Recorded in notes, not as data: no quantity holds the Delta k = 0 conditions of the Xe-Ar mixtures (see the decision below):

  • p. 1171: 6.8 Torr Xe with 800 Torr Ar (ratio 0.0085) phase-matches at 439.62 nm (harmonic 146.54 nm), 1.26 nm from the 6s line at 440.88 nm.

  • Fig. 11: 0.76 Torr Xe with 202.2 Torr Ar phase-matches at 440.3 nm.

  • Fig. 8: ratio 0.0198 at 1.004 nm from 5d[3/2]1.

  • Fig. 10: 4.04 Torr Xe with 701 Torr Ar, 5d[3/2]1.

  • The Fig. 6 annotations: kappa = 2.48e14 P_Xe and Delta k_R = -0.057 P_Ar, in cm^-1 and Torr.

  • The fitted F_01 = 0.26 and 2 beta = 1e-4 P_Xe P_Kr.

• Checked:

  • Against fit/Kr, the Kr value is 0.14 % above (27.99 au; the model’s sigma there is 0.20 %).

  • It is ferrell_1987’s 2.607e-23 at 146.413 nm, rounded.

  • The Fig. 6 constants reproduce the printed -1.26 nm for the 6.8/800 mixture (computed: -1.27 nm).

  • The 6.8/800 condition gives Ar (n - 1)/N at 146.54 nm of 1.428e-23. That is ferrell_1987’s 146.542 nm point (1.427e-23) within 0.1 %.

  • The Fig. 10 condition puts the harmonic at 119.12 nm, which is ferrell_1987’s 119.120 nm argon point.

• Finding (misprint): for Fig. 10’s Delta lambda_m, the text prints -2.47 nm and the caption -0.247 nm. The caption is correct:

  • Eq. (12) scales Delta lambda_m with P_Xe/P_Ar, and Fig. 8’s -1.004 nm at 0.0198 gives -0.29 nm at 0.00576.

  • -0.247 nm reproduces ferrell_1987’s 119.120 nm.

  • It is not a dataset value, so there is no erratum entry.

• Doubt:

  • Fig. 6’s raster axis puts the peaks 0.2-0.4 nm from where the printed constants place them, so the figure is not digitised.

  • The temperature behind “per Torr” is not stated.

  • The pressure shift of the Xe lines by several hundred Torr of Ar is not given.

• Decision:

  • The Kr point is check: it is the same determination as ferrell_1987/experiment_Kr and never enters a fit beside it.

  • The mixture ratios are not stored. phase_match_density_ratio is Shelton’s equal-mismatch ratio (rho_gas/rho_ref = Delta alpha_ref/Delta alpha_gas > 0), whereas a mixture with Delta k = 0 has N_A/N_B = -Delta alpha_B/Delta alpha_A. That needs a new quantity or a parameter (reported).

  • No third-order data: Omega_3 is not measured, and no chi(3) is printed.

• Status: decided (2026-09-29).

TC-718 cotter_1979 (Cotter, Opt. Lett. 4, 134 (1979)) (2026-09-29)

• Where: src/optmat/data/sources/cotter_1979.toml.

• Transcribed: none as data. The paper’s one dispersion number is calculated, not measured: Delta k = -140 p cm^-1, p in atm (p. 135), with Delta k = 6 pi (n_3 - n_1)/lambda_1, tripling 337.1 nm to 112.4 nm in Kr.

  • It comes from an eleven-term Sellmeier formula: ten lines with literature f values, plus one lumped term fitted to visible and ultraviolet indices.

  • The temperature behind “per atm” is not stated, so the value is not a mismatch per atom.

• Recorded in notes:

  • An optimum Kr pressure exists for each lens (3-5 atm for the short lenses, p. 134; Fig. 1 plots bar), which requires Delta k < 0 at 112.4 nm.

  • The confocal parameter is not measured and the beam is not Gaussian, so b Delta k = -4 gives no number.

  • Dye-laser tripling gave output at 111.6-116.5 nm. In the note added in proof it was 110.0-116.5 nm, “closely” the range of calculated Delta k < 0 (p. 135).

• Checked: against fit/Kr, evaluated at 112.37 nm, below its 125 nm range limit, with warnings suppressed.

  • 112.37 nm lies blue of both resonance lines (116.49 and 123.58 nm), between them and the effective oscillator at 99.88 nm.

  • fit/Kr gives Delta alpha = alpha(112.37) - alpha(337.1) = -10.9 au. That is Delta k = -149 cm^-1/atm at 0 C and -139 at 20 C, against Cotter’s -140.

  • fit/Kr’s own sigma on alpha(112.37 nm) is 5.5 au (77 %), about 50 % on Delta k.

  • fit/Kr’s Delta alpha changes sign at a 110.07 nm harmonic (330.21 nm fundamental). The model’s sigma there puts the crossing within about +-2 nm.

  • This matches the observed short-wavelength limit of the tunable output, 110.0 nm.

• Doubt: the paper does not say whether the 110.0 nm limit is set by phase matching or by the dye’s tuning range, so it is not used as a constraint.

• Decision: a method-only record. There is no measured dispersion, and a calculated per-pressure mismatch at an unstated temperature fits no quantity. No third-order data: the efficiencies are not reduced to a susceptibility.

• Status: decided (2026-09-29).

TC-719 junginger_1981 (Junginger, Puell, Scheingraber & Vidal, IEEE J. Quantum Electron. 17, 557 (1981)) (2026-09-29)

• Where: src/optmat/data/sources/junginger_1981.toml.

• Transcribed: Table I, note 2 (p. 560): Kr “linear susceptibility”, 2.59e-24 ESU at 431.0 nm and 4.37e-24 ESU at 143.7 nm.

  • These are per-atom values with n^2 - 1 = 4 pi N chi, i.e. the polarizability volume, stored as polarizability in cm3.

  • The paper interpolated them from Leonard 1974 and Chashchina & Shreider (120 measurements, 670-135 nm, p. 559), so they are check with reproduced_from.

  • The wavelength medium is not stated. The values are recorded as vacuum; the 0.03 % air-vacuum difference is below their three digits.

• Not transcribed: magnesium is not a material of the package. This covers:

  • Table I’s Mg susceptibilities;

  • the Mg third-order table, whose first row is printed chi_T^(1)(3 omega) for chi_T^(3) (image checked);

  • sigma(3 omega) = (4.5 +- 0.7)e-19 cm^2;

  • the pressure-broadening coefficient.

• Checked:

  • The convention: 2.59e-24 cm3 is 17.48 au. fit/Kr gives 17.42 au at 431.0 nm, 0.31 % below the paper (model sigma 80 ppm; the printed three digits allow +-0.19 %).

  • At 143.7 nm the paper is 1.37 % above fit/Kr (model sigma 0.25 %). This matches Chashchina & Shreider’s own offset from fit/Kr: +0.92 % at 140.4 nm and +1.55 % at 152.5 nm (bideau_mehu_1981/chashchina_shreider_1969_Kr).

  • The mixture condition: from Table I, N_Kr/N_Mg = -Delta chi_Mg/Delta chi_Kr is 12.84 with the measured chi_Mg(3 omega) (-5.35e-24) and 11.92 with the calculated one (-3.72e-24). The printed ratios are 12.7 and 11.8, 1.1 % and 1.0 % lower.

• Doubt:

  • The residual 1 % in the ratio reproduction is unexplained. It may be rounding of the Kr digits or a density detail of the heat pipe.

  • The PDF’s first page is an unrelated correction by Byer and Eggleston.

  • The library title drops “in”.

• Decision:

  • The Kr values are check. They are an interpolation of others’ data (the Chashchina & Shreider scale), never fitted.

  • The measured P_Kr/P_Mg = 12.7 at 431.0 nm (the Delta k = 0 condition of a mixture) is not stored. Mg is not a material, and no quantity holds a mixture ratio.

  • The ratio determines Mg’s chi(3 omega) given Kr’s, so it cannot test Kr.

• Status: decided (2026-09-29).

TC-720 voronin_2017 (Voronin & Zheltikov, Sci. Rep. 7, 46111 (2017)): the generalized Sellmeier equation for air; its CO2, N2, O2 and Ar terms (2026-09-29)

• Where: src/optmat/data/sources/voronin_2017.toml, tools/extract/voronin_2017.py.

• Transcribed: Table 1 (JSON cells, checked against the image): the CO2 rows r = 1-4 and the electronic rows of N2, O2 and Ar (r = 12-14) as formulas without a form, coefficients in e-notation with the printed digits (the cells lose the superscripts of x 10^-k; the script reads them back and asserts every coefficient). The water rows (r = 5-11, 15), the air SSE (Ciddor 1996’s coefficients as printed) and Fig. 5’s single-term formulas are in the notes. The GSE is n - 1 linear in each species’ density (no Lorentz-Lorenz, ideal gas); per molecule each term is a Lorentz oscillator f = 2A at E = hc/lambda.

• Checked: (1) A is dimensionless, not ‘ps^2’ as headed: the electronic rows sum to half the electron count (N2 7.000, O2 8.000, H2O 5.000). Eq. (4) misprints the second numerator as A_2r lambda_1r^2 (Eqs. 5-6: lambda_2r^2; only lambda_2r^2 reproduces S(-2) below). (2) The N2, O2 and H2O terms reproduce Margoliash & Meath’s (1978) S(0) and S(-2) to 1e-6 and S(-4) to 1e-4 and 1.2e-3. (3) Against the stored fits, per molecule: N2 +185 ppm at 633 nm, +174 ppm static; O2 +178 and +277 ppm; Ar -6.53 % at 633 nm and -6.50 % static (10.357 against 11.077 au). (4) The four electronic terms at the Fig. 1 densities reproduce Ciddor’s standard-air formula to 1e-5 over 300-1500 nm. (5) The CO2 terms’ strengths are HITRAN’s principal isotopologue’s (within 0.10-0.15 % in the 15 and 4.3 um regions) and 1.6-1.7 % below optmat’s all-isotopologue HITRAN 2024 bands; static 2.0837 against 2.1212 au.

• Doubt: the fitting procedure, weights and spectral range of the pole wavelengths are not stated. The Fig. 1 densities (total 2.551e19 cm^-3) are those of 1 atm near 15 degrees C, not the 296 K stated. The Ar term matches Peck & Fisher’s 0 degrees C formula only at Fig. 5’s argon density 2.879e19 cm^-3 (7.1 % above 0 degrees C, 1 atm): it is not argon’s polarizability. No CO2 electronic term. The stated 1e-10 accuracy is against the authors’ own line sum, which shares the electronic terms.

• Decision: method source and formulas for comparison only; nothing enters a fit. The Ar term must not be used for argon.

• Status: verified (2026-09-29).

TC-721 mathar_2004 (Mathar, Appl. Opt. 43, 928 (2004)): line-by-line refractivity of water vapour and moist air from HITRAN; method only (2026-09-29)

• Where: src/optmat/data/sources/mathar_2004.toml.

• Transcribed: nothing as data. The notes record the method (Eq. 1, a linear superposition of Lorentz oscillators in eps with n = sqrt(eps); f from HITRAN’s squared transition moments, Eq. 2), the line counts (water 31,646 lines, 441 nm-24.96 mm; CO2 27,123 lines, 1.036-22.6 um; HITRAN 2000), the ultraviolet oscillators used per species (Margoliash & Meath for N2, O2, H2O, CH4; Padial et al. for CO2; Eggarter and Chan et al. for Ar, S(0) = 13.3; Hibbert et al. and Chan et al. for Ne) and the stated comparisons (pp. 929-931).

• Checked: the pure-N2 value at 28 um and 833.3 hPa, 2.31e-4 (p. 931), against fit/N2: 2.2050e-4 at 26 degrees C (the temperature of the air calculation it sits beside) and 2.3135e-4 at 12 degrees C. The value is a 12 degrees C one.

• Doubt: the temperature of the N2 comparison is not stated. No Lorentz-Lorenz local field (eps linear in density; the successor mathar_2007 adds it).

• Decision: method source for the OEP (line-by-line HITRAN plus ultraviolet pseudospectra); nothing fitted or checked against it.

• Status: decided (2026-09-29).

TC-722 mathar_2007 (Mathar, J. Opt. A 9, 470 (2007)): polynomial fits to a line-by-line index of humid air, 1.3-24 um; compared with optmat’s dry air (2026-09-29)

• Where: src/optmat/data/sources/mathar_2007.toml.

• Transcribed: nothing as data. The notes record Eqs. (5)-(6) (fifth-degree polynomial in sigma - sigma_ref, each coefficient quadratic in 1/T, p and relative humidity H with cross terms), the reference values (290.65 K, 75,000 Pa, H = 10 %), the five windows with sigma_ref (1.3-2.5, 2.8-4.2, 4.35-5.2, 7.5-14.1, 16-24 um) and each table’s c_0ref (cells of the five tables, image-checked; the text rendering loses the captions of Tables 3 and 5, read on the page), and the method (Eq. 2 line sum, Lorentz-Lorenz Eq. 4, virial densities, temperature-dependent line strengths, 370 ppm CO2 fixed, stated accuracy 2e-4 of the susceptibility).

• Checked: the tables evaluated at 17.5 degrees C, 750 hPa and H = 0 (linear extrapolation from 5-60 %) against the stored fits of the CIPM-2007 dry-air constituents (CO2 at 370 ppm) by Lorentz-Lorenz at CoolProp’s air density. Dispersion within each window agrees within 0.23e-8 (1.3-2.5 um), 0.34e-8 (4.49-5.2 um) and 1.4e-8 (3.0-4.0 um); departures of 2-3.4e-8 at the band edges (2.8, 4.2, 4.35 um), -1.25 to +2.4e-8 over 7.5-14.1 um and up to 7e-8 over 16-24 um. Level: Mathar is 5.0-5.4e-8 (2.7e-4) higher at 1.3-2.5 um, rising to 7.8e-8 at 10.8 um and 16e-8 at 20 um; the same optmat sum lies 3.0e-8 below Edlen 1966 at 15 degrees C, 1013.25 hPa, 0.5-2 um (within Edlen’s +-5e-8), and Mathar states his raw theory lies about 4e-8 above dry-air measurements.

• Doubt: the comparison’s H = 0 is an extrapolation; the mixture density in the comparison is CoolProp’s pseudo-pure air (x_CO2 changed without re-solving the density). The level offset growing into the far infrared (16e-8 at 20 um) is not explained; it lies where water’s rotational band and CO2’s 15 um band dominate.

• Decision: method source; no dataset or formula (moist air). Not a validator for optmat’s CO2 bands: at 370 ppm CO2’s infrared term is 1e-9 to 6e-8 of n - 1 in the windows, below the comparison’s resolution except at band edges.

• Status: decided (2026-09-29).

TC-723 tang_1972 (Tang, J. Opt. Soc. Am. 62, 644 (1972)): bounds on the one-term Sellmeier formula, and what they say about optmat’s one pole per infrared band (2026-09-29)

• Where: src/optmat/data/sources/tang_1972.toml.

• Transcribed: no values (atomic hydrogen only, in figures). The notes record the three constructions of alpha_a = alpha0 eta^2/(eta^2 - omega^2): eta = omega_1 (upper bound below omega_1; Eqs. 11-13, 36); eta^2 = N/alpha0 = S(0)/S(-2) (lower bound; Eqs. 14-19, 37); eta fixed by one value alpha(omega0) (upper bound below omega0, lower bound above, one crossing only; Eqs. 20-38), and the refinement with f_1 known (Eqs. 39-45). Three text misprints noted (Eq. 21 for 20; f_omega for f_1 in Eq. 43; ‘.V’ for N in Eq. 19), none affecting a coefficient.

• Checked: derived here: the omega0 -> 0 limit of Eq. (20) is eta^2 = S(-2)/S(-4) (the one-term formula that keeps the first Cauchy coefficient), a lower bound and the tighter one, since omega_1^2 <= S(-2)/S(-4) <= S(0)/S(-2). optmat.gas.infrared’s pole per band, E^2 = sum S / sum(S/nu^2), is Tang’s Eq. (14) applied to a band’s lines; by the same argument as Eqs. (10)-(19), it lies below the band’s true contribution at frequencies below the band and above it (smaller in magnitude) at frequencies above the band. Size, from Voronin & Zheltikov’s P/R-branch pair for CO2’s 4.3 um band (voronin_2017): the one pole is 1.5 % low at 2200 cm^-1, 1.6 % small at 2500 cm^-1, 0.1 % at 3000 cm^-1, 2e-4 at 4000 cm^-1 and 6e-6 at 633 nm.

• Doubt: the error estimate uses a two-pole model of the band, not its lines; the bounds need all f >= 0 (true of HITRAN’s net intensities).

• Decision: method source for the OEP; no change to the band poles (their error at optical frequencies is 1e-5 of a band’s small contribution).

• Status: decided (2026-09-29).

TC-724 egan_2024_correction (Egan & Yang, Int. J. Thermophys. 45, 177 (2024)): the Gouy phase correction to egan_2023 (2026-09-29)

• Where: egan_2024_correction.toml (new, no datasets); egan_2023.toml ([[errata]] of A_R_Ar and A_R_N2; notes).

• Transcribed: the correction’s whole text (2 pages): the Gouy phase shift of the Fabry-Perot cavity does not depend on the refractive index (the beam waist depends on the wavelength in the medium), so the working equation loses the factor (1 + eps_d) (corrected Eq. (3)); the reported molar refractivities of Ar and N2 were “fractionally small by 0.3 x 10^-6 A_R”.

• Applied: errata of egan_2023: A_R(Ar) 4.195735 -> 4.1957363 and A_R(N2, 303 K) 4.446175 -> 4.4461763 cm^3/mol at 632.9908 nm (the stated factor applied; the correction prints no new values). One tenth of each standard uncertainty (3.1e-6).

• Effect: egan_2023’s argon value moves from -2.7 ppm to -2.4 ppm of fit/Ar, and the argon S(-4) derived from it in TC-707 (27.965(9)) by +0.001 %: nothing in TC-707’s conclusions changes.

• Doubt: N2’s temperature coefficient A_theta is not addressed (a common relative factor leaves it unchanged to first order, not stated). Whether yang_2025 (same cavity, 2025) used the corrected equation, and whether lang_2026’s reproduced egan_yang_303K is the corrected value, is not stated in either paper.

• Status: corrected (2026-09-29).

TC-725 The refits of 2026-09-29: new magnetic terms, egan_2023 in fit/Ar, new validators; CO2’s lower minimum (2026-09-29)

• Where: data/gas/fits/{He,Ne,Ar,N2,O2}.toml; every stored fit re-run in dependency order (models/fitted/*.json), robustness records of He, Ne, Ar, N2, Kr, Xe, O2, CO2, CH4, SF6; the tables of docs/accuracy.md and docs/gas_models.md.

• Decisions:

  • fit/Ne and fit/Ar take Lesiuk & Jeziorski’s relativistic chi_0 (TC-706): -8.4786e-5 and -2.29545e-4 a.u. (before -8.484e-5 and -2.30e-4). Effect on n - 1 +0.02 ppm (Ne); Ar below.

  • fit/Ar fits egan_2023/A_R_Ar (TC-707, TC-724) beside egan_2019: an independent apparatus and pressure scale, 3.1 ppm. Chi-squared of the two 0.12 and 0.76.

  • fit/N2 takes Lang et al.’s ab initio chi_0 = -1.75e-4 a.u. (TC-708; before 0). Refraction fixes alpha + chi_0, so n - 1 moves by -0.01 ppm; the electric static value by 15 ppm.

  • Validators added: fit/He puchalski_2020/alpha_static (electric; chi-squared 0.003); fit/Ar thalman_2014/bbces_Ar (+0.17 %, chi-squared 1.1 for 4); fit/N2 thalman_2014/crds_N2_405 (-0.07 %), crds_N2_532 (+0.25 %), egan_2023/A_R_N2 (+8 ppm at 303 K, chi-squared 5.8: the model has no temperature dependence and N2’s A_R rises 1.2 ppm/K, so it tests the temperature), lang_2026/cauchy_303K (chi-squared 26 for 4, the ab initio moments 3-4 sigma low, TC-708) and lang_2026/semi_empirical_303K (chi-squared 3.0 for 2); fit/O2 thalman_2014/bbces_O2_370, _405, _660 (+0.25, +0.08, +0.93 %).

  • Not done: the helium retardation term (TC-705, open); fitting egan_2023’s N2 value (the temperature question, TC-707).

• Effect on the models (new against old): fit/Ar n - 1 -1.30 ppm at 633 nm, -1.03 ppm at 800 nm, GVD at 800 nm -55 ppm (0.3 of its statistical sigma); through Shelton’s ratios fit/Kr -0.28 ppm and GVD -31 ppm, fit/Xe -1.32 ppm and -26 ppm; He, Ne, N2, O2, CH4, SF6 change by 0.02 ppm or less; H2, D2, CO, N2O, O3 unchanged.

• Finding (CO2): re-run with its configuration unchanged and its N2 partner moved by 0.01 ppm, fit/CO2 lands in another minimum: chi-squared 234.3 against the stored 239.3 (72 degrees of freedom; 1.5 after the Birge scaling), the same with 12 and with 40 starts, so the stored fit had been a local minimum. The second effective oscillator now sits on its modelling bound, 0.225 hartree (202 nm, the absorption onset), with f = 0.0033. The datasets trade: Old, Gentili & Peck 85 -> 53 (17 points), Egan 2026 27.8 -> 5.9 (2), against Hohm’s shape 6.6 -> 46 (5) and Shelton’s 1986 ratios 8.1 -> 18.6 (5). New against old: n - 1 +9 ppm at 633 nm, -159 ppm at 343 nm, +508 ppm at 250 nm; GVD -0.35 % at 633 nm, -0.69 % at 500 nm, -0.08 % at 800 nm, -0.27 % at 343 nm, +32 % at 250 nm. Leave-one-out at 343 nm now 1.9 % (Shelton 1986; before 0.46 %): working estimate there raised from 1 % to 2 %.

• Doubt: a pole on its bound is a sign that the two-oscillator form and the bound decide the ultraviolet shape; the near-infrared (800 nm) is stable to 0.08 %. Whether to move the bound, add an oscillator or narrow the range below 300 nm is a modelling decision not taken here. SF6’s leave-one-out record also changed without a change of the fit (largest at 800 nm now shelton_1985_sf6, 1.3 %, before shelton_1990, 1.8 %): the refits without a dataset are sensitive to their starting point.

• Status: decided (2026-09-29) for the changes above; CO2’s ultraviolet form decided (2026-09-29) by TC-726.

TC-726 fit/CO2: the two weak bands below 10 eV as lines; the effective oscillators from 10 eV (2026-09-29)

• Where: data/gas/fits/CO2.toml ([[model.lines]], effective_min_energy_hartree, starts, description); models/fitted/CO2.json, models/robustness/CO2.json; the accuracy and gas-model pages.

• The problem (TC-725): with two free effective oscillators bounded at 0.225 hartree (202 nm), the lowest minimum put one on the bound with f = 0.0033. Tried in memory, the minimum follows the bound: bound 0.27 hartree, chi-squared 207.3 with f = 0.018 on it (7.35 eV); bound 0.30, 243.6 with no oscillator below 11.8 eV; the GVD at 250 nm varies by 25 % across these. chan_1993_co2 (Table 2, curated) shows CO2’s only strength below 10 eV is two weak diffuse bands, 1Delta_u (f = 0.00565, about 8.38 eV) and 1Pi_g (0.00753, about 9.30 eV), and none at 6-7.5 eV: the low-bound solutions stand in for these bands with a misplaced and too strong pole.

• Decision: the two bands are lines at 147.95 and 133.32 nm (the table’s peak energies, approximate; the bands are diffuse), f priors 0.00565 and 0.00753 with sigma 0.0012 each, the spread of the other measurements the table compares (1Delta_u 0.0040-0.0062, 1Pi_g 0.0053-0.0075); the effective oscillators are bounded at 0.37 hartree (10.07 eV, just below the strong 1Pi_u and 1Sigma_u+ bands near 11 eV); 24 starts.

• Result: chi-squared 237.45 for 70 degrees of freedom (reduced 3.39); the lines fit at f = 0.00601 and 0.00761 (within 0.4 and 0.1 of their priors’ sigma); effective oscillators at 0.431 and 0.708 hartree (11.7 and 19.3 eV). Moving the bound to 0.40 hartree changes the GVD by at most 0.3 % at 250 nm and 0.03 % from 300 nm to 1 um (checked in memory). Against the fit before TC-725: n - 1 within 6 ppm and the GVD within 0.32 % (250 nm) and 0.05 % (300-1064 nm), 0.09 % at 1300 nm; against TC-725’s: the GVD -24 % at 250 nm, +0.26 % at 343 nm, +0.35 % at 633 nm.

• Held out: Bideau-Mehu et al.’s 181-254 nm interferometry (a validator, TC-178): chi-squared 57 for its points, against 17363 with TC-725’s solution; other validators unchanged within 1 %.

• Robustness: the largest leave-one-out shift of the GVD at 343 nm is 0.50 % (Shelton 1986), 0.20 % at 800 nm (Old, Gentili & Peck); no dataset moves the model by more than 3.3 sigma. The working estimate at 343 nm returns to 1 %.

• Doubt: the band energies are approximate peak energies of diffuse bands; as poles they matter only below about 200 nm, outside the declared range (250 nm). The tension between Old, Gentili & Peck with Egan 2026 and Hohm with Shelton’s 1986 ratios (TC-148, TC-400) remains, and is what the reduced chi-squared of 3.4 reflects.

• Status: decided (2026-09-29).

TC-727 Third-party data files moved to the paper library; the UDM parameters in the records (2026-09-29)

• Where: src/optmat/data/external/ (weaver/, mcpeak_2015/, nifs_photoab/, newad2/ and schott/ removed), the records babar_2015, weaver_1981, ordal_1983, johnson_1972, mcpeak_2015, sakamoto_2010, franta_2015b, franta_2016, franta_2017, franta_2025 and schott_2023, optmat.solid.models.formulas, optmat.solid.udm, optmat.solid.fitting, data/solid/fits/SiO2.toml and its stored fit, tools/extract/, tools/newad2/udm_check.py, tests/solid/test_udm.py.

• Decision (J. C. Travers, 2026-09-29): the package keeps no third-party file whose redistribution terms are not stated. Babar & Weaver’s workbook, McPeak et al.’s Supporting Information data files, the NIFS database’s text tables, Franta et al.’s newAD2 parameter files and tables, and the text layer of SCHOTT’s N-BK7 data sheet are attached byte for byte to their papers in the curators’ paper library (paperextract’s attach, with each file’s URL, retrieval date and a note). The SCHOTT data sheet is in the library as a document without a DOI (Unverified_b3287ae9ef98, named from the PDF’s SHA-256); c-Si’s newAD2 files, an unpublished model, go with franta_2017. A dataset read from an attached file names it as table = "data/<file>". The Mainz ozone spectra (open access, cited), HITRAN’s band totals, NIST’s tables, Henke’s factors, the refractiveindex.info snapshot (CC0) and the tRecX runs stay.

• The UDM parameters: the four newAD2 parameter files that published formulas use (franta_2016/udm_lithosil_q2; franta_2015b/udm_SiO2_X2551, udm_MgF2_X2935, udm_Al2O3_X2890) are held in the records as the formulas’ terms: the file’s first line as attributes and every value as the file prints it (194, 131, 101 and 23 values). The silica fit starts from franta_2016/udm_lithosil_q2 in place of the file.

• Checked:

  • The library-lane tests pass against a copy of the library with the files attached: every affected extraction (babar_2015, weaver_1981, mcpeak_2015, sakamoto_2010, franta_2015b, franta_2016, schott_2023) writes the committed data files unchanged from the attached copies; the records’ terms equal the attached parameter files string for string; and the implementation reproduces the authors’ tables of all seven models as before (TC-321).

  • Re-running the silica fit from the formula gives the stored fit to the last digit; only the recorded start and the configuration’s digest change.

  • Attaching republishes a library paper: its text, document.json and tables are unchanged, but the figure crops of a paper’s supplement are re-rendered with slightly different pixels. paperextract’s reprocess does the same without an attachment, so it is not the attachment’s doing.

• Also: the remaining files’ PROVENANCE.md notes, the materials registry’s comments and three extraction scripts no longer describe the curation’s internal process; the facts are unchanged. The tRecX extraction scripts’ local directory is replaced by a placeholder, and their SHA-256 are updated in their PROVENANCE.md.

• Status: decided (2026-09-29).

TC-728 fit/He: the retardation term in the refractive polarizability; the Thomas-Reiche-Kuhn sum as a prior (2026-09-29)

• Where: optmat.gas.models.oscillator (OscillatorModel.retardation_au: a term c omega^2 in the refractive polarizability, its derivative and the dispersion derivatives), optmat.gas.fitting ([model] retardation_au, added like chi_0 to refractive observations and harmonic differences, never to electric data or moments), optmat.gas.models.fitted (loaded from the stored fit); data/gas/fits/He.toml; every stored fit re-run in dependency order and every robustness record; the conventions, fitting, gas-model and accuracy pages; tests in tests/test_fitting.py and tests/test_fitted.py.

• Decision (the term, TC-705): fit/He takes Pachucki & Puchalski’s retardation term, c = kappa alpha_nrel alpha_em^2 = -0.5069525 x 1.3831922 x alpha_em^2 = -3.73405e-5 a.u. (omega in hartree; kappa and alpha_nrel = (2/3) alpha_0(0) from pachucki_2019’s Table I, recomputed here), fixed, outside the covariance. The convention is extended, not changed: the refractive polarizability is what refraction measures, electric plus chi_0 plus, where known, retardation. Neglected for the other gases (kappa not known; of the order of 1e-5 of their dispersion by the same scaling).

• Decision (the prior): with the term, fit/He’s fourth effective oscillator ran away (5e13 hartree, f = 4e-18) at the same chi-squared, 38.09, leaving a singular covariance; three effective oscillators give chi-squared 135 (the moments alone 96). The Thomas-Reiche-Kuhn sum S(0) = 2 (the electron count) is added as a prior, sigma 0.001 (a judgement): chi-squared 38.09 for 66, the fourth oscillator at 10.5 hartree with f = 0.24, S(0) = 2.000, and the moments fitted at chi-squared 0.008 (before 0.13). Before this entry the fits had S(0) = 1.81.

• Effect on fit/He (new against the stored fit before): n - 1 -0.14 ppm at 633 nm, -0.09 ppm at 800 nm (the term); GVD -23.6 ppm at 633 nm, -23.9 ppm at 800 nm (6 of its statistical sigma, 4.0 ppm) and -22 to -24 ppm from 300 nm to 1.55 um. Toward the resonance the refitted electric terms move it by -4.4 ppm at 100 nm, -6 ppm at 80 nm (5 and 2 statistical sigma: the freedom of the highest oscillator, which the covariance does not contain), and -51 to -577 ppm at 65 to 60 nm (0.4 to 0.5 sigma, the 1s2p strength moving by 0.00045, 0.5 of its sigma). All within the working estimate (< 0.01 %).

• Validated: yang_2025’s measured two-colour A_2 of helium (formula he_A2, 1.332468(6)e-4 cm^3/mol) against the fit’s refractive omega^2 coefficient: 4.81 sigma without the term, -0.56 sigma with it (test in tests/test_fitted.py, bound 2 sigma). puchalski_2020/alpha_static unchanged (0.007 ppm).

• Partners: through Shelton’s He/X ratios fit/Ne’s GVD at 800 nm moves -9.8 ppm, fit/H2 n - 1 -0.18 ppm and D2 -0.03 ppm; every other fit by 0.2 ppm or less.

• Status: decided (2026-09-29).

TC-729 fit gallery: observation conventions and normalised residuals (2026-09-29)

• Where: docs/gallery/_helpers.py (_fit_data, fit_overview), tests/test_fit_gallery.py, docs/fitting.md.

• Checked: the gallery previously compared every direct datum with the full refractive polarizability, ignoring the fitter’s electric, infrared, correction_au, shape_relative and wavelength-window options. For gaiser_2018/molar_polarizability_Ar, it showed +8.988 sigma against fit/Ar instead of +0.408 sigma: the electric datum was compared with the refractive prediction, including chi_0 = -2.29545e-4 a.u. (TC-706). The former point was outside the panel’s +/-6 sigma limits. The corrected squared residual is the stored contribution to chi-squared, 0.166264. These are checks against the existing source records, configuration, fitting code and stored fit; no primary paper was re-examined.

• Decision: use the fitter’s observation conversion and forward prediction for configured direct datasets. Remove a fitted scale from both values and uncertainties. Compare each observation in its configured convention; express the difference in the top panel as a percentage of the full refractive polarizability, equivalent to translating the observation onto that convention. Its error bar uses the observation’s full uncertainty. The bottom panel is the data-minus-prediction residual divided by that uncertainty, with the opposite sign to the optimiser. Configured wavelength windows apply to both panels.

• Checked: regression tests compare every plotted fitted dataset’s point count and sum of squared residuals with its stored fit, including the molecular shape allowances, wavelength selections and ozone’s additive correction. Independent oscillator sums check electric comparisons for argon and helium (including the retardation distinction) and electronic-only methane theory. The existing eligibility filter, which omits datasets marked check or excluded, is retained.

• Doubt: other direct datasets without fitting or validator options still use their stored convention. Cauchy moments, ratios, Rayleigh cross sections and priors are absent from these panels; the stored reduced chi-squared describes the full fit. The fixed plotting limits can hide outliers.

• Status: corrected (2026-09-29).

TC-730 The molecules’ reference temperature: 293.15 K, and datasets brought to it (2026-09-29)

• Where: optmat.gas.fitting ([model] reference_temperature_k; the dataset option temperature = { measured_k, coefficient, sigma }, for fitted datasets and validators; stored as reference_temperature_k); data/gas/fits/{N2,O2,CO2,N2O,H2,D2}.toml; the conventions, fitting, gas-model and accuracy pages; tests in tests/test_fitting.py.

• Finding: a state’s temperature enters the index only through the density and Lorentz-Lorenz; every polarizability model is independent of temperature. For the molecules the fitted level carries the temperature of the data that set it: N2 and N2O about 293 K (Egan et al. 2019 at 293.15 K), CO2 and O2 303 K (Egan 2026, 4.6e-6 and 7.2e-6 of A_R, most of each level’s weight), CH4 and CO 297.5 K (Zhao et al. 2026), SF6 mostly 373 K (Achtermann et al.), H2 and D2 293 K (Raj et al.’s rotational average). Peck & Khanna set N2’s shape, not its level (systematic 3.3e-4).

• Decision: a fit may declare a reference temperature, and a dataset measured elsewhere is brought to it by the factor 1 + c (T_ref - T), with sigma_c |T_ref - T| added in quadrature, where the coefficient c is measured. 293.15 K (20 degrees C, the metrology laboratories’ temperature and the accuracy page’s) for N2, O2, CO2, N2O, H2 and D2. Brought to it: egan_2026/A_R_CO2 (303 K, c = 4.22e-6 per K at 633 nm, combined u 8 %, sigma 0.34e-6; 4.13e-6 at 1542 nm, inside it) and egan_2026/A_R_O2 (2.11e-6, u 9.4 %, sigma 0.20e-6; 2.02e-6 at 1542 nm) (egan_2026, pp. 4, 7-8); the N2 validator egan_2023/A_R_N2 (303 K, 1.18(4)e-6, egan_2023 p. 17). The other datasets are left at their temperatures: their weight in the levels is small, and most state none. CH4, CO and SF6 declare no reference temperature: their levels rest on 297.5 and 373 K data and no coefficient is curated.

• Effect: fit/CO2 n - 1 -39.8 ppm at 633 nm (-38.7 at 343 nm, -37.9 at 1550 nm), GVD -0.018 % at 800 nm (0.37 of its statistical sigma), chi-squared 237.45 -> 236.76 (egan_2026 27.1 -> 20.3); fit/O2 n - 1 -20.7 ppm, GVD -12 ppm at 800 nm; N2, N2O, H2, D2 unchanged. The N2 validator egan_2023: +7.6 ppm (chi-squared 5.8) at 303 K becomes -4.1 ppm (1.6) at 293.15 K.

• Not modelled: the evaluation at other temperatures. A model’s polarizability does not change with the state’s temperature; at 20 K from the reference the omission is about 24 ppm (N2), 42 ppm (O2) and 85 ppm (CO2) of n - 1.

• Status: decided (2026-09-29).

TC-731 The real-gas density returns a condensed phase past saturation (2026-09-30)

• Where: optmat.gas.eos (_fluid, number_density, compressibility); OEP 1, §4.2.

• Finding: number_density(gas, State(p, T)) asks CoolProp (8.0.0, through pyfluids 4.0.0) for the state at the given pressure and temperature, and CoolProp returns the stable phase there. Past saturation that is a liquid, and its density is returned without a warning. At 294 K, SF6 has Z = 0.688 at 20 bar (phase Gas) and Z = 0.107 at 25 bar (Liquid), a density eight times larger. SF6 at 50 bar is SupercriticalLiquid (T < T_c, p > p_c), as is Xe at 60 bar and 280 K, and CO2 at 50 bar and 280 K is Liquid. solprop’s own density (from CoolProp’s mass density) behaves alike.

• Checked: the 122 distinct gas states at which curated datasets are stated are all gaseous or supercritical (none Liquid, SupercriticalLiquid or two-phase), so no reduced dataset is affected.

• Decision (OEP 1, §4.2): the forward law and its inverse share one domain, the gas below saturation and the fluid above the critical temperature. A state CoolProp reports as Liquid, SupercriticalLiquid or two-phase raises StateError.

• Status: open: the refusal is made in OEP 1’s Phase 2c.

TC-732 O3’s measured-absorption derivative is not the derivative of its evaluator (2026-09-30)

• Where: optmat.gas.absorption.MeasuredAbsorption (real_derivative_au, _derivatives), used by OscillatorModel.dpolarizability_domega_au and dispersion_au for fit/O3; OEP 1, §4.1.

• Finding: the real part of the measured term is a cubic spline of the grid’s Kramers-Kronig transform inside the grid (0 to 96 787 cm⁻¹, 0.5 cm⁻¹ steps), and a trapezoid sum over the grid outside it. real_derivative_au is instead numpy.gradient of the grid values, applied repeatedly for the higher orders, then linearly interpolated, and it clamps to the end value outside the grid. Against the spline’s own derivative it differs by up to 4.6e-5 of the largest |d Re alpha / d omega| over 185-3800 nm (-1333.341 against -1333.302 a.u. at 255 nm). Outside the grid it has the wrong sign (-4.81e5 against a central difference of the evaluator of +176 at 100 nm and +1.56 at 50 nm), and at omega = 0 it gives 2.9e-4 a.u. where the derivative of the even real part is 0. The real part itself is discontinuous at the grid’s upper end (-25.6 a.u. just inside, -3115 just outside), outside O3’s range.

• Effect: inside O3’s range, 4.6e-5 of the first derivative. The orders 2-4 of dispersion_au (fit/O3’s GVD uncertainty, its robustness record, its gallery page) are gradients of gradients; they were not compared.

• Decision (OEP 1, §4.1): the new SI derivative uses the spline’s derivative inside the grid, the differentiated trapezoid sum outside it, and the segment slopes of the imaginary part’s interpolant (the mean of the two at a knot).

• Status: open: the first derivative is replaced in OEP 1’s Phase 2b; the higher orders need their own treatment (roadmap).

TC-733 Two docstrings that no longer describe their code (2026-09-30)

• Where: optmat.gas.models.registry.default_model, optmat.gas.ionisation_rates.IonisationRateModel.instantaneous_rate.

• Finding: default_model said it raises for ozone “for now”; defaults.toml names fit/O3, and it has not raised for ozone since. instantaneous_rate said the rate is the cycle-averaged rate divided by cycle_average_factor; that holds only for averaging = "tunnelling". The default, "consistent", divides by the model’s own cycle average (cycle_average of its slope and curvature; TC-662).

• Decision: both docstrings corrected; no number changes.

• Status: corrected (2026-09-30).

TC-734 The silica tensor Raman default: Lin & Agrawal’s own f_R, with the fitted total n2 (2026-09-30)

• Where: optmat.solid.raman_response, optmat.solid.kerr (kerr/SiO2); OEP 1, §4.7 and §7.10; solprop SEP 3, D11.

• Finding: the copolarised Stokes gain at 330 cm⁻¹ for a 526.0 nm pump, with kerr/SiO2’s n2(526 nm) = 2.792e-20 m²/W, against Stolen & Ippen’s 1.5e-11 cm/W +- 10 % (stolen_1973/gain_amplifier, TC-693):

  • Hollenbeck & Cantrell, the Kerr fit’s f_R = 0.219 (paired, the scalar default): 1.354e-11, -9.7 % (TC-696);

  • Lin & Agrawal’s shape at f_R = 0.219: 1.233e-11, -17.8 %;

  • Lin & Agrawal’s own f_R = 0.245, holding the total n2: 1.382e-11, -7.9 %;

  • the same, holding the fit’s electronic part (total 1.035 n2): 1.430e-11, -4.7 %.

  Lin & Agrawal’s normalised response has an imaginary part 9 % below Hollenbeck & Cantrell’s at 330 cm⁻¹ (peak gain 1.71 against 1.91e-11 cm/W at f_R = 0.219, both near 435 cm⁻¹). The gain set the fit’s f_R through Hollenbeck & Cantrell’s shape, so this is a consistency check; Hellwarth et al.’s nuclear share, 0.21 +- 0.03 (TC-694), is the validator of f_R, and 0.245 lies 1.0 sigma from the fit’s 0.219 +- 0.026.

• Decision (J. C. Travers, 2026-09-30, on OEP 1’s recommendation): the tensor default is Lin & Agrawal’s form with its own f_R = 0.245 and kerr/SiO2’s total n2; the variant scaled to the fit’s f_R is not added. Every silica bundle holds the total n2 and takes its shape’s f_R; the tensor default’s electronic part is then 3.3 % below the fit’s and its Raman part 12 % above it. A second Kerr fit with Lin & Agrawal’s shape in the gain’s prediction stays a possible refinement.

• Status: decided (2026-09-30).

TC-735 Reject incomplete resolved Raman bands (2026-09-30)

• Where: optmat.gas.raman._vibrational, the internal raman.toml loader; tests/test_raman_contracts.py.

• Finding: with ground-state rotational constants present, omitting all three upper-state prescriptions (upper, fit_lines, b_difference) silently produced an unresolved band, even when resolved = true. Explicitly requesting resolution without a lower ladder also silently produced one line. Three regression cases demonstrated the missing rejection before the correction.

• Decision: a resolved band requires both ladders; reject an incomplete request with DataError. Where lower constants exist, resolution remains the default; resolved = false still explicitly selects an unresolved band. With no lower constants and no resolution request, the existing unresolved behaviour is retained.

• Checked: every existing curated configuration supplies the required prescriptions or deliberately uses an unresolved band. Before/after comparisons of all eight gases and ten vibrational bands at 295 and 350 K, and one and two amagat, give exact equality for all 160 arrays of frequencies, amplitudes, linewidths, levels and branch labels. Regression tests also check the valid resolved and explicitly unresolved neighbours. No curated record, fit, default or numerical result changed.

• Doubt: no new primary-source reading was required or performed; this corrects configuration validation, not a choice of rotational constants or physical model.

• Status: corrected (2026-09-30).

TC-736 Fail clearly when a continuum constraint has no usable secant step (2026-09-30)

• Where: optmat.gas.euv.constrained; tests/test_euv.py.

• Finding: a synthetic line of strength 0.5 at one hartree and a continuum of 0.3 per hartree at 2, 3 and 4 hartree expose two failures. A split below the first continuum sample leaves no adjustable value and a changed target causes division by zero. A static-sum target corresponding to a factor 0.05 below 3.5 hartree causes the local secant iteration to propose a negative scale; its logarithm then gives NaNs. These are synthetic numerical tests, not material data.

• Decision: reject a zero secant slope or a proposed non-positive/non-finite scale with DataError, before division or logarithmic interpolation. Keep the bounded six-step iteration and the returned last iterate for valid steps. The method is for adjustments within measured uncertainties; it is not a general solver for arbitrary large changes. An invalid trial does not imply that the physical target is impossible.

• Checked: both failure cases were reproduced before the correction. A factor-0.2 target uses all six updates and agrees with an independent piecewise analytic integral to 1e-6 relative, allowing the existing 20,000-point quadrature’s O(h^2) error. All five curated EUV models retain exactly the same scale factors, dipole sums S(-4), S(-2), S(0), and polarizabilities at frequencies 0, 0.01, 0.05 and 0.1 au. No source data, stored fit or recommended model changed.

• Doubt: large changes can still require a different root solver; this correction reports an invalid step explicitly rather than extending that numerical method. No primary paper was re-examined for these numerical failure cases.

• Status: corrected (2026-09-30).

TC-737 wilke_1950 (Wilke, J. Chem. Phys. 18, 517 (1950)): the mixture-viscosity rule of OEP 1, checked against the page (2026-09-30)

• Where: src/optmat/data/sources/wilke_1950.toml; OEP 1, §4.3 and Q17.

• Transcribed: no values. The notes record the multicomponent rule, Eqs. (13)-(14) (p. 519), the binary Eq. (11) (p. 518), the viscosities’ state (the mixture’s temperature and pressure) and the paper’s stated accuracy: 0.97 % average deviation for the binary data of Fig. 1, 0.49 % without H2-Ar, and 1.9 % for thirteen multicomponent mixtures.

• Checked:

  • Eq. (14) against the page image at 600 dpi. It prints (M_j/M_i)^(1/4), and (4/sqrt 2)[1 + M_i/M_j]^(1/2) in the denominator. With phi_ii = 1, Eqs. (13)-(14) are exactly OEP 1’s form: mu_mix = sum_i x_i mu_i / sum_j x_j Phi_ij, with Phi_ij = [1 + (mu_i/mu_j)^(1/2) (M_j/M_i)^(1/4)]^2 / [8 (1 + M_i/M_j)]^(1/2).

  • Reproduced: Table I’s phi_12 and phi_21 from Eq. (14), with the printed viscosities and modern molar masses. He-Ar at 20 C gives 2.4192 and 0.2716 (printed 2.417 and 0.2716), Ne-Ar at 200 C 1.6057 and 0.6166 (1.606, 0.6166), and Ne-He at 200 C 0.4863 and 1.5523 (0.4862, 1.552). Nine pairs agree within 0.3 %.

• Doubt:

  • The library’s extracted text renders Eqs. (10), (11) and (14) with the exponent 1/2 on M_j/M_i. That is an extraction error; the page and Table I both give 1/4.

  • Table I’s N2-O2 phi_21 = 1.014 is inconsistent with its own phi_12 = 0.994 through phi_21 = phi_12 (mu_2/mu_1)(M_1/M_2), which gives 1.005. It is a slip in the table, and no value is taken from it.

• Decision: OEP 1’s Q17 is resolved: its formula is Wilke’s. The paper’s evidence for the noble gases is the He-Ar binary at 20 C (Fig. 1) and the Ne-Ar-He ternary at 200 C (Table II: 360.0 against a measured 357.4, 0.7 %). The manual page states it.

• Status: verified (2026-09-30).

TC-738 buckingham_1955 (Buckingham & Pople, Trans. Faraday Soc. 51, 1029 (1955)): the second dielectric virial of a non-polar gas, and OEP 4’s pair law (2026-09-30)

• Where: src/optmat/data/sources/buckingham_1955.toml; OEP 4, §4.1.

• Transcribed: no values. The notes record Eqs. (2.12) and (3.1) (p. 1031) and the three terms of the coefficient:

  • the change of the pair’s mean polarizability with separation;

  • dipole-induced-dipole (Eqs. 3.5-3.8);

  • the orientational term of a pair’s field-free dipole (Eq. 3.18).

• Checked:

  • Against the page images: for atoms the result is B = (2 pi N^2/3) integral Delta alpha exp(-u/kT) d^3r in Gaussian units. That is B = N_A^2/(6 eps0) integral Delta alpha exp(-U/kT) d^3R in SI, OEP 4’s form, factors 1/2 and 1/3 included, with Delta alpha one third of the pair polarizability’s trace.

  • Reproduced: Eq. (3.8) gives Table 1’s argon value, 1.99 cm^6/mol^2 at 25 C.

  • The orientational term vanishes at optical frequencies (p. 1035), so the optical coefficient keeps the pair’s excess mean polarizability only.

• Doubt:

  • The paper treats a single gas. The pair count extends it to mixtures, but an unlike atom pair has an interaction-induced dipole. Its static cross coefficient therefore carries an orientational term that the optical one lacks. OEP 4’s pair records keep the two apart (its §7.3).

  • For molecules the integral also averages over relative orientations.

  • The library’s text misreads the second author as ‘POPLLE’ and fuses Table 1’s reference marks into values.

• Status: verified (2026-09-30).

TC-739 garberoglio_2020 (Garberoglio & Harvey, J. Res. NIST 125, 125022 (2020)): ab initio dielectric and refractivity virials of He, Ne and Ar (2026-09-30)

• Where: src/optmat/data/sources/garberoglio_2020.toml; OEP 4, §4.1 and §5.

• Transcribed: no values. The notes record the definitions (Eqs. 1-3), with B_R = B_eps + omega^2 B_R^(2), and the tabulated values near 300 and 350 K (Tables 1-3): He B_R -0.0550, Ne -0.097 and Ar 1.73 cm^6/mol^2 at 300 K and 632.99 nm.

• Checked:

  • The classical limit, Eq. (13), is Buckingham and Pople’s (TC-738). Its printed 8 pi^3 is a misprint for 8 pi^2.

  • The calculation agrees with the package’s like terms for He (Achtermann’s -0.068(10), ‘slightly below’ but consistent) and Ar (1.76(5) against about 1.70).

  • Quantum corrections at 300 K are 0.9 % for He and 0.5 % for Ne, well below the measurements’ uncertainties.

  • The pair term’s dispersion, from B_eps to B_R at 633 nm, is a few per cent. OEP 4’s convention lets it disperse like the linear term.

• Doubt: neon’s calculation has no stated uncertainty and may be about 25 % off (Bich’s independent value). See TC-744 for neon’s measured values.

• Status: verified (2026-09-30).

TC-740 kunz_2012 (Kunz & Wagner, J. Chem. Eng. Data 57, 3032 (2012)): GERG-2008, the multi-fluid mixture model (2026-09-30)

• Where: src/optmat/data/sources/kunz_2012.toml; OEP 4, §4.2 and §7.4.

• Transcribed: no values. The notes record:

  • the form, Eqs. (1)-(17) and (34)-(38);

  • the 21 components;

  • the binary parameters of the pairs OEP 4 needs (Tables A6 and A8);

  • the stated uncertainties (Table 6).

• Checked:

  • The form reduces to each component’s equation at x_i = 1 (§2.2).

  • He-Ar, He-O2, He-H2, He-CO, Ar-H2, H2-O2 and O2-CO have every reducing parameter 1 and no departure function: Lorentz-Berthelot, unfitted. That confirms the six placeholder pairs GPT-6’s review found in CoolProp. CoolProp’s He-Ar is Tkaczuk et al.’s instead (TC-742).

  • N2-O2, N2-Ar and O2-Ar have fitted reducing functions only. For that class the gas-phase density uncertainty is 0.3-1 %, near the lower value for these pairs. Air as a whole is 0.1-0.2 %.

  • CoolProp 8.0.0’s N2-O2 parameters are GERG-2008’s.

• Doubt:

  • The paper states no quadratic mixing rule for the second virial; the model’s B is not quadratic in composition in general. OEP 4 cites Gernert (TC-743) for the quadratic law it contrasts with the models.

  • GERG-2008’s pure-fluid equations are technical ones (O2 to 303 K), while CoolProp uses the reference equations with these binary parameters.

  • The library’s text garbles Eqs. (42), (43) and (45).

• Status: verified (2026-09-30).

TC-741 lemmon_2000 (Lemmon, Jacobsen, Penoncello & Friend, J. Phys. Chem. Ref. Data 29, 331 (2000)): dry air, pseudo-pure and as a mixture (2026-09-30)

• Where: src/optmat/data/sources/lemmon_2000.toml; OEP 1, §5 (the density of air); OEP 4, §7.4.

• Transcribed: no values. The notes record:

  • the pseudo-pure equation (§4) and its composition: N2 0.7812, O2 0.2096, Ar 0.0092 (Jones 1978, without CO2);

  • its range and its uncertainty: 0.1 % in density (k = 2) to 873 K and 70 MPa;

  • the mixture model (§5, Table 15) and its verified ranges (Table 17).

• Checked:

  • CoolProp 8.0.0 names its ‘Air’ equation Lemmon-JPCRD-2000. This is OEP 1’s pseudo-pure air, the density of Gas.Air, and settles that row of its §5.

  • CoolProp’s multi-fluid N2/O2/Ar pairs are not this paper’s mixture model, whose reducing functions have a different form. They are GERG-2008’s (N2-O2) and Gernert’s (N2-Ar, O2-Ar; TC-743).

  • Against air p-rho-T data both of the paper’s models have an average deviation of 0.097 %.

• Doubt:

  • Ar-O2’s p-rho-T data are only at 70-90 K; the pair is unverified at 70-400 K (0.5 % or more).

  • The mixture model’s second virial is less accurate than the air equation’s.

  • The library’s text renders the tables’ minus signs as ‘2’.

• Status: verified (2026-09-30).

TC-742 tkaczuk_2020 (Tkaczuk, Bell, Lemmon, Luchier & Millet, J. Phys. Chem. Ref. Data 49, 023101 (2020)): He-Ne, He-Ar and Ne-Ar mixture models, and their accuracy near ambient (2026-09-30)

• Where: src/optmat/data/sources/tkaczuk_2020.toml; OEP 4, §3, §7.4 and §8.

• Transcribed: no values. The notes record:

  • the reducing parameters of the three pairs (Table 6);

  • the data sets with their ranges and average deviations (Tables 3-5);

  • the second-virial sets, compared but not fitted.

• Checked:

  • These are the parameters CoolProp 8.0.0 uses (reference key Tkaczuk-JPCRD-2020). For Ne-Ar, beta_T 1.033, gamma_T 0.967, beta_v 0.919, gamma_v 1.035.

  • GPT-6’s quotation of §3.1 is exact: 0.5-2.5 % for 95 % of the He-Ar data, and 3 % for 90 % of the Ne-Ar density data. It covers the fitted data below 10 MPa, cryogenic and ambient together.

• Finding: near ambient, the models’ average deviations from the measured mixture densities are:

  • He-Ne: 0.08-0.26 % (Kestin et al. 1981 at 298 K; Vogl and Hall 1972).

  • He-Ar: 0.72 % (Blancett et al., 223-323 K to 73 MPa).

  • Ne-Ar: 0.43 % (Kestin et al. 1981 at 298 K to 13.7 MPa).

  These exceed the models’ difference from the partial-pressure rule at 10 bar in OEP 4’s §3 (1.6e-3 for He/Ar, 3.4e-4 for Ne/Ar). So the paper does not establish that the multi-fluid density is closer to experiment there. OEP 4’s Phase 2 compares every density method with the measured mixture densities and cross second virials near ambient, and the default for each mixture follows from that comparison (OEP 4, §7.4).

• Doubt:

  • The library copy is the accepted manuscript. Its text drops Table 4’s deviation column on p. 4, which was read from the page.

  • The text’s figure numbers and upper temperatures and pressures are inconsistent in places. No parameter is affected.

• Status: verified (2026-09-30); the finding is carried by OEP 4.

TC-743 gernert_2013 (Gernert, doctoral thesis, Ruhr-Universität Bochum (2013)): humid-gas and CCS binaries, and the virial limitation of multi-fluid models (2026-09-30)

• Where: src/optmat/data/sources/gernert_2013.toml; OEP 4, §4.2, §7.4 and §8.

• Transcribed: no values. The notes record:

  • the fifteen binaries of CO2, H2O, N2, O2, Ar and CO, and which are refitted;

  • the cross-second-virial data sets (Table A2.1);

  • the stated density uncertainties (Table 6.1).

• Checked:

  • §5.2.4 (pp. 127-130): the model’s second virial ‘is clearly not quadratic’ in composition, a consequence of the corresponding-states approach, and the quadratic mixing rule, Eq. (5.11), ‘is not correctly reproduced by the model’. It is shown for H2O-N2, and is small when the components’ critical temperatures are similar.

  • Table A2.1 (p. 198) lists Bose and Cole’s CO2-Ar cross virials, 5 points at 320-322 K, none used.

  • CoolProp 8.0.0’s N2-Ar, O2-Ar and CO2-Ar pairs carry this thesis’s key; its N2-O2 parameters are GERG-2008’s, which the thesis kept.

  • Stated gas-phase density uncertainty at reduced density below 0.6: N2-O2 < 0.1 %, N2-Ar < 0.5 %, O2-Ar < 1.0 %, CO2-Ar < 0.5 %.

• Doubt:

  • O2-Ar rests on one 1923 data set at 298 K, reproduced within +-2 %.

  • The Elshayal and Lu citation of Table A2.1 appears to be misprinted.

  • The library’s extraction is partial (two empty pages), and Table 6.1’s header is garbled; the table was read from the pdf’s text layer.

• Status: verified (2026-09-30).

TC-744 Finding: neon’s refractivity virial, Orcutt & Cole’s static B_eps against the ab initio and optical values (2026-09-30)

• Where: data/gas/refractivity_virial.toml ([Ne]: orcutt_1967/B_this_work_Ne, -0.30(10) cm^6/mol^2 at 322 K, static); garberoglio_2020 (TC-739).

• Finding: the package’s neon B_R is Orcutt and Cole’s static dielectric coefficient. It is about three times the magnitude of the others:

  • Garberoglio and Harvey’s ab initio B_eps, about -0.098 at 323 K, and B_R, about -0.101 at 633 nm;

  • Huot and Bose’s B_eps, about -0.12(6) (Garberoglio and Harvey’s Fig. 5);

  • Achtermann et al.’s 1993 optical B_R, about -0.11(2) at 303 K (their Fig. 6).

  Orcutt and Cole’s value is about two of its standard uncertainties from the calculation. Burns et al.’s optical -0.14(14), which the configuration’s note cites as agreeing, agrees with both.

• Size: the difference, 0.2 cm^6/mol^2 against neon’s A_R of 1.0 cm^3/mol, is about 8e-6 of n - 1 at 1 atm and 294 K, and about 8e-4 at 100 bar.

• Doubt: the values other than Orcutt and Cole’s are read from Garberoglio and Harvey’s figures. Achtermann et al. 1993 and Huot and Bose are not in the library.

• Decision: none yet. The choice is between Garberoglio and Harvey’s calculation and Achtermann et al.’s 1993 measurement, once that paper is curated.

• Status: open.

TC-745 Model identity, ownership and qualified intervals: OEP 1, Phase 1 (2026-09-30)

• Where:

  • optmat.identity (new, core): ModelIdentity, the canonical record, the SHA-256 digest, FrozenMapping, frozen, the status vocabulary;

  • optmat._validity (new, core, private): the qualified intervals;

  • every model class of the surface, which now derives from Identified: the gas dispersion models (Model, OscillatorModel, FittedModel, FormulaModel, DatabaseModel) and MeasuredAbsorption; HyperpolarizabilityModel; both rate models; GasRamanResponse; the solid models (Model, FormulaModel, UdmModel, FittedModel, TabulatedModel); KerrModel; SilicaRamanResponse.

• The digest is the SHA-256 of canonical JSON of:

  • the class;

  • the EVALUATION_VERSION of each class along its MRO that declares one, and of the evaluator modules it names (lorentz_lorenz, ionisation_rates, molecular_ionisation_rates, nonlinear, raman_response of the gases, raman_response of silica, conditions for Edlén’s air); all are 1;

  • every field except the status;

  • extras: the refractivity virial ratio of every gas dispersion model, the reference density of a formula or refractiveindex.info entry, the digests of the linear model and Kerr fit behind silica’s Raman kernel, and of the N2 model behind a solid formula relative to nitrogen.

• Deviations from OEP 1, section 4.8:

  • the values resolved from another component (the reference density, the virial ratio, the bound models) are resolved once per object on first use (functools.cached_property), not at construction. Resolving them eagerly would make building the gas registry import CoolProp (about 0.5 s) and fail without the optional pyfluids, and would make every solid model load the gas fits. The value is still fixed for the object’s life and enters its record;

  • optmat.gas._tunnelling is not a shared evaluator: it computes the molecules’ orientation-averaged structure factors at construction, which are stored fields and so in the digest. The atomic evaluator lives in ionisation_rates, which the rate models name.

• Not in scope of an identity: TabulatedEntry (a comparison table, not a model), and the registry dictionaries, which are still shared mutable caches; the models in them are read-only.

• Checked:

  • golden values of 358 quantities of every registry model (gas dispersion, hyperpolarizability, the rates at 800 nm, the Raman responses of the eight molecules and dry air, the solids, the Kerr fit and the silica responses) were recorded on main before any change and are bitwise unchanged after it;

  • the digests: identical across processes and hash seeds; changed by any field, an interval, an evaluator version or a bound component; every model’s digest is distinct; storage read-only after construction, replace and pickling;

  • every model has one interval, its range, and warns exactly where it did: the message for one interval is unchanged, and a NaN wavelength still does not warn.

• Status: decided (2026-09-30).

TC-746 The status of every curated model (2026-09-30)

• Where: the builders of each registry; the status keys of data/gas/molecular_ionisation_rates.toml and data/gas/raman_response.toml.

• Decision (OEP 1, sections 6.2 and 7.3):

  • gas dispersion: the model data/gas/defaults.toml recommends is validated (every gas’s fit), with the file’s reason; every other published formula and every refractiveindex.info entry is comparison;

  • solids: a material’s recommended model (any axis) is validated; the others are comparison;

  • atomic ionisation rates: default is validated, Kr and Xe with their suggested constant included: Wallace et al.’s yields test them, and their uncertainty factor of 2 says how well (OEP 1, section 7.3). The other four models (three forms of the literature and the default’s one-electron rate) are comparison;

  • molecular rates: default is validated except SF6, untested (no calculated or measured rate to test it against, TC-678, TC-684); the six literature forms are comparison (TC-673);

  • Raman responses: CO2 and N2O are provisional (TC-542: CO2 has no Q-branch width and borrows the S coefficient; N2O is vibrational only with rho = 0 and Chen et al.’s T2 taken as collisional); the other gases are validated; a mixture takes the least trusted status of its Raman-active constituents, so dry air is validated;

  • silica: hollenbeck_2002, the default, is validated; lin_2006 and blow_1989 are comparison until OEP 1’s Phase 2g names the tensor default (TC-734);

  • kerr/SiO2 and every hyperpolarizability fit are validated;

  • a model built directly by a caller is user.

• Status: decided (2026-09-30).

TC-747 golub_1969 (new; Golub and Welsch, Gauss quadrature from the Jacobi matrix) (2026-09-30)

• Where: data/sources/golub_1969.toml; optmat.gas.infrared.gauss_rule; OEP 3, section 4.

• Transcribed: no values. The record states the method: the nodes of an N-point Gauss rule are the eigenvalues of the weight’s Jacobi matrix, and the weights the squared first components of the orthonormal eigenvectors times the zeroth moment.

• Checked:

  • Eq. (2.6) against the page image (journal p. 223, pdf p. 3): w_j = q_{1,j}^2 / p_0^2(t_j) = q_{1,j}^2 / k_0^2 = q_{1,j}^2 mu_0.

  • The exactness for polynomials of degree up to 2N - 1 (p. 222, the Theorem).

  • gauss_rule builds the Jacobi matrix by the Lanczos process on the band’s lines, with full reorthogonalisation, and applies Eq. (2.6). Tests: synthetic measures reproduce mu_0 to mu_{2n-1} to 1e-12; a measure with fewer distinct lines than n gives its exact rule.

• Doubt: the library’s resolver took the received and revised dates for the year; the DOI was confirmed by the curator.

• Status: verified (2026-09-30).

TC-748 The derivation of the molecular gases’ windows, band rules and bound: OEP 3, Phase 1 (2026-09-30)

• Where: tools/hitran/windows.py; the derived tables data/external/hitran/<gas>_band_rules.csv, _windows.csv, _bound.csv and _absorption.csv for CO, CO2, CH4 and N2O; optmat.gas.infrared (band_systems, infrared_windows, bound_cells, fold_poles); tools/hitran/feasibility.py.

• Method (OEP 3, sections 4 and 7):

  • the settings are those of section 7: sigma 1 cm^-1; a_sigma below 0.1 m^-1 for the pure gas at 101325 Pa and 296 K; tolerance 0.1 of the parent fit’s statistical sigma of alpha and 1 % of max(|D_2 ref|, |D_2 electronic|); at most 8 nodes, each system within a tenth of the tolerance; windows at least 50 cm^-1 wide;

  • the analysis runs from 12.5 um to each fit’s shortest wavelength.

• The reference.

  • The resonant term of the lines farther than 30 cm^-1, and the antiresonant term of every line, are FFT convolutions on a 0.005 cm^-1 grid. The lines nearer than 30 cm^-1 are summed directly. Above the line lists’ 11000 cm^-1, everything is summed directly.

  • The smoothed kernel is Dawson’s function and its derivatives. Beyond |x| = 15 the asymptotic series takes over; the two agree to 1e-10 in every order there.

• Checked:

  • On synthetic lines, the reference and all three derivatives agree with the direct sum over every line to 1e-8.

    • A first version convolved every line by FFT; its roundoff near strong lines reached 5e-5 of D_2 in a window 500 cm^-1 away. The near and far parts were split for that reason.

  • The smoothed absorption agrees with the direct Gaussian sum to 1e-5.

  • feasibility.py reproduces the first table of OEP 3, section 8, for CO’s 2.52-4.34 um window (1 to 8 nodes: n - 1 error 2.0e-3, 6.7e-5, 2.9e-7, 4.1e-11; GVD medians 0.73, 5.6e-3, 8.1e-7; below 1 % over 2, 55, 88, 98 % of the window), and the second table’s 98 % (core 100 %).

  • The committed tables satisfy the invariants of section 8 (tests/test_infrared_windows.py):

    • positive strengths, with the nodes inside their spans;

    • each system’s M_0 and M_-2 kept;

    • the rules’ totals equal to the band tables’ to their six digits;

    • windows at least 50 cm^-1 wide, with no pole inside any window;

    • the bound’s cells tiling every window;

    • one provenance for the four tables of a gas.

  • The bound: each 0.25 cm^-1 cell was checked at its midpoint, and near a pole at a tenth of the distance to it. A check above the cell’s bound resampled the cell on the fine grid (CO 1324 cells of 38444, CO2 3231 of 20812, CH4 1530 of 13386, N2O 3406 of 24664); none failed the tolerance.

• The poles needed (Q6; the fits hold today CO 30, CO2 4296, CH4 295, N2O 2518). With the rotational systems and the folds, the rules need CO 97, CO2 4188, CH4 944 and N2O 6060 poles. Most band systems keep one node: CO2 2598 of 2879, N2O 1691 of 2380. 131, 66 and 403 systems of CO2, CH4 and N2O reach the cap of 8.

• Status: decided (2026-09-30).

TC-749 Decision: the optical ranges keep their data’s qualification, and only absorption splits them (2026-09-30)

• Where: tools/hitran/windows.py (enforced); the four windows tables.

• Finding:

  • Near weak near-infrared bands, the reference smoothed at sigma = 1 cm^-1 carries GVD structure from their individual lines that no pole model follows. For CO2 the model’s GVD differs from the reference by:

    • 1600 electronic GVDs at 1064 nm (4.4e4 fs^2/m at 1 atm);

    • 39 at 1542 nm;

    • 2e4 at 1.3 um.

  • In alpha the difference is 1.3 and 1.5 times the tolerance at 1.4 um and 1542 nm, and 0.04 at 1.2 um.

  • Enforcing the tolerance inside the present optical ranges would have ended CO2’s, N2O’s and CH4’s qualified ranges near 0.9 um (today 1400, 2000 and 1400 nm). It would have split CO’s at its overtones, with new warnings at 1064 and 1542 nm and at fitted and validating data (CO2’s 1542 nm metrology, CO’s 1566 nm refractometry).

• Decision (J. C. Travers, 2026-09-30): each fit’s optical range (its range_nm) keeps the qualification its data give it.

  • It is split only where the pure gas absorbs (a_sigma at or above 0.1 m^-1).

  • The representation tolerance qualifies windows beyond that range, at longer wavelengths.

  • Inside the range the bound is stored and reported, not enforced, and an in-window band there is always folded, so that no pole lies in a qualified interval.

  • This deviates from OEP 3, section 4, which splits an optical interval where a band “cannot be represented”.

  • The manual is to say that a picosecond pulse near a weak band sees structure the model does not hold.

• The reported bound inside the optical ranges (the largest over the tolerance): CO 1.6 (alpha) and 194 (GVD); CO2 2.8 and 168; CH4 up to 330 and 2.6e6; N2O up to 118 and 3.4e6. The extremes are at single lines of the weak bands.

• Status: decided (2026-09-30).

TC-750 The qualified intervals of CO, CO2, CH4 and N2O, and OEP 3’s Q1, Q2, Q3 (2026-09-30)

• Where: the four <gas>_windows.csv.

• The intervals (vacuum wavelength; the gaps’ dominant conditions in brackets):

  • CO: 0.167-2.288 um, then 2.565-4.340 and 5.191-12.5 um. The first interval is the fit’s range (to 2000 nm) extended by the tolerance to 2.288 um. [2.288-2.565: the 2-0 band, kept, and its absorption; 4.340-5.191: the fundamental’s absorption.]

  • CO2: 0.250-1.400 um (the range, which absorbs nowhere above 0.1 m^-1); then 2.302-2.380, 2.381-2.475, 2.541-2.590, 3.203-3.350, 3.357-3.593, 5.549-6.946 and 8.435-8.941 um. [1.400-2.302: representation (80 %) near the weak 1.4-2.1 um bands; 3.593-5.549: the 4.3 um band; 6.946-8.435 and 8.941-12.5: kept bands, among them the 9.4 and 10.4 um laser bands.]

  • CH4: 0.240-1.123 um, 1.137-1.149, 1.177-1.187 and 1.188-1.313 um (the range, split by absorption at 1.123-1.137, 1.149-1.177 and 1.187-1.188 um, and ending at 1.313 um, where absorption and representation begin); then 11.123-12.088 um. [1.313-11.123: representation 52 %, absorption 46 %.]

  • N2O: 0.320-1.516 and 1.518-1.950 um (the range, split by absorption at 1.517 um and ending at 1.950 um); then 4.814-4.956 and 6.752-7.048 um. [1.950-4.814: representation 50 %, absorption 44 %.]

• Against OEP 3, section 8:

  • CO’s two infrared windows qualify as the feasibility study found.

  • CO2’s short-wave windows qualify over most of the candidates, and its 4.65-12.2 um candidate over 5.55-6.95 um. The part 8.44-8.94 um also qualifies here, where section 8 found none of 8.41-8.95 um with its draft keep rule.

  • N2O and CH4 qualify narrow mid-infrared windows only, as section 8 foresaw: their weak bands dominate the local dispersion.

  • Pure CO2 is not qualified at its laser lines.

• Q1 settled: the transparency criterion is a_sigma below 0.1 m^-1 at 101325 Pa and 296 K. Each window’s record states its largest a_sigma, the values at its edges, the largest self-broadened single-line Lorentz peak at 1 atm, and the Lorentz far-wing absorption beyond 25 cm^-1 of every line (an estimate from above; real wings are sub-Lorentzian). The largest far wings are 0.23 m^-1 (N2O at 4.81-4.96 um), 0.052 m^-1 (N2O at 6.75-7.05 um) and 0.041 m^-1 (CO2 at 3.36-3.59 um).

• Q2 settled: the tolerance of section 7 is kept, enforced beyond the optical ranges (TC-749). No window there exceeds it (largest ratios 0.999 in alpha, CO2 at 3.36-3.59 um; 0.997 in the GVD, CO2 at 3.20-3.35 um).

• Q3 settled: fold or keep per band, chosen per candidate window for the widest qualified span among keeping none or the bands above 1e-5, 1e-6, 1e-7 or 1e-8 of the molecule’s M_0. The choice: CO keeps 3 bands in its 2.40-4.44 um candidate; CO2 keeps 11 in its 4.65-12.5 um candidate and folds the rest (472); CH4 and N2O keep none.

• Status: decided (2026-09-30).

TC-751 The rotational systems (2026-09-30)

• Where: the rotational system of each <gas>_band_rules.csv; OEP 3, section 4.

• Finding:

  • The rotational system is every line whose upper and lower vibrational states are equal. For CO that includes the hot rotational groups (v = 1, 2, …): 1631 lines to 298.6 cm^-1.

  • CO2 has 836 such lines, below 51 cm^-1, of its asymmetric isotopologues, where OEP 3, section 7, says it has none. Their static sum is 4.5e-8 au.

  • CH4’s are the ground and nu4 rotational groups, 10029 lines to 477 cm^-1.

• Checked: the systems’ static sums are the orientation terms of TC-156:

  • CO 0.651 au, against mu^2/3kT = 0.664 au at 296 K (mu = 0.1098 D);

  • N2O 1.448 au (TC-156: 1.45), against mu^2/3kT = 1.424 au.

  • The vibrational sums equal the band tables’ (CO2 2.1212 au), and CO’s 0.1223 au agrees with bishop_1982’s 0.1213 au (TC-202).

• Decision: the rotational system is part of every rule table, one node each (their share is below a tenth of the tolerance in every window). Phase 2 keeps it out of the static and electric validators.

• Status: decided (2026-09-30).

TC-752 Data and validators outside the new intervals (2026-09-30)

• Where: data/gas/fits/CO2.toml; the four windows tables.

• Finding:

  • Old, Gentili and Peck’s CO2 values at 1695 and 1817 nm, the validators OEP 3 would add (TC-148), lie in CO2’s 1.400-2.302 um gap. There the weak bands’ representation fails, by 8 times the tolerance in alpha at 1.6 um.

  • Simmons’s and Willetts and Harris’s 10.6 um values, and Marchetti’s (2006, 2007), lie in the laser bands’ gap.

  • CO’s 1566 nm (zhao_2026) and CO2’s 1542 nm data stay inside the kept optical ranges (TC-749).

• Decision: for Phase 3: these data are compared, not qualified. Whether Old’s two points are fitted is Phase 3’s decision (OEP 3, section 7).

• Status: open (for OEP 3, Phase 3).

TC-753 marchetti_2006 and marchetti_2007: one apparatus, one systematic (2026-09-30)

• Where: data/sources/marchetti_2006.toml, marchetti_2007.toml; OEP 3, section 5.

• Finding:

  • Both use the same differential two-Fabry-Perot method, with the same 209 cm cell and ZnSe windows.

  • Both use the same pressure measurement. Its stated limit, 0.4 % (2007, p. 79), is common to every line and to both papers.

  • The 2006 value at 10.57 um, scaled from 23 to 21 degrees C, agrees with the 2007 1P18 line to 0.03 % (the records’ notes).

• Decision: marchetti_2006 is a reproduction check of marchetti_2007, not an independent validator of a fit to it. Both lie outside pure CO2’s qualified intervals (TC-750).

• Status: decided (2026-09-30).

TC-754 Finding: SF6 absorbs inside its declared range (2026-09-30)

• Where: fit/SF6 (230-5000 nm); the HITRAN cross-section of Ref. [1164] (298.1 K, N2-broadened, 0.112 cm^-1).

• Finding: at 1 atm and 296 K the pure gas absorbs, inside the model’s declared range:

  • up to 3.9 m^-1 at 4.49 um (2227 cm^-1; 3.4 m^-1 smoothed over 1 cm^-1);

  • up to 0.64 m^-1 at 3.53 um (3 nu3).

  • Above 3200 cm^-1 the spectrum is at the file’s noise level (zeros, with medians of 0.05-0.1 m^-1 over 1 cm^-1), and no band there is established.

• Decision: none now. SF6’s model is unchanged (OEP 3, Q14): its infrared treatment is deferred to its own proposal, which is to qualify its range. It is on the roadmap’s item The infrared beyond OEP 3.

• Status: open.

TC-755 The collisional widths against the resolution sigma = 1 cm^-1 (2026-09-30)

• Where: tools/hitran/windows.py (collisional); OEP 3, section 4 (“Phase 1 assesses its effect”).

• Method: the reference neglects collisional broadening. The resonant kernel of every line within 200 cm^-1 of a window was replaced by the Voigt kernel. That kernel is the Faddeeva function, with the S-weighted mean self-broadened HWHM times the pressure: CO 0.066, CO2 0.098, CH4 0.075 and N2O 0.097 cm^-1/atm. The change of D_0 and D_2 was compared with the tolerance at each 1 cm^-1 of every window, at 1, 3 and 10 atm.

• Finding:

  • In every window beyond the optical ranges, where the tolerance qualifies the window, the change is at most 0.13 of the tolerance at 1 atm and 0.31 at 3 atm. At 10 atm it is at most 0.58 in the GVD (CO2 2.54-2.59 um) and 0.81 in alpha (N2O 4.81-4.96 um).

  • The resolution therefore stands to a few atmospheres. At 10 atm the model’s own error, up to 0.999 of the tolerance, and the collisional change can together exceed the tolerance.

  • Inside the optical ranges, where the bound is reported only (TC-749), the GVD near weak lines changes by 88 to 3500 times the tolerance at 1 atm. There the resolved structure depends on the pressure, as it does on sigma.

• Decision: sigma = 1 cm^-1 is kept (OEP 3, section 7). The manual is to state that the windows’ qualification assumes a few atmospheres at most (OEP 3, Phase 3).

• Status: decided (2026-09-30).

TC-756 The infrared refractivity of CO, CO2, CH4 and N2O: a literature search (2026-09-30)

• Where: OEP 3, section 5 (“to be sought in Phase 1”); the roadmap.

• Finding: a search of the literature and of the works citing Old, Gentili and Peck (1971), Marchetti and Simili (2006) and Rollefson and Havens (1940) found, besides the CO2-laser values in hand (Marchetti and Simili, Simmons, Willetts and Harris):

  • Rollefson and Havens, Phys. Rev. 57, 710 (1940), CH4 at wavelengths from about 1.7 to 15 um, the one broadband mid-infrared set;

  • H. Matsumoto, Appl. Phys. B 44, 147 (1987), CO2 at 10.6 um (2 % stated);

  • F. Legay, Nuovo Cimento 2, 781 (1955), dispersion across vibration-rotation bands (the gases not stated in the abstract);

  • Tsankova et al., ChemPhysChem (2018), CO’s static polarizability to 52 ppm (k = 2);

  • Mitrofanov et al., Sci. Rep. 7, 2103 (2017), the group delay of air at 3.6-4.2 um, through CO2’s 4.3 um band wing.

  No gas-phase refractivity of CO or N2O between 2 and 12 um was found. The theory the search found (Bishop and Cheung 1982, Hohm 2013, Jhanwar and Meath 1982, Thomas and Meath 1977) and the static measurements (Schmidt and Moldover 2003, Zhao et al. 2026) are curated already.

• Doubt: the entries come from abstracts and bibliographic records; none has been read in full or curated. Rollefson and Havens’s uncertainty and states are not yet known.

• Decision: the five are on the roadmap’s wanted list, to be curated as validators in OEP 3’s Phase 3.

• Update (2026-10-01): all five are curated (TC-802 to TC-806). Tsankova et al.’s 52 ppm (k = 2) is the uncertainty of the permittivity; the polarizability’s is 1.01 % (TC-804). Legay (1955) measured HCl alone (TC-805).

• Status: resolved (2026-10-01).

TC-757 The polarizability’s frequency derivative, and the temperatures as metadata: OEP 1, Phase 2b (2026-09-30)

• Where: Model.dpolarizability_domega (every gas dispersion model); MeasuredAbsorption.complex_derivative_au; lorentz_lorenz.dpolarizability_dsusceptibility; FittedModel.reference_temperature, infrared_temperature, temperature_coefficient; data/gas/temperatures.toml.

• Method (OEP 1, section 4.1):

  • Each class differentiates its own evaluator analytically, in omega. The static limit is 0 with no chain rule through lambda, and NaN for the seven refractiveindex.info form-2 entries, as their value is.

  • A formula is differentiated in 1/lambda and reduced through inverse Lorentz-Lorenz’s Jacobian, d alpha/d chi = 9 eps0 / [N P (chi + 3)^2] with d chi/d(n - 1) = 2n, at its reference density.

  • O3’s measured term is differentiated branch by branch: the spline inside the grid, the differentiated trapezoid sum above it, and the linear interpolant’s slope for the imaginary part (the mean of the two slopes at a knot).

• Checked:

  • Every registry model (106) against a four-point central difference of complex_polarizability in omega: within 1e-5, and converging at fourth order where the difference is above its rounding floor.

  • O3 between its knots, to 1e-7 in both parts; at a knot, the mean slope; above the grid, the real part to 1e-7 and the imaginary part 0.

  • Helium’s retardation term adds 2 c omega.

  • The Jacobian against a difference of polarizability_from_susceptibility, to 1e-7.

• Finding and change (TC-732, OEP 1, section 10):

  • O3’s first derivative, dpolarizability_domega_au and dispersion_au at order 1, now takes the spline’s own derivative, not a gradient of the grid.

  • It moves by at most 4.5e-5 of its maximum within O3’s range (at 265 nm; median 3e-9 of the local term). The largest local change is 4e-4 of the term, in the Hartley band, apart from its zero crossing near 281 nm.

  • The higher orders of dispersion_au stay gradients of the grid, as the roadmap records.

  • OscillatorModel.EVALUATION_VERSION is 2, so every oscillator model’s digest changes. The golden values are unchanged, and the derivatives were added to them.

• The temperatures (OEP 1, section 4.9):

  • A fit’s reference temperature is read from its stored record.

  • The infrared terms’ temperature is 296 K (HITRAN), or 298.1 K for SF6’s cross-section.

  • The measured coefficients of N2 (egan_2023), O2 and CO2 (egan_2026) are all at 632.9908 nm. They are curated in temperatures.toml, and a test checks them against the fits’ temperature options.

  • All three enter the identity; evaluation does not follow them.

• Status: decided (2026-09-30).

TC-758 The equation-of-state object, its inverse and its phase domain: OEP 1, Phase 2c (first part) (2026-09-30)

• Where: optmat.gas.eos: EquationOfState, equation_of_state, pressure, SATURATION_MARGIN, ROUND_TRIP_TOLERANCE; the gas extra now names coolprop>=8.

• Method (OEP 1, section 4.2):

  • CoolProp’s Helmholtz-energy equations are called directly, through their HEOS backend, not through pyfluids, which wraps the same library. Over 218 states of every gas, the compressibility factors of the two are bitwise equal. The golden values of every model, whose formulas reduce through these densities, are unchanged.

  • The phase domain is the gas below its vapour pressure and the supercritical fluid to the equation’s stated pressure, within its temperatures.

    • It ends 1e-5 below the vapour pressure, because CoolProp’s pressure-temperature solve refuses pressures within 1e-6 of it.

  • The inverse starts from the backend’s own (density, temperature) solve, in the equation’s molar density and gas constant. A bracketed Brent solve on the forward law then brings it to a round trip of 1e-12 in N, or raises.

  • The identity names CoolProp’s version, the fluid, its reference key and its gas constant.

• Checked:

  • On every gas’s domain, at 0.01 bar to the domain’s top (below T_c) or 100 bar, and at four temperatures within each equation, the round trip holds to 1e-12 and the pressure to 1e-9.

  • The ideal gas is recovered at 1 Pa to 1e-6.

  • A liquid (SF6 at 294 K and 25 bar; CO2 at 280 K and 50 bar), a supercritical liquid (CO2 at 290 K and 100 bar), the saturated vapour’s density and denser states, states above p_max, and temperatures outside the equation are refused, forward and inverse.

  • The speed of sound of argon at 1 kPa is the ideal gas’s (5 R T / 3 M)^1/2 to 1e-4.

• Change: the forward law now refuses condensed states, which it returned silently before (TC-731, which this resolves). No curated state is affected: the full suite, which reduces every curated dataset, passes unchanged.

• Status: decided (2026-09-30).

TC-759 Named air compositions, the air model and ciddor_1996: OEP 1, Phase 2d (2026-09-30)

• Where:

  • optmat.gas.composition (REDUCED: "dry air (N2, O2, Ar)", "dry air (N2, O2)");

  • optmat.gas.air (AirModel, air_model);

  • optmat.gas.eos.air_equation_of_state (CoolProp’s pseudo-pure Air, lemmon_2000);

  • optmat.gas.raman_response and data/gas/raman_response.toml (the named mixtures);

  • the source record data/sources/ciddor_1996.toml.

• ciddor_1996 (new):

  • The standard dry air of Eqs. (1)-(2), p. 1567, with Appendix A’s constants (p. 1571): k0 = 238.0185, k1 = 5792105, k2 = 57.362 and k3 = 167917 um^-2, and the CO2 factor 1 + 0.534e-6 (x_c - 450). These were read from the page image.

  • Its range is “approximately 300 nm to 1690 nm” (p. 1571), and its stated overall uncertainty 2-5e-8 in n (p. 1568).

  • The formula is recorded, not built as a model, since its medium is air, not a curated species. At 633 nm Eq. (1) gives 10^8 (n_as - 1) = 27653.0.

• The air model:

  • Its polarizability is the mole-fraction sum of the constituents’ recommended models, value and derivative, bound to their digests.

  • Its intervals are their intersection: 195 nm to the static limit for the reduced compositions, and 320-1400 nm for the full one, which N2O and the molecules limit.

  • The full composition is renormalised by its printed sum. Its density comes from the pseudo-pure dry air.

  • Lorentz-Lorenz takes no pair terms, which are OEP 4’s.

• Checked:

  • The full composition against Ciddor’s standard dry air at 15 C, 101325 Pa and 400 umol/mol of CO2: within 1.1e-8 in n from 400 to 1400 nm, and -2.7e-8 at 320 nm, inside Ciddor’s 2-5e-8.

  • The omission of the reduced compositions, 320-1400 nm: N2/O2/Ar is -1.88 to -1.95e-4 of the full composition’s polarizability, and N2/O2 +1.50 to +1.86e-4, as OEP 1, section 4.4, states.

  • The pseudo-pure air against the partial-pressure sum at 294 K: 1.9e-4, 1.76e-3 and 5.98e-3 above it at 1, 10 and 50 bar (OEP 1: 1.9e-4, 1.8e-3, 6.0e-3).

• Finding: solprop’s recipes (0.7808, 0.2095 and 0.0093, renormalised) are not CIPM-2007’s to their rounding, as OEP 1, section 8, expects. CIPM-2007’s O2 fraction, 0.20939, lies 1.1e-4 below solprop’s older 0.2095, beyond four-digit rounding. N2 and Ar agree within 7.3e-5.

• Changes:

  • The Raman response of "dry air" is now that of "dry air (N2, O2, Ar)", with the same fractions and a new identity name, so its digest moved. "dry air (N2, O2)" is added.

  • The full composition is refused, since its CO2 has no broadening coefficients by N2 and O2.

• Status: decided (2026-09-30).

TC-760 D2’s dilute viscosity: Assael et al.’s Table 2, whose printed equations do not reproduce it (2026-09-30)

• Where: the source record data/sources/assael_1987.toml, its dataset table2 (data/values/transport/D2/, tools/extract/assael_1987.py), and data/gas/transport.toml.

• The source (OEP 1, Q14): Assael, Mixafendi and Wakeham, J. Phys. Chem. Ref. Data 16, 189 (1987), the zero-density viscosity of normal deuterium from 30 K to 2200 K. Above 350 K it is the authors’ hydrogen correlation scaled by the square root of the mass ratio (Eq. 3). Below, the same form times a function f(T*) fitted to four primary data sets (Table 1).

• Extraction: four cells of the extracted Table 2 differ from the page. They were checked against a 400 dpi rendering and against their neighbours: the header 1060 is 1080; 280 K is 12.06; 840 K is 25.68; 1200 K is 32.99. The page’s 34.90 at 1300 K is one unit off the smooth run and is kept as printed.

• Finding: Eqs. (1) and (4)-(7) as printed, with sigma = 0.2968 nm and epsilon/k = 33.3 K, miss Table 2 by -12 % at 30 K, +1.3 % at 300 K and -2.9 % at 2200 K. The table is smooth. Above 350 K, where Eq. (3) applies, it lies 0.1-1.1 % below Muzny et al.’s normal hydrogen scaled by (m_D2/m_H2)^(1/2), and 0.04 % above it at 300 K. The authors’ hydrogen correlation (J. Phys. Chem. Ref. Data 15, 1315 (1986)) would show which printed constant is wrong. It is not in hand.

• Decision: optmat serves Table 2 as a cubic spline in log eta against log T, provisional. The spline recovers left-out knots to 7.2e-4 at doubled spacing, and so to about 5e-5 at the table’s own spacing, below its rounding. The stated uncertainty is 1 % at 250-350 K, 2 % below and at most 4 % above.

• Against solprop: solprop’s D2 table evaluates REFPROP’s normal-hydrogen correlation for deuterium. Assael et al.’s values differ from it by -0.41 % at 200 K, +0.01 % at 300 K and +0.69 % at 600 K.

• Status: provisional (2026-09-30), until Assael et al. 1986 is curated; resolved by TC-765 (the printed Eq. 4 is the universal functional; D2 validated); the spline superseded by TC-839 (the correlation is served).

TC-761 SF6’s transport served from CoolProp unchecked (2026-09-30)

• Where: data/gas/transport.toml ([gases.SF6]).

• Finding: solprop’s twelve gases include SF6. CoolProp’s viscosity correlation for it (Quiñones-Cisneros, Huber and Deiters, J. Phys. Chem. Ref. Data 41, 023102 (2012), doi:10.1063/1.3702441) and its equation of state (Guder and Wagner, J. Phys. Chem. Ref. Data 38, 33 (2009), doi:10.1063/1.3037344) are not in the library. The citations are from CoolProp 8.0.0’s bibliography.

• Decision: SF6’s transport model is served from CoolProp, provisional, with no source record and no stated uncertainty, until both papers are curated. The viscosity range is the equation’s, 223.555-625 K.

• Status: provisional (2026-09-30); resolved by TC-765 (both papers curated and reproduced; SF6 validated).

TC-762 The dilute viscosity against one bar: up to 1.7e-3, not a few parts in 1e4 (2026-09-30)

• Where: tests/test_transport.py; OEP 1, section 4.3.

• Finding: OEP 1 says the viscosity at 0.1 MPa differs from the dilute limit by a few parts in 1e4. CoolProp’s correlations at one bar lie above optmat’s dilute values as follows, over solprop’s 200-600 K:

  • He: 5e-5 to 4.9e-4;

  • H2: -1.7e-5 to 2.3e-4;

  • Ar: 1.9e-4 to 1.6e-3;

  • N2: 1.8e-4 to 1.7e-3;

  • O2: 4.1e-4 to 1.6e-3;

  • CH4: 4.7e-4 to 1.2e-3. The largest offsets are at 200 K; at 294 K they are 1.9e-4, 6.5e-5, 7.6e-4, 7.5e-4, 1.1e-3 and 1.1e-3. The WebBook’s tables at 0.1 MPa lie above Huber’s dilute form by 0.028 % (Ne), 0.33 % (Kr), 0.54 % (Xe) and 0.52 % (N2O) at 200 K, and by 0.013 %, 0.13 %, 0.21 % and 0.21 % at 298.15 K.

• Consequence: every offset is below its gas’s stated uncertainty, so OEP 1’s rule stands: a table at 0.1 MPa may serve a dilute value, with its offset stated. The phrase “a few parts in 1e4” understates it below room temperature. The OEP’s Part II report corrects the text.

• Status: decided (2026-09-30).

TC-763 The transport models: sources, forms, ranges and statuses (OEP 1, Phase 2c, second part) (2026-09-30)

• Where:

  • optmat.gas.transport and data/gas/transport.toml;

  • two quantities, dilute_viscosity and ideal_gas_heat_capacity, in the new family transport;

  • sixteen source records: arp_1998, lemmon_2004, muzny_2013, laesecke_2017, quinones_cisneros_2006, huber_2018, assael_1987, harvey_2023, tegeler_1999, lemmon_2006, leachman_2009, richardson_2014, span_2000, schmidt_1985, span_1996 and setzmann_1991;

  • the WebBook tables in data/external/nist_webbook.

• CoolProp’s correlations: He, Ar, H2, N2, O2, CH4 and CO2 take CoolProp’s viscosity at 1e-6 mol/m^3. Each reproduces its paper’s printed dilute form to below 1e-9, with the constants recorded as formulas and tested. CoolProp reports helium’s whole viscosity as its “critical” term, so optmat takes the total at vanishing density, not the “dilute” contribution.

• Deviation (OEP 1, sections 5 and 6.5): Ne, Kr, Xe and N2O take Huber’s dilute Chapman-Enskog form (NISTIR 8209, Eqs. 6-7 times F_c, his Tables 1-2), not the WebBook’s tables at 0.1 MPa. It is the quantity OEP 1 defines, the dilute limit. It covers each equation of state’s temperatures where the tables stop at 200-400 K, and it is what the tables evaluate. It reproduces Huber’s Table 7 check values to 2.4e-7 with REFPROP’s constant 0.026692. Eq. (6) evaluated with CODATA’s k_B gives 1.38e-4 more. The tables are kept as the check.

• Ranges: each correlation’s stated temperatures:

  • He 110-1500 K (Maitland and Smith’s dilute values above 110 K);

  • H2 13.957-1000 K;

  • CH4 95-600 K;

  • CO2 200-2000 K, where Laesecke and Muzny state an uncertainty;

  • Ar, N2 and O2 their equations of state’s, over which Lemmon and Jacobsen’s equations hold;

  • Ne, Kr, Xe and N2O their equations of state’s, within Neufeld’s 0.3 < T* < 100;

  • D2 30-2200 K. The heat capacity takes each equation of state’s temperatures. A temperature outside a range raises StateError.

• Heat capacity (decision): c_p0 is the equation’s c_p0/R times CODATA’s R, the CODATA convention of the number density (TC-758). The noble gases give (5/2) R exactly; CoolProp’s helium equation carries R 1.47e-6 below Harvey et al.’s.

  • O2’s ideal part in CoolProp is Stewart et al.’s (1991, not in hand). Schmidt and Wagner’s agrees with it to within 3e-6 from 60 K to 1000 K.

  • N2O’s is Lemmon and Span’s Eq. (10), reproduced to 2e-16.

  • Neon’s equation (Thol et al., listed as submitted in CoolProp’s bibliography) is not obtainable. Its c_p0 is the monatomic gas’s.

• Molar mass: each equation of state’s, as the papers print it; Leachman et al. print none for H2, which is 2.01588 g/mol in CoolProp and Muzny et al.

• Statuses:

  • validated, with the stated uncertainty in each model, for He, Ne, Ar, Kr, Xe, H2, N2, O2, N2O and CO2. Helium’s stated uncertainty is Arp et al.’s “maximum of +-10 percent” above 100 K, for the correlation as a whole.

  • provisional for D2 (TC-760) and SF6 (TC-761), both since resolved by TC-765, and for CH4: Quiñones-Cisneros and Deiters state no uncertainty for the dilute-gas term, only the fit’s 0.31 % average deviation, and a validated model needs a stated uncertainty.

• Wilke’s rule: mixture_viscosity is Eqs. (13)-(14) of wilke_1950. It reduces to the pure gas, does not depend on the order of the gases, and lies 8-9e-4 below Lemmon and Jacobsen’s pseudo-pure air (CoolProp’s, 1 % in the dilute gas) for “dry air (N2, O2, Ar)” at 250-400 K. CIPM-2007’s full composition is refused, because CO has no transport model.

• Not in hand (asked for):

  • Assael et al. 1986 (hydrogen; TC-760);

  • Quiñones-Cisneros, Huber and Deiters 2012 and Guder and Wagner 2009 (SF6; TC-761);

  • Stewart, Jacobsen and Wagner 1991 (O2’s ideal part);

  • Muzny et al.’s erratum, J. Chem. Eng. Data (2022), doi:10.1021/acs.jced.2c00523.

• Status: decided (2026-09-30).

TC-764 Explicit parameters and overrides: OEP 1, Phase 2a (2026-09-30)

• Where: optmat.identity (Identified.with_parameters, INPUTS, DERIVED, modified, base, describe), with each class’s inputs and rebuild:

  • IonisationRateModel.from_parameters and MolecularRateModel.from_parameters;

  • OscillatorModel.from_parameters, and the inputs of the gas dispersion models;

  • GasRamanResponse.from_lines;

  • FormulaModel.sellmeier and TabulatedModel.from_arrays for the solids, and the fitted UDM’s values;

  • SilicaRamanResponse’s shape and fraction.

• The mechanism: with_parameters(**changes) accepts only a class’s declared inputs and refuses its derived fields by name. It rebuilds through the class’s constructor. The result has the status user, the changes in identity.modified, the curated digest in identity.base, and no stated uncertainty unless the changes give one (a rate’s uncertainty_factor, a fit’s covariance and chi-squared become NaN). modified and base, like the status, are not in the digest, which covers the numbers.

• Through one path: the curated rate, molecular-rate and Raman builders now construct through from_parameters and from_lines. Every golden value and digest is unchanged, which shows that the two paths agree bit for bit. That includes the Raman damping groups and density range, now derived from the lines by one rule for both paths.

• Custom species (OEP 1, section 7.4): the rate models’ and gas dispersion models’ species may be a plain name, the identity’s material. A custom species has no curated virial ratio (0) or equation of state, so its index takes the ideal-gas density, as ozone’s does.

• Deviations from OEP 1, section 6.3:

  • The overrides of a dispersion model name its fields, in atomic units (section 7.5), while OscillatorModel.from_parameters takes SI: strengths, pole energies in J and an offset in C m^2/V, the form of OEP 2.

  • A fitted model’s term count is fixed, except through infrared.

  • MolecularRateModel stores no structure coefficients, so an override not naming them keeps the curated orientation average, passed to from_parameters as structure_factors.

  • The equation-of-state, transport, air, hyperpolarizability, Kerr and measured-absorption models declare no inputs: section 6.3 gives them no rules, and a different one of those is a curated choice.

• The Raman density range needs each band’s strongest line’s Doppler width (Herring et al.’s Eq. 4, TC-688). The response stores only the Dicke caps, so from_lines computes it from the species’ molecular mass: the curated mass_u for a curated species, or a caller’s mass=.

• Status: decided (2026-09-30).

TC-765 Transport follow-up: D2 settled, SF6 checked, O2’s ideal part bounded (2026-09-30)

• Where: new source records assael_1986, quinones_cisneros_2012, guder_2009 and stewart_1991; assael_1987, muzny_2013 and schmidt_1985 updated; data/gas/transport.toml; TransportModel.heat_capacity_range.

• D2 (resolves TC-760):

  • Assael, Mixafendi and Wakeham’s hydrogen correlation (1986) is Eq. (1) with ln Omega* = sum a_i (ln T*)^i, a = 0.354125, -0.427581, 0.149251, -0.037174, 0.003176 (their Eq. 3 and Table 2). Their Eq. (13) is a different, universal corresponding-states functional, which they found to miss hydrogen’s data by up to 6 %.

  • The 1987 D2 paper prints Eq. (13)’s coefficients as its Eq. (4). With Eq. (3)’s instead, the D2 mass and Eq. (7)’s f(T*) applied at every temperature, the D2 Table 2 is reproduced within 1.5 units of its last digit (5.1e-4). The 1987 text says f applies below 350 K, but the table applies it throughout: 1 - f is 2e-3 at 360 K and 1e-4 at 1000 K.

  • The exception is the 90 K cell, 6.5 units off. The scan there is degraded but reads 5.410, where the correlation and the neighbours give 5.416; it is kept as printed.

  • D2 is now validated, with the paper’s stated uncertainty. Its values are unchanged.

• SF6 (resolves TC-761):

  • CoolProp’s viscosity equals Quiñones-Cisneros, Huber and Deiters’s Eq. (6) (Table 2, T_c = 318.7232 K) to 1.4e-10. Their stated uncertainty is 0.3 % (k = 2) at 298-700 K, rising to 1.5 % at the triple point and at 1000 K. The range is now theirs, 223.555-1000 K.

  • The paper’s zero-density check values are 3-4e-5 above Eq. (6) with the printed coefficients.

  • CoolProp’s c_p0 equals Guder and Wagner’s Eq. (15) (Table 21, checked against the image) to 2e-16, with the same M and R. The paper’s uncertified OCR tables (pp. 25, 39-58) are not used.

  • SF6 is now validated.

• O2’s ideal part (finding): CoolProp’s ideal-gas heat capacity for oxygen is a refit of Wagner, Ewers and Schmidt’s equation (Stewart et al. 1991, Eq. 11; the ideal part of Schmidt and Wagner 1985). It agrees within 3.3e-6 from 60 K to 1500 K, then departs: -1.6e-5 at 1600 K, -4.9e-5 at 1700 K, -1.1e-4 at 1800 K and -3.5e-4 (-0.013 J/(mol K)) at 2000 K. From 1800 K that exceeds Eq. (11)’s stated agreement with its data, 0.003 J/(mol K). O2’s heat-capacity range therefore stops at 1700 K (heat_capacity_range_k), below the equation of state’s 2000 K. This is a restriction; no value changes.

• Muzny et al.’s erratum (2022): it corrects Eqs. (6), (7) and (9), the initial-density and residual terms. The dilute-gas Eqs. (3)-(4) that optmat uses are untouched, and the erratum’s zero-density check, 1.9772 uPa s at 40 K, is reproduced.

• Identity: TransportModel gains heat_capacity_range, so every transport digest moved (the golden values are re-recorded). No value changed.

• Status: decided (2026-09-30).

TC-766 The Raman groups, line identifiers and tensor parts: OEP 1, Phase 2e (2026-09-30)

• Where: optmat.gas.raman_response (RamanGroup; GasRamanResponse.groups, line_id, check_densities); the band keys in data/gas/raman.toml; tools/raman_line_ids.py and tests/data/raman_line_ids.json; the manual page’s sections on the groups and the two tensor parts.

• The groups: each group carries its lines, their identifiers, the width law in SI (gamma_c = pi c, gamma_d = pi d N_amg, gamma_D = pi Delta nu_D, gamma_beta = pi beta / N_amg), the shift sigma = 2 pi s / N_amg, and the zero-density frequencies and amplitudes. decay_rate(N) is defined for N >= 0, with the limit of OEP 1, section 4.5 at N = 0, and does not warn. The groups’ responses sum to the response. The only group with a shift is H2’s Q branch.

• The limits at 295 K: zero for every line of N2, O2, dry air, N2O and CO2 and some of D2’s; finite for H2 (152.8 MHz in Gamma/pi at least; OEP 1 says 153), CH4 and SF6. This is as OEP 1, section 4.5, states.

• Band keys (decision): the curated bands’ descriptions (“v = 0 -> 1 (Q branch)”, “the 1388 cm-1 member of the nu1/2nu2 Fermi dyad (unresolved Q branch)”) are long, and one contains “/”. Each vibrational band now has a short curated key (v1, nu1, nu3, fermi_1285, fermi_1388), which is the response’s band and part of line_id, species/band/branch/J. The description stays as the band’s mode.

• Identity: the Raman responses’ band values changed, so their digests moved (golden values re-recorded; no value changed).

• Status: decided (2026-09-30).

TC-767 The channel rates and the energy per event: OEP 1, Phase 2f (2026-09-30)

• Where: IonisationRateModel and MolecularRateModel: channel_rates, energy_loss_rate, energy_per_event, energy_kind; the rates page’s section.

• The channel rates: the atomic model now forms each channel’s term separately (_log_channel_terms). A channel’s rate is its term times the one factor the model applies to the sum (N_eff and the averaging), so the channel rates sum to instantaneous_rate to roundoff. The energy per event, the rate-weighted mean energy, is formed from the terms’ logarithms. The factor cancels in it, and it stays defined where the rates underflow; it is the lowest channel’s energy at zero field.

• Checked: argon at 800 nm gives 15.797 eV at 5e9 V/m and 15.814 eV at 5e10 V/m, as OEP 1, section 4.6, states. The molecular models have one channel, so their energy per event is their ionization_energy.

• Energy kinds: the molecular models state their own (vertical for every default). The atoms’ curated kind is adiabatic (the two coincide for an atom), and not stated for a custom species or an overridden energy.

• Unchanged: every rate; the golden values are unchanged.

• Status: decided (2026-09-30).

TC-768 The silica nonlinear bundles: OEP 1, Phase 2g (2026-10-01)

• Where: optmat.solid.bundle (SilicaNonlinearBundle, silica_bundle, silica_bundles, GainCheck); the tensor default in data/solid/raman/SiO2.toml (tensor = "lin_2006"); the silica page’s section; the n0 = 1 rule in raman_coefficient’s docstring.

• The bundles: default (Hollenbeck and Cantrell, the Kerr fit’s f_R = 0.219, paired), tensor (Lin and Agrawal, their f_R = 0.245; TC-734), and one per silica response. Each holds the Kerr fit’s total n2(lambda) and its shape’s f_R, gives n2, (1 - f_R) n2, f_R n2 and h_R, and binds the Kerr fit’s and the response’s digests.

• The gain checks (Stolen and Ippen, 526.0 nm pump, 330 cm^-1, 1.5e-11 cm/W +- 10 %), computed with each bundle’s total n2 and f_R: default 1.35e-11 cm/W (-9.7 %), tensor 1.38e-11 (-7.9 %), blow_1989 1.46e-11 (-2.5 %). These reproduce OEP 1, section 4.7, and every bundle lies within the measurement’s stated uncertainty.

• Statuses: validated for the default and tensor bundles and for the bundles of their two responses; comparison for Blow and Wood’s.

• Unchanged: every existing model.

• Status: decided (2026-10-01).

TC-769 The solid tables’ rule outside their knots: OEP 1, Phase 2h (2026-10-01)

• Where: TabulatedModel.out_of_range and with_out_of_range; the metals and crystals pages.

• The rule: outside its knots a table holds its end values, with a ModelRangeWarning ("hold", the default, as before). With "raise", a finite wavelength outside the knots raises StateError, while a NaN is not refused. with_out_of_range(mode) switches the rule without changing the status, since the numbers the table returns are the same; it is not an override.

• Identity: the rule is a field, so the four metal tables’ digests moved (golden values re-recorded; no value changed).

• Capability notes (OEP 1, section 6.10): N-BK7’s model is lossless, and its absorption is the curated transmittance. BK7 and N-BK7 are distinct materials. Identity and status on every solid model came with Phase 1 (TC-745).

• Status: decided (2026-10-01).

TC-770 Several qualified intervals per fit, and the representation bound: OEP 3, Phase 2 (2026-10-01)

• Where:

  • optmat.gas.fitting ([model] band_nodes and windows; FitConfig.rotational, intervals_nm, gap_reasons, derived_sha256; the record’s fields);

  • optmat.gas.infrared (qualified_windows, derived_digest);

  • FittedModel (gap_reasons, n_rotational, derived_sha256, representation_bound_au, the gap’s reason in the range warning);

  • the fitting and identity pages.

• band_nodes: the infrared terms become every band system’s derived rule, in place of the band poles up to infrared_max_wavenumber; the two keys are exclusive. band_nodes below the tables’ own node count (8) is refused, since the rules would have to be rederived.

• Term classes: the rotational system is a class of its own (TC-751). It enters refractive observations with the infrared terms and harmonic differences, and is left out of electric observations (static dielectric data, which hold the orientation polarizability or have it removed) and of the moments.

• windows = true: the model’s qualified intervals are the derived windows, in ascending wavelength, with the reason of each gap between two of them. A gap beyond the longest window is not one. The range warning names the gap’s reason.

• The record: a fit that uses either key records band_nodes, windows, intervals_nm, gap_reasons, n_rotational and derived_sha256, the SHA-256 of the four derived tables. The bound’s tables enter the digest through it. A fit that uses neither records nothing new, so every stored fit, its digest and its warnings are unchanged.

• representation_bound_au(omega, order), order 0, 2 or 3, reads the gas’s bound cells. It is NaN outside every qualified interval (with a warning), and raises for a fit that read no derived tables.

• Deviations from OEP 3, section 6:

  • band_nodes is added beside infrared_max_wavenumber rather than replacing it, so the present fits, SF6 and O3 keep theirs.

  • The derivation’s own settings stay in the tables’ provenance rather than in a separate configuration file.

• Tests rewritten: the stored fits’ physicality test runs per interval; the rotational-band test also checks the derived rules’ one rotational system.

• Status: decided (2026-10-01).

TC-771 Achtermann et al. 1993 and Huot and Bose 1991 curated; neon’s, krypton’s and xenon’s B_R compared (OEP 4, Phase 1) (2026-10-01)

• Where: achtermann_1993 (13 datasets: Table II’s “this work” A_R, B_R and C_R of He, Ne, Ar, Kr and Xe at 632.99 nm, 3 sigma); huot_1991 (28 datasets: Table I’s static B_eps and C_eps of the five atoms at 77.4 to 407.6 K, uncertainty level not stated); tools/extract/achtermann_1993.py, tools/extract/huot_1991.py. Both tables were checked against the page images.

• Neon (TC-744): Achtermann et al.’s optical B_R, -0.11(2) cm^6/mol^2 at 303 K, agrees with Huot and Bose’s static B_eps, -0.12(6) at 323 K, and with Garberoglio and Harvey’s ab initio -0.101 at 633 nm. It does not agree with Orcutt and Cole’s static -0.30(10), the present choice. TC-744’s doubt is resolved: the values that were read from Garberoglio and Harvey’s figures are confirmed against the papers.

• Krypton: Achtermann et al.’s 5.96(6) at 303 K against Orcutt and Cole’s static 5.6(3), the present choice, which agrees with it within its uncertainty.

• Xenon: Achtermann et al.’s 28.5(5) at 348 K against Burns et al.’s 25.5(29) at 632.8 nm and 298 K, the present choice; they agree within Burns et al.’s uncertainty, which is six times larger.

• Third coefficients: Achtermann et al.’s C_R of Kr (-275(10) at 303 K) and Xe (-1802(50) at 348 K), “presented for the first time”, now set those gases’ third-term bound in a mixture (TC-773). They do not enter the index.

• Decision: no recommended B_R is changed here. Switching neon (and possibly krypton and xenon) to Achtermann et al. 1993 changes a recommended value. It is prepared on its own branch for the author’s decision.

• Status: open (the choice of B_R); the curation is done.

TC-772 Achtermann et al. 1991’s third and fourth coefficients extracted; the contribution of a static B_R (OEP 4, Phase 1) (2026-10-01)

• Where: achtermann_1991 (16 new datasets: Table II’s C_R, order 3, and SF6’s D_R, order 4, from the rows of the existing B_R); tools/extract/achtermann_1991.py; data/gas/refractivity_virial.toml (C_R pointers for Ar, Kr, Xe, H2, N2, CH4, CO2 and SF6, C_R_bound = 1.0 for He, and contribution for Ne and Kr); optmat.gas.virial (like_term, third_term, pair_rules).

• Quantity: C_R needs no new quantity. refractivity_virial_coefficient with order = 3 already holds C_eps values, so this deviates from OEP 4, section 5, which lists a third-virial quantity as new. The record’s former note that C_R was “a format gap” is removed.

• He: Achtermann et al. give only a bound, -1.0 < C_R < 0.4 cm^9/mol^3 at 323 K (p. 5680), entered as |C_R| <= 1.

• Contribution (OEP 4, section 7.3): a static B_R is taken as an optical term only where its induced part is stated, and the loader refuses one that does not state it. Neon’s and krypton’s static values are those of atoms, which have no orientational part: contribution = "induced".

• Status: decided (2026-10-01).

TC-773 The optics of gas mixtures: law, pair terms and domain (OEP 4, Phase 1) (2026-10-01)

• Where: optmat.gas.mixture (mixture_optics, MixtureOptics, PairTerm); data/gas/refractivity_virial.toml [pairs]; the vocabulary’s unlike_pair_refractivity_virial_coefficient, which has no datasets yet; the page Gas mixtures at finite density; tests/test_mixture.py.

• The law: y = sum_s A_s rho_s + sum_{s,t} B_st rho_s rho_t, inverted once, as OEP 4, section 4.1 states.

  • Like terms are b_s A_s, with the curated b.

  • Unlike terms are the mean of the like terms, each with its own A (section 7.2).

  • refractivity uses each constituent’s real polarizability, susceptibility its complex one.

  • The derivatives are the closed forms of section 4.1.

• Pure limit: for every one of the 15 gases, refractivity equals Model.refractivity within 1e-13 relative, and sqrt(1 + susceptibility) equals Model.refractive_index within 1e-15 relative. The frequency derivative matches the pure law’s chain rule within 1e-13.

• R8 reproduced: for O3 at 255 nm, 1 bar and 294 K, the real convention gives 4.5393908e-4, the complex index 4.5388635e-4 and its imaginary part 5.6189256e-4. Their difference, -5.2724e-8, equals -(Im chi)^2/24 at second order. OEP 4, section 6, calls it “5e-8 of n - 1”; it is an absolute difference, about 1.2e-4 of n - 1.

• Statuses: a mixture is provisional where any term is unknown (a like term without a curated B_R: O2, D2, N2O, CO, O3), else validated, following section 7.2. No unlike term has been checked against a measurement, and the page says so.

• The domain:

  • The bound is the lower of the third-term bound (the largest |C_R/A_R| present) and the pair-term bound (the estimated and unknown terms’ uncertainty at 1e-3 of y). Both are taken as the smallest over 48 geometric wavelengths per qualified interval, plus the static limit.

  • Argon 6961 and N2 6675 mol/m^3, where OEP 4, section 4.3, says about 7000 and 6700.

  • 50/50 He/Ar 2446 mol/m^3, where section 7.2 says about 2700. That figure is at one wavelength; the smallest over the interval is lower.

  • Air 1296 mol/m^3, set by oxygen’s unknown term; a pure gas with an unknown like term 500 mol/m^3.

• Interface: a Gas and its name are one dictionary key (Gas is a string enum), so no mapping can repeat a species. The refusal of a repeated key that OEP 4, section 6, lists is therefore not implemented: the case cannot arise.

• Sensitivity (section 8): the page tabulates n - 1, its sensitivity and the GVD’s for He/Ar, Ne/Ar, He/Ne and air at 10 and 30 bar, 800 nm, and a test recomputes the table. The relative sensitivity of n - 1 is 0.8e-4 to 4.6e-4 for the noble pairs and 2.9e-4 to 8.6e-4 for air.

• Golden values: 8 new records (four mixtures, susceptibility and its frequency derivative); no existing value or digest changed.

• Status: decided (2026-10-01).

TC-774 Finding: the declared scales of OEP 4 against the curated coefficients (2026-10-01)

• Where: data/gas/refractivity_virial.toml [pairs] (unknown_b = 2.0, third_ratio = 600.0).

• unknown_b: OEP 4, section 7.2, sets |b| <= 2 cm^3/mol as “the largest |b| of the curated gases (SF6 and Xe)”. The curated b are SF6 2.005 and Xe 2.462 (Burns et al.’s 25.5/10.36). Xe’s exceeds the scale. Burns et al.’s three other lines give b of 1.4 to 1.8 (TC-178), and Achtermann et al. 1993’s 28.5/10.344 is 2.76 at 348 K.

• third_ratio: section 4.3 sets |C_R| <= 600 B_R^2/A_R from “the largest measured ratio, N2’s 560”. Computed from the curated values, |C_R| A_R / B_R^2 is:

  Gas	Ratio
  H2	1679
  N2	560
  CO2	528
  Ar	117
  He (bound)	113
  SF6	61
  CH4	58
  Kr	55
  Xe	29

  H2’s is the largest, but its B_R is 0.13(8) at 3 sigma, so B_R^2 is not resolved. At its upper value, 0.21, the ratio is about 640.

• Effect: the scale enters only neon’s third-term bound (4295 mol/m^3 with 600) and the unknown like terms’ uncertainty and pair bound. No index value depends on either.

• Decision: the scales are kept as OEP 4 decided them. Whether to raise unknown_b to 2.5 (the rule as worded) and to state H2’s exclusion is for the author.

• Status: open.

TC-775 The search for unlike-pair refractivity coefficients and for oxygen’s B_R (OEP 4, Phase 1) (2026-10-01)

• Searched: the library and the web, for measured or ab initio unlike-pair refractivity or dielectric virial coefficients of He-Ar, Ne-Ar, He-Ne and N2-O2, and for a measured B_R of O2.

• Unlike pairs: none found for these pairs.

  • Garberoglio and Harvey’s path-integral calculation (garberoglio_2020) and Garberoglio et al.’s review (garberoglio_2023) give like pairs only.

  • Bose and Cole’s CO2-Ar B_eps,12 assumes its induced part, so it is not an optical coefficient (OEP 4, section 7.3).

  • Egan et al. (egan_2026, section 5) state that nothing appears known about the refractivity cross virial of N2-O2.

  • The unlike-pair quantity therefore has no datasets.

• Oxygen: Egan et al. give b_R(sigma, T) = (0.194 + 0.00641 sigma^2)[1 + 1.4e-3 (T/K - 303)] cm^3/mol. Its static part is Hohm’s heuristic estimate, with 50 % assumed uncertainty; their two-colour data indicate that Hohm’s dispersion term is 50 % too small. It is a candidate for O2’s like term, about 0.2 cm^3/mol against the declared scale of 2. Adopting it would make O2’s mixtures estimate rather than unknown, and raise air’s optical bound from 1296 mol/m^3 to about 6650: the pair bound would be about 13600, and the third-term bound becomes the lower, about 6650 for O2 at the declared scale and 6675 for N2 (estimated by hand from the rules, not from the code). It is also a change to a recommended value (the O2 index at finite density), so it is left for the author’s decision with neon’s (TC-771).

• Also found, for Phase 2: Egan et al.’s N2-O2 cross second density virial coefficient (in egan_2026, not extracted), and “Recommended second virial coefficients for nitrogen and oxygen” (arXiv:2607.24634, not in the library).

• Status: done for Phase 1; open for the choice of O2’s like term.

TC-778 The acceptance rule for the mixture equations of state, fixed before the comparison (OEP 4, Phase 2) (2026-10-01)

• Why now: OEP 4, section 7.4, requires the rule to be fixed before the multi-fluid models are compared with the measured data. This entry is written before any measured cross virial or mixture density has been compared, and before the curated data of the comparison are in the repository.

• Points compared: every curated measured value of the pair between 250 and 350 K:

  • each cross second virial coefficient B_12;

  • each excess second virial coefficient E;

  • each mixture’s second virial coefficient;

  • each mixture compressibility factor or density, at total densities up to the mixture’s optical-domain bound at its composition (MixtureOptics.density_bound).

  Smoothed, correlated or combining-rule values (use = "check") are reported, not counted.

• Model values:

  • Z (or the density) of the multi-fluid model, at the measured pressure, temperature and composition.

  • For a cross coefficient, its effective B_12 = [B_mix(x) - x^2 B_11 - (1 - x)^2 B_22] / [2x(1 - x)]: at the measured composition where one is stated, else at x = 1/2. The spread over x from 0.1 to 0.9 is reported, since the effective coefficient of a multi-fluid model depends on composition (TC-743).

  • For an excess coefficient, the model’s B_12^eff - (B_11 + B_22)/2, with its own pure fluids. Where a source measures E and prints a B_12 derived from it with literature pure-gas values, the E is counted and the B_12 only reported, so that the old pure values do not enter the comparison.

• Combined uncertainty:

  • Start from the measurement’s standard uncertainty, read from its stated level. A value whose level is not stated is read as a standard uncertainty, as the package reads it everywhere.

  • For densities and Z, add in quadrature the model’s own stated density uncertainty where its paper states one: Gernert’s N2-O2 0.1 %, N2-Ar 0.5 % and O2-Ar 1.0 % (gernert_2013), each read as a standard uncertainty. Tkaczuk et al. state none (tkaczuk_2020), so none is added for the noble pairs.

  • The pure fluids’ second virials enter the effective B_12. Their uncertainty is not stated by CoolProp and is not added.

• Pass: a point passes where |model - measured| <= 2 u_c. A point without a stated uncertainty is compared and reported, and not counted.

• Qualification: a pair qualifies when two conditions hold. First, at least 95 % of its counted points pass, in each kind (virial coefficients; densities and Z) that has counted points. Second, it has at least three counted points in all. A pair that fails is reported with its deviations, and its mixtures fall back (section 7.4).

• The fallback’s cross virial: each pair’s cross_virial is the measured B_12 set with stated uncertainties that has the most points in 250-350 K, ties going to the smaller median uncertainty. Outside its measured temperatures the virial method refuses the state.

• Default method per mixture: multi-fluid where every pair qualifies; else virial where every pair has a cross virial; else partial-density, provisional (section 7.4).

• Amended (2026-10-01), still before the comparison: the excess coefficients and the reading of an unstated level were added, once the first curated record (brewer_1969) showed that its measurement is E.

• Status: decided (2026-10-01), before the comparison.

TC-779 The mixture equations of state against the measured data: results, defaults and statuses (OEP 4, Phase 2) (2026-10-01)

• Where: optmat.gas.mixture_validation (comparisons, pair_results, fallback_comparisons, fallback_results, effective_cross_virial); data/gas/mixture_pairs.toml; tests/test_mixture_validation.py, which keeps the records in step with the comparison.

• The multi-fluid models, under TC-778’s rule: no required pair qualifies.

  Pair	Model	Result
  He-Ar	Tkaczuk-JPCRD-2020	E about 10 cm^3/mol below the measured (9.3 against Brewer and Vaughn’s 20.1 and Martin et al.’s 20.4 at 298-300 K). Kalfoglou and Miller’s B_12, 18.77 at 303 K, against 7.5. Blancett et al.’s Z 5e-4 to 1e-2 above it. 0 of 15 virial and 0 of 103 density points pass.
  Ne-Ar	Tkaczuk-JPCRD-2020	E 3.4 against 13.0 at 298 K; 0 of 3 virial and 1 of 10 density points (Kestin et al.) pass.
  He-Ne	Tkaczuk-JPCRD-2020	E -2.6 against 0.76; Vogl and Hall’s Z 2.2e-3 above it at 36 bar (sigma 1.7e-4). 0 of 5 virial and 0 of 36 density points pass.
  N2-O2	Gernert-Thesis-2013	E -0.34 against Martin et al.’s -1.0(2); 0 of 3 pass.
  Ar-N2	Gernert-Thesis-2013	E -0.16 against -0.57(10) (Brewer and Vaughn) and -0.6(2) (Martin et al.); 0 of 6 pass.
  Ar-O2	Gernert-Thesis-2013	3 of 4 pass (Martin et al.’s 290 K value by 0.42 against 2 x 0.2).
  Ar-CH4, CH4-CO2, CH4-N2	Kunz-JCED-2012	Martin et al.’s E, 3 of 3 each: qualified, and curated in mixture_pairs.toml.

  The effective cross coefficient of a multi-fluid model depends on composition: He-Ar’s runs from +16.0 (x_Ar = 0.1) to -4.2 cm^3/mol (0.9) at 298 K (TC-743). In the noble pairs the departure function sets the gap: with it switched off, He-Ar’s B_mix(1/2) moves from 2.77 to 8.87 cm^3/mol, against the 8.13 Brewer and Vaughn’s B_12 implies.

• CoolProp reproduces the published models: Tkaczuk et al.’s Table 8 check values (p at 200 K and 10 mol/dm^3, equimolar) agree within 3.4e-7 for He-Ne and 2.7e-6 below for both argon pairs; the cause of that common offset is not established. CoolProp’s He-Ne and He-Ar parameters are Table 6’s with the component order swapped (beta inverted), and its Ne-Ar parameters are Table 6’s directly. So the gap is the models’: Tkaczuk et al. compared the second virials and did not fit them (tkaczuk_2020).

• Amended after the comparison: the fallback’s cross_virial may name a measured excess E. B_12 is then built as E + (B_11 + B_22)/2 with the reference equations’ pure B, the sources’ own relation (Brewer and Vaughn’s Eq. 12) with modern pure values. Without the amendment, TC-778’s selection would leave He-Ar with Kalfoglou and Miller’s single point in range, and the other pairs with none: the measured B_12 sets are either derived from E with 1929 pure values and state no uncertainty (Brewer and Vaughn, Martin et al.), or lie above 350 K (Vatter et al.). The choices are the E sets of Brewer and Vaughn (He-Ar, Ne-Ar, He-Ne, Ar-N2: sigma 0.1) and of Martin et al. (N2-O2, Ar-O2: sigma 0.2, 290-320 K).

• The fallback against the densities: the same rule as TC-778, applied within the fallback’s truncation bound and measured temperatures. This can only demote a default to provisional, never qualify a multi-fluid model.

  • He-Ne: Vogl and Hall’s Z, 35 of 36 pass: qualified.

  • He-Ar: Blancett et al.’s Z, 16 of 78 pass. The fallback lies up to 7.0e-4 below at 273 K and 28 bar (sigma 4e-5): Brewer and Vaughn’s B_12 is 0.5 cm^3/mol below Blancett et al.’s own at 273 K, and the unlike third virials are left out. It is five to ten times closer than the multi-fluid model.

  • Ne-Ar: Kestin et al.’s densities, 7 of 8 pass (worst 3.2 sigma at 0.1 %).

  • Air’s pairs: no density data. Dry air’s fallback agrees with CIPM-2007’s Z within 1.8e-6 over 600-1100 hPa and 17-27 C, against u(Z) = 1.5e-5. The multi-fluid N2/O2/Ar agrees within 8.6e-6, and the pseudo-pure air within 2.1e-5; the reduced composition’s missing CO2 accounts for about 1.4e-6. The CIPM comparison is evidence for the mixture, not a counted comparison of a pair.

• Defaults, by TC-778’s order: He/Ne virial (validated); He/Ar and Ne/Ar virial (provisional); dry air virial (provisional, 290-320 K); the three Kunz pairs multi-fluid (validated); others partial-density (provisional).

• At 10 bar and 294 K:

  • The default He/Ar density is 2.1e-3 below the multi-fluid model’s.

  • Dry air’s default is 1.8e-4 above the multi-fluid N2/O2/Ar.

  • The multi-fluid N2/O2/Ar is 2.0e-4 below the pseudo-pure air, as OEP 4, section 7.4, states.

• For the author (OEP 4, Q19):

  • Whether to accept these defaults.

  • Whether air’s range should stay limited to Martin et al.’s 290-320 K, or take the multi-fluid model outside it.

  • Whether to seek a complete copy of Blancett et al. (TC-784) and more Ne-Ar and air-pair density data.

• Status: decided (2026-10-01) under TC-778; the defaults are open for the author.

TC-780 Brewer and Vaughn 1969 curated (OEP 4, Phase 2) (2026-10-01)

• Where: brewer_1969 (20 datasets), tools/extract/brewer_1969.py; J. Chem. Phys. 50, 2960 (1969), Table IV, p. 2966.

• Transcribed: the excess E and interaction B_12 second virial coefficients (cm^3/mol) of ten pairs (Ar-H2, Ar-He, Ar-N2, Ar-Ne, H2-He, H2-N2, H2-Ne, He-N2, He-Ne, N2-Ne) at -125 to 50 C in 25 C steps, 8 values each.

  • E carries 0.1 cm^3/mol, level not stated: the stated precision (“reproduced usually within 0.1 cc/mole”, p. 2960).

  • B_12 states no uncertainty: it is E plus the literature pure values of Table I (Otto 1929; Michels for Ar), so a fit or comparison uses one or the other (TC-778 counts E).

  • Table I and II’s literature values, Table III’s runs, the figures and the E = alpha T^beta correlation are not extracted.

• Checked:

  • All 160 numbers and 80 labels of Table IV against the table image, and Tables I and III against theirs.

  • Eq. 12, from the printed E and Table I, reproduces all 80 B_12 within 0.005 cm^3/mol; the script checks this on every run.

  • Table III’s averages equal Table IV at -125 C.

• Corrected: the 25 C row printed “H2-Ne” (E 2.83, B_12 16.01) is H2-He, for four reasons:

  • Ne-H2 has its own 25 C row.

  • H2-He would otherwise lack a 25 C row.

  • 2.83 lies on the H2-He run of E.

  • Eq. 12 gives 16.015 with He’s pure value against 15.92 with Ne’s.

  The script files the row under H2-He and keeps the printed label.

• Doubt: gas purity is not stated; the pure values behind B_12 date from 1929. Ar-N2’s E is small and negative without a trend, as the paper notes.

• Status: corrected (2026-10-01).

TC-781 Martin et al. 1982 curated; Bose and Cole’s pressure virials added (OEP 4, Phase 2) (2026-10-01)

• Where: martin_1982 (44 datasets), tools/extract/martin_1982.py; bose_1970 (8 datasets added), tools/extract/bose_1970.py extended (the existing datasets rewrite byte for byte).

• Martin et al.: Aust. J. Chem. 35, 1525 (1982), Tables 1-3, p. 1526.

  • Transcribed:

    • E of 17 pairs at 290, 300 and 320 K (nominal): primary, +-0.2 cm^3/mol, “approximately” (p. 1528), level not stated.

    • Their B_12, which is E plus Dymond and Smith’s pure B: check.

    • The Ar-N2 runs of Table 2: check.

    • Table 1’s pure B, reproduced from Dymond and Smith 1980.

    • The CF4 pairs are skipped (CF4 is not an optmat gas).

  • Checked:

    • Every grid against its table image. The library attaches Tables 2 and 3 to the wrong captions; the page image settles which is which.

    • B_12 = E + (B_11 + B_22)/2 reproduces all 51 cells within 0.10.

    • Eq. 3 reproduces Table 2’s six Ar-N2 E to the printed rounding.

  • Doubt: CH4-CF4 at 300 K is internally inconsistent (skipped). He-N2 differs from Brewer and Vaughn by 0.7-0.9, which the authors call beyond their error.

• Bose and Cole: J. Chem. Phys. 52, 140 (1970), Tables III and IV.

  • Transcribed:

    • B_p of Ar (-15.8(10)) and CO2 (-109.3(44)) at 49.7 C.

    • Five CO2-Ar mixtures’ B_p, filed under Ar with x_Ar = 1 - X(CO2), one at 47.7 C.

    • B_p,12 = -30.1 at 49.7 C, as a check without a stated uncertainty.

  • Checked: the tables and text against the page images. The authors’ alternative -38.0 reproduces as -37.9.

  • Doubts:

    • A refit of Table III gives -32.3, not -30.1, within the stated 2-3 cm^3/mol.

    • Table III prints X = 0.217 where Table I gives 0.2196.

    • Their dielectric cross term B_eps,12 is defined without the factor 2 of the usual sum over x_s x_t B_st. Their 14.3 is therefore twice the coefficient of OEP 4’s convention, which matters if it is ever curated as an unlike-pair term (it is not an optical one, OEP 4, section 7.3).

• Status: verified (2026-10-01); the B_p,12 refit is open.

TC-782 Vatter et al. 1996 curated (OEP 4, Phase 2) (2026-10-01)

• Where: vatter_1996 (9 datasets), tools/extract/vatter_1996.py; Ber. Bunsenges. Phys. Chem. 100, 73 (1996), Table 1, p. 75.

• Transcribed: B_12 of Ar-N2, Ar-O2, Ar-CO, Ne-N2, Ne-O2 and Ne-CO, and pure CO’s B, at 296.15-463.15 K, with the printed errors (level not stated: “estimated”, later “error bounds”). Two 296.15 K cells with table notes (Ewing and Trusler for Ar-N2, Michels et al. for CO) are reproduced datasets. B_12 rests on measured mixture-minus-reference differences with literature pure B’s, which the notes list. There is no N2-O2 pair.

• Checked:

  • Every cell and both notes of Table 1 against the image.

  • Table 4’s Boyle temperatures of the argon pairs reproduced from Table 1 (403.4, 363.1, 368.4 K against 404, 365, 368).

  • Table 3’s combining rules reproduced, except Ne-O2’s v_c12 (58.0 computed, 56.5 printed).

• Doubt: Table 2 repeats two of this work’s values differently (Ar-N2 at 353 K -1.5 against -1.4; Ne-N2 at 463 K 20.0 against 20.2), within the errors; Table 1 is kept.

• Status: verified (2026-10-01).

TC-783 Vogl and Hall 1972 and Kalfoglou and Miller 1967 curated (OEP 4, Phase 2) (2026-10-01)

• Where: vogl_1972, kalfoglou_1967 and their scripts.

• Vogl and Hall: Physica 59, 529 (1972).

  • Transcribed:

    • Z of the 49.4 % He-Ne mixture at 40, 0 and -40 C against pressure (two Burnett runs each, per-point sigma_z, 1 sigma).

    • The mixture’s B (primary).

    • Pure He’s and Ne’s B and B_12 (checks: B_12 is derived from them).

  • Checked:

    • Every mixture cell of Table I and Tables II and III against the images.

    • B_mix reproduced from the printed Z within 0.01 cm^3/mol, and B_12 by Eq. 2 within 0.03.

  • Doubt: their neon B is 4 % above the reference equation at 40 and 0 C, as they say themselves, and it enters their B_12.

• Kalfoglou and Miller: J. Phys. Chem. 71, 1256 (1967).

  • Transcribed: Table II’s He-Ar B_12 at 30-500 C, with probable errors.

  • Not transcribed: Table I’s B_mix and C_mix in atm^-1, because the vocabulary has no 1/atm unit.

  • Checked:

    • Table II’s cc/mole column equals its atm^-1 column times RT.

    • B_12 reproduced from Table I by Eq. 4 within the last digit.

  • Doubt: the “probable errors” match the fits’ standard errors, so the stored uncertainty may be 1.48 times too large. The pure He and Ar B lie up to 0.8 cm^3/mol below the reference equations.

• Status: verified (2026-10-01); Kalfoglou and Miller’s level is open.

TC-784 Blancett et al. 1970 and Kestin et al. 1981 curated (OEP 4, Phase 2) (2026-10-01)

• Where: blancett_1970, kestin_1981 and their scripts.

• Blancett et al.: Physica 47, 75 (1970).

  • Transcribed:

    • Z of four He-Ar mixtures (x_Ar 0.2000-0.7801) at 323.15, 273.15 and 223.15 K up to 150 atm, both runs, with sigma (1 sigma): 198 values.

    • The mixtures’ and pure gases’ B.

  • Checked:

    • Every cell against the images.

    • Every Z reproduced from Table II’s virial series within 1e-5. This also identifies the three pages whose composition labels the scan clips.

  • Doubt:

    • The library’s scan clips pp. 82-88: the B_HeAr row is unreadable, and some low-pressure and top rows are probably missing. A complete copy is needed.

    • Table I’s Z are fitted-series values, correlated within an isotherm. A printed sigma of 0 means below 0.5e-5.

• Kestin et al.: Physica A 106, 415 (1981), a viscosity paper with equation-of-state data.

  • Transcribed:

    • Table III’s measured Ne-Ar densities at x_Ar = 0.2727 and 0.7722 at 25 C (0.1 %, level not stated), with their Z as checks.

    • E_Ne-Ar = 12.95 (text, no uncertainty).

    • Tables IIA and IIB’s mixture B as checks.

  • Checked:

    • Every cell against the images.

    • Z = P/(rho R T) reproduced except one row (x_Ar = 0.7722, 0.7032 MPa, whose P and rho disagree with its printed Z); that row is excluded, since the misprinted number cannot be identified.

    • E refitted to Table III gives 12.99.

• Status: verified (2026-10-01); Blancett et al.’s missing rows and the excluded Kestin row are open.

TC-785 The mixture equation of state (OEP 4, Phase 2) (2026-10-01)

• Where: optmat.gas.mixture_eos (mixture_equation_of_state, MixtureEquationOfState, PairDensity, METHODS, TRUNCATION_BOUND); data/gas/mixture_pairs.toml; the vocabulary’s thermodynamic family (second_virial_coefficient, cross_second_virial_coefficient, excess_second_virial_coefficient, mixture_second_virial_coefficient, mixture_compressibility_factor, mixture_density), the pressure units kPa, MPa and psia, and the density units mol/m3, mol/cm3 and mol/L; tests/test_mixture_eos.py.

• Methods:

  • multi-fluid is CoolProp’s HEOS mixture. Its forward law takes the PT flash and checks for a single gas phase; its inverse refines the (rho, T) pressure on the forward law.

  • virial and partial-density are section 4.2’s sum, each constituent’s pressure at its partial density in the CODATA convention, explicit in density, with a one-dimensional root for the density at a pressure.

  • Both preserve the composition exactly and round-trip pressure to density to pressure within 1e-12.

• Pure limit: at x = 1 the multi-fluid method equals the pure equation within 1e-13, and the fallback within 1e-10 (the fallback’s direct (rho, T) evaluation against the pure inverse’s solve).

• The pair records: loaded with each curated model key checked against CoolProp’s. A placeholder pair (all reducing parameters one and no departure function) counts as unfitted, and a pair CoolProp lacks (Ar-Xe) refuses the multi-fluid method by name.

• Deviations from OEP 4, section 6:

  • The function lives in optmat.gas.mixture_eos, not optmat.gas.mixture.

  • It returns a MixtureEquationOfState, not OEP 1’s EquationOfState: the class has the same method names, plus partial_densities, method and qualified.

  • Its status uses the package’s vocabulary (validated or provisional), with qualified as a field, in place of a “qualified” status.

  • The fallback’s range is the constituents’ temperatures intersected with its cross coefficients’ measured ones.

• Status: decided (2026-10-01).

TC-786 The helium-argon example and the combined sensitivity (OEP 4, Phase 3) (2026-10-01)

• Where: the gallery example docs/gallery/accuracy/plot_mixture_he_ar.py; the section How much each piece matters of Gas mixtures at finite density; tests/test_mixture.py recomputes its table.

• What it shows: a 50/50 He/Ar fill at 294 K and 800 nm, against the full law: the default equation of state’s densities and the mixture optics. Each change is relative, in n - 1 / in the GVD:

  Left out or replaced	10 bar	30 bar	60 bar
  The local field (the dilute law)	-1.1e-3 / -2.1e-3	-3.3e-3 / -6.2e-3	-6.5e-3 / -1.2e-2
  The pair terms	-1.5e-4 / -1.6e-4	-4.4e-4 / -4.8e-4	-8.6e-4 / -9.4e-4
  The mixture’s equation of state, by the partial-pressure density	+6.0e-3 / +6.3e-3	+1.8e-2 / +1.9e-2	+3.6e-2 / +3.8e-2
  The default density, by the multi-fluid model’s	+2.1e-3	+5.7e-3	+9.1e-3

  The unlike-pair estimate’s declared uncertainty is +-1.5e-4 at 10 bar and +-9.0e-4 at 60 bar.

• Finding: the density, not the optics, limits a helium-argon fill. The two density methods differ by ten times the optics’ pair terms, and neither meets Blancett et al.’s data (TC-779).

• Status: decided (2026-10-01).

TC-787 The solprop parity fixtures at one commit; the transport and density baselines (OEP 1, Phase 3) (2026-10-01)

• Where: every tests/data/solprop_*.json, re-recorded at solprop main d57741490dbc; the new solprop_transport.json and solprop_eos.json (tools/solprop_transport.py, tools/solprop_eos.py); tests/test_solprop_baseline.py; the page Transport of the dilute gases.

• Re-recorded: the seven existing fixtures, with each tool run in solprop’s own environment, reading it only. Their values are unchanged against the five commits they recorded before (8aaee858, 9d81dff5, b871f18c, 2dc84d00, c099545c); only the commit moves.

• Transport baseline: for solprop’s twelve gases over its ranges:

  • The molar masses agree exactly.

  • solprop’s heat-capacity ratio (CoolProp’s at 1e-3 bar) is within 2.9e-5 of optmat’s ideal-gas value (Xe).

  • The viscosities differ by up to:

    • 6.8e-3 for D2 at 600 K (REFPROP’s hydrogen correlation for deuterium, TC-760);

    • 5.4e-3 for Xe and 5.2e-3 for N2O at 200 K, and 4.7e-3 for SF6 at 225 K (the WebBook tables and CoolProp at one bar against the dilute forms);

    • 1.7e-3 or less for the rest.

  The page tabulates them, and a test recomputes the table.

• Correction: the page gave Assael et al.’s D2 viscosity as -0.41 % at 200 K to +0.69 % at 600 K against solprop’s table. Against solprop’s recorded values the signs are the reverse: +0.41 % at 200 K, -0.68 % at 600 K. The page is corrected; TC-760’s values are unaffected.

• Density baseline: at 0.1, 1, 10 and 30 bar and 273.15 and 294 K, solprop’s densities and optmat’s differ by the equations’ gas constant alone: R_eos / R_CODATA - 1, 5.7e-6 for Ar, N2 and CH4, 1.47e-5 for O2, and within 3e-10 of it for every gas.

• Finding for solprop: at 30 bar SF6 is condensed at both temperatures (its vapour pressure is 12.5 bar at 273 K). solprop returns a liquid’s density, 8 times the ideal gas’s; optmat refuses the state (OEP 1, section 4.2). solprop SEP 3’s changed-results report should name it.

• To repeat: OEP 3’s refits change CO, CO2, CH4 and N2O. The fixtures holding them (solprop_sellmeier.json, solprop_gamma3.json) are compared against the refitted models when the refits land, and re-recorded if solprop has moved.

• Status: decided (2026-10-01).

TC-788 The page for propagation codes (OEP 1, Phase 4) (2026-10-01)

• Where: docs/propagation.md, Using optmat from a propagation code, in the getting-started section; its snippets run in tests/test_docs_snippets.py.

• What it covers (OEP 1, section 9):

  • the surface, as a table of what a code calls;

  • the units: SI, vacuum wavelength, per particle, the state and its real-gas density;

  • which third-order helper follows solprop’s convention (gamma3) and which do not;

  • what to store: the identity, the digest and the version;

  • the status;

  • the qualified intervals and the range, absorption and phase refusals;

  • the Raman groups, line identifiers and zero-density decay;

  • the rates’ channels and energy per event;

  • the silica bundle;

  • overrides;

  • transport and mixtures.

  It links the pages that hold the detail rather than repeating them.

• Status: decided (2026-10-01).

TC-789 The release test, and the sdist’s contents (OEP 1, Phase 5) (2026-10-01)

• Where: tests/test_clean_install.py (marker release, lane poe test-release, left out of the default lane); pyproject.toml ([tool.hatch.build.targets.sdist]).

• The test (OEP 1, section 6.12):

  • It builds the wheel and the sdist from the checkout.

  • It installs each with the gas extra into a fresh environment, offline (from uv’s cache), away from the source tree and without PAPER_LIBRARY.

  • In that environment it runs the quickstart’s and the propagation page’s snippets, and resolves every name of the public-surface snapshot.

  • It checks that the wheel ships every tracked data file, and that the sdist holds the tracked tree and none of the local state.

  It passes for both artifacts (about 2 minutes).

• Finding, fixed: the first build’s sdist was 265 MB and held 95,860 files under .claude/worktrees/, agents’ worktrees with their docs builds. hatchling reads only the repository’s .gitignore, and .claude/ is ignored by a global ignore file, so hatchling did not exclude it. The sdist target now excludes /.claude and /.codex, and the test guards it.

• The tag is left to the author (OEP 1, section 12).

• Status: decided (2026-10-01).

TC-792 Decision: neon’s B_R from Achtermann et al. 1993 (OEP 4, Q18) (2026-10-01)

• Where: data/gas/refractivity_virial.toml [Ne]: achtermann_1993/B_R_this_work_303_Ne and A_R_this_work_Ne, in place of orcutt_1967/B_this_work_Ne and A_this_work_Ne; fit/Ne refitted.

• Why: TC-744 and TC-771. Achtermann et al.’s optical -0.11(2) cm^6/mol^2 at 632.99 nm and 303 K (3 sigma) agrees with three values: Huot and Bose’s static -0.12(6), Garberoglio and Harvey’s ab initio -0.101 at 633 nm, and Burns et al.’s -0.14(14). Orcutt and Cole’s static -0.30(10) is about two of its standard uncertainties from them. The value is optical, so no contribution need be stated.

• Effect:

  • Neon’s b = B_R/A_R goes from -0.301 to -0.110 cm^3/mol.

  • At a given state, n - 1 rises by 7.9e-6 (relative) at 1 atm and 294 K, and 7.5e-4 at 100 bar (TC-744 estimated 8e-6 and 8e-4).

  • The refit’s polarizability moves by at most 1.7e-8 relative (200 nm), since the fit rests on the ab initio moments and the dielectric-constant data.

  • Reduced chi^2 goes from 2.627 to 2.625; sigma at 800 nm from 8.7 to 8.6 ppm.

  • Neon’s formula models reduce their n through the new b. Their polarizabilities change, as do their digests, the CIPM-2007 air’s, and the neon mixtures’.

  • The neon third-term scale, 600 B_R^2/A_R, falls with B_R^2. The pure-neon bound rises from 4295 to 11750 mol/m^3, and He/Ne’s sensitivity falls to 3.0e-5 at 10 bar.

• Status: decided (2026-10-01): accepted by the author (OEP 4, Q18).

TC-793 Decision: krypton’s B_R from Achtermann et al. 1993 (OEP 4, Q18) (2026-10-01)

• Where: data/gas/refractivity_virial.toml [Kr]: achtermann_1993/B_R_this_work_303_Kr and A_R_this_work_Kr, in place of orcutt_1967/B_this_work_Kr and A_this_work_Kr; fit/Kr refitted.

• Why: an optical value, five times more precise than the static one it replaces, and from the same fit as the C_R that krypton’s mixture domain already uses (TC-772). Orcutt and Cole’s 5.6(3) at 322 K agrees with 5.96(6) at 303 K, as does Burns et al.’s 6.23(155).

• Effect:

  • Krypton’s b goes from 0.894 to 0.929 cm^3/mol.

  • At a given state, n - 1 rises by 1.35e-6 at 1 atm and 294 K, and 1.85e-4 at 100 bar.

  • The refit’s polarizability moves by -1.2e-7 at 800 nm (-1.4e-6 at 200 nm), within its 78 ppm.

  • Reduced chi^2 goes from 1.2254 to 1.2264.

  • Krypton’s formula models change through the new b.

• Xenon keeps Burns et al.’s value (the author’s decision, 2026-10-01). Achtermann et al.’s 28.5(5) is at 348 K, Burns et al.’s 25.5(29) at 298 K, and the temperature dependence of B_R is not modelled.

• Status: decided (2026-10-01): accepted by the author (OEP 4, Q18).

TC-794 Decision: O2’s refractivity virial from Egan et al.’s published estimate (OEP 4, Q18) (2026-10-01)

• Where: data/gas/refractivity_virial.toml [O2] (b_formula = "egan_2026/o2_b_R", at 632.99 nm and 303 K, relative_uncertainty = 0.5, status = "provisional"); optmat.gas.virial (a gas’s b from a published formula; the like-term status provisional); optmat.gas.mixture (a provisional like term is known for the pair estimate, enters the sensitivity with its uncertainty, and makes its mixtures provisional); fit/O2 refitted.

• Source checked: Egan et al. 2026, p. 8, against the paper’s text layer:

  • The formula, b_R / (cm^3/mol) = (0.194 + 0.00641 sigma^2)[1 + 1.4e-3 (T/K - 303)].

  • “With an assumption of 50 % uncertainty.”

  • “The recommendation is tied to Hohm’s b_eps estimate, but the sigma^2 and T dependencies are derived from this work.”

  • It matches the record’s formula o2_b_R, whose check said “Not checked”; that check now cites this entry.

• The value: 0.2100(1050) cm^3/mol at 632.99 nm and 303 K (sigma = 1/0.63299 um^-1). It is the estimate’s optical value at the other gases’ wavelength, as they are used.

• Why (the author’s decision, 2026-10-01): a published estimate with a stated uncertainty is more than the unknown term’s b = 0 +- 2. O2 had no measured B_R (TC-775).

• Effect:

  • O2’s n - 1 at a state rises by 8.7e-6 at 1 atm and 294 K, and 9.1e-4 at 100 bar.

  • The refit’s polarizability moves by -1.2e-5 at 200 nm and under 3e-7 above 400 nm. Reduced chi^2 goes from 0.232 to 0.233.

  • The air models’ polarizabilities, through fit/O2.

  • Air’s optical domain goes from 1300 to 6150 mol/m^3, now set by O2’s third term at the declared scale. Air’s sensitivity in n - 1 goes from 2.9e-4 to 3.2e-5 of n - 1 at 10 bar.

  • O2’s mixtures stay provisional.

• Status: decided (2026-10-01).

TC-795 Decision: the declared scales of OEP 4 (Q17) (2026-10-01)

• Where: data/gas/refractivity_virial.toml [pairs].

• Decision (the author, 2026-10-01; TC-774 gives the grounds):

  • unknown_b goes from 2.0 to 2.5 cm^3/mol, the largest curated |b| (Xe’s 2.46), as OEP 4, section 7.2, words the rule.

  • third_ratio stays 600. N2’s measured 560 is the largest ratio among the gases whose B_R is resolved. H2’s 1679 is excluded, because its B_R, 0.13(8), is not resolved.

• Effect: the unknown like terms (D2, N2O, CO, O3) and their pairs carry a 25 % larger scale. A pure gas with an unknown like term has its optical bound at 400 mol/m^3 (was 500). No index value changes.

• Status: decided (2026-10-01).

TC-796 Decision: dry air’s equation of state is the multi-fluid model at every temperature (OEP 4, Q19) (2026-10-01)

• Where: data/gas/mixture_pairs.toml (prefer_multi_fluid = true on N2-O2, Ar-N2 and Ar-O2); optmat.gas.mixture_eos (a mixture whose pairs all prefer it takes the multi-fluid model as its default, unqualified and provisional).

• Decision (the author, 2026-10-01): it overrides the default order of TC-778 for dry air.

  • Under that order, air’s default was the fallback, which holds only at Martin et al.’s 290-320 K and refuses other temperatures.

  • The multi-fluid N2/O2/Ar agrees with CIPM-2007’s Z within 8.6e-6, against CIPM-2007’s u(Z) = 1.5e-5. The fallback’s 1.8e-6 does not justify refusing every state outside 290-320 K, nor a switch of method at its edges.

  • The noble-gas defaults of TC-779 stand.

• Effect:

  • Air’s density moves to the multi-fluid model’s, 1.8e-4 below the fallback’s at 10 bar and 294 K.

  • Air’s temperature range becomes its constituents’.

  • The fallback stays available by name (method="virial").

  • The comparison of TC-779, and the pairs’ qualified = false, are unchanged.

• Status: decided (2026-10-01).

TC-797 The molecules refitted with their bands as rules and their windows (OEP 3, Phase 3) (2026-10-01)

• Where: data/gas/fits/{CO,CO2,CH4,N2O}.toml (band_nodes = 8 and windows = true, in place of infrared_max_wavenumber); the stored fits and robustness records; the pages The gas models, Accuracy, Conventions and Fitting; the gallery example CO2 from the ultraviolet to its infrared windows.

• The change:

  • Every band system is now its derived Gaussian rule, in place of one pole per band below a cut-off; the polar molecules’ rotational systems are a term class of their own (TC-751, TC-770).

  • The qualified intervals are the derived windows. Each fit keeps its optical range, split only where the pure gas absorbs (TC-749), plus the windows between the bands beyond it.

  • The configurations’ descriptions state the new intervals.

• The fits: reduced chi-squared, before -> after:

  • CO 0.367 -> 0.367;

  • CO2 3.38 -> 4.01 (Old et al. 81.7 -> 94.2; 3.69 with Marchetti’s values still fitted, 77.1 -> 85.8);

  • CH4 0.696 -> 0.685;

  • N2O 3.014 -> 3.015.

• Against the present fits, inside the new intervals (the change in alpha in units of the present fit’s sigma, 200 points over each optical range):

  • CO 0.05;

  • CO2 0.26 (0.24 with Marchetti’s values fitted);

  • N2O 0.67;

  • CH4 1.86 at 1194 nm, and 1.0 to 1.1 across 276-1200 nm.

  CH4’s change exceeds one sigma: its near-infrared overtone bands are now rules rather than single poles, which moves the fitted electronic terms by about one sigma. Its statistical sigma at 800 nm is 45 -> 44 ppm in n - 1, and 9.3e-4 -> 7.6e-4 relative in the GVD.

• The intervals:

  • CO: 167-2288 nm, 2.56-4.34 and 5.19-12.5 um.

  • CO2: 250-1400 nm and seven windows from 2.30 to 8.94 um.

  • CH4: 240-1123, 1137-1149, 1177-1187.4 and 1187.9-1313 nm, and 11.1-12.1 um. Its optical range now ends at 1313 nm, where the pure gas’s smoothed absorption reaches 0.1 m^-1, against 1400 nm before.

  • N2O: 320-1516 and 1518-1950 nm, 4.81-4.96 and 6.75-7.05 um. The 1516-1518 nm gap is absorption, and N2O now ends at 1950 nm, against 2000.

• The static limit: CO and N2O now carry their rotational systems, whose static contribution is the orientation polarizability mu^2/3kT: +0.65 au (CO, 13.20 -> 13.85) and +1.45 au (N2O, 20.89 -> 22.34). Christiansen et al.’s electronic-plus-vibrational static CO is now compared as an electric observation, which leaves the rotational system out; it stays at -0.12 % (it would have been -4.8 %). The conventions page states the static convention.

• Found:

  • CO2’s last window ends at 8.94 um. Its laser bands at 9.4 and 10.4 um are kept, so Marchetti’s 9.2-10.7 um values lie outside every qualified interval. The page now says pure CO2 is not qualified at its laser lines.

  • Decided (the author, 2026-10-01; OEP 3, Q22): Marchetti’s values are validators, and the laser bands stay kept. Dropping them from the fit moves the model by at most 0.27 sigma (their leave-one-out record). They lie 0.76 % above the model. CO2’s reduced chi-squared goes from 3.69 to 4.01, because their chi-squared per point (3.2) was below the fit’s, and its Birge-scaled sigma at 800 nm from 7.8 to 8.1 ppm.

  • Decided (the author, 2026-10-01; Q23): the windows are not rederived from the refitted parents.

  • Old et al.’s 1695 and 1817 nm points stay outside the fit’s intervals (TC-752).

  • CH4’s optical range now ends at 1313 nm, so Shelton’s fitted 1319 nm N2/CH4 ratio lies just beyond it, as Zhao et al.’s 1566 nm value did before.

  • Bose et al.’s static CH4 now agrees to -59 ppm (+68 before), Schmidt et al.’s to +502 ppm (+629).

  • The full CIPM-2007 air now has four intervals (320-1123, 1137-1149, 1177-1187 and 1188-1313 nm), set by its trace CH4 and N2O under the intersection rule. The reduced air of the air models and the Raman response keeps one. The mixture rule that would widen the trace constituents’ intervals (OEP 3, Q13) is not implemented: it needs the mixture’s own representation tolerance, which no OEP defines.

• Checks: the gate, test-fits (16 passed) and the robustness records of the four. solprop’s parity fixtures for these gases (OEP 1, section 6.11) still pass against the refits.

• Golden values: only fit/CO, fit/CO2, fit/CH4, fit/N2O and the CIPM-2007 air change. A windowed model’s golden grid is taken on its first interval.

• Status: decided (2026-10-01): accepted by the author (OEP 3, Q21).

TC-798 Finding: OEP 2’s tolerance cannot be met in OEP 3’s windows (2026-10-01)

• Where: a feasibility calculation of OEP 2’s reduction (section 7: constrained least squares with the M_0 and M_-2 equalities, F >= 0, one set of energies per absorbing region) on the refitted CO of TC-797. It is not in the repository: OEP 2 is not implemented.

• Finding: with OEP 2’s tolerance, every residual within 0.1 of the parent’s statistical sigma in alpha, D_2 and D_3, the windows cannot be met by a compact model. There the fixed infrared terms carry no statistical uncertainty, so the sigma is the electronic terms’ alone, while the infrared contribution is many orders larger. For CO the worst residual over all its intervals, in units of the parent’s sigma (K poles in its two vibrational regions, one at the rotational fold), is:

  K per region	alpha	D_2	D_3
  1, 1	155	8.4e5	3.6e7
  3, 3	3.2	2.0e3	8.1e4
  5, 5	0.086	56	2.3e3

• With the representation bound as the tolerance in the windows (the larger of the sigma and the bound beyond the optical range, the sigma inside it), K = 4, 4 reaches 0.024, 1.7 and 2.3, and K = 5, 5 does no better.

• On the optical range alone (OEP 2’s original setting), K = 2 for the fundamental and 1 for the overtone meets the tolerance in alpha and D_2 (0.007 and 0.026), with D_3 at 0.32.

• Consequence: OEP 2 needs, before it is built on these parents, a decision on what its compact models cover and to what tolerance:

  • (a) the optical intervals only, with the stated tolerance;

  • (b) every interval, with the representation bound as the tolerance in the windows, and more poles than OEP 2 estimated;

  • (c) the windows left to the full model.

• Decided (the author, 2026-10-01): (a), the optical intervals only, with OEP 2’s tolerance. OEP 2’s Part II records it.

• Status: decided (2026-10-01).

TC-799 The compact models of the molecules (OEP 2, Phase 1) (2026-10-01)

• Where: optmat.gas.models.compact (the reduction, the loader and the reproduction check); tools/fit/compact.py; data/gas/compact/<gas>.toml and data/gas/models/compact/<gas>.json for CO, CO2, CH4, N2O and SF6; the registry; FittedModel.dispersion_sigma_au; the page Fitting dispersion models, section Compact infrared terms.

• The method (OEP 2, sections 4 and 7): each fit’s vibrational poles, its fixed terms after the rotational system, become a few compact poles fitted to their alpha, D_2 and D_3 over the compact intervals, weighted by the fit’s absolute statistical sigma (Birge-scaled, from the covariance), with M_0 and M_-2 kept exactly by an equality-constrained non-negative solve over every support. The electronic terms, covariance and rotational system are the fit’s. The energies are searched in log E within each absorbing region, from a Gaussian rule, the strongest bands, two spreads and seeded random starts; of the candidates, the lowest cost among those meeting the tolerance on the check grid is kept.

• The intervals: the fit’s qualified intervals inside its optical range (OEP 2, Part II; TC-798); for CH4 and N2O they end earlier, at 1070 and 1500 nm (TC-800).

• The regions: besides OEP 2’s region below the intervals and those between them, the region above them: OEP 3’s fold puts a share of each top band system on a node beyond the fit’s short-wavelength end (CO 147 nm, f/M_0 = 2.5e-5; CO2 148 nm; CH4 107 nm; N2O 125 nm). No compact model needs a pole there: its share is taken by the others, within both moments.

• The results (the worst |residual| / sigma on 1600 points per interval, against 0.1):

  Model	Interval	Fit’s vibrational poles	Compact poles	alpha	D_2	D_3	One fewer: D_3
  compact/CO	167-2000 nm	96	3	0.0017	0.0057	0.049	1.85
  compact/CO2	250-1400 nm	4187	5	0.0022	0.0015	0.046	2.73
  compact/CH4	240-1070 nm	943	5	0.0007	0.0006	0.010	0.29
  compact/N2O	320-1500 nm	6059	5	0.0006	0.0002	0.069	5.86
  compact/SF6	230-5000 nm	3	3 (kept)	0	0	0	-

  The compact poles, cm^-1: CO 2143.7, 3582.3, 4274.5; CO2 763.3, 2409.9, 4355.7, 6976.2, 6983.5; CH4 1508.2, 3474.1, 7283.7, 8638.4, 8889.2; N2O 1172.5, 2347.7, 4382.1, 6589.9, 6596.7. M_0 and M_-2 hold to 1e-15.

• Reproduction: every fitted dataset and validator through the fit’s own observation code, scales and partner models fixed: inside the compact intervals the largest change of any datum is 0.003 of its sigma (CO2, Old et al.); the static validators are equal to 6e-16. Beyond (reported): CO2’s window data move by up to 23 sigma (Marchetti & Simili at 9-11 um) and CH4’s 1566 nm value (Zhao et al.) by 1.5 sigma, where the compact models warn and name their parents.

• Also checked: at 10 bar and 293.15 K the relative error in n - 1 equals that in alpha to 1e-3 of itself (OEP 2’s estimate, 8e-4). The re-derivation reproduces the stored models (the fits lane, 100 s). The golden values of every existing model are unchanged.

• Deviations from OEP 2’s text: the region above the intervals (above); SF6’s poles reordered by energy; FittedModel.dispersion_sigma_au, a public method, for the absolute sigma of section 4.

• Status: implemented (2026-10-01).

TC-800 Finding: CH4’s and N2O’s optical intervals end at band-rule poles (OEP 2) (2026-10-01)

• Where: OEP 2’s reduction on fit/CH4 and fit/N2O (TC-797), over their qualified intervals inside the optical range, as decided (TC-798).

• Finding: CH4’s optical range holds four intervals (240-1122.6, 1136.6-1148.5, 1176.9-1187.4 and 1187.9-1312.7 nm) and N2O’s two (320-1515.7 and 1517.6-1950.2 nm), split where the pure gas absorbs (TC-749). The parents’ band-rule poles lie in those gaps and just beyond the last interval, within 0.2 to 3 cm^-1 of the interval edges (CH4 8418.7-8421.6 cm^-1 in the 0.46 nm gap at 1187.6 nm, and 7615.3 cm^-1 against the 7618 cm^-1 edge; N2O 6589.9-6597.2 cm^-1 in its 1.8 nm gap, and 5127.1 cm^-1 against 5127.8). There a single parent pole contributes up to 8e16 (CH4) and 3e14 (N2O) of the parent’s sigma in D_3, so a compact model must reproduce every nearby pole: with three to five poles per region the worst residuals are 1e14 to 3e16 sigma. The parents’ own representation bound there is of the same size (bound / sigma up to 8e16 in D_3), so the structure followed is the rules’, not the gas’s.

• Shortening the interval (one region below, K poles):

  Gas	Compact interval ends	K	worst D_3 / sigma
  CH4	1050 nm	4	0.077
  CH4	1070 nm	4	0.29
  CH4	1070 nm	5	0.010
  CH4	1080 nm	6	0.074
  CH4	1100 nm	6 / 7	0.10 / 2.0
  N2O	1500 nm	5	0.069
  N2O	1505 nm	5	0.50
  N2O	1515 nm	7	5e5

  Keeping the parents’ poles in the gaps instead would need 36 (CH4) and 20 (N2O) poles kept unchanged, with more beyond the last interval: hundreds of terms.

• Proposed and implemented: CH4’s compact interval ends at 1070 nm (5 poles; it covers 1064 nm), 4.7 % short of the first gap, and N2O’s at 1500 nm (5 poles), 1.0 % short; beyond them the full models hold. CO’s and CO2’s optical ranges end clear of their bands (13.5 % and 2.2 % above their highest pole below) and need no change.

• Decided (the author, 2026-10-01): the shortened intervals, CH4 240-1070 nm and N2O 320-1500 nm, a deviation from the decided scope (TC-798) recorded in OEP 2’s Part II.

• Status: decided (2026-10-01).

TC-801 The compact models’ printed forms (OEP 2, Phase 2) (2026-10-01)

• Where: optmat.gas.models.compact.coefficients, CompactCoefficients and format_coefficients; the section The compact coefficients of the page The gas models (both forms for each molecule, tested against the formatter); the gallery example The compact models against their parents.

• The forms (OEP 2, sections 4 and 6): the polarizability form, f_k and lambda_k in descending energy (electronic, infrared, then the rotational term), which goes through the package’s density conversion; and the Sellmeier form at a state, B_k = N alpha_au f_k / (2 epsilon_0 E_k^2) and C_k = lambda_k^2, with N the real-gas density. Each carries the intervals, the reduction’s residuals, both identity digests and the electronic terms’ covariance transformed to the printed parameters (it reproduces the parent’s polarizability sigma to rounding: 5e-7 for CO2, whose effective terms are correlated to 0.9998).

• The digits: eleven significant digits, not OEP 2’s ten. On the present parents ten digits change CO2’s D_3 by 0.0101 of its sigma at 1.4 um, above the 0.01 rounding budget (its compact poles at 1.43 um, 2 % beyond the interval); eleven give at most 0.0017 over every molecule. The rounding error is not monotonic in the digits (CO2: 0.0052 at nine).

• The Sellmeier form’s stated error at 101325 Pa and 293.15 K, against the full parent (Lorentz-Lorenz, the real-gas density, the virial), on the check grid: in n - 1, CO 8.7e-5, CO2 8.8e-5, CH4 1.2e-4, N2O 8.3e-5 and SF6 2.1e-4 relative (OEP 2’s section 8: 5e-5 to 1.2e-4 for the four); in beta_2, 2.1e-4, 1.7e-4, 2.1e-4, 1.8e-4 and 2.6e-4 of its largest value.

• A deviation: beta_2’s error is stated relative to its largest value over the intervals, not pointwise: beta_2 changes sign inside the interval of CO (1969 nm), CO2 (1315 nm), N2O (1465 nm) and SF6 (1271 nm), where a relative difference is unbounded and its largest value depends on the grid (0.2 to 0.5 % on 1600 points).

• Status: implemented (2026-10-01).

TC-802 rollefson_1940: methane’s refractivity at 1.68-14.8 um (2026-10-01)

• Where: rollefson_1940 (3 datasets), tools/extract/rollefson_1940.py; Phys. Rev. 57, 710 (1940), Table I, p. 713, and the text, pp. 710-717. For OEP 3’s infrared validators (TC-756).

• Transcribed:

  • experiment_CH4: Table I’s (n - 1)_EXP x 10^6 at 49 wavelengths, 1.68-14.8 um, by the prism method (the change of deviation with pressure), averages of several runs. “Reduced to standard conditions (0°, 760 mm)” with the International Critical Tables’ expansion coefficient 0.003683 and pv data (p. 712): state 1 atm, 0 C, density real. Primary.

  • calc_CH4: the authors’ two-band model column: check.

  • koch_1909_CH4: Koch’s 419.20 and 450.06 x 10^-6 at 6.557 and 8.678 um, quoted on p. 712: reproduced (Koch 1909 not in the library; his state assumed, his density reduction unknown).

  • Not extracted: Friberg’s extrapolated column (a model of other data, adjusted vertically), the differences and band constants (derived), Fig. 2.

• Uncertainty: none is stated as a number.

  • Per point 0.28 x 10^-6 (rms): the rms of EXP - CALC over the 38 rows below 11 um whose band constants are not parenthesised.

  • 0.4 % more for the 11 parenthesised rows (3.000 and 6.79-7.00 um, near the bands; all beyond 11 um, where the points “scatter rather badly”, p. 713), which scatter by 1.7 x 10^-6 rms.

  • Scale 1 % (one sigma): the values lie 4 x 10^-6, “about 1 percent”, above Friberg’s extrapolated visible data, which the authors allow may be “systematic error … or impurity” (pp. 711-712).

  • The wavelengths’ medium and accuracy are not stated; taken as vacuum (an air wavelength moves no value by more than 0.08 x 10^-6).

• Checked:

  • Table I against its image and the PDF’s text layer (all 49 rows); refractiveindex.info’s copy agrees at all 49.

  • Delta(n - 1) = |EXP - EXT| at all rows (the script checks it on every run).

  • CALC = EXT + K3/(nu3^2 - nu^2) + K4/(nu4^2 - nu^2), with K3 = 16.50, K4 = 7.50, nu3 = 3019.6 and nu4 = 1304 cm^-1 (nu in 1000 cm^-1): within 0.013 at the 20 rows printed to 0.01, 0.15 at 6.79-7.00 um, 0.10 beyond 8 um. The band constants reproduce within 0.10.

  • The derived numbers reproduce: n_inf - 1 = 442.1 x 10^-6 and n_inf^2 - 1 = 884.4 x 10^-6 (p. 716); the effective charges 0.562 and 0.277 x 10^-10 e.s.u. to 1 % with 2K (p. 715); the values at Koch’s wavelengths (426.35, 458.10) and the differences 31.75 and 30.86 (p. 712).

• Finding: against fit/CH4 at 1 atm, 0 C (real gas):

  • Inside the qualified intervals, only 11.46 and 11.89 um: +4.6 and +3.3 x 10^-6 (+1.04 %, +0.74 %).

  • In the gaps, a level offset: +3.0 x 10^-6 (+0.69 %) below 7 um, scattering 0.33-0.41 x 10^-6 about it; +3.2 (+0.73 %) at 8.9-10.9 um; +0.9 to +2.0 on the 7.7 um band’s wing (8.36-8.48 um); +7.0 at 8.63 um, where the fit resolves a line that the prism averages; +2.7 to +7.6 beyond 11 um.

  • Koch’s two values lie 1.0 % and 1.2 % below the fit.

  • The shape agrees; the level is the authors’ own 1 % against the visible data, within the stated scale.

• Doubt:

  • Purity: “corroborative evidence and not conclusive proof of purity” (p. 711).

  • The measurement pressures, temperature and wavelength calibration are not stated.

  • Near the bands an asymmetric absorption of the slit image can shift it (p. 712).

  • The text defines K for n^2 - 1 (p. 712), the table’s K is for n - 1 (a factor 2; the data are unaffected).

• Decision: a fit/CH4 validator, refractive with its infrared part (the defaults), qualified at 11.46 and 11.89 um and compared elsewhere, as TC-752 (TC-807).

• Status: verified (2026-10-01).

TC-803 matsumoto_1987: CO2 at the 10.6 um CO2-laser line (2026-10-01)

• Where: data/sources/matsumoto_1987.toml; tools/extract/matsumoto_1987.py; data/values/refractive/CO2/matsumoto_1987__measured_CO2.csv. One of the validators sought for OEP 3 (TC-756).

• Transcribed: Table 2 (p. 148, image checked), column (n - 1)_m x 10^6, scale 1e-6: CO2 at 101325 Pa and 20 degrees C on the 10.4 um band’s P(20) line, at its centre and 25 MHz either side: 409.1, 412.4 and 405.3. The abscissa is the printed 10.6 um (p. 148; Fig. 2), as vacuum; the paper prints no wavelength of the line, which is 944.2 cm^-1 in marchetti_2007 (0.03 % in n - 1). The uncertainty is 2 % relative, level not stated (‘better than 2%’, p. 149). The density is unknown: the state comes through Koch’s visible formula, whose density convention the paper does not give (real and ideal differ by 0.5 %). use = "check".

• Not transcribed:

  • Table 1’s ratios R = (n - 1)_10.6um / (n - 1)_0.63um (0.981, 0.989, 0.972; sigma 0.024, 0.016, 0.011 of single measurements, N = 14, 7, 5). They are the measurement itself, but the vocabulary has no quantity for a gas’s refractivity over its own at another wavelength.

  • Table 2’s (n_m - n_c) column against Koch’s formula, a calculation.

• Checked:

  • Table 2 is R x 417.0e-6, Koch’s visible value at the state, to the printed digit in every row (implied 416.97-417.03). That value is 0.12 % above fit/CO2 at 632.99 nm with the real-gas density, 0.66 % with the ideal.

  • Against fit/CO2 at 10.6 um (real-gas density): -0.87, -0.07 and -1.79 %, mean -0.91 % (ideal: -0.33, +0.47, -1.25 %). The weighted mean ratio, 0.9794 +- 0.0033, which needs neither Koch’s formula nor the density, is 1.17 % below the model’s 0.9909. The rows scatter beyond their standard errors (chi-squared 4.8, 2 degrees of freedom).

  • Against the other CO2-laser data, relative to the rows’ mean polarizability: Marchetti and Simili +1.4 % (1P20, 2007) and +1.5 % (10.57 um, 2006); Simmons -1.0 % (NTP) and -1.6 % (LL); Willetts and Harris -1.9 %. All are within its 2 %. Against fit/CO2, Marchetti 2007 is +0.46 % at 1P20 (+0.76 % over its 27 lines), and Simmons and Willetts are -2.0 to -2.8 %: the model lies between the two groups, as this source does.

• Doubt:

  • Table 2’s last (n_m - n_c) value is printed 5.0 (image checked). The first two rows give Koch’s 10.6 um value as 410.4 and 410.3; the third implies 400.3, unless it should be -5.0. The column is not extracted, so there is no erratum.

  • The 2 % has no stated level.

  • The He-Ne vacuum wavelength used in the comparison is quoted from memory.

• Decision: a check dataset, not fitted: 2 %, against Marchetti and Simili’s 0.3-0.7 %, and beyond fit/CO2’s last window (8.94 um; TC-797). A validator of fit/CO2 beside Willetts and Harris, its three rows being one line (TC-807). A quantity for the ratio R, the cleaner validator, is not added.

• Status: verified (2026-10-01).

TC-804 tsankova_2018: CO’s static electric polarizability from dielectric measurements (2026-10-01)

• Where: data/sources/tsankova_2018.toml (dataset alpha_e_CO, formula eq4_CO); zhao_2026/tsankova_2018_dp_CO, re-pointed to it; OEP 3, Q20 (TC-756).

• Transcribed: from the text (no table holds it), alpha_e = (2.176 +- 0.022) x 10^-40 C^2 m^2 J^-1, relative combined expanded uncertainty 1.01 % (k = 2; pp. 789, 791), as a static polarizability in SI, level 2 sigma: 13.198 au, one sigma 0.067 au (0.51 %). The regression’s mu_e = 3.584e-31 C m (0.107 D) and b_eps = 1.015 +- 0.044 cm^3/mol (k = 2) are in the formula eq4_CO. Not extracted, for want of a quantity: Table 2 (eps_r and the molar polarization at each p and T), mu_e and b_eps.

• What it is: a 395 MHz re-entrant-cavity permittivity, 255-313 K and 2-8 MPa, densities from Lemmon and Span’s equation of state (0.3 %, k = 2). alpha_e is the electronic plus vibrational polarizability (“the vibrational contribution is already included”, p. 785). The orientation term mu^2/3kT is removed by Debye’s 1/T regression, and there is no magnetic term: an electric value, as Christiansen et al.’s total static CO (TC-751). It is temperature-independent by assumption.

• Corrects TC-756: the “52 ppm (k = 2)” is the uncertainty of eps_r, not of the polarizability; alpha_e’s is 1.01 % (k = 2).

• Checked:

  • With CoolProp’s Lemmon-Span densities, a fit of Eq. (4) to Table 2’s eps_r gives alpha_e = 2.1772e-40, mu_e = 0.1069 D, b_eps = 1.007 cm^3/mol (printed 2.176, 0.107, 1.015). With the printed values, eps_r - eps_fit lies within +-22 ppm, with the isotherm pattern p. 790 describes.

  • The +0.37 % (Maroulis) and +0.28 % (Hohm plus Bishop and Cheung) comparisons recompute.

  • Zhao et al.’s 4.888 cm^3/mol is (alpha_e - 0.020e-40) N_A/3 eps0.

• Finding: Table 2’s P_meas column is offset from its eps_r column by the equivalent of -47.7 +- 3.3 ppm in eps_r. Fitted instead of eps_r, it would give alpha_e = 2.172e-40 (-0.18 %, 0.37 sigma) and b_eps = 2.03. It does reproduce the paper’s Fig. 4b comparison. The paper’s parameters follow the eps_r column.

• Compared (in units of its one sigma, 0.067 au):

  • fit/CO’s electronic and vibrational static value, 13.196 au (the rotational system left out): +0.011 %, +0.02 sigma;

  • Christiansen et al.’s 13.18: +0.26 sigma;

  • Zhao et al.’s static value plus the fit’s vibrational 0.122 au: +0.25 sigma;

  • Hohm’s RI mean plus Bishop and Cheung: +0.54 sigma.

  Its mu_e gives an orientation term of 0.635 au at 296 K, 2.4 % below fit/CO’s rotational system (0.651 au).

• Doubt: mu_e’s uncertainty is 1.3 % (k = 2) on p. 790 but +-0.001 D on p. 791. b_eps is 1.014 on p. 791 and printed in cm^-3 mol^-1. The regression’s weighting is not stated, and alpha_e and mu_e are strongly anticorrelated. The Fig. 6b statement (0.78 % and 0.20 %) is not reproduced. Zhao et al.’s 0.045 cm^3/mol is not this paper’s uncertainty.

• Decision: a check, fit/CO’s static validator with electric = true (infrared terms included, rotational system and chi_0 excluded), not fitted (TC-807).

• Status: verified (2026-10-01).

TC-805 legay_1955: HCl’s fundamental band, no datasets (OEP 3, Q20) (2026-10-01)

• Where: data/sources/legay_1955.toml; TC-756’s candidate list; OEP 3, Q20.

• Transcribed: no values. The record states:

  • the gas: HCl alone, in its fundamental band at 3.4 um (p. 781);

  • the method: Twyman interferometry and channelled spectra through a grating spectrograph resolving about 0.3 cm^-1 (pp. 781-783);

  • the state: the values reduced to 76 cm Hg and 15 degrees C (p. 784);

  • the earlier prism measurements the paper cites: Statescu 1915 (CO2), Rollefson and Rollefson 1935 (HCl), Rollefson and Havens 1940 (CH4).

• Checked: every page image, against the library text. Fig. 2 (p. 783) is a raster figure: the ordinate ‘(n_σ - 1) 10^6’ from -50 to +50; the curve, the vibrational fundamental’s term alone, with the rotational and electronic terms neglected; and some 35-40 measured index variations between P(1) and R(0), about 2866-2903 cm^-1. The ordinate changes sign near 2877 cm^-1. It is not HCl’s refractivity.

• Doubt:

  • The points’ zero, the reference wavelength and index of the channelled spectrum, and the density reduction are not stated.

  • No uncertainty is stated (‘assez bien sur la courbe théorique’, p. 784), nor the wavelength medium.

  • The library’s identity rests on a bibliographic search (the scan prints no DOI); the header, title, author and page numbers agree.

• Decision: no datasets.

  • HCl is not a registered material.

  • The values are relative, with an unstated zero, inside an absorption band.

  • They exist only in a raster figure (TC-699).

  • The paper holds nothing for CO, CO2, CH4 or N2O, so it gives no validator for Q20. TC-756’s question of which gases it measured is answered: HCl alone.

  • Statescu (Phil. Mag. 30, 737, 1915) on CO2 in the infrared is a further candidate, not yet in hand.

• Status: decided (2026-10-01).

TC-806 mitrofanov_2017: the group delay of air at 3.7-4.15 um, recorded without a dataset (2026-10-01)

• Where: src/optmat/data/sources/mitrofanov_2017.toml; tools/extract/mitrofanov_2017.py; OEP 3, Q20 (TC-756).

• Transcribed: nothing into data. The paper (Sci. Rep. 7, 2103, 2017; pdf pages are article pages 1-7) measures only the differential group delay Delta tau_g = tau_g - tau_0 of 60 m of room air over 3.70-4.15 um (Fig. 1d, p. 3; definition p. 4). It comes from SHG FROG with a transform-limited and a chirped (-0.007 ps^2) 80 fs probe. Its zero is arbitrary and no reference wavelength is stated. The text prints one number, “Delta tau_g ~ 1.8 ps … from 3.70 to 4.15 um” (p. 6). Measured CO2 1.32e16 cm^-3 (p. 6; 527 ppm at 1 atm and 20 degrees C, converted here); L ~ 60 m (p. 4). Temperature, pressure, humidity, wavelength medium and every uncertainty are not stated. The paper’s n0 = 1.000270232 at 3.9 um (Fig. 1 caption) is a model value and is not taken.

• Why no dataset: the vocabulary has no quantity for a group delay with an unstated zero (group_delay is absolute per unit length; data rule 7), air is not a registered material, and the values are in a raster figure only (Figure 1, one 1650 x 1478 image).

• Checked: every statement the record quotes, against the pdf’s text layer on its page (by the script). Figure 1d traced by the script from the native image, its axes calibrated from the tick marks (137.5 px per 0.1 um, 136 px per ps; curves about 6 px wide, +-0.02 ps). The transform-limited curve relative to 3.70 um: +0.130 ps at 3.90 um, +0.280 at 4.00, +0.859 at 4.10, +1.409 at 4.13 and +1.781 at 4.15 (the text’s 1.8 ps).

• Comparison (a check; outside every qualified interval): fit/N2, fit/O2 and fit/Ar at CIPM-2007’s ratios (101325 Pa, 20 degrees C, assumed), plus fit/CO2 at 1.32e16 cm^-3, n_g - 1 = N (alpha + omega d alpha/d omega) / (2 eps0), warn=False. tau_g(4.15) - tau_g(3.70) = 2.18 ps against 1.8 ps; the model reaches 1.8 ps at 4.142 um, where the delay rises by 0.045 ps per nm. With the free zero fitted over 3.70-4.13 um the transform-limited curve departs from the model by 0.023 ps rms, the chirped curve by 0.045 ps rms and the authors’ calculation by 0.017 ps rms, against a 1.4 ps rise. As a scale of the CO2 term the curve asks for 0.995 of the monitored density (0.978 to 4.10 um). At 4.14 and 4.15 um the curve lies 0.13 and 0.35 ps below the model, at the plot frame’s corner. fit/CO2 agrees with HITRAN’s CO2 lines summed directly (smoothed by 1 cm^-1) to 0.2 % in this delay at 4.15 um. 3.6-4.2 um lies in fit/CO2’s gap 3592.6-5549.4 nm (reason “representation”) and beyond the CIPM-2007 air model’s intervals.

• Finding: the full CIPM-2007 air model, evaluated beyond its intervals, diverges at fit/N2O’s band-rule pole at 2596.19 cm^-1 (3851.8 nm): a 68 ps spike over 60 m on a 1 nm grid from 0.3 ppm of N2O. It warns there; with warn=False it is unusable in the mid-infrared.

• Doubt: whether the plotted curves are clipped at the frame (4.150 um, 1.5 ps), and so whether the 1.8 ps is a bound. FROG’s resolution near the band edge. “Six 10-m round trips” against L ~ 60 m (the comparison supports 60 m). Water vapour, which optmat does not model and the paper does not state. The CO2 monitor’s uncertainty.

• Decision: recorded as a source without a dataset; not a validator until a quantity for a relative group delay (reference wavelength or free offset, path length, CO2 density) and a material for air exist. Its weight would be check-level: it tests N_CO2 times CO2’s band-wing dispersion at a few per cent.

• Status: open (the quantity and the material for air).

TC-807 The infrared validators and Old’s points, compared (OEP 3, Q19 and Q20) (2026-10-01)

• Where: data/gas/fits/{CO2,CH4,CO}.toml (validators only), their stored fits and robustness records, and the compact models re-derived from them; optmat.gas.fitting (a validator may take range_nm; one that is also fitted is compared at its fitted scale).

• Added as validators (the fits are unchanged: chi-squared CO2 172.26, CH4 21.22, CO 12.10, as before):

  • fit/CO2: Old et al.’s 1695 and 1817 nm points (old_1971/experiment, 1600-2000 nm, at the fitted scale 1.000713), in the 1.40-2.30 um gap, where the weak bands’ rules miss the tolerance (TC-752): -68 and -96 ppm (-10 and -14 of their 6.9 ppm). The gap’s representation fails by about this much, so they are not a test of the fit’s electronic terms (Q19). Matsumoto’s 10.6 um line (TC-803): -0.91 % on average, chi-squared 1.0 for its three rows at their 2 %.

  • fit/CH4: Rollefson and Havens’s 49 points at 1.68-14.8 um (TC-802): +0.70 % on average, the authors’ own level against the visible data; chi-squared 4783 at the per-point scatter alone, without the 1 % scale. Inside the intervals only 11.46 and 11.89 um.

  • fit/CO: Tsankova et al.’s static electric value (TC-804), compared without the rotational system: +110 ppm, chi-squared 0.00.

• Status: decided (2026-10-01).

TC-808 The fits’ representation error inside their optical ranges, at coarser resolutions (OEP 3, Q18) (2026-10-01)

• Where: tools/hitran/resolution.py (prints; writes nothing); the page Accuracy, What the uncertainties leave out.

• The question (OEP 3, Q18): inside a fit’s optical range the representation bound against the line-by-line reference smoothed at sigma = 1 cm^-1 is reported, not enforced (TC-749). Would a coarser sigma qualify it?

• Measured: for each stored molecular fit, over its qualified intervals inside its optical range, |D_m[fit] - D_m[reference]| on the 0.25 cm^-1 grid and the direct grid above it, for sigma = 1, 10 and 100 cm^-1. In alpha the error stays within the fit’s statistical sigma for CO and CO2 (at most 0.16 and 0.26 sigma at 1 cm^-1) and exceeds it only at 1 % (CH4) and 0.1 % (N2O) of the points, at their narrow gaps’ edges (29 and 12 sigma). In D_2, against OEP 3’s tolerance (1 % of the larger of |D_2| and the electronic |D_2|), the shortest wavelength where it fails:

  Gas	sigma 1 cm^-1	10 cm^-1	100 cm^-1
  CO	955 nm	1176 nm	1466 nm
  CO2	909 nm	1032 nm	1183 nm
  CH4	903 nm	903 nm	939 nm
  N2O	909 nm	919 nm	1137 nm

  At 1 cm^-1 the largest errors in D_2 are 6e6 (CO), 3e6 (CO2), 3e11 (CH4) and 5e9 (N2O) of the statistical sigma; at 100 cm^-1, 107, 1100, 3e11 and 5e9. For CH4 and N2O smoothing does not help: the worst points are next to the fits’ own band-rule poles at the edges of their narrow absorbing gaps, which no smoothing of the reference removes.

• Decision (the author, 2026-10-01, on the recommendation): the intervals are unchanged; the accuracy page states that the group-velocity dispersion holds to 1 % up to about 900 nm at every resolution, and how far a broadband pulse’s smoothing extends it. Q18 is closed.

• Status: decided (2026-10-01).

TC-809 A mixture’s intervals widened across a trace constituent’s gaps (OEP 3, Q13) (2026-10-01)

• Where: optmat.gas.air (_widened, the tolerances); optmat.gas.infrared.gap_cells; tools/hitran/gap_bound.py and src/optmat/data/external/hitran/<gas>_gap_bound.csv for CO, CO2, CH4 and N2O; the page Choosing a model, the air models.

• The rule (OEP 3, Q13, with the mixture’s tolerance the author accepted): a mixture’s intervals are the intersection of its constituents’, widened only where, at its mole fractions, all of these hold:

  • its smoothed absorption, the sum of each unqualified constituent’s pure-gas absorption (at 101325 Pa and 296 K) times its mole fraction, is below 0.1 m^-1;

  • no unqualified constituent has a pole there;

  • the mole-fraction sums of their representation errors are within 0.1 of the mixture’s statistical sigma in alpha (the constituents’ sigmas combined as independent) and 1 % of the larger of the mixture’s |D_2| and its electronic |D_2|: OEP 3’s own tolerance, applied to the mixture.

  A widened interval that adds a piece narrower than 50 cm^-1 is dropped (OEP 3’s minimum width). Widening changes where the model warns, not its values.

• The tables: the windows tables hold each molecule’s bound only in its windows, so tools/hitran/gap_bound.py measures, in each stored fit’s gaps from 12.5 um to the top of the absorption grid (11 050 cm^-1), the largest |D_m[fit] - D_m[reference]| (m = 0, 2, 3) against the same smoothed line sum (sigma = 1 cm^-1) and the largest smoothed absorption, per geometric cell (ratio 1.001), on the 0.25 cm^-1 grid and the half-step offset grid; a cell holding a pole of the fit is marked and unbounded. Each table records its inputs’ SHA-256, the fit’s configuration and stored digests, the settings and the tool’s commit; the air model’s identity carries the tables’ digests.

• Not widened: where an unqualified constituent has no table (the atoms and diatomics, qualified wherever air is), and beyond the tables’ span: below N2O’s 320 nm, whose ultraviolet absorption is not assessed, and beyond 12.5 um.

• The result: the reduced compositions keep one interval, unchanged. The full CIPM-2007 air gains two pieces, 1499-1516 and 1548-1562 nm, beyond its intersection (320-1123, 1137-1149, 1177-1187 and 1188-1313 nm). Its trace gases’ other gaps stay closed: their band-rule poles fill them, and no interval may hold a pole. Widening further would need the trace constituents in another representation, with their bands folded (OEP 3, Q13), a different model.

• Status: implemented (2026-10-01).

TC-810 The propagation surface defers the slow scipy modules and the source catalogue (2026-10-01)

• Where: optmat.gas.absorption (gaussian_filter1d, fftconvolve, CubicSpline), optmat.gas.eos, optmat.gas.models.compact and optmat.solid.kerr (scipy.optimize), optmat.gas.nonlinear (least_squares), optmat.gas.transport (CubicSpline), optmat.solid.models.tabulated (PchipInterpolator) and optmat.gas.ionisation (the fitted models). Each is now imported inside the function that uses it.

• Why: importing optmat.gas.models.registry or optmat.gas.ionisation_rates on its own took about 1.2 to 1.4 s. Most of it was scipy.signal, which brings scipy.stats, and scipy.optimize, which only O3’s measured absorption, the equation of state’s inverse and the fitting code use. scipy.interpolate imports scipy.optimize (scipy 1.18.1), so the spline imports are deferred too. optmat.gas.ionisation imported the fitted dispersion models for one function, so every rate model loaded the whole dispersion chain.

• Result: after importing gas.models.registry, gas.ionisation_rates, gas.molecular_ionisation_rates, gas.raman_response, gas.air, gas.eos, gas.transport, gas.nonlinear, solid.models.registry and solid.bundle, none of scipy.signal, stats, ndimage, interpolate or optimize is loaded; scipy.constants, special and linalg remain (tested in tests/test_package.py). Cumulative python -X importtime, median of six interleaved runs against main at f714ec2 in the same session: gas.models.registry 1.24 s to 0.40 s, gas.ionisation_rates 1.39 s to 0.55 s. Inside a solprop run, which loads scipy.signal and stats itself, the saving is about 0.1 s.

• Unchanged: the evaluation code and every number. The golden values and identity digests (tests/test_golden_models.py) and the public-API snapshot pass without regeneration; no EVALUATION_VERSION is raised. scipy.constants (in optmat.constants and optmat.gas.infrared) stays at module level, since avoiding it would mean copying CODATA values.

• The first lookup: the first registry.default_model or registry.model call for any gas, argon included, took about 2.5 s, and the first call of nearly every other model solprop uses about 2 s. The profile shows the source catalogue (optmat.datasets.sources: 562 records and about 6500 point files) loaded to read a few records. registry.model built every registry through _all_models(), and the published formulas read every record. The rest looked up one dataset or record in datasets() or sources(): O3’s measured absorption (ogawa_1958/absolute), the refractivity virial (virial), the ionisation parameters and rates, the gas Raman parameters and response, transport, the hyperpolarizability formulas, the metal tables and silica’s Raman response (the bundle). The smoothing and the Kramers-Kronig transform themselves take about 0.1 s.

• The change: a private module, optmat._catalogue, reads one record with load_source (the loader the catalogue uses, so a record read alone is the catalogue’s own, tested point for point; once the catalogue is loaded it serves the catalogue’s records). source(id), dataset(key), records() (by id) and by_key(material, quantity=...) (by key, filtered as datasets() filters) read on lookup; iterating over them loads the catalogue as before. formula_sources() reads only the records whose text has a [[formulas]] table (226 of 562), and is tested to give exactly the sources with formulas, in the catalogue’s order. The call sites above use them in place of the catalogue; scans over the catalogue (the fits, the validations, the cross-checks) are unchanged. registry.model, for gases and solids, builds only the registry its name’s prefix names (fit/, compact/, refractiveindex.info/, table/; otherwise a published formula); registry.models and the full listing are unchanged, and every listed name resolves to the same model (tested by digest).

• Result: in a fresh process none of solprop’s entry points loads the catalogue (tested). Imports and the first call, median of three interleaved runs against main at 4c1ebb1 in the same session: gas default_model("Ar") 2.96 s to 1.21 s; N2’s refractive index 3.79 s to 1.70 s; CaF2’s 2.79 s to 2.04 s; SiO2’s 2.11 s to 0.36 s; silica_bundle() 2.07 s to 0.37 s; ionisation_rate_model("Ar", 800e-9) 2.57 s to 1.23 s; ionisation_parameters("Ar") 2.60 s to 1.27 s; raman_response("N2", 293.15) 2.27 s to 0.44 s. The digests are unchanged.

• Open: about 0.6 s of a gas’s first lookup is importing scipy.signal and scipy.ndimage, since fitted_models() still builds O3’s term with every fit; deferring it means a lazy fitted_models() mapping (its public return type changes) or a lazy MeasuredAbsorption, whose fields are in the digest. Not pursued (2026-10-01): about 1 s is acceptable. The published formulas read their 226 records with their data files (0.75 s, the most of CaF2’s remaining cost beyond its N2); reading the formulas alone (0.2 s) would need a loader beside load_source.

• Status: implemented (2026-10-01).

TC-811 The equation of state’s domain: the melting line and the triple point (2026-10-01)

• Where: optmat.gas.eos (EquationOfState.phase_domain and its private _domain_top and _melting_pressure; the forward check and the inverse); the manual’s Conventions, the phase domain.

• Finding (solprop SEP 3, Phase 1a; its open question Q2): above the critical temperature phase_domain declared (0, p_max), with p_max the equation’s stated pressure. CoolProp also refuses a state below its melting line, T < T_melt(p). Wherever the melting pressure p_melt(T) is below p_max, part of the declared domain was solid. The inverse’s guard evaluated the density at p_max first, so it raised at every density, 1 bar included. CoolProp 8.0.0’s melting lines cross the equations’ pressures at these temperatures, and the inverse failed from T_c up to each one:

  Gas	T_c (K)	p_max (GPa)	Failed up to (K)
  He	5.2	1.0	61.1
  Ne	44.4	1.0	109.8
  Ar	150.7	1.0	254.0
  H2	33.1	2.0	171.3
  D2	38.3	2.0	172.0
  N2	126.2	2.2	283.8
  CH4	190.6	1.0	255.6
  CO2	304.1	0.8	327.7
  dry air (Lemmon 2000)	132.5	2.0	236.2

  Kr, O2 and CO were not affected: their melting lines end below T_c, at 205, 80.7 and 114 MPa, at or above their equations’ pressures. Xe, SF6 and N2O have no melting line in CoolProp.

• Also found: at exactly the lower end of an equation’s temperatures, its triple point, CoolProp refuses the gas below the triple pressure. Only a sliver at p_sigma (1 - 1e-5) passed, so the declared (0, p_sigma) was false there too.

• Decision: the domain is made true, and one bound serves phase_domain, the forward check, the inverse’s guard and its bracket. At and above T_c the upper end is the lower of p_max and p_melt(T) (1 - 1e-5), wherever CoolProp’s line covers the temperature. Above the line’s own temperatures the line is beyond its top pressure, which is at or above p_max for every fluid (tested). Below T_c the vapour pressure binds, as before. A state above the melting bound is refused as solid, and the inverse’s refusal names the bound. The triple point is excluded from the domain (the author, 2026-10-01). The 1e-5 margin is not needed at the line’s own value (CoolProp 8.0.0 accepts p_melt itself, at 40 temperatures per gas), but keeps the domain’s end clear of CoolProp’s numerical solve for T_melt(p), as SATURATION_MARGIN does for the vapour pressure.

• Checked: for the fourteen gases with an equation and for dry air, a scan over T from just above the triple point to 400 K in 4 K steps (with T_c and either side of where the melting line crosses p_max), at densities from 1e20 m^-3 to just below the density at the domain’s top. The round trip N(p(N, T), T) / N - 1 is within 1e-12 everywhere, and every density above the top is refused, naming the vapour pressure, the melting pressure or the equation’s pressure (tests/test_equation_of_state.py). Below T_c the vapour pressure is below the melting pressure wherever the line is defined. The exception is CO2 within about 1e-5 K of its triple point: the equation puts the triple point at 517 964 Pa, the melting line at 517 950 Pa (2.7e-5 apart), and the lower bound is taken. The golden values, the identity digests and the solprop parity fixtures (tests/data/solprop_eos.json) pass unchanged.

• EVALUATION_VERSION: unchanged. phase_domain enters no identity record, and no number the forward law or the inverse returned before has changed. The states that raised now return values; at the triple point the sliver that passed is now refused.

• Doubt: for Xe, SF6 and N2O the high-pressure domain is bounded only by p_max, since CoolProp has no melting line for them. The mixtures’ virial fallback (optmat.gas.mixture_eos) still checks a constituent’s partial density only below T_c. At exactly a constituent’s triple point it now raises through phase_domain.

• Status: corrected (2026-10-01).

TC-812 travers_2026_trecx: the 6 fs one-electron yields as the ionised fraction; the model’s dependence on frequency (2026-10-01)

• Where: src/optmat/data/external/trecx/scan_6fs_v2/results.csv, PROVENANCE.md there (its section on the 6 fs runs again), src/optmat/data/sources/travers_2026_trecx.toml (ionised_gauss6_Ar_m0, ionised_gauss6_Ar_m1, ionised_gauss6_He, and the record’s notes), tools/extract/travers_2026_trecx.py (six_fs_uncertainty), optmat.gas.ionisation_validation.TDSE_YIELDS, tools/ionisation_rate_tables.py, docs/ionisation_rates.md, docs/gallery/ionisation/plot_ionisation_frequency.py, src/optmat/data/gas/ionisation_rates.toml (the reasons of coulomb and Ar’s uncertainty_factor).

• Transcribed: the ionised fraction, 1 - (ground + bound states up to n = 10) at the end of the pulse, of the three 6 fs scans of TC-666 repeated by J. C. Travers on 29 September 2026 (tRecX a987d7c7, the build of TC-702): Ar 3p m = 0 and m = 1 at the ten intensities, He 1s at rows 0 to 7, the pulse from a file, 1000 au without field after it, cutEnergy 100. Tier 3. Rows within a factor 10 of the loss of a run without a field are excluded (Ar m = 0 row 0, Ar m = 1 rows 0-1, He rows 0-1). The uncertainty, 0.05 to 1.8 %, is the runs’ rule (convergence runs at three or four intensities per family), recomputed by the extraction script from the archived table and tested against the record.

• Checked: every run complete; the initial energies (spread 5e-11, 1.3e-10); the drift (1.0e-9 Ar, 3.2e-8 He); the June chi-loss reproduced to 0.99-1.03 above the floor; the norm at every print step (He row 7’s excursion to 1.085 changes the yield by at most 0.05 %); every warning (PROVENANCE.md). Helium at June’s cutEnergy 60 was not converged in the step, so June’s He values at rows 0-2 are mostly numerical loss.

• Decision: the validator’s 6 fs yields (TDSE_YIELDS) are the ionised fraction alone; the June measures stay in the record, not compared. They supersede TC-666’s datasets as the 6 fs yield.

• Finding: against the ionised fraction the one_electron model is 1.07 to 1.67 times the calculation for argon (m = 0) at Keldysh parameters 0.5 to 2.3, the most at the largest, and 1.15 to 1.22 times for helium at 0.3 to 0.9. Against June’s chi-loss it had been 0.93 to 1.21: that measure counted the Rydberg states. With the 42 fs result (0.99 to 1.8, TC-702) the model is too high for one electron in the multiphoton regime. Its static limit is not the cause: it is 0.94 to 1.01 times the static rates of the same electron (TC-813). No Coulomb factor follows the calculations: Ilkov et al.’s and Popruzhenko et al.’s are 2 to 3 times low at gamma = 1.8 to 2.3 and up to 1.7 times high at 0.6; the static factor has the smallest error over gamma = 0.3 to 2.3, so TC-653’s decision stands, on a narrower margin than it stated. The m = 1 electron’s yield is 2 to 39 % of m = 0’s.

• Doubt: one carrier-envelope phase; the rows between convergence rows take their neighbours’ uncertainty.

• Status: verified (2026-10-01); the dependence on frequency is open with TC-660.

TC-813 travers_2026_trecx: static rates of Ar 3p, m = 0 and m = 1; Zhang et al.’s displaced cell (2026-10-01)

• Where: src/optmat/data/external/trecx/static_rates/ (results.csv, results_nearest.csv), PROVENANCE.md there, travers_2026_trecx.toml (static_Ar_m0, static_Ar_m1), tools/extract/travers_2026_trecx.py (static_uncertainty), optmat.gas.ionisation_validation.STATIC_REFERENCES, src/optmat/data/sources/zhang_2014.toml (the excluded row of tableIX_tonglin_Ar and tableIX_muller_Ar).

• Transcribed: Gamma = -2 Im E (au) of the complex-scaled resonance of H0 + F z continuing Ar 3p (Tong and Lin’s potential), m = 0 and m = 1, traced from F = 0, at the seven fields of Zhang et al.’s Table IX up to 0.2 au: J. C. Travers’s tRecX runs of 29 September 2026. Tier 3. The uncertainty is the largest change among direct solves with the discretisation varied (angular functions, radial elements and order, ECS angle 0.3 and 0.6, ECS radius 30 and 20 bohr): 0.016 to 1.4 % (m = 0) below 0.19 au, 7.7 % at 0.197 au; 0.006 to 0.86 % (m = 1). The ECS radius moved out to 60 bohr loses the resonance and is left out.

• Checked: m = 0 reproduces Zhang et al.’s Tong-Lin column to 0.04 to 2.4 % at the six fields kept (tested); every run exited normally.

• Finding: at the excluded field, 0.12177 au, Gamma/2 = 1.3232e-2, the printed Muller cell (1.3229e-2) to 0.02 %. The row’s cells are very likely displaced: the Tong-Lin value printed in the Muller column, the GSZ value repeated in the Tong-Lin column, the Muller value not printed. The m = 1 rate, not published elsewhere, is 2.1 % of m = 0’s at 0.053 au and 22 % at 0.197 au.

• Decision: Zhang et al.’s row stays excluded in both columns; the exclusions now give the finding. It is not corrected: the value would come from this calculation, not the paper. static_Ar_m0 is a static reference of the one_electron model, which it puts at 0.94 to 1.01.

• Status: verified (2026-10-01).

TC-814 Decision: until the measured yields agree, the default follows Wallace et al. (2026-10-01)

• Where: docs/ionisation_rates.md (Measured yields; Open questions); the default model (src/optmat/data/gas/ionisation_rates.toml), unchanged.

• Context: Wallace et al. (2016) and Wahlstrand et al. (2018) differ by about 3 in the rate (TC-660). The calculations do not settle it: one electron of argon in Wahlstrand et al.’s pulse is 1.3 to 4.1 times their atom (TC-702), all-electron rates point both ways (TC-669, TC-701), and the maintainer doubts that the in-house all-electron (haCC) runs can settle it.

• Decision (J. C. Travers, 2026-10-01): prefer Wallace et al. The default stays as it is, matching their yields within their calibration, and is not adjusted towards Wahlstrand et al.’s (no change of the effective number of electrons, no scale). The accuracy factors stay as stated.

• Why Wallace et al.: their intensities rest on atomic hydrogen, whose yield is calculated exactly; their three gases are matched with one scale each within the calibration; and the one-electron calculations lie above Wahlstrand et al.’s atom.

• What it does not settle: Wallace et al.’s argon tests the rate where the yield bends towards saturation, near 3e14 to 5e14 W/cm2 (Keldysh parameter about 0.6), where the one-electron model is 1.07 to 1.12 times the calculation (TC-812). Below 1.5e14 W/cm2, where the model is up to 1.7 times the calculation, the only absolute yields are Wahlstrand et al.’s. A further absolute measurement of argon is wanted; Kübel et al., Phys. Rev. A 93, 053422 (2016), cited by Sarkadi (2021) for a model needing the measured intensity times 2.5, is to be read.

• Status: decided (2026-10-01); open with TC-660. The absolute yields as intensity scales, and the hydrogen calibration’s limits: TC-819.

TC-815 The rates of Luna.jl and solprop against the default (2026-10-01)

• Where: tests/data/legacy_ionisation_rates.json, written by tools/legacy_ionisation_rates.jl (Luna) and tools/legacy_ionisation_rates.py (solprop, optmat); tools/legacy_ionisation_measured.py; tools/ionisation_rate_tables.py (legacy_table); docs/ionisation_rates.md (Luna.jl and solprop); tests/test_legacy_ionisation_rates.py.

• Transcribed: the instantaneous rate each code applies to the noble gases at 800 nm, at 28 fields (the amplitudes of 1e13 to 1e15 W/cm2), and the yields of 6 and 30 fs Gaussian pulses at 19 peak intensities, computed with each code: Luna.jl de9db7c (branch modal-fixed, clean), Ionisation.IonRatePPTCached, the rate its Interface.makeplasma! builds for plasma = true; solprop 05172a4 (main, clean), driver.simulation._ionisation_rate, its capillary driver’s rate, PPT with its defaults. The pulses are gaussian_pulse’s, reproduced in Julia to 6.7e-11 of the peak field.

• Checked: Luna’s cached spline equals its direct rate to 2.4e-14 and the caches on disk; solprop’s production table equals its direct rate to 1.6e-9; solprop without its barrier-suppression factor equals Luna to 2.5e-7 (tested).

• Finding: both are the rate of Perelomov, Popov and Terent’ev in Ilkov et al.’s form, with the Hartree coefficient, the sum over m, two electrons per orbital, and for He, Ne and Ar a Stark shift and exp(-2 alpha+ F) (not for Kr, Xe). solprop is NOT Luna: it multiplies by Tong and Lin’s factor (alpha 7 for He, 9 for the others), so its rate is 0.89 (He, 5e13 W/cm2) to 0.13 (Kr, 5e14) times Luna’s. The default is 1.1 to 1.6 times Luna’s rate for argon and 2.4 to 5.2 times solprop’s; below Luna’s by 1.35 to 10 times for Ne, Kr and Xe, the most at high intensity; 0.85 to 1.9 times for He. Through the tests on measured yields, the intensity scale against Wallace et al. is 1.05 (Ar), 0.955 (Kr), 0.895 (Xe) for Luna and 0.935, 1.06, 1.13 for solprop, against calibrations of 1.3, 1.5 and 2.5 % (the default: 0.98, 1.00, 1.00); over Wahlstrand et al.’s yields Luna’s are 1.0 to 3.1 (Ar), 1.4 to 7.3 (Kr), 1.8 to 9.4 (Xe) times, solprop’s 0.64 to 1.6, 0.9 to 3.5, 1.1 to 4.2. Luna stops with an error above twice the barrier-suppression field (xenon above 3.5e14 W/cm2); solprop has no limit, and its argon rate falls with the field above 1.8 times it.

• Doubt: the tests on measured yields use the codes’ rates interpolated on the 28 fields; Luna’s xenon is held constant above its limit, which Luna does not do. Which Luna branch earlier production runs used is not recorded here.

• Status: verified (2026-10-01).

TC-816 Finding: the rate is erratic above its maximum field (2026-10-01)

• Where: optmat.gas.ionisation_rates.IonisationRateModel.instantaneous_rate and cycle_averaged_rate, above maximum_field (twice the barrier-suppression field F_b), where they warn (ModelRangeWarning).

• Finding: at 800 nm the default’s instantaneous rate first falls with the field at 2.1 to 2.4 F_b, and between 2 and 4 F_b it swings between 2.4e12 and 1.3e17 /s (Ar: 4.0e15 at 2.7 F_b, 2.4e15 at 3.1, 4.8e15 at 3.3, 9.4e12 at 3.7); the cycle-averaged rate exceeds the instantaneous one near 3.1 F_b. Below 2 F_b it is smooth. A propagation that reaches such fields and ignores the warning takes these values.

• Doubt: the cause is not established; the averaging from the rate’s own slope and curvature (TC-662) is the suspect, where the slope of the logarithm passes through zero.

• Status: closed by TC-828 (2026-10-02): the erratic values came from the averaging’s expansion; the rate is now averaged by quadrature and held above its maximum field, as the maintainer decided.

TC-817 nambu_2026 (Nambu, Nie, Marsh & Joshi, J. Opt. Soc. Am. B 43, 750 (2026)): absolute ionisation of Ar, Kr, Xe at 800 and 400 nm by plasma interferometry; the phase-shift validator (2026-10-01)

• Where: src/optmat/data/sources/nambu_2026.toml (12 datasets), tools/extract/nambu_2026.py, tools/extract/_figure.py (Painted, painted, texts: colours, form XObjects, text objects), the quantity ionization_phase_shift (optmat.vocabulary, docs/data.md), optmat.gas.ionisation_validation (plasma_phase_shift, phase_shift_test, circular_yield), tools/ionisation_rate_tables.py (phase_shift_table), docs/ionisation_rates.md.

• Transcribed: the measured points of Fig. 6 (800 nm pump, 55 fs) and Fig. 7 (400 nm, 130 fs), Ar, Kr, Xe, linear and circular polarisation: the phase shift of the probe (rad, normalised to 1 atm) against the pump’s peak intensity (W/cm2), with error bars, 251 points; read from the vector drawing (data rule 8, digitised = "vector", use = "check"). The beams (Table 2: pump and probe durations and 1/e^2 radii; M^2 = 1.25, App. C) are parameters of every dataset, checked by the script against the library’s table. Fig. 8 (267 nm) and the theory curves are not taken.

• Checked: every tick of every panel on its fitted scale (worst 0.0045 pt); the gamma = 1 lines of Fig. 6 where the paper’s ionisation energies put them, to 0.075 %; the intensities on grids of set pulse energies (multiples of 1.6078e13 and 6.475e11 W/cm2, within 2e-4); each panel’s marker count against the drawing’s outlines; overlays of every point on the page rendered at 10x. The error bars are symmetric in rad: sigma is half a bar, level not stated; 181 bars shorter than their marker are kept from the drawing. No number of the same quantity is printed.

• The validator: the phase is Eq. (3) of the paper (Nie et al. 2022’s Eq. (3) likewise): the electron density each point of the focus is left with, n_e/2n_c, averaged over the probe’s Gaussian profile and integrated along the axis, with Gaussian pump and probe beams of the stated radii and M^2, the density 2.7e19 cm^-3 at 1 atm that Nie et al. state (Fig. 4), and the yield of the local peak intensity (the cycle-averaged rate on the envelope). Checked: a fully ionised column gives its analytic phase (doctest); a power law through the ionised fraction Nie et al.’s Fig. 3(b) shows for He at 5e14 W/cm2 (about 5.5e-3, slope 7) gives 0.30 rad against their averaged 0.27 (Fig. 3c, read by eye); the radii taken as diameters would give 0.08. The test fits the scale on the measurement’s intensities, in the logarithm, weighted by the bars.

• Finding (800 nm, linear): the default fits Ar, Kr, Xe at intensity scales 1.01, 0.96, 0.89, the phase 0.83, 1.13, 1.30 times the measured on geometric average; ppt_ilkov 1.09, 1.00, 1.04; ppt_popruzhenko 1.11, 0.99, 0.96. At 800 nm the measurement does not separate the Coulomb factors.

• Finding (400 nm, linear, Keldysh parameters 2 to 6): the default is 2.9 to 5.2 times the measured phase (scales 0.50 to 0.69); ppt_popruzhenko fits at 1.05 to 1.19, ppt_ilkov at 1.08 to 1.41. The static Coulomb factor’s excess at large Keldysh parameter now has four indications: the one-electron calculations at 800 nm (TC-812), the R-matrix rates of Ar at 390 nm (TC-701), Parker et al.’s He at 390 nm (TC-660) and this measurement.

• Circular polarisation: optmat has no rate for it. The static rate at the turning field’s magnitude (circular_yield), a lower estimate near gamma = 1, is about 10 times below the measured phase of Ar at 800 nm. The data are curated, not compared.

• Doubt: no intensity calibration or uncertainty is stated; the 800 nm points differ from Nie et al.’s, which the paper says it reproduces (TC-818); the probe for each pump is from Nie et al.; self-focusing is left out at 800 and 400 nm, as the authors do.

• Status: verified (2026-10-01); the Coulomb factor at large Keldysh parameter is open (TC-819).

TC-818 nie_2022 (Nie, Nambu, Marsh et al., Opt. Express 30, 25696 (2022)): the plasma-interferometry yields of He, Ar, Kr, Xe and H2 (2026-10-01)

• Where: src/optmat/data/sources/nie_2022.toml (10 datasets), tools/extract/nie_2022.py, the validator of TC-817.

• Transcribed: the measured phase shifts (rad, normalised to 1 atm) against the pump’s peak intensity, 93 points: Fig. 3(a), He, 800 nm, linear, with the gas pressure of each point (raster); Fig. 4, Ar, Kr, Xe, 800 nm, linear and circular (raster); Fig. 6, H2 at 800, 400 and 267 nm, linear (vector). The beams of Table 1 (checked by the script); M^2 = 1.25 is stated for the 800 nm laser only, so the H2 datasets at 400 and 267 nm cannot be modelled; the density at 1 atm, 2.7e19 cm^-3, from Fig. 4’s caption. Intensities from ‘carefully measuring the spot size, pulse duration, laser energy and gas pressure at each experimental condition’ (p. 7), the duration by SPIDER; no uncertainty is stated. Data ‘may be obtained from the authors upon reasonable request’.

• Checked: every tick on its scale (raster: worst 0.31 px; vector: 0.011 pt); the overlays; Fig. 3’s pressures (read from the image) give similar raw phases, 12 to 26 mrad; Fig. 6’s intensities on round values (0.1 to 0.2 % above at 800 nm, 0.995 of them at 400 nm).

• Doubt: Fig. 4’s markers sit on theory curves of their colour: each was seeded at a pixel picked on the image and then located by rule; caps touching a marker are not read, so 17 of its 57 points have a sigma. Digitising: 4 % (Fig. 3), 5 % (Fig. 4), 0.2 % (Fig. 6) in the phase.

• Finding (against nambu_2026): at equal phase Nambu et al.’s 800 nm intensities are 0.88 to 0.89 times these for Ar and Kr and 0.82 for Xe (medians; 0.80 to 0.95 point by point), alike for linear and circular polarisation; Nambu et al. omit the lowest Ar and Kr points and draw more points at more pressures. The reproduction changes the intensity scale by 11 to 18 %, unexplained.

• Finding (the models, 800 nm, linear): at these intensities the default fits at scales 0.93 (Ar), 0.875 (Kr), 0.77 (Xe), the phase 1.40, 1.62, 1.99 times the measured; ppt_ilkov 0.97, 0.94, 0.89; ppt_popruzhenko 1.00, 0.93, 0.83. He: the default 0.90 (2.3 times the phase), ppt_popruzhenko 0.99. H2: the default 0.85 (2.0 times).

• Status: verified (2026-10-01).

TC-819 Finding: the absolute yields as intensity scales, and the papers read for them (2026-10-01)

• Where: docs/ionisation_rates.md (Measured yields); TC-814.

• Finding: expressed as the scale on each measurement’s intensities at which the default fits it (below 1: the model ionises too much):

  Measurement	Ar	Kr	Xe
  Wallace et al. 2016, 5.5 fs, intensity from atomic hydrogen (TC-658)	0.98	1.00	1.00
  Nambu et al. 2026, 55 fs, plasma interferometry (TC-817)	1.01	0.96	0.89
  Nie et al. 2022, 55 fs, the same method (TC-818)	0.93	0.875	0.77
  Wahlstrand et al. 2018, 42 fs, plasma interferometry	0.84	0.82	0.69

  Wahlstrand et al.’s by the fit of their yield fits with the intensities scaled (measured_yields), the residual a factor of 1.5. The factor of about 3 in the rate between the measurements (TC-660) is 15 to 20 % in the intensity, the size of the change between one group’s two publications of its own data (TC-818). Pullen et al. (2013) and Kielpinski et al. (2014), read: the hydrogen calibration is good to 1 to 2 % statistically, with no systematic budget, demonstrated at 6.3 fs on 1.1 to 4.8e14 W/cm2; their careful conventional calibration was 7 % high, Wallace et al.’s (2016) 56 % (eta_1 = 0.641).

• Finding (xenon): within each absolute measurement, where one intensity calibration serves all gases, xenon’s scale is 0.82 to 0.88 of argon’s (Nambu 0.88, Nie 0.83, Wahlstrand 0.82) and krypton’s 0.94 to 0.98: the three absolute measurements put the default’s xenon high against its argon by about 15 % in the intensity, a factor of 2 to 3 in the rate, the size of the spread of xenon’s structure coefficient (TC-657). Wallace et al.’s test, of the shape of the yield, does not see it.

• Read, not curated: Kübel et al., PRA 93, 053422 (2016) (Ar2+/Ar+ ratios only; the target length varied to hold the count rate; its factor 2.5 was fitted to momentum widths and attributed by the authors to the semiclassical model); Chen et al., Sci. Rep. 7, 7488 (2017) (a calculation on Kübel et al.’s data); Ruden, arXiv:2508.07500 (Guo et al.’s data with intensity and count scales fitted to PPT for Ar: circular); Mosert & Bauer, CPC 207, 452 (2016) (t-SURFF with the Coulomb potential switched off before the surface, the cure of TC-703); Bauer & Koval (2006) and Patchkovskii & Muller (2016) (codes, no benchmark yields of use here).

• Status: open: the Coulomb factor at large Keldysh parameter (TC-817) and xenon’s rate against argon’s are the maintainer’s to decide; TC-814 stands.

TC-820 The rate in a circularly polarised field (2026-10-01)

• Where: optmat.gas.ionisation_rates (circular_saddle_point, circular_enhancement, IonisationRateModel.circular_rate), optmat.gas.ionisation_validation.circular_yield and the circular branch of phase_shift_test, tests/test_circular_rate.py, docs/ionisation_rates.md.

• Decision: the rate of an atom in a circularly polarised field of magnitude F is each fine-structure channel’s static rate (its tunnelling rate with Tong et al.’s coefficient, the static correction, the effective number of electrons, as in linear polarisation) times the factor by which the field’s turning raises the shell’s short-range rate over its value at zero frequency, and times the model’s Coulomb factor over its static limit. The factor is Barth & Smirnova’s (PRA 87, 013433 (2013)) simple formulas, eqs. (97) and (100)-(105), summed over the shell’s three orbitals p+, p-, p0 (the magnetic quantum number along the direction of propagation; the s orbital for helium); the saddle point zeta_0 is the root of eq. (94), by bisection, and Appendix F’s series below a Keldysh parameter of 0.01. The common factor |C|^2 Ip F/2F0 cancels, so the coefficient’s normalisation does not enter, and the static limit is the default’s static rate at the magnitude.

• Checked: zeta_0 against Appendix F’s series (1e-5 at gamma = 0.05) and eq. (94) itself up to gamma = 1e7; g and h against eqs. (106) and (109); the enhancement tends to 1; the simple formulas against the approximate photon sums, eqs. (89)-(90), at the paper’s example (Ip = 0.5, omega = 0.057, F = 0.03 to 0.06) within 8 % (‘coincide within graphical resolution’, Fig. 2); a static model gives its static rate; at 800 nm and 1e14 W/cm2 the circular rate is below a tenth of the linear one. Argon at 800 nm and 2e14 W/cm2: 3.74 times the static rate at the same magnitude.

• Finding: against the measured circular yields (TC-817, TC-818) the default fits at intensity scales close to the linear ones: Nambu et al. 1.08, 1.00, 0.98 (linear 1.01, 0.96, 0.89; Ar, Kr, Xe), Nie et al. 0.98, 0.895, 0.81 (linear 0.93, 0.875, 0.77). At 400 nm the default is 2.8 to 3.5 times the circular phase (scales 0.66 to 0.73) as in linear polarisation; there ppt_ilkov and ppt_popruzhenko overshoot the other way (1.17 to 1.82).

• Doubt: how the Coulomb correction enters in circular polarisation is not derived here; the model’s linear-polarisation factor over its static limit is applied, as Nambu et al. (2026, App. A) do with Popruzhenko et al.’s. Barth & Smirnova’s rates are of a short-range potential.

• Status: decided (2026-10-01); open with TC-819: the Coulomb factor at large Keldysh parameter, in both polarisations.

TC-821 bahl_2016, santra_2006, otobe_2004: static rates of Ne, Ar, Kr, Xe (2026-10-01)

• Where: src/optmat/data/sources/bahl_2016.toml, santra_2006.toml, otobe_2004.toml, their scripts in tools/extract/, optmat.gas.ionisation_validation.STATIC_REFERENCES (Bahl for Ne, Ar, Kr, Xe; Santra’s total for Kr).

• Transcribed:

  • Bahl, Wright & Kolesik (PRA 94, 023850 (2016)): the static rate Gamma = -2 Im E of one active electron (m = 0, implied by the method) of Ne, Ar, Kr, Xe, from the publisher’s data files attached to the library entry (*_imE_nlp.dat, scale = -2); the rows below where the rate rises smoothly are excluded with reasons (Ne below 0.043, Ar 0.025, Kr 0.020, Xe 0.018 au). Argon’s potential is Tong and Lin’s (the rates equal tRecX’s and Zhang et al.’s to 0.2 %); Kr and Xe’s are not identified (Cloux et al. 2015 is not in the library). He is not taken: its printed fields are rounded from a grid of (k - 1/2) x 0.001 au, off by 0.0005 au (8 % in the rate at 0.1 au), and 20 appear twice.

  • Santra, Dunford & Young (PRA 74, 043403 (2006)), Table I: Kr 4p, spin-orbit resolved, three channels at 0.10 au (rates of one electron in one spin-orbital), and the text’s total, 0.036 au = 2 x the sum (0.0362), which the record checks.

  • Otobe, Yabana & Iwata (PRA 69, 053404 (2004)), Table II: Xe 5p (‘2p’ in the paper) complex orbital energies at 4 to 9e13 W/cm2 (I = c eps0 F^2/2, checked against p. 5), the per-orbital rate w = -2 Gamma/hbar (scale to au); the library’s table is scrambled, so the script transcribes the image and checks it against the library’s cells. The 8e13 row grows irregularly and is flagged, not excluded.

• Finding: the one_electron model over Bahl et al.’s rates: Ne 1.08 to 1.35, Ar 0.91 to 1.12, Kr 1.10 to 1.22, Xe 0.88 to 1.05: the model’s static limit holds for krypton and xenon too, so the xenon excess of TC-819 is not in the static one-electron rate. The default over Santra et al.’s Kr total at 0.10 au: 0.77. Over Otobe et al.’s Xe total (2 x the three orbitals, density functional theory with the polarisation of the atom), 0.48 to 0.97 from 4 to 9e13 W/cm2 (not in the validator: a total of three datasets).

• Doubt: Bahl et al.’s Kr and Xe potentials are unknown, so the comparison tests the model against one-electron rates in some potential, not in Tong and Lin’s.

• Status: verified (2026-10-01).

TC-822 dewitt_2001, loriot_2008, dura_2012, sharma_2018: molecule-to-atom ratios and O2’s eight-photon cross-section (2026-10-01)

• Where: src/optmat/data/sources/dewitt_2001.toml, loriot_2008.toml, dura_2012.toml, sharma_2018.toml, their scripts in tools/extract/; the quantity ionization_yield_ratio (optmat.vocabulary, docs/data.md).

• Transcribed:

  • DeWitt, Wells & Jones (PRL 87, 153001 (2001)), 790 nm, 100 fs, gas mixtures: O2:Xe (Fig. 1, 18 points, 1.9e13 to 9.5e13 W/cm2) and N2:Ar (Fig. 2, 34 points, 4.4e13 to 6.1e14) read from the vector drawings, and the text’s ‘between 0.15 and 0.2’ (O2:Xe, as 0.175 +- 0.025, a bound) and ‘approximately 1.7’ (N2:Ar). No ion-detector efficiency correction (their ref. 19: Guo et al.’s ‘effectively reduced their O2:Xe ionization ratio by a factor of 2’); dissociative and double ionisation added to the single channel. Intensity from the onset of double ionisation of the noble gases; no uncertainty stated.

  • Loriot, Hertz, Lavorel & Faucher (J. Phys. B 41, 015604 (2008)), 800 nm, 100 fs, all-optical (cross-defocusing calibrated by field-free alignment): N2’s ionisation probability for parallel and perpendicular polarisations (Fig. 4, vector; the parallel set reproduced from their earlier work, not in the library) and N2/Ar (Fig. 7, 7 points, 0.72 to 0.89; text 0.8 +- 0.1). O2/Xe ‘lower than 0.2 for I_0 < 40 TW cm^-2’ is in the notes only (a bound, not a value). The intensity calibration is not described.

  • Durá et al. (J. Phys. Chem. A 116, 2662 (2012); online 2011), Fig. 4 read from its image: O2/Xe 0.115, 0.239, 0.273 at 800, 1300, 1400 nm, N2/Ar 0.71 to 0.89, at 3e13 W/cm2, with the Z/sqrt(M) correction of the detector (quoted). The intensity rests on Guo et al.’s Xe+ yields; the OPA pulses’ durations are not stated.

  • Sharma et al. (Sci. Rep. 8, 2874 (2018)): O2’s eight-photon cross-section (3.3 +- 0.3)e-130 W^-8 m^16 s^-1 at 800 nm, 164 fs, below 2.7e13 W/cm2, from absolutely counted electrons and beam metrology (Table 1, checked by the script). The +-0.3 is the fit’s; the duration’s 5.3 % is about 37 % in sigma_8 (proportional to tau^7), and the electron number rests on an assumed collision frequency.

• Checked: the texts’ numbers against the figures (DeWitt’s O2:Xe median 0.183 below 1e14 W/cm2, N2:Ar 1.82; Loriot’s mean 0.811 +- 0.070; Durá’s rise by 2.4); Loriot’s Fig. 7 redraws ten of DeWitt’s N2:Ar points, which match the reading of DeWitt’s Fig. 2 to 0.21 % in intensity and 0.005 in the ratio; overlays of every figure.

• Finding (the models):

  • O2/Xe: the default’s yield ratio (100 fs, 790 nm) is 0.23 to 0.70 of DeWitt et al.’s uncorrected ratio. With their detector’s correction (Guo’s 2.03) it would be 0.47 to 1.4 of it. At 3e13 W/cm2 the default gives 0.037 to 0.039 from 0.78 to 1.4 um, against Durá et al.’s corrected 0.115 to 0.273: three to seven times low, and without the measured rise with wavelength.

  • N2/Ar: the measurements disagree with each other: DeWitt 1.05 to 2.03 (uncorrected), Loriot 0.72 to 0.89 (optical), Durá 0.71 to 0.89 (corrected). The default (0.84 to 1.39) lies between: 0.43 to 0.95 of DeWitt’s, 1.11 to 1.63 of Loriot’s, 1.6 to 1.9 of Durá’s.

  • O2’s multiphoton rate: the default’s cycle-averaged rate over sigma_8 I^8 is 11.9 at 1e13, 2.7 at 2e13 and 1.3 at 2.7e13 W/cm2 (Keldysh parameter 3.2 to 1.9), too high and too shallow at large Keldysh parameter, as for the atoms (TC-817).

• Doubt: the three ratio measurements’ intensities are weakly calibrated, and their detection conventions differ by a factor of about 2 for O2/Xe; xenon’s own rate against argon’s is in question (TC-819), which moves O2/Xe and not N2/Ar.

• Status: verified (2026-10-01); open with TC-683 (O2 against xenon) and TC-819.

TC-823 lin_2012 (Lin et al., Phys. Rev. Lett. 108, 223001 (2012)): O2/Xe and N2/Ar at 800 and 2000 nm (2026-10-01)

• Where: src/optmat/data/sources/lin_2012.toml, tools/extract/lin_2012.py.

• Transcribed: Fig. 2, read from the vector drawing: O2+/Xe+ at 800 nm (28 points, 3.7e13 to 2.4e14 W/cm2, 0.071 to 0.354) and 2000 nm (44 points, 3.6e13 to 2.2e14, 0.076 to 0.526); N2+/Ar+ at 800 nm (25 points, 0.88 to 1.01) and 2000 nm (32 points, 1.01 to 1.27), as ionization_yield_ratio, use = "check". No error bars; the uncertainty is the digitising’s (0.1 %). Not stated in the paper: the pulse durations, the intensity calibration and its uncertainty, any correction of the detector’s efficiency (Z/sqrt(M) would lower O2/Xe by 2.03 and N2/Ar by 1.194), the 800 nm polarisation, and whether each pair was a mixture.

• Checked: every tick on its scale (0.028 pt); Fig. 2(a) is the quotient of Fig. 1(a)’s yields at every one of its 72 points within 0.7 % (2000 nm) and 0.4 % (800 nm), except 800 nm at 110.5 TW/cm2 (0.156 against 0.133); Fig. 2(b) is not Fig. 1(b)’s quotient throughout (up to 25 % and 45 % apart at shared intensities; the paper does not say how it was made); the text’s ‘around 1’ (N2/Ar median 1.024), the 2000 nm ratio at least 1.41 times the 800 nm one above 60 TW/cm2, and the 800 nm ratio rising as I^0.96 (‘about 4 times’ for 4 times the intensity); overlays.

• Finding: with an assumed 50 fs pulse and no focal average, the default’s O2/Xe is 0.55 to 2.3 times Lin et al.’s at 800 nm (median 0.95) and 0.29 to 1.17 at 2000 nm (median 0.46): at 1e14 W/cm2 and 2000 nm 0.074 against 0.243. The measured ratio rises with the wavelength above 6e13 W/cm2 and the default’s does not, as for Durá et al. (TC-822). N2/Ar: 0.85 to 1.23 (800 nm) and 0.72 to 0.96 (2000 nm) of the measured.

• Doubt: the uncalibrated intensity scale; Fig. 2(b) against Fig. 1(b); the one 800 nm point; the unstated detection convention, which decides whether the default’s O2/Xe at 800 nm is right (median 0.95 uncorrected) or twice too high (1.92 corrected).

• Status: verified (2026-10-01); open with TC-683 and TC-822.

TC-824 travers_2026_trecx: argon’s one-electron ionised fraction at 400 nm; the Coulomb factor at large Keldysh parameter (2026-10-01)

• Where: src/optmat/data/external/trecx/scan_wavelength/results_400.csv, PROVENANCE.md there, travers_2026_trecx.toml (ionised_gauss10_400nm_Ar_m0, _m1), tools/extract/travers_2026_trecx.py, optmat.gas.ionisation_validation.TDSE_YIELDS, tools/ionisation_rate_tables.py, docs/ionisation_rates.md.

• Transcribed: the ionised fraction, 1 - bound(n <= 10) at the end of the pulse, of Ar 3p m = 0 and m = 1 in Tong and Lin’s potential at 400 nm, a 10 fs Gaussian, ten intensities from 3e13 to 1.5e15 W/cm2 (Keldysh parameter 4.19 to 0.59): J. C. Travers’s tRecX runs of 1 October 2026, the A2 set-up (TC-812). Tier 3. Uncertainty 0.046 to 0.32 % by A2’s rule, recomputed by the script and tested; m = 1 takes m = 0’s.

• Checked: every run complete; the drift (every yield 250 times above the floor); the pulse; the norm; convergence in the step and cutEnergy (PROVENANCE.md).

• Finding (the Coulomb factor): the one_electron model, with the default’s static factor, is 1.4 to 3.9 times the calculation at Keldysh parameters 1.4 to 4.2 (1.03 to 1.29 below 1.2): Nambu et al.’s measured excess at 400 nm (TC-817) appears for one electron, so it lies in the model’s dependence on frequency, not in the atom. With only the Coulomb factor changed to Popruzhenko et al.’s, the model is 0.23 to 0.36 of the calculation at 2.2 to 4.2 and 0.43 to 0.80 at 1.1 to 1.8. The calculation lies between, as at 800 nm (TC-812). A factor between them, static x (1 + 2 gamma/e)^(-2 n* beta), scanned over beta on the three one-electron argon sets (400 nm 10 fs; 800 nm 6 fs and 42 fs; yields below 0.75), fits best at beta = 0.3: the model over the calculations is then 1.36, 0.93 and 0.84 on geometric average (rms factor 1.29, against 1.64 for the static factor, beta = 0, and 2.87 for Popruzhenko’s, beta = 1). 400 nm alone would take beta about 0.45, 800 nm about 0.2 to 0.3: the Keldysh parameter alone does not order the excess. The scan is not a model in optmat.

• Doubt: one carrier-envelope phase; one wavelength more (1030 nm) is still to run.

• Status: verified (2026-10-01); the Coulomb factor at large Keldysh parameter is the maintainer’s to decide (TC-819, TC-820).

TC-825 zhao_2016 (Zhao, Le, Jin, Wang & Lin, Phys. Rev. A 93, 023413 (2016)): one-electron TDSE yields of H, He, Ne, Ar, Kr, Xe; the Coulomb factor’s dependence on wavelength (2026-10-01)

• Where: src/optmat/data/sources/zhao_2016.toml, tools/extract/zhao_2016.py, src/optmat/data/materials.toml (atomic hydrogen, H, a material named only by such reference calculations; not one of optmat’s gases), optmat.gas.ionisation_rates.coulomb_factor (its docstring).

• Transcribed: from the vector drawings, the one-electron TDSE ionisation probability (1 - the bound states, Eq. 6; generalized pseudospectral method) for a 15 fs Gaussian: H at 600, 800, 1000 and 1200 nm (Fig. 2, 25 points each), He and Ne at 400 nm, Ar, Kr and Xe at 800 nm (Fig. 3, 29 to 41 points), ionization_yield, use = "check", 2 % digitising; Xe’s potential parameters (text). The authors’ correction factors of PPT (Fig. 1) are in the notes. Not stated: which m was propagated, the pulse’s FWHM convention (an intensity FWHM reproduces their PPT curves), Kr’s potential’s parameters (Garvey et al.).

• Checked: every tick on its scale; the insets against the main panels (0.1 % in intensity, 1.3 to 1.6 % in probability); the gamma arrows against the intensities (1.1 and 1.3 %); the printed 1.49 and the legends’ 1.42, 1.49, 1.36, 1.26 against Fig. 1; their PPT reproduced by optmat’s PPT with Popruzhenko et al.’s factor and the discrete channel sum to 0.92 to 1.00.

• Finding:

  • Hydrogen: the TDSE is 1.3 to 1.8 times PPT with Popruzhenko et al.’s factor and 0.38 to 0.58 of PPT with the static factor (averages over 6 to 13e13 W/cm2; the static factor 2 to 2.6 times high). At equal Keldysh parameter the ratio still moves with the wavelength, by about 35 % from 800 to 1200 nm (TDSE over the static form 0.43, 0.50, 0.58 at 800, 1000, 1200 nm and gamma = 1): the correction depends on the wavelength beyond gamma.

  • The noble gases, one electron (one_electron, 15 fs, m = 0 assumed): the static factor is 1.23 times the TDSE for Ar at 800 nm (the tRecX calculations: 1.24 at 42 fs, TC-702), 2.23 for Kr and 1.75 for Xe at 800 nm, 1.43 for He and 1.59 for Ne at 400 nm; Popruzhenko et al.’s 0.34 to 0.60 (geometric means). The model’s excess for one electron of Xe over Ar’s, 1.4, is part of the excess of Xe against Ar that the absolute measurements show (TC-819).

  • The excess orders with s = n* omega/2 I_p, the parameter of Perelomov, Popov and Kuznetsov’s (1968) range of validity of the static factor (TC-670: s = 0.046, 0.055, 0.068 for Ar, Kr, Xe at 800 nm, twice that at 400 nm, against a critical value of about 0.04 at gamma = 3): a correction of the Coulomb factor in gamma and s is the candidate the data suggest.

• Doubt: the TDSE’s own accuracy is not stated; the unstated m and Kr potential.

• Status: verified (2026-10-01); open with TC-824 (the Coulomb factor).

TC-826 travers_2026_trecx: argon’s one-electron ionised fraction at 1030 nm; the Coulomb factor’s dependence on frequency (2026-10-02)

• Where: src/optmat/data/external/trecx/scan_wavelength/results_1030.csv, PROVENANCE.md there, travers_2026_trecx.toml (ionised_gauss10_1030nm_Ar_m0, _m1), tools/extract/travers_2026_trecx.py (WAVELENGTH_TABLES), optmat.gas.ionisation_validation.TDSE_YIELDS, docs/ionisation_rates.md.

• Transcribed: the ionised fraction, 1 - bound(n <= 10) at the end of the pulse, of Ar 3p m = 0 and m = 1 in Tong and Lin’s potential at 1030 nm, the 10 fs Gaussian of TC-824 (2.9 cycles), ten intensities from 1e13 to 5e14 W/cm2 (Keldysh parameter 2.82 to 0.40): J. C. Travers’s tRecX runs of 2 October 2026. BOX 80, and 120 at the two highest intensities. Tier 3. Uncertainty 0.22 to 4.2 % (m = 1: up to 7.1 %, its drift) by A2’s rule, recomputed by the script and tested. Rows within a factor 10 of the loss without a field (m = 0: 0 and 1; m = 1: 0 to 2) are excluded as upper bounds; the test checks that the excluded rows are exactly those.

• Checked: every run complete; the drift; the pulse; the norm; convergence in BOX, angular momentum, the step, cutEnergy and the ECS angle, whose halving moves n = 9 and 10 states out of the labelled set (+0.9 to 1.3 %; 1 - bound(n <= 8) changes by 0.1 %) (PROVENANCE.md).

• Finding: the one_electron model with the default’s static factor is 1.02 to 1.35 times the calculation at Keldysh parameters 0.4 to 1.8. At gamma = 1.8 it is 1.1 times at 1030 nm, 1.6 at 800 nm (6 fs, TC-812) and 2.0 at 400 nm (the same 10 fs pulse, TC-824): at equal Keldysh parameter the excess grows with the frequency. With only the Coulomb factor changed to Popruzhenko et al.’s, the model is 0.22 to 0.38 of the calculation at 1.2 to 1.8 (the literature’s form, ppt_popruzhenko, 0.31 to 0.62 on the envelope). The scan of TC-824 (static x (1 + 2 gamma/e)^(-2 n* beta), yields below 0.75, on the carrier), now on four sets: the geometric mean of model over calculation is 1 at beta = 0.15 (1030 nm, 10 fs), 0.16 (800 nm, 42 fs), 0.24 (800 nm, 6 fs) and 0.48 (400 nm, 10 fs); a single beta of 0.25 to 0.3 leaves an rms factor of 1.28 (static 1.57). The fraction grows with the frequency, but the two 800 nm pulses differ by as much as 800 and 1030 nm, so the pulse length (or the number of cycles) is mixed in: an 800 nm run with the 10 fs pulse is to separate them. The scan is not a model in optmat.

• Doubt: one carrier-envelope phase; 2.9 cycles, so the yield of the central half-cycles dominates.

• Status: verified (2026-10-02); open with TC-824 (the Coulomb factor).

TC-827 Correction of TC-825: hydrogen against the static Coulomb factor with Tong and Lin’s static correction (2026-10-02)

• Where: docs/ionisation_rates.md, optmat.gas.ionisation_rates.coulomb_factor (its docstring), CHANGELOG.md.

• The error: TC-825 compared Zhao et al.’s one-electron hydrogen with the short-range rate times the Coulomb factor alone, without the static correction that every model of optmat’s noble gases carries. At Zhao et al.’s intensities (6 to 13e13 W/cm2) the field is 0.69 to 0.95 of hydrogen’s barrier-suppression field, where Tong and Lin’s factor with alpha = 6 (their Table 2 for H; tong_2005’s notes, not curated) is 0.5 to 0.6. So TC-825’s “static factor 2 to 2.6 times high for hydrogen” was about half the over-barrier correction. Its noble-gas comparisons used one_electron, which has it, and stand. Pointed out by a review of Le et al. (2016) and Bauer and Deng (2018).

• Corrected: hydrogen as a from_parameters model like one_electron (C_l = 2, l = 0, one electron, Tong and Lin alpha = 6, the default’s channel sum and averaging), 15 fs, the instantaneous rate on the carrier, geometric mean over 6 to 13e13 W/cm2: model over TDSE 1.09 (1200 nm), 1.17 (1000), 1.28 (800), 1.53 (600) with the static factor (without Tong and Lin’s: 1.93, 2.05, 2.24, 2.61). The excess still grows with the frequency at equal Keldysh parameter, as for argon (TC-826). The fraction beta of TC-824’s blend that makes the mean 1 is 0.10, 0.15, 0.20, 0.28: beta/s = 2.6 to 3.7 with s = n* omega/2 I_p, against 3.5 to 5.3 for the four argon sets (TC-826).

• Status: corrected (2026-10-02).

TC-828 The average over a cycle by quadrature; the rate held above its maximum field; the molecules’ ranges (2026-10-02)

• Where: optmat.gas.ionisation_rates (_log_cycle_averages, _held, IonisationRateModel._log_rate_au, EVALUATION_VERSION 2), optmat.gas.molecular_ionisation_rates (correction_range, maximum_field, EVALUATION_VERSION 2), molecular_ionisation_rates.toml (correction_range per molecule, with reasons), docs/ionisation_rates.md, docs/molecular_ionisation_rates.md, tests/data/golden_models.json, tests/data/legacy_ionisation_rates.json.

• Found: solprop’s agent reported that the 0.1.1 rates turn over just above their maximum field (1.04 to 1.07 times for Ar, Kr, Xe, 1.16 to 1.19 for N2 and He) and carry about 3e-9 of rounding noise (He). Both reproduced, and traced to the “consistent” averaging (TC-662): the average over a cycle was a second-order expansion in the logarithmic slope and curvature of the rate, by finite differences with a step of 1e-3. Near the maximum field Tong and Lin’s factor bends the rate (curvature -7 at slope 2 for Ar) and the expansion fails: the cycle-averaged rate was 1 % low at the barrier-suppression field F_b, 5 % at 1.5 F_b and 24 % (Ar), 13 % (He) at 2 F_b, turned over at 1.01 to 1.14 times the maximum field while the rate it averages rises to 1.34 to 1.57 times, and above it swung erratically (TC-816). The rounding of the second difference gave the noise, rising to 3.6e-9 near the maximum. TC-662 had tested the expansion up to F_b only.

• Changed:

  • The average over a cycle by quadrature for the atoms and the molecules alike: with cos(phi) = exp(-t^2) the integrand is smooth and falls as exp(-(1 + s)t^2); 32-point Gauss-Legendre over t sqrt(1 + s) in [0, 5], s the rate’s own slope. Against 4000-point quadrature in the phase it is within 4e-7 up to the maximum field and 5e-5 at three times it, for He to Xe and N2, O2 from 400 nm to static. The noise is 2e-14. The cost is about four times the expansion’s (10 microseconds per field per rate). The average of the instantaneous rate over a cycle is the cycle-averaged rate to 4 % at 400 nm (Xe, 3.9 %) and 1.5 % at 800 nm.

  • The rate held above its maximum field for models with a static correction, at its value there, with the warning (the maintainer’s decision); the literature’s forms without one keep their rising formula. Every rate now rises monotonically.

  • Each molecule’s range (correction_range, in F_b), the maintainer’s choice among three: the largest field its alpha was fitted to or checked against, not the former 1.5 for all, which would have held O2 at 0.30 of jagau_2018’s rate at 0.10 au, where alpha was fitted: H2, D2 1.61; N2 and the molecules that take its alpha (CO, CO2, N2O, SF6) 1.71; O2 1.96; CH4 1.72. Each is below the field where its rate would turn over (2.0 to 3.4 F_b).

• Effect on the values: at 800 nm the default’s cycle-averaged rate rises by 0.3 % (Ar, 1e14 W/cm2) to 12 % (He) and 30 % (one-electron Xe) at 0.95 to 0.98 of the maximum field, the instantaneous rate by -10 % to +0.2 %; above the maximum field the golden values change by up to 250 times (the held value against the old erratic one). Parker et al.’s helium at 390 nm: 1.27 to 1.45. The comparisons with the TDSE, the measurements and Luna and solprop (the page’s tables) are regenerated. Golden values re-recorded (the identity digests change with the evaluation version).

• Status: implemented (2026-10-02); closes TC-816.

TC-829 Luna.jl, solprop and the default through every test at 800 nm (2026-10-02)

• Where: tools/legacy_ionisation_measured.py (TabulatedRate, now a subclass of IonisationRateModel; substituted, phase_shift_references, parker_ratios), tools/ionisation_rate_tables.py (legacy_tests_table), docs/ionisation_rates.md (Luna.jl and solprop), ionisation_rates.toml (the reasons’ ratios, after TC-828).

• Why: the maintainer asked whether solprop should take optmat’s default for the noble gases now. TC-815 tested the codes on Wallace et al. and Wahlstrand et al. only; the phase shifts curated since (TC-817, TC-818) and the two-electron helium had not been applied to them.

• Done: each code’s rate (the fixture’s, interpolated) through intensity_scale_test (Wallace et al.), phase_shift_test (Nambu et al., Nie et al.: 800 nm, linear), measured_yields (Wahlstrand et al.) and helium_laser_rates (Parker et al. at 780 nm against the codes’ 800 nm, up to the fixture’s 1e15 W/cm2), with optmat’s default at its own wavelength and at 800 nm; a generated table on the page, tested to be current. The reasons’ ratios moved by TC-828 are updated (Ar one electron 1.08 to 1.67; He 1.16 to 1.23; Parker et al. 0.95 to 1.19 at 780 nm, 1.27 to 1.45 at 390 nm).

• Finding: the best intensity factors (1 a match; below 1 the code is high):

  • Wallace et al. (Ar, Kr, Xe; calibration 1.3 to 2.5 %): Luna 1.05, 0.95, 0.90; solprop 0.94, 1.06, 1.13; the default 0.98, 1.00, 1.00, the only one within the calibration for all three;

  • Nambu et al. (Ar, Kr, Xe): Luna 1.08, 0.85, 0.88; solprop 1.19, 0.99, 1.03; the default 1.01, 0.95, 0.89;

  • Nie et al. (He, Ar, Kr, Xe): Luna 0.90, 0.98, 0.80, 0.75; solprop 0.93, 1.12, 0.92, 0.89; the default 0.90, 0.93, 0.87, 0.77;

  • root mean square over the ten: 1.15 (Luna), 1.10 (solprop), 1.12 (the default);

  • over Wahlstrand et al.’s yields: Luna 0.97 to 3.1 (Ar), 1.4 to 7.3 (Kr), 1.8 to 9.4 (Xe); solprop 0.64 to 1.6, 0.88 to 3.5, 1.1 to 4.2; the default 1.7 to 4.0, 1.7 to 4.0, 4.2 to 7.9;

  • Parker et al.’s helium (two electrons): the default 0.86 to 1.11 at 800 nm (0.95 to 1.12 at its 780 nm), Luna 0.59 to 1.44, solprop 0.50 to 0.88.

  The measurements differ among themselves (xenon’s factor 0.77 to 1.00 for the default) by more than the codes do; on the best-calibrated measurement and on the calculation of a whole atom the default is the closest. Against the one-electron calculations the codes’ Coulomb factor (Ilkov et al.’s) is 2.8 times low at gamma = 2.3 and 1.7 times high at 0.6, the default’s 1.08 to 1.67 high (the page’s table).

• Recommendation to the maintainer (not a decision here): solprop can take the default for the noble gases in the near infrared now, pinned by its identity; at 400 nm and below and gamma > 1.5 no code is good (the default 1.4 to 4 times high against the one-electron calculations, Ilkov et al.’s form low by a similar factor).

• Doubt: the codes’ rates are interpolated on 28 fields and held above 1e15 W/cm2 (and above Luna’s limit); the 2.5 % between Parker et al.’s 780 nm and the codes’ 800 nm.

• Status: verified (2026-10-02).

TC-830 travers_2026_trecx: argon’s one-electron ionised fraction at 800 nm with the 10 fs pulse; one electron at haCC’s ionisation energies archived (2026-10-03)

• Where: src/optmat/data/external/trecx/scan_wavelength/results_800.csv, ip_matched/results_ci.csv, ip_matched/results_c3m1.csv, PROVENANCE.md there, travers_2026_trecx.toml (ionised_gauss10_800nm_Ar_m0, _m1), tools/extract/travers_2026_trecx.py (WAVELENGTH_TABLES), optmat.gas.ionisation_validation.TDSE_YIELDS, docs/ionisation_rates.md.

• Transcribed: the ionised fraction, 1 - bound(n <= 10) at the end of the pulse, of Ar 3p m = 0 and m = 1 in Tong and Lin’s potential at 800 nm, the 10 fs Gaussian of TC-824 and TC-826 (3.75 cycles), ten intensities from 1.5e13 to 8e14 W/cm2 (Keldysh parameter 2.97 to 0.41): J. C. Travers’s tRecX runs of October 2026. Tier 3. Uncertainty 0.096 to 2.3 % by A2’s rule, recomputed by the script and tested; the rows within a factor 10 of the loss without a field are excluded (m = 0: row 0; m = 1: rows 0 and 1).

• Checked: every run complete; the drift; the pulse; convergence in angular momentum, radial discretisation, BOX, the step, cutEnergy and the ECS angle, whose halving moves n = 9 and 10 out of the labelled set (2.3 %; 1 - bound(n <= 8) changes by 0.2 %). The BOX 160 check at 8e14 W/cm2 had a transient norm above 1 near the peak of the field; its yield agrees with BOX 120 to 0.03 % (PROVENANCE.md).

• Finding: with one pulse at three wavelengths, the one_electron model with the static factor is, at gamma = 1.8, 1.1 times the calculation at 1030 nm, 1.7 at 800 nm and 1.9 at 400 nm: the excess grows with the frequency at fixed pulse length, so it is not the pulse length of the 6 fs set. At 800 nm the 10 fs excess, 1.75 to 1.05 over gamma 2.4 to 0.5, is a little above the 6 fs one. In TC-824’s blend the fraction beta whose geometric mean is 1 (yields below 0.75) is 0.15 (1030), 0.29 (800) and 0.48 (400 nm), 4.2, 6.4 and 5.3 times s = n* omega/2 I_p.

• Also archived, not curated: one electron in Tong and Lin’s potential with its short-range terms scaled (Zhao et al. 2016, Eq. 3) to haCC’s ionisation energies, 0.560275 au (configuration interaction) and 0.563940 au (the 3-channel mMax 1 set-up’s effective energy), A2’s 6 fs pulse at haCC’s three intensities, the ionised fraction and the norm-loss (convergence 0.62 %). Raising the energy by 0.65 % lowers the yield by 1.24, 1.12 and 1.05 at 4.0e13, 9.6e13 and 2.3e14 W/cm2; the scaled potential at 0.560275 au gives 2.30, 1.98 and 1.33 times the unscaled potential’s yield. Interim (the haCC runs with mMax 1 are still running): the all-electron haCC norm-loss with 4 channels and mMax 0 is 0.76 (4.0e13) and 0.80 (9.6e13) of one m = 0 electron’s at the same effective ionisation energy (interpolated in log yield between the two energies), 0.81 with 3 channels. They are to be curated together with the final haCC runs.

• Doubt: one carrier-envelope phase; the haCC comparison is interim (mMax 0, lMax 20, the interpolation in the energy).

• Status: verified (2026-10-03); open with TC-824 (the Coulomb factor) and TC-660 (one active electron).

TC-831 A candidate Coulomb factor that depends on the frequency; the models frequency and one_electron_frequency (2026-10-03)

• Where: optmat.gas.ionisation_rates (CoulombFactor gains frequency; _FREQUENCY_CONSTANT; coulomb_factor), ionisation_rates.toml (frequency, one_electron_frequency, status provisional), docs/ionisation_rates.md (A candidate Coulomb factor), tests/test_ionisation_validation.py.

• Why: the one-electron calculations (TC-812, TC-824, TC-826, TC-830, TC-825) put the static factor too high at gamma > 1 by an amount that grows with the frequency at fixed gamma; Popruzhenko et al.’s factor is too low. A review of the literature found no derived correction that depends on more than gamma: every first-order Coulomb correction (Popruzhenko et al. 2008; Karnakov et al. 2015 eq. 5.8; the analytical R-matrix theory of Kaushal and Smirnova 2013, circular) depends on gamma alone; Perelomov, Popov and Kuznetsov’s (1968) term in s has the wrong sign; Popruzhenko’s (2014) invariant correction gives no rate. A dependence on the frequency at fixed gamma needs a term of order s = n* omega/2 I_p.

• The form: Q = (2 F_0/F)^(2n*) (1 + 2 gamma/e)^(-2 n* c s), per channel; it is TC-824’s blend with beta = c s, and tends to the static factor as omega -> 0.

• The fit: c minimising the root-mean-square logarithm of model (one_electron with this factor, the instantaneous rate on the carrier) over calculation, on the three 10 fs sets of argon (400, 800, 1030 nm; yields below 0.75), over c = 0 to 10 in steps of 0.5, refined by a parabola: c = 5.26, rounded to 5.25; rms factor 1.17 against 1.78 at c = 0; geometric means per set 1.00, 1.06, 0.96 at c = 5.25.

• Tested on data not fitted (geometric mean of model over calculation, static -> candidate): tRecX argon 6 fs 1.34 -> 1.00, 42 fs 1.24 -> 0.91, helium 6 fs 1.20 -> 1.12; Zhao et al. He and Ne (400 nm) 1.42, 1.57 -> 1.15, 1.14; Ar, Kr, Xe (800 nm) 1.23, 2.22, 1.75 -> 0.95, 1.53, 0.99; H at 600, 800, 1000, 1200 nm (Tong and Lin’s alpha = 6) 1.52, 1.28, 1.17, 1.09 -> 0.84, 0.89, 0.91, 0.91; Parker et al.’s helium at 390 nm 1.27 to 1.45 -> 0.85 to 1.28, at 780 nm 0.95 to 1.19 -> 0.85 to 1.13. Measurements, the intensity scale of the best fit (1 a match): Nambu et al. at 400 nm (Ar, Kr, Xe, linear and circular) 0.50 to 0.73 -> 0.90 to 1.11 (Xe circular 1.41; the static Xe linear fit is at the search’s bound of 0.5); Nambu et al. and Nie et al. at 800 nm (16 fits) rms 1.114 -> 1.083; Wallace et al. 0.98, 1.00, 1.00 -> 1.03, 1.07, 1.13, beyond the calibration of 1.3 to 2.5 %; Wahlstrand et al., rate over measured, 1.7 to 7.9 -> 1.0 to 4.6.

• Doubt: fitted to one gas, one pulse length and one carrier-envelope phase; hydrogen alone would take c = 2.6 to 3.7 (TC-827). The analysis was run with the form patched into the model (scripts not kept in the repository); the test checks the committed models against the 10 fs and 6 fs sets and Wallace et al.

• Status: implemented as provisional models (2026-10-03). Not the default: the maintainer’s decision waits for the all-electron haCC calculation of argon (TC-830) and the measurements to be reconciled.

TC-832 The equations of state’s molar mass; CoolProp’s pseudo-pure air against lemmon_2000 (2026-10-02)

• Where: EquationOfState.molar_mass and MixtureEquationOfState.molar_mass (optmat.gas.eos, optmat.gas.mixture_eos); the manual’s Conventions and Mixtures. Asked for by solprop (SEP 3), whose mass terms, dilute sound speed and mean free path for Gas.Air need the molar mass that goes with air_equation_of_state()’s density.

• Decision: a pure gas’s equation of state, and air’s, gives the molar mass its backend uses, CoolProp’s molar_mass(), the one its mass density and speed of sound are formed with. It equals the transport models’ molar_mass for the thirteen transport gases. A mixture’s gives its composition’s, sum x_s M_s over its constituents’ equations, for every method. The value is resolved from the backend, which the equation’s fluid and backend version fix, so it is not a field: no identity digest and no number changes, and the number densities do not use it (the CODATA convention).

• Finding: CoolProp 8.0.0’s pseudo-pure air (“Air”, Lemmon-JPCRD-2000) holds 0.02896546 kg/mol. Lemmon et al. (2000) print M = 28.9586 ± 0.0002 g/mol for the air of their equation (the unlabelled table “Fixed Points for Air”, p. 334, read from the image), the mean of their composition (Table 3, p. 337: N2 0.7812, O2 0.2096, Ar 0.0092; 28.9586007 g/mol with their constituents’ masses). The two differ by 2.37e-4 relative. CoolProp’s number equals the CIPM-2007 M_a of dry air (picard_2008, TC-570) to the last digit; where CoolProp took it from is not established. The pure gases agree with the paper: Ar 39.948, N2 28.01348, O2 31.9988 g/mol, as CoolProp holds them.

• Checked: CoolProp’s speed of sound of air uses its own molar mass: w equals sqrt((c_p / c_v) (dp/drho_molar)_T / M) to rounding with M = 0.02896546 kg/mol, and would be 1.18e-4 higher with Lemmon’s (tests/test_equation_of_state.py). The N2/O2/Ar mixture gives 28.9597 g/mol, its normalised composition’s mean.

• Decision on air (the maintainer, 2026-10-02): expose CoolProp’s value, so that the molar mass is consistent with the speed of sound and the mass density of the equation optmat evaluates. Lemmon’s printed value differs from it by less than the equation’s density uncertainty (0.1 %, k = 2).

• Status: decided (2026-10-02).

TC-833 Hydrogen as a test of the rate: Tong and Lin’s alpha for H, pulses in cycles, the yield against the frequency, and the hydrogen comparisons (2026-10-03)

• Where: tong_2005.toml (alpha_H, ip_H), tools/extract/tong_2005.py; optmat.vocabulary (ionization_yield_spectrum), docs/data.md; optmat.gas.ionisation_validation (cycle_pulse, pulse_yield(..., cycles=), hydrogen_model, HYDROGEN_YIELDS, hydrogen_yields, HYDROGEN_SPECTRA, hydrogen_spectra; RateComparison.gas may be "H"); tools/ionisation_rate_tables.py (hydrogen_table); docs/ionisation_rates.md (One-electron calculations of hydrogen); tests/test_ionisation_validation.py.

• Transcribed: Tong and Lin’s (2005) Table 2 column H, alpha = 6.0 and I_p = 0.500 au, skipped until atomic hydrogen became a material (TC-825); its Table 1 row (the bare Coulomb potential) stays uncurated.

• Added: a quantity for a yield against the photon energy or wavelength at a fixed peak intensity, with the pulse counted in cycles (Bauer and Deng’s Figs. 7 and 8); cycle_pulse, sin^2 ramps of the vector potential with an optional plateau (Le et al.’s sin^2, Bauer and Deng’s 2-10-2 flat top), the field -dA/dt (checked against the numerical derivative to 1e-3 of the peak, no static part); the hydrogen model, one_electron’s form for the 1s electron (C_0 = 2 exactly, l = 0, Tong and Lin’s alpha), compared on each calculation’s envelope (no calculation states its carrier-envelope phase), points whose stated uncertainty exceeds 10 % left out (Bauer and Deng’s Fig. 1 at low yield, read on a linear axis); the spectra at their vertices nearest to frequencies 0.005 au apart up to 0.25 au, below 350 nm without the model’s range warning.

• Finding (geometric means, yields below 0.75): below gamma = 1 every set agrees - static 1.05 to 1.32, the candidate frequency (TC-831) 0.92 to 1.03, Popruzhenko et al.’s 0.44 to 0.59; gamma 1 to 2: static 1.1 to 1.5 at 600 nm and longer, 2.6 to 3.7 at 400 nm, the candidate 0.76 to 0.95 (1.4 at 400 nm); above 2, in the multiphoton regime with resonances, static 0.9 to 4.4, the candidate 0.37 to 0.83 (low in every set: fitted to argon, it overcorrects hydrogen, which alone would take c = 2.6 to 3.7, TC-827). Against the frequency at 0.063 au (Bauer and Deng’s Fig. 8) static 1.14, 2.22, 2.90 and the candidate 0.94, 1.26, 0.75 in the three ranges; at 0.02 au (gamma >= 2 throughout) static 13 times high, and no form follows it. Zhao et al.’s comparison of TC-827 is now reproduced by the code (the model on the envelope here, on the carrier there: within a few per cent).

• Status: verified (2026-10-03); open with TC-824 (the Coulomb factor).

TC-834 bauer_2018 (Bauer and Deng, Chinese Phys. B 27, 093202 (2018)): one-electron TDSE of hydrogen in a flat-top pulse, against intensity and frequency (2026-10-03)

• Where: src/optmat/data/sources/bauer_2018.toml, tools/extract/bauer_2018.py, src/optmat/data/values/ionisation/H/bauer_2018__*.csv.

• Transcribed (vector figures, matplotlib drawings in form XObjects with real text labels; axes from the bottom and left ticks, every tick within 0.021 pt of its fitted scale; use = "check", digitised = "vector"): the TDSE ionisation probability of H(1s) (generalized pseudospectral method, length gauge, m = 0), a 2-10-2 cycle flat top (sin^2 ramps of A), I = F^2 in atomic units:

  • Fig. 5(a), 800 nm (omega = 0.057 au), 35 markers, 7.99e12 to 3.20e14 W/cm2, 1 %;

  • Fig. 1, 800 nm, 44 markers on a linear axis, 4.9e12 to 4.0e14 W/cm2, 0.001 absolute;

  • Fig. 6(a), 400 nm (0.114 au), 38 markers, 1.0e13 to 4.0e14 W/cm2, 1 %;

  • Figs. 7 and 8, against omega 0.040 to 0.645 au at F = 0.02 and 0.063 au (1.404e13 and 1.393e14 W/cm2), 640 and 4511 curve vertices (all kept), 20 % (the curves are smoothing splines: the grey TDSE curves of Figs. 5(a) and 6(a) depart from their own markers by up to 5 to 18 %). Not curated: the excitation and ground-state probabilities (no quantity), the five model curves (in the notes).

• Checked: Fig. 5(b) repeats Fig. 1 within 0.0003 and Figs. 6(a), (b) repeat Fig. 2 (6(a) within 0.75 %), as the captions say; the I_BSI lines at 1.3703e14 to 1.3705e14, the printed 1.37e14; the six printed F-I pairs agree with I = F^2 (3.51e16 W/cm2 per au^2); ground + excited + ionised sum to 1.0005 to 1.0012; the resonances the text names (Fig. 7: 0.375, 0.444 au, humps read at 0.379, 0.457; Fig. 8: 0.114, 0.228, read at 0.118, 0.228); overlays inspected (every marker captured once, the curves followed). The text’s excitation statements against the figures: ‘less than 10 %’ at 0.057 au (max 0.069); ‘up to 30 % near 1.5e14’ at 0.114 au (0.29 there, the maximum 0.34 at 1.7e14); ‘some 10 %’ excited at 3.5e14 (0.15).

• Finding (the source): Fig. 5(a)’s markers, which the caption says are Fig. 1’s calculations, are on another intensity grid and up to 20 % higher where the two share intensities (1.4e14: 0.313 against 0.261; 1.6e14: 0.472 against 0.393; 2e14: 0.852 against 0.797); Fig. 8 at 0.057 au, 0.063 au reads 0.317, siding with Fig. 5(a) (0.309) against Fig. 1 (0.260). Both are curated, with the discrepancy in the notes.

• Not stated: how the ionisation probability is computed, the grid, step and partial waves, the carrier-envelope phase, whether F = 0.063 is 0.0625, the frequencies of the calculations behind Figs. 7 and 8, ω = 0.057 au is 799.4 nm.

• Status: verified (2026-10-03). The comparison with the model: TC-833.

TC-835 le_2016 (Le, Wei, Jin and Lin, J. Phys. B 49, 053001 (2016)): one-electron TDSE of hydrogen in sin^2 pulses at 400, 800 and 1600 nm (2026-10-03)

• Where: src/optmat/data/sources/le_2016.toml, tools/extract/le_2016.py, src/optmat/data/values/ionisation/H/le_2016__fig12*.csv.

• Transcribed (Fig. 12, PDF page 19, vector; use = "check", digitised = "vector", 1 %): the TDSE curves’ points the drawing passes through (segment and Bezier ends, not control points), every one on the 1e12 W/cm2 grid of the calculation within 0.008e12: (a) 400 nm, 12-cycle sin^2, 8 points in three clusters (two single Beziers span 1.2 to 7.9e13 and 8.1 to 14.8e13; use with care); (b) 800 nm, 6 cycles, 38 points, 1.0e13 to 1.5e14 W/cm2; (c) 1600 nm, 6 cycles, 106 points, 2.0e13 to 1.5e14 W/cm2 (point-to-point structure up to 10 %, the calculation’s). Not curated: the ADK, PPT (Eq. 91, the static factor, scaled by 0.33, 0.33, 0.5), SFA and SFA-CC curves.

• Checked: axes from the frames’ ticks (within 0.009 pt and 0.001 pt), mirrored edges; the legend’s samples; the gamma = 1 dotted lines at 1.1413e14 (800 nm) and 2.8541e13 (1600 nm) against hydrogen’s 1.1384e14 and 2.8460e13 with I = c eps0 F^2/2 (+0.25 %, +0.28 %: a peak intensity, linear polarisation); the ranges against the text’s ‘1x10^13 to 1.5x10^14’; overlays inspected. The text’s ‘at 4x10^13 the ADK underestimates by almost two orders of magnitude’ (800 nm): the drawing gives 1/17 there (1/78 at 3e13). optmat’s static PPT without correction reproduces the drawn PPT curves to 0.90 to 0.98 (1600 nm) and 0.83 (800 nm) with sin^2 on the field, 1.33 and 1.15 on the intensity: the field is taken (TC-833).

• Not stated: the TDSE method, its accuracy and its measure of ionisation, the polarisation (linear, by the gamma lines), whether sin^2 is of the field or the intensity, the carrier-envelope phase.

• Status: verified (2026-10-03). The comparison with the model: TC-833.

TC-836 travers_2026_trecx: argon’s one-electron ionised fraction in Wallace et al.’s pulse; the calculation through their test (2026-10-03)

• Where: src/optmat/data/external/trecx/scan_wallace/results_cep0.csv, results_cep90.csv, PROVENANCE.md there, travers_2026_trecx.toml (ionised_wallace_cep0_Ar_m0, _m1, ionised_wallace_cep90_Ar_m0, _m1), tools/extract/travers_2026_trecx.py (WALLACE_TABLES, wallace_uncertainty), optmat.gas.ionisation_validation (TDSE_YIELDS, which now compares each calculation at its own carrier-envelope phase; WALLACE_TDSE, tdse_intensity_scale_test), docs/ionisation_rates.md.

• Transcribed: the ionised fraction, 1 - bound(n <= 10) at the end of the pulse, of Ar 3p m = 0 and m = 1 in Tong and Lin’s potential, in Wallace et al.’s (2016) pulse: a 5.5 fs Gaussian (intensity FWHM, 2.06 cycles) on the vector potential at 800 nm, carrier-envelope phases 0 and pi/2, twelve intensities from 5e13 to 6e14 W/cm2 (Keldysh parameter 1.62 to 0.47), into saturation: J. C. Travers’s tRecX runs of 2 October 2026. Tier 3. Uncertainty 0.33 to 1.5 % by A2’s rule at phase 0, recomputed and tested; phase pi/2 and m = 1 take phase 0’s m = 0.

• Checked: every run complete; the drift (9.5e-10, every yield far above it); the pulse; the norm; convergence (PROVENANCE.md).

• Finding:

  • The phase changes the m = 0 yield by -6.1 to +6.0 %, oscillating with the intensity (at equal envelope intensity the pi/2 field’s largest value is 0.981 E0).

  • Against the calculation (each phase on its own carrier) the one_electron model with the static factor is 1.06 to 1.45 times it, with the candidate frequency factor (TC-831, not fitted to these) 0.86 to 1.04.

  • Put through Wallace et al.’s test in place of a model (the m = 0 yield averaged over the two phases, the focal average, the intensity scale fitted to the shape of their measured yield), the calculation matches their argon at 1.002, within the calibration of 1.3 %: the measured saturation is that of exact one-electron physics. The test barely sees the rate’s magnitude: the calculation’s rate times 0.8 gives 1.016 (0.87: 1.012; 1.65: 0.966). The models: one_electron 0.970 and one_electron_frequency 1.019, either side of the calculation; default 0.984, frequency 1.033 (the fine structure moves them by about 1.4 %). So Wallace et al.’s argon does not discriminate between the static and the candidate factor, nor between an atom of 0.8 and 1 electron (TC-830); the 3 to 13 % beyond calibration that TC-831 reported for the candidate is for argon no evidence against it. Krypton’s and xenon’s calculations in the same pulse are to come.

• Doubt: the calculation is of one electron (m = 0) in a model potential; the extrapolation of the calculated yields beyond 5e13 to 6e14 W/cm2 in the focal average (the yields below are small, those above saturated).

• Status: verified (2026-10-03); open with TC-824 and TC-814.

TC-837 The rates’ evaluation: three to four and a half times faster, the same to the last bit (solprop SEP 3, Q46) (2026-10-02)

• Where: optmat.gas.ionisation_rates (_log_cycle_averages, _log_sum_exp, _closed_forms, IonisationRateModel._log_term) and optmat.gas.molecular_ionisation_rates (MolecularRateModel._log_term); tools/benchmark_rates.py.

• Finding (where the time went): solprop measured the default argon model at 800 nm at 1.2 ms a call plus 15 us a field. channel_sum = "integral" is not an integral evaluated per field: it is the closed form of the integral of Perelomov et al.’s eq. (55) over the number of photons (channel_factor), already vectorised. The cost per field is the average over a cycle by 32-node quadrature (TC-828), which evaluated every channel’s static and frequency-dependent terms at 67 fields for each field asked for. Each of its two 32-node passes kept one of the two terms, so the expensive one was evaluated at the cheap one’s nodes and discarded, and the terms at the amplitude were computed twice. The cost per call was scipy.special.logsumexp, some 70 us of dispatch a call, ten calls a rate call, and the Gauss-Legendre nodes, an eigenvalue problem solved at every call.

• Change:

  • Each rate is evaluated alone at its own nodes, and the terms at the amplitude are passed in.

  • The nodes are computed once.

  • _log_sum_exp repeats logsumexp’s arithmetic over the first axis step by step (SciPy 1.18) without its dispatch.

  • The closed forms of channel_factor and ppt_exponent_function share arsinh gamma and (1 + gamma^2)^(1/2) where every gamma is past the series (_closed_forms).

  • A molecule’s projections +-m’, of equal B^2(m’), are evaluated once each. Every expression and its order are kept. The 32-node arrays are the same, so even channel_sum = "sum", whose truncation depends on the whole array, is unchanged.

• Unchanged, checked:

  • Every curated atomic and molecular rate model (every named model; channel_sum = "sum" and both averagings), at 248, 400, 800, 1030 and 3900 nm and in a static field, at 101 fields from 1e-3 to 4 times the barrier-suppression field, zero, 1e-300 V/m and a negative field: instantaneous_rate, cycle_averaged_rate, circular_rate and channel_rates, 4734 cases, equal to 9af79f6’s to the last bit.

  • The golden values and identity digests; EVALUATION_VERSION is not raised.

  • The tests compare _log_sum_exp with SciPy (ties, one row, infinities, NaN), each rate alone with the pair, and the shared closed forms with the public functions, all bit for bit.

• Timings (tools/benchmark_rates.py --against, 9af79f6 and this tree in alternate rounds on one loaded machine, best of five; ms for 1 / 64 / 4096 fields):

  Model	Before	After	Faster
  Ar, default, 800 nm	0.83 / 1.48 / 45.7	0.20 / 0.41 / 14.2	4.1 / 3.6 / 3.2
  N2, molecular default	1.75 / 4.33 / 175	0.40 / 0.97 / 37.4	4.4 / 4.5 / 4.7
  H2, molecular default	1.43 / 3.32 / 111	0.38 / 0.80 / 28.8	3.7 / 4.2 / 3.9

  For argon: 0.2 ms a call and 3.4 us a field, from 0.8 ms and 11 us.

• Not done: what remains per field is the model at 2 x 32 + 2 fields. Fewer nodes, or a table of the averages against the field, would change the numbers (the quadrature is accurate to 3e-5 or better; TC-828); such a change would raise EVALUATION_VERSION, and it is not made here.

• Status: decided (2026-10-02).

TC-838 The derivative of a formula made absolute: a jitter of 1e-8 from differencing the air’s squared index (solprop SEP 3, Q38) (2026-10-02)

• Where: optmat.solid.models.formulas.FormulaModel._dpermittivity_domega (and _air_refractivity, _AIR_STEP); tests/solid/test_models.py.

• Finding: solprop found the analytic dindex_domega of CaF2 (daimon_2002, relative to nitrogen) to jitter by about 2e-8 between neighbouring frequencies, with alternating second differences, where the Sellmeier formula itself is smooth. The Sellmeier part of the derivative is analytic. The reference gas entered through a central difference of its squared index (1 + r)^2 with a step of 1e-6 omega. That squared index is about 1.0005 and is rounded at 1e-16 of 1, which is 1e-8 of its change over the step. The comment’s “1e-12 relative” was the truncation error alone. Every formula made absolute had the jitter, measured as the rms departure of the derivative from a quartic through 41 frequencies 1e-5 apart:

  • Daimon’s CaF2 (nitrogen): 4e-9 to 9e-9;

  • the air-relative formulas (Malitson’s SiO2, CaF2, MgF2, Al2O3 and BaF2; Dodge’s, Weber’s, Schott’s N-BK7), which also difference the standard-air wavelength: 2e-9 to 1.3e-8. The absolute formulas (Leviton, Arosa) had 5e-16. The fused-silica fit is a UDM with a complex-step derivative: 5e-13.

• Fix:

  • The refractivity r is differenced on its own; it keeps its digits.

  • d(n_air^2)/d omega = 2 (1 + r) dr/d omega.

  • The standard-air wavelength’s d(lambda^2)/d omega is -2 lambda^2 (1/omega + r_s’/(1 + r_s)), with r_s’ differenced alike.

  • The step is 1e-4 omega. Against Edlen’s formula differentiated by hand, the truncation error is below 8e-9 of dr/d omega from 250 nm to 3.5 um, and the rounding error is about 1e-10. The air’s term is below 1e-3 of the derivative.

  • The jitter is now 1e-14 to 9e-14 everywhere, the rounding of the formula.

• Changed values: the derivatives of the eleven formulas made absolute move by 2e-9 to 2.5e-8, the old error. Their indices are unchanged to the last bit. FormulaModel.EVALUATION_VERSION is raised from 1 to 2, so the digests of all thirteen formula models change, and the golden values are re-recorded. No other model’s record changed.

• Status: corrected (2026-10-02).

TC-839 D2’s viscosity from Assael et al.’s correlation, not a spline through their Table 2 (solprop SEP 3, Q33) (2026-10-02)

• Where: optmat.gas.transport (the form "assael", _assael; the form "table" and its spline removed) and data/gas/transport.toml ([gases.D2]); docs/transport.md; tests/test_transport.py.

• Finding: solprop found transport_model("D2").viscosity not smooth near 86-92 K: a Chebyshev series over 60-600 K or wider could not represent it to 1e-6. The spline interpolated Table 2 (TC-760) and passed through every cell. Two things made it wiggle:

  • the 90 K cell, 5.410 where the correlation and its neighbours give 5.416 (degraded in the scan, kept as printed; TC-765), which bent it most between 86 and 94 K;

  • the cells’ four-digit rounding, 2e-4, everywhere.

  Fitted in ln T over 60-600 K, the spline’s best Chebyshev series of degree 10 to 80 missed ln eta by 8.3e-4 to 7.1e-5. With the 90 K knot left out, 4.7e-4 to 7.1e-5. Narrowing the range would not have helped.

• Decision: D2’s viscosity is the correlation that reproduces the table (TC-765):

  • assael_1986’s Eqs. (1) and (3) (sigma = 0.2968 nm, epsilon/k = 33.3 K, the a_i of their Table 2) with the equation of state’s D2 molar mass;

  • times assael_1987’s 1 - exp(-f T*^(1/3)), f = 2.8105 (Eq. 7), at every temperature.

  The two source records are cited in its identity. Table 2 stays curated, as the check. Against it the correlation is within 1.5 units of its last digit, 5.1e-4 at most (at 250 K), except for the 90 K cell, 1.2e-3. Both are below the stated 1 % (250 to 350 K) and 2 % (below). A Chebyshev series of degree 20 in ln T reaches 2e-12 of ln eta over 60-600 K, and below 1e-9 over 30-2200 K.

• Unchanged: the range (30-2200 K, the table’s and the paper’s), the stated uncertainty, the status (validated) and the heat capacity.

• Changed values: the served viscosity moves by up to 5.1e-4 (1.2e-3 at 90 K). Against solprop’s recorded values it is now 0.42 % above at 200 K (0.41 % before) and 0.68 % below at 600 K. The model’s digest changes, and its golden values are re-recorded.

• Status: decided (2026-10-02).

TC-840 The status of a gas’s Raman response without the response (solprop SEP 3, Q42) (2026-10-02)

• Where: optmat.gas.raman_response.raman_response_status (and _status, the rule it shares with raman_response); docs/propagation.md, docs/raman_response.md; tests/test_raman_response.py.

• Need: solprop built a whole GasRamanResponse to learn whether a gas’s response is validated, provisional or absent. Building one computes every line at four densities: 0.6 ms for N2 and 5 ms for dry air.

• Decision:

  • raman_response_status(gas) reads the status and its reason from raman_response.toml’s choices: the worst status of the Raman-active constituents. It takes 1.5 us for N2 and 0.3 ms for dry air.

  • The rule is one function, used by both, so the two cannot differ. A test compares them for every curated gas and both air mixtures.

  • It returns None where no constituent is Raman-active: the noble gases, which have no rotational or vibrational Raman response, alone or mixed.

  • It refuses what raman_response refuses from the composition alone: a molecule without curated choices (CO, O3), and CIPM-2007’s full air.

• Limitation: the collision partners are not checked. A mixture whose constituents have no broadening coefficients by one another (CO2 with N2) has a status here, and raman_response refuses it.

• Status: decided (2026-10-02).

TC-841 Fused silica near 2 um: the dispersion of Lithosil Q2’s OH bands, not an artefact of the fit; its evaluation noise (solprop SEP 3, Q37, Q32) (2026-10-02)

• Where: fit/SiO2 (data/solid/models/fitted/SiO2.json, data/solid/fits/SiO2.toml); docs/silica.md. No code or data changed.

• The question (Q37): fit/SiO2’s GVD differs by 1.7 % from Malitson’s formula near 2 um, and its beta3 has structure that a finite-difference stencil resolves. solprop asked whether this is the refit to the absolute data or an artefact.

• Finding: the structure is the Kramers-Kronig dispersion of absorption bands in Franta’s model of the Lithosil Q2 plate, which the refit keeps unscaled (Nph36-52; TC-399). The bands:

  • the 2.73 um fundamental, Nph36-41, 3600-3697 cm^-1;

  • a narrow group at 4449, 4467 and 4526 cm^-1 (2.25, 2.24 and 2.21 um), FWHM 293, 122 and 51 cm^-1, Nph45-47, with k up to 1.05e-5 at 2212 nm (alpha = 0.6 cm^-1);

  • weaker bands at 1.90-2.59 um (Nph42-43, 48-49) and at 1.38 um (Nph50-52).

  At 2.0 um the fit’s beta2 is 1.73 % above Malitson’s made absolute. With the bands set to zero (and nothing refitted) it would be 0.33 % below, so the bands give +2.07 %: the fundamental 1.31 %, the 2.2 um group 0.77 %, the rest 0.0-0.1 %. The 2.2 um group alone changes beta3 at 2 um by 6.8 % (a 1 nm stencil; 7.8 % at 50 nm). Near 2.2 um the GVD swings to +712 fs^2/mm, against -149 fs^2/mm for Malitson’s. The refit itself contributes -0.3 % to -0.5 % to beta2 from 1.5 to 2.0 um.

• What the data say:

  • The absolute refractometry agrees with the fit, bands included, to about 1e-5 from 1.5 to 2.44 um: Malitson’s three prisms (Corning 7940, Dynasil, GE 151) at 1.53, 1.66-1.81, 1.97, 2.06, 2.15, 2.33 and 2.44 um, and Leviton’s Corning 7980 at 1.6-2.5 um (2.6 um: 3e-5).

  • Without the bands, and not refitted, the residuals grow to -2e-5 to -4e-5 at 2.15-2.44 um and -1e-4 at 2.6 um. Most of that is the smooth tail of the 2.73 um fundamental, which a refit could partly absorb.

  • The 2.2 um group’s swing in n is 1.2e-5 peak to peak (2196-2278 nm), about the refractometry’s precision, and its wavelengths are 0.1-0.2 um apart. The absolute data therefore neither confirm nor exclude the group at Lithosil Q2’s strength in their grades.

• Source checked: Franta et al. (2016), Fig. 23 (left), plots the plate’s k “in the region of OH vibrations” to 5000 cm^-1 on a scale (0-0.045) on which these bands do not show. The text discusses the 3600 cm^-1 OH peak and the films’ water but does not assign the 4450-4530 cm^-1 bands. They are in the newAD2 parameter file (the curated model). Their assignment is not taken from a curated source here.

• Decision: none to the fit; keeping or dropping Lithosil Q2’s 2.2 um bands for other grades is a curated choice for the maintainer. The silica page now states the bands, their effect on beta2 and beta3, and that Malitson’s and Leviton’s formulas have none.

• Evaluation noise (Q32): fit/SiO2’s n carries 1e-15 to 6e-15 relative rounding noise at 0.8-3.5 um (rms about a quartic over 41 frequencies 1e-5 apart), and its dn/domega 1e-13 to 6e-13. The noise comes from the cancellation of the UDM’s closed forms below a term’s characteristic energy, where the series takes over only below 0.05 E_g (TC-321). It is left as it is: moving the switch would change values far below any physical effect. The derivative is a complex step, exact to that noise.

• Status: decided (2026-10-02). The bands’ fate is left open to the maintainer.

TC-842 Argon at 390 nm: van der Hart’s all-electron rates against the candidate Coulomb factor; the atom at about 0.87 of one electron (2026-10-03)

• Where: tools/ionisation_rate_tables.py (rmatrix_table: a column for one_electron_frequency), docs/ionisation_rates.md (All-electron rates at 390 nm), tests/test_ionisation_validation.py.

• Finding: TC-701 found the default 1.6 to 2.9 times van der Hart’s all-electron R-matrix rates of argon at 390 nm (Keldysh parameter 2.1 to 1.4) and left open how much was the model’s and how much the atom’s. With the candidate frequency-dependent Coulomb factor (TC-831), which the one-electron calculations ask for, one electron (one_electron_frequency) is 0.85 to 1.37 times the R-matrix rates below gamma = 2.2: 1.17 times the Floquet rates (vanderhart_2006, 16 points) and 1.07 times the time-dependent ones (vanderhart_2007 Fig. 4, 4 points), 1.36 at Table I’s one point; 1.155 over all 21 on geometric average. So most of TC-701’s gap is the Coulomb factor’s, and the atom ionises at about 0.87 of one electron, as haCC’s interim all-electron calculation of argon at 800 nm finds (0.76 to 0.87 at matched ionisation energy, TC-830): two all-electron methods, at two wavelengths, agree. At higher gamma (multiphoton, resonant) the candidate is still 1.7 to 4.5 times the calculations. Helium: one_electron_frequency is 0.64 to 0.86 of the two-electron Floquet rate away from its resonance, an atom at 1.2 to 1.6 electrons, as Parker et al.’s static rates (1.27 to 1.59, TC-658) and haCC at 800 nm (1.65) give.

• Doubt: the candidate is fitted to one-electron argon (TC-831); the R-matrix calculations have one state of the ion (van der Hart’s one-state basis); haCC’s result is interim (mMax 0).

• Status: verified (2026-10-03); bears on TC-660 (one active electron) and TC-824.

TC-843 travers_2026_trecx: atomic hydrogen at 400 and 800 nm, 15 fs; a second code for Zhao et al.’s hydrogen (2026-10-03)

• Where: src/optmat/data/external/trecx/scan_hydrogen/results_400.csv, results_800.csv, PROVENANCE.md there, travers_2026_trecx.toml (ionised_gauss15_400nm_H, _800nm_H), tools/extract/travers_2026_trecx.py (HYDROGEN_TABLES), optmat.gas.ionisation_validation.HYDROGEN_YIELDS, docs/ionisation_rates.md (One-electron calculations of hydrogen), tests/test_ionisation_validation.py.

• Transcribed: the ionised fraction, 1 - bound(n <= 10) at the end of the pulse, of H 1s in the bare Coulomb potential, a 15 fs Gaussian (intensity FWHM) on the vector potential at 400 and 800 nm, carrier-envelope phase 0, ten intensities from 5e13 to 3e14 W/cm2 (Keldysh parameter 3.02 to 1.23 and 1.51 to 0.62): J. C. Travers’s tRecX runs of 2 October 2026 (part D of the runs). Tier 3. Uncertainty 0.002 to 0.058 % by A2’s rule, recomputed and tested.

• Checked: every run complete; initial -0.5; the pulse; the drift (2.1e-9 to 2.6e-9); convergence in every variation (BOX and the ECS angle the largest, through n = 9 and 10).

• Finding:

  • Zhao et al.’s 800 nm hydrogen (TC-825, read from their vector figure), the same 15 fs pulse and measure: 0.96 times tRecX’s on geometric average, 0.72 to 1.17 point by point (18 points, 5.5e13 to 1.4e14 W/cm2; tRecX’s ten intensities, interpolated, are coarser than the resonances): a second code confirms the reading of their figure and the intensity-FWHM convention assumed there.

  • Against the hydrogen model (TC-833), geometric means of the yields below 0.75: 800 nm, the static factor 1.19 (gamma below 1) and 1.21 (1 to 2), the candidate frequency 0.96 and 0.81, Popruzhenko et al.’s 0.56 and 0.32; 400 nm, static 2.19 (gamma 1 to 2) and 1.65 (above 2), the candidate 1.07 and 0.47. Excitation reaches 0.78 of the ionised population at 1.65e14 W/cm2 (400 nm, a resonance). As for the other sets, the candidate fits below gamma = 2 and is too low above it.

• Status: verified (2026-10-03); open with TC-824.

TC-844 travers_2026_trecx: argon’s one-electron ionised fraction at 400 and 1030 nm with a 30 fs pulse; the candidate on a pulse it was not fitted to (2026-10-03)

• Where: src/optmat/data/external/trecx/scan_wavelength/results_400_30fs.csv, results_1030_30fs.csv, PROVENANCE.md there, travers_2026_trecx.toml (ionised_gauss30_400nm_Ar_m0, _m1, ionised_gauss30_1030nm_Ar_m0, _m1), tools/extract/travers_2026_trecx.py (LONG_TABLES), optmat.gas.ionisation_validation.TDSE_YIELDS, docs/ionisation_rates.md, tests/test_extraction.py (which now checks the stated uncertainty of every tRecX yield set: the 10 and 30 fs, Wallace-pulse and hydrogen sets, the last two untested in TC-836 and TC-843), tests/test_ionisation_validation.py.

• Transcribed: the ionised fraction, 1 - bound(n <= 10) at the end of the pulse, of Ar 3p m = 0 and m = 1 in Tong and Lin’s potential with the 400 and 1030 nm set-ups and intensities of TC-824 and TC-826 and a 30 fs Gaussian (intensity FWHM; 22.5 and 8.7 cycles): J. C. Travers’s tRecX runs of 3 October 2026 (part D of the runs). Tier 3. Uncertainty 0.15 to 0.34 % (400 nm) and 0.14 to 4.1 % (1030 nm; m = 1 to 6.0 %) by A2’s rule, recomputed and tested; rows within a factor 10 of the loss without a field excluded (1030 nm: m = 0 rows 0 and 1, m = 1 rows 0 to 2).

• Checked: every run complete; the drift (3.4e-9 in 8441 au); the pulse; the norm; convergence (PROVENANCE.md).

• Finding:

  • Away from saturation the 30 fs pulse ionises 2.3 to 5.4 times the 10 fs pulse’s at 400 nm and 2.5 to 3.8 times at 1030 nm, the most at the lowest intensities and near resonances: about the 3 that a rate gives for a Gaussian three times longer. The dependence on the pulse length beyond the rate’s is small.

  • The candidate frequency factor (TC-831), fitted to the 10 fs sets, is 0.87 (400 nm, 0.48 to 1.36 over gamma 4.2 to 1.4) and 0.955 (1030 nm, 0.80 to 1.04 over gamma 1.8 to 0.6) times these on geometric average (yields below 0.75); the static factor 2.01 and 1.175. The candidate carries over to a pulse three times longer.

• Status: verified (2026-10-03); open with TC-824.

TC-845 travers_2026_trecx: krypton and xenon, one electron, 800 nm (6 fs), and their static rates (2026-10-03)

• Where: src/optmat/data/external/trecx/scan_kr_xe/results.csv, static_results.csv, PROVENANCE.md there, travers_2026_trecx.toml (ionised_gauss6_Kr_m0, _Xe_m0, static_Kr_m0, static_Xe_m0), tools/extract/travers_2026_trecx.py (KR_XE, _kr_xe_static, kr_xe_static_uncertainty; a2grid among the variations), optmat.gas.ionisation_validation (TDSE_YIELDS, STATIC_REFERENCES), tools/ionisation_rate_tables.py (the TDSE table covers every gas of TDSE_YIELDS), docs/ionisation_rates.md, tests/test_ionisation_validation.py, tests/test_extraction.py.

• Transcribed: the ionised fraction, 1 - bound(n <= 10) at the end of the pulse, of Kr 4p and Xe 5p (m = 0, one active electron) in zhang_2014’s potentials (Kr: GSZ, Table II; Xe: Tong and Lin’s form, Table I; valence energies +0.27 % and -0.21 % against the measured, not adjusted), A2’s 6 fs pulse at A2’s ten intensities (Xe: 4.4e-5 to 0.963; Kr: 5.5e-7 to 0.975), and their static rates (-2 Im E, traced resonance) at 0.03 to 0.10 au: J. C. Travers’s tRecX runs of 2 and 3 October 2026 (part G of the runs). Tier 3. Uncertainty 0.1 to 1.5 % (scans), 0.02 to 1.2 % (static) by the runs’ rules, recomputed and tested.

• Checked: every run complete, exit 0; no drift; the potentials against the table images; the static traces’ smallest step overlap 0.815 (Xe) and 0.889 (Kr), every variation on the same eigenvalue (PROVENANCE.md).

• Finding:

  • Against the calculations (yields below 0.75, geometric means): the one_electron model with the static factor 1.74 (Kr, 1.34 to 2.23) and 1.61 (Xe, 1.34 to 2.29); with the candidate frequency factor (TC-831, not fitted to these) 1.16 (Kr, 0.90 to 1.45) and 0.94 (Xe, 0.81 to 1.07).

  • Krypton’s 1.16 is its static normalisation: in a static field the one-electron model is 1.08 to 1.17 times tRecX’s rates of the same potential, as against Bahl et al.’s (1.10 to 1.22, TC-821); xenon’s is 0.84 to 1.04. The Coulomb factor’s dependence on the frequency is right for both.

  • Zhao et al.’s krypton (TC-825), 2.2 times below the static factor and 1.5 below the candidate, used Garvey et al.’s potential; with Zhang et al.’s the excess over the static factor is argon’s and xenon’s (1.6 to 1.7). Their xenon: 1.75 and 0.99, as here.

  • With the candidate, one electron of xenon is not ionised more against argon’s (Ar 6 fs: 1.00; Xe: 0.94) than the model says, so the measured excess of xenon over argon (factor 2 to 3 in the rate, TC-819) is not in the one-electron physics: it is the atom’s (or the measurements’).

  • Saturation: Xe from 3.5e14 W/cm2 and Kr from 5.5e14 at 0.94 to 0.97, 2.5 to 4.9 % of the population left in excited states.

• Doubt: one electron, m = 0 only; cutEnergy 100 sets the 1.3 to 1.5 % of the lowest rows (150 would remove it).

• Status: verified (2026-10-03); bears on TC-819 (xenon against argon), open with TC-824.

TC-846 travers_2026_trecx: krypton in Wallace et al.’s pulse; the krypton atom ionises like about 1.35 electrons (2026-10-04)

• Where: src/optmat/data/external/trecx/scan_wallace/results_kr_cep0.csv, results_kr_cep90.csv, PROVENANCE.md there, travers_2026_trecx.toml (ionised_wallace_cep0_Kr_m0, _cep90_Kr_m0), tools/extract/travers_2026_trecx.py (WALLACE_KR_TABLES; wallace_uncertainty takes the tables), optmat.gas.ionisation_validation (TDSE_YIELDS, WALLACE_TDSE), docs/ionisation_rates.md, tests/test_ionisation_validation.py, tests/test_extraction.py.

• Transcribed: the ionised fraction, 1 - bound(n <= 10) at the end of the pulse, of Kr 4p, m = 0, one active electron in part G’s potential (TC-845), in Wallace et al.’s 5.5 fs pulse at carrier-envelope phases 0 and pi/2 and twelve intensities from 5e13 to 6e14 W/cm2 (4.4e-4 to 0.96): J. C. Travers’s tRecX runs of 3 and 4 October 2026 (part B of the runs). Tier 3. Uncertainty 0.27 to 0.73 % by the runs’ rule, recomputed and tested; phase pi/2 takes phase 0’s.

• Checked: every run complete, exit 0; no drift; the norm; one GMRES tolerance warning in a convergence run whose yield is within 0.012 % of the base (PROVENANCE.md).

• Finding:

  • The phase changes the yield by -10.3 to +9.2 % (argon: -6.1 to +6.0 %), oscillating with the intensity.

  • Against the calculation (yields below 0.75): the one_electron model with the static factor 1.63 (CEP 0) and 1.61 (pi/2), with the candidate frequency factor 1.21 and 1.20 (krypton’s static normalisation, 1.08 to 1.17, TC-845, is in it).

  • Through Wallace et al.’s test (tdse_intensity_scale_test), the exact one-electron calculation needs the intensities scaled by 1.045, beyond the calibration of 1.5 %; argon’s matched at 1.002 (TC-836). The calculation’s rate times 1.47 gives 0.989, times 0.8 gives 1.077: the measured krypton atom ionises more than one m = 0 electron, by about 1.35 to 1.45.

  • Santra et al.’s all-electron static rate of krypton (all 4p electrons, spin-orbit coupled; TC-821) is 1.34 times tRecX’s one-electron rate at 0.10 au. A measurement and an all-electron calculation agree: the krypton atom ionises like about 1.35 electrons, argon’s like 0.8 to 1 (TC-830, TC-842). This is the size of the excess of krypton over argon in the measurements, and points the same way as xenon’s (TC-819, TC-845): the heavier atoms’ excess over one electron is the atom’s.

  • The models through the same test: default 0.998, frequency 1.072, one_electron 0.953, one_electron_frequency 1.026. The default matches through a cancellation: its static Coulomb factor’s excess makes up for krypton’s missing electrons. With the candidate, krypton’s effective number of electrons would be about 1.35 (Santra et al.’s ratio) rather than argon’s 1.

• Doubt: one potential (GSZ); m = 0 only; Santra et al.’s one field; the test’s sensitivity to the rate’s magnitude is weak (a factor 0.8 moves it 3 %).

• Status: verified (2026-10-04); bears on TC-819 (xenon against argon) and on the effective number of electrons of Kr (and Xe) if the candidate is adopted. Santra et al.’s rate is an independent-electron sum, not all-electron: TC-851.

TC-847 travers_2026_trecx: the argon atom in haCC against one electron at its ionisation energy (2026-10-04)

• Where: src/optmat/data/external/trecx/ar_hacc/results.csv, ip_matched/ (from TC-830), PROVENANCE.md there, travers_2026_trecx.toml (hacc_normloss_gauss6_Ar_c4, _c3; normloss_ipmatched_{ci,c3m1}_Ar_m{0,1}, ionised_ipmatched_{ci,c3m1}_Ar_m{0,1}), tools/extract/travers_2026_trecx.py (HACC_RUNS, hacc_uncertainty, IP_MATCHED_TABLES; _six_fs and six_fs_uncertainty take the measure’s column), optmat.gas.ionisation_validation (HACC_YIELDS, IP_MATCHED_YIELDS, AtomRatio, hacc_ratios), docs/ionisation_rates.md (The effective number of electrons), tests/test_ionisation_validation.py, tests/test_extraction.py.

• Transcribed:

  • haCC’s argon atom (all electrons antisymmetrised; the Scrinzi group’s Ar_qz, its 3p ionisation energy 3.2 % low, no spin-orbit, added by its author as preliminary for an XUV tutorial), A2’s 6 fs pulse at 800 nm, the norm-loss 1000 au after the pulse: 4 ion channels (3p^-1 x 3, 3s^-1), mMax 0, at 4.03e13, 9.61e13 and 2.29e14 W/cm2 (8.83e-6, 2.114e-3, 0.1151; effective I_p 0.5631718 au); 3 channels at 9.61e13 (2.177e-3; 0.5626988 au). Uncertainty 1.2 to 7.3 %, the angular momentum (lMax 20 high by up to 7 %; a bias).

  • One electron in Tong and Lin’s argon potential scaled to haCC’s ionisation energies 0.560275 and 0.563940 au (part J of the runs), the same pulse and intensities, m = 0 and m = 1, the norm-loss and the ionised fraction (uncertainty 0.24 to 1.6 %). J. C. Travers’s tRecX runs of 29 September to 3 October 2026. Tier 3.

• Checked: every curated run complete over A2’s window; the uncertainty rules recomputed and tested; the one-electron runs’ initial energies equal their targets to 1e-10 au (PROVENANCE.md).

• Not yet curated: the decisive run with all three 3p channels and mMax 1 at 9.61e13 W/cm2 finished on 4 October after the table was written; the runs’ report gives 2.2203e-3 at +1000 au (I_p 0.563940 au, exactly part J’s second energy): 0.857 of one m = 0 electron, about 0.79 with the angular-momentum correction the report derives (lMax 20 to 30 at 3 channels, -6.8 %; 30 to 40, -0.7 %). It is to be added when the table is re-extracted.

• Finding: the argon atom’s yield over one m = 0 electron’s at the same ionisation energy and measure (hacc_ratios; one electron interpolated in the log between the two energies): 0.76, 0.80 and 0.87 at 4.0e13, 9.6e13 and 2.3e14 W/cm2 (4 channels), 0.81 (3 channels, 9.6e13); with mMax 1, 0.86 (0.79 corrected). Six independent electrons would give 2 x (m = 0) + 4 x (m = 1): the atom is 0.38 to 0.41 of that. So argon ionises like about 0.8 of one electron in this pulse, as van der Hart’s all-electron R-matrix rates at 390 nm give with the candidate Coulomb factor (about 0.87, TC-842); the default’s effective number of electrons, 1 from Jagau’s static rates (TC-669), is within 20 %. Krypton, by Santra et al. and Wallace et al., ionises like about 1.35 electrons (TC-846).

• Doubt: one data set of uncertain provenance (questions put to its author by the maintainer); one pulse (a 20 fs point is requested for the runs); the ratio’s rise with the intensity (0.76 to 0.87) is the opposite of Jagau’s static trend over the same fields.

• Status: verified (2026-10-04); bears on TC-660 (one active electron) and the effective number of electrons (TC-669).

TC-848 Decision: the default ionisation rate takes the frequency-dependent Coulomb factor; krypton’s effective number of electrons 1.35 (2026-10-04)

• Where: src/optmat/data/gas/ionisation_rates.toml (default and one_electron: coulomb = "frequency"; default Kr electrons = 1.35; the reasons; the models default_static and one_electron_static, status comparison, the former two; the provisional frequency and one_electron_frequency of TC-831 retired), optmat.gas.ionisation_rates (the module’s and coulomb_factor’s docstrings; the citation of the frequency form), tools/ionisation_rate_tables.py (the tables give both factors), tools/molecular_rate_tables.py (molecules against the atoms’ static model), docs/ionisation_rates.md (Three parts, each tested against what isolates it, new; The frequency-dependent Coulomb factor, formerly the candidate), docs/molecular_ionisation_rates.md, tests/ (findings made with the static factor now name default_static or one_electron_static), tests/data/golden_models.json, tests/data/legacy_ionisation_rates.json.

• Decided by: the maintainer (2026-10-04), “switch now”, with xenon’s number of electrons provisional.

• Why: the model is three parts, each set against the references that isolate it:

  • the Coulomb factor’s dependence on the frequency, one-electron physics, one constant for all gases: c = 5.25 fitted to one-electron calculations of argon (TC-831), and within 0.84 to 1.16 of every one-electron calculation it was not fitted to below gamma = 2 (Ar in 6, 30 fs and Wallace et al.’s pulse; H, He, Ne, Kr, Xe; TC-833 to TC-845). It tends to the static factor in a static field, so the static references and the numbers of electrons set from them are unchanged.

  • the static normalisation per gas (C_l, alpha), against exact one-electron static rates: unchanged.

  • the effective number of electrons per gas, against all-electron calculations and measurements, with the Coulomb factor fixed: argon 1 (Jagau’s static rates 0.83 to 1.00; haCC 0.76 to 0.87 in a pulse, TC-847; R-matrix about 0.87 at 390 nm, TC-842), neon 1, helium 1.47 (Parker et al.’s static rates), krypton 1.35 (Santra et al.’s all-electron static rate is 1.34 times the one-electron rate; Wallace et al.’s yields need about 1.4 on the exact one-electron calculation, TC-846), xenon 1, provisional. The static factor’s excess above gamma = 1 had made up for krypton’s missing electrons, so the old default matched Wallace et al.’s krypton with 1 electron; the three parts are now set separately.

• Effect on the values: at 800 nm the default’s cycle-averaged rate of argon at 1e14 W/cm2 falls by 24 % (8.020e11 to 6.112e11 /s), helium’s at 1e15 by 5 %; krypton’s rises by the factor 1.35 at low field. The one-electron model is now 0.90 to 1.07 times argon’s TDSE at 6 fs (was 1.08 to 1.67). Through the measurements: Wallace et al.’s intensity scales 1.033 (Ar), 1.023 (Kr), 1.13 (Xe, provisional; was 0.98, 1.00, 1.00); Nambu et al.’s and Nie et al.’s ten fits rms 1.08 (was 1.12), and Nambu et al.’s 400 nm brought near 1; Wahlstrand et al.’s rate over measured 1.2 to 4.6 (was 1.7 to 7.9); Parker et al.’s helium 0.85 to 1.13 (780 nm) and 0.85 to 1.28 (390 nm); Santra et al.’s krypton 1.04 (was 0.77). Golden values and the Luna/solprop fixture re-recorded; the page’s tables regenerated.

• Not changed: the molecules’ default keeps the static Coulomb factor (its alphas and electron counts were set from static rates, and no calculation tests a molecule’s dependence on the frequency); whether it follows the atoms is open. The molecular page compares molecules with the atoms’ default_static.

• Open: xenon’s number of electrons (part B of the runs, xenon in Wallace et al.’s pulse); helium’s (haCC and Parker et al. differ by 1.25 at 390 nm, the two-electron runs to settle it); above gamma = 2 the factor is low for hydrogen.

• Status: decided and implemented (2026-10-04); supersedes the interim choice of TC-814 for the Coulomb factor. Santra et al.’s rate is an independent-electron sum, not all-electron: TC-851.

TC-849 travers_2026_trecx: xenon in Wallace et al.’s pulse; one electron of xenon passes their test (2026-10-06)

• Where: src/optmat/data/external/trecx/scan_wallace/results_xe_cep0.csv, results_xe_cep90.csv, PROVENANCE.md there, travers_2026_trecx.toml (ionised_wallace_cep0_Xe_m0, _cep90_Xe_m0), tools/extract/travers_2026_trecx.py (WALLACE_XE_TABLES), optmat.gas.ionisation_validation (TDSE_YIELDS, WALLACE_TDSE), docs/ionisation_rates.md, tests/test_ionisation_validation.py, tests/test_extraction.py, the counts in README.md and docs/index.md.

• Transcribed: the ionised fraction, 1 - bound(n <= 10) at the end of the pulse, of Xe 5p, m = 0, one active electron in part G’s potential (TC-845), in Wallace et al.’s 5.5 fs pulse at carrier-envelope phases 0 and pi/2 and twelve intensities from 5e13 to 6e14 W/cm2 (0.013 to 0.96): J. C. Travers’s tRecX runs of 3 to 6 October 2026 (part B of the runs). Tier 3. Uncertainty 0.03 to 1.2 % by the runs’ rule, recomputed and tested; phase pi/2 takes phase 0’s.

• Checked: every run complete, exit 0; no drift; the norm. 23 phase-0 runs were stopped by a time limit and continued from their checkpoints; the norm continues across the restart, and the six missing expectation rows lie after the pulse, where nothing is read (PROVENANCE.md). One GMRES tolerance warning in a convergence run whose yield is within 0.015 % of the base. The report’s prose gives the Keldysh parameter 1.41 at row 0, its table and the potential’s I_p 1.42.

• Finding:

  • The phase changes the yield by -17.7 to +9.4 %, oscillating with the intensity (krypton -10.3 to +9.2 %, argon -6.1 to +6.0 %), and by 0.3 % or less in saturation.

  • Against the calculation (yields below 0.75): one_electron (the frequency-dependent factor) 0.80 to 1.18, geometric means 0.96 (phase 0) and 1.00 (pi/2), as at 6 fs (0.94; TC-845): the factor holds for xenon in a second pulse. one_electron_static 1.24 to 1.73.

  • Through Wallace et al.’s test (tdse_intensity_scale_test), the exact one-electron calculation matches at 1.019, within the calibration of 2.5 %, as argon’s does (1.002, TC-836) and krypton’s does not (1.045, TC-846). A factor of 1.09 on its rate gives 1.000; the calibration allows about 0.93 to 1.27. The xenon atom ionises like about 1.1 electrons without the spin-orbit splitting.

  • The model’s N_eff multiplies the rate weighted over the ion’s two levels (2/3 at 2P3/2, 1/3 at 2P1/2), which for xenon is 0.71 to 0.79 times the one-level rate at 800 nm from 5e13 to 2e14 W/cm2 (krypton 0.78 to 0.85, argon 0.91 to 0.95; in a static field at 0.06 to 0.10 au xenon 0.74 to 0.82, krypton 0.80 to 0.88, argon 0.93 to 0.96). In the model’s terms xenon’s ratio is about 1.5. The default, with xenon’s provisional 1, is at 1.133; with 1.5 it would be at 1.026 (argon 1.033, krypton 1.023), with 1.6 at 1.009.

  • The cost: with 1.5, Nambu et al.’s xenon scale at 400 nm moves from 1.11 to 0.98, at 800 nm from 1.00 to 0.92, Nie et al.’s from 0.87 to 0.80 (their argon 0.90, 1.06, 0.98), and Wahlstrand et al.’s rate over measured from 1.9-4.6 to 2.9-6.8: the excess of xenon over argon in those measurements (TC-819) grows.

  • N_eff is the atom’s rate over the model’s own one-electron rate (its C_l and the levels’ weights), as argon’s (Jagau), helium’s (Parker et al.) and krypton’s (Santra et al.: the default is 1.04 times it) were set; a ratio to an exact one-electron calculation is converted through the weighting and the model’s ratio to the calculation before it is compared. Krypton’s 1.35 needs no change: its model is 1.08 to 1.17 above the exact rate of one potential (TC-845), but Bahl et al.’s one-electron rates span 0.88 to 1.22, and Santra et al.’s all-electron rate of the real atom is the anchor.

• Doubt: one potential (Tong and Lin’s form, I_p 0.21 % below the measured); m = 0 only; the test’s weak sensitivity to the rate’s magnitude (a factor 0.8 moves it about 3 %); the calculation has no spin-orbit coupling, so the conversion through the levels’ weights is the model’s, not tested by a calculation of xenon.

• Status: verified (2026-10-06). Xenon’s N_eff: TC-850.

TC-850 Decision: xenon’s effective number of electrons 1.5 (2026-10-06)

• Where: src/optmat/data/gas/ionisation_rates.toml (default, Xe: electrons = 1.5, uncertainty_factor = 3.0, their reasons), optmat.gas.ionisation_rates (the module’s docstring), docs/ionisation_rates.md, tests/test_ionisation_validation.py, tests/data/golden_models.json (rate/default/Xe@800nm only), tests/data/legacy_ionisation_rates.json.

• Decided by: the maintainer (2026-10-06), on the recommendation below.

• Why: N_eff is the atom’s rate over the model’s own one-electron rate (its C_l and the ion’s two levels weighted 2/3 and 1/3), as argon’s (Jagau), helium’s (Parker et al.) and krypton’s (Santra et al.) were set. Xenon has no all-electron calculation; its atom-level reference is Wallace et al.’s yields, whose intensities are calibrated on atomic hydrogen and which the default follows (TC-814). The exact one-electron calculation passes their test with a factor of 1.09 on its rate (TC-849); the model’s one electron is 0.96 to 1.00 times the calculation in their pulse, and the weighting 0.71 to 0.79: 1.09/(0.98 x 0.75) = 1.48, taken as 1.5. Derived, not fitted to the scale: it lands at 1.026, beside argon’s 1.033 and krypton’s 1.023. Krypton’s 1.35 is unchanged (the default is 1.04 times Santra et al.’s all-electron rate; TC-849).

• Effect on the values: xenon’s default rate rises by 1.5 at every field. Through the measurements: Wallace et al.’s scale 1.133 to 1.026; Nambu et al.’s at 800 nm 1.00 to 0.92, at 400 nm 1.11 to 0.98 (circular 1.03); Nie et al.’s 0.87 to 0.80; Wahlstrand et al.’s rate over measured 1.9-4.6 to 2.9-6.8; rms of the ten 800 nm intensity fits 1.08 to 1.10. Golden value and the Luna/solprop fixture re-recorded; the page’s tables regenerated.

• Against: within the absolute measurements at 800 nm, where one calibration serves all gases, xenon’s intensity scale is now 0.86 (Nambu et al.) and 0.81 (Nie et al.) of argon’s, the model’s xenon high against its argon by 2 to 3.5 in the rate (TC-819); at 400 nm Nambu et al.’s is 1.09. The uncertainty factor is raised from 2 to 3 to cover it. TC-848’s reason for xenon’s provisional 1 read TC-819 the wrong way (“probably above 1”); those measurements argue for fewer electrons, Wallace et al.’s for more.

• Status: decided and implemented (2026-10-06); resting on one measurement until an all-electron calculation of xenon exists. Santra et al.’s rate is an independent-electron sum, not all-electron: TC-851.

TC-851 Correction of TC-846, TC-848 and TC-850: Santra et al.’s krypton rate is not all-electron; what the effective number of electrons is (2026-10-06)

• Where: src/optmat/data/gas/ionisation_rates.toml (krypton’s reasons), docs/ionisation_rates.md (Three parts, The effective number of electrons, the krypton findings, Open questions), tests/test_ionisation_validation.py (a comment). No value changes.

• Found by: a reading of the literature on the many-electron factor for the ionisation-rate paper (2026-10-06), checked at first hand: santra_2006, p. 043403-2, “the effective one-electron potential V_HS is calculated using the Hartree-Fock-Slater code written by Herman and Skillman”; p. 043403-4, “the sum over all gamma_{j,m} weighted by the number of electrons in the respective j,m subshell”. The record (TC-821) describes it correctly; TC-846, TC-848 and TC-850, krypton’s reasons, the manual and the changelog of 0.3.0 called it all-electron.

• Consequence: the ratio 1.34 (Santra et al.’s sum over tRecX’s one electron at 0.10 au) measures the Herman-Skillman potential’s rate per electron against Zhang et al.’s, summed over six spin-orbitals as independent electrons; it is no evidence on the many-electron factor. Krypton’s 1.35 rests, as xenon’s 1.5 does, on Wallace et al.’s yields through the exact one-electron calculation (a factor of about 1.4, TC-846), and with it the three gases sit at the same intensity scale (Ar 1.033, Kr 1.023, Xe 1.026). The value stands; its support is one measurement, through a test that is weakly sensitive to the rate’s magnitude.

• What N_eff is: the explicit statements of the literature give a factor of 2 for a doubly occupied orbital against a one-electron rate with the exact asymptotic coefficient, in the weak-field limit (tolstikhin_2014, section II G; also Parker et al. 2007, van der Hart et al. 2007, Majety & Scrinzi 2015’s Fig. 1, which plot single-electron rates times 2). The N_eff here (about 1 to 1.5) are against this model’s formula (Tong, Zhao & Lin’s C_l, Tong & Lin’s correction, the Coulomb factor) and part of their distance from 2 is the formula’s. The manual now says so: N_eff is a calibration of the formula, not a count of active electrons; what it rules out is the occupancy of 2 per m (6 for a p shell) of some propagation codes. The rise towards 2 at low field (TC-669) is consistent with the weak-field limit.

• Status: corrected (2026-10-06).

TC-852 tolstikhina_2014 (Tolstikhina, Morishita & Tolstikhin, Phys. Rev. A 90, 053413 (2014)): the weak-field limit on the formula’s scale (2026-10-06)

• Where: src/optmat/data/sources/tolstikhina_2014.toml, tools/extract/ tolstikhina_2014.py, optmat.gas.ionisation_validation (WEAK_FIELD_ATOMS, WeakFieldFactor, weak_field_factors), tools/ionisation_rate_tables.py (ionisation-rate-weak-field), docs/ionisation_rates.md (The effective number of electrons), tests/test_ionisation_validation.py, tests/test_ionisation_rates_page.py, the counts.

• Transcribed: Table I (p. 053413-4; the cells checked against the table image): for He, Ne, Ar, Kr and Xe the Hartree-Fock orbital exponent kappa, the relaxation coefficient R_N, the ionising orbital’s asymptotic coefficient g_N and the atom’s g = sqrt(p) R_N g_N (p = 2) of the many-electron weak-field asymptotic theory, Gamma = |g|^2 W(F). Theory, Hartree-Fock, nonrelativistic, leading order at weak field. Found by the literature search of 2026-10-06 on the many-electron factor (TC-851).

• The comparison: their Eq. (11) with Tong, Zhao & Lin’s tail C_l r^(1/kappa-1) e^(-kappa r) gives one electron of the model g_1 = sqrt(2(2l+1)/kappa) 2^(-1/kappa) C_l, with which their Eqs. (1)-(2) are the static ADK rate exactly (checked algebraically; hydrogen: C_l = 2, kappa = 1, g = sqrt 2 as printed). (g/g_1)^2 at the HF kappa is the atom’s weak-field rate over the model’s one electron.

• Finding:

  • He 1.67, Ar 1.72, Kr 1.78, Xe 1.82: the literature’s factor 2 of the doubly occupied orbital, less the 9 to 17 % by which tong_2002’s C_l^2 exceed Hartree-Fock’s (with relaxation). This reconciles TC-851’s “2 in the literature” with this model’s numbers at weak field.

  • At working fields the references give less: helium 1.47 (Parker et al.), argon about 1 (Jagau, haCC, R-matrix), rising towards low field (1.2 at 0.07 au, 1.6 at 0.06 au; TC-669); krypton’s 1.35 and xenon’s 1.5 multiply the fine-structure weighting (0.75 to 0.85), about 1.1 without it. The many-electron factor falls with the field from its weak-field value; a constant N_eff does not follow it.

  • Neon 0.53: its g_N is half of what tong_2002’s C_l implies, while Jagau’s coupled-cluster rates agree with the formula and 1 electron (1.03 to 1.10, TC-669). One of the two coefficients is wrong for neon; not settled.

  • For helium the accurate two-electron g (2.932, quoted p. -5) is the Hartree-Fock one within 0.4 %.

• Doubt: Hartree-Fock, nonrelativistic (the paper flags Kr and Xe); kappa_HF 0.8 to 3.6 % above the measured; the comparison is of coefficients at one kappa, not of rates at the measured ionisation energy.

• Status: verified (2026-10-06); bears on TC-658, TC-669 and TC-851. No model value changes.

TC-853 uiterwaal_1998 (Uiterwaal et al., Phys. Rev. A 57, 392 (1998)): saturation intensities and multiphoton cross sections at 248.6 nm; the rate in the multiphoton regime (2026-10-06)

• Where: src/optmat/data/sources/uiterwaal_1998.toml (inline points), tools/extract/uiterwaal_1998.py (checks, no data file), optmat.vocabulary and docs/data.md (the quantity saturation_intensity, family ionisation), optmat.gas.ionisation_validation (SATURATION_INTENSITIES, SaturationTest, saturation_test), tools/ionisation_rate_tables.py (ionisation-rate-saturation), docs/ionisation_rates.md (Multiphoton saturation at 248.6 nm, Open questions), tests/test_ionisation_validation.py, tests/test_ionisation_rates_page.py.

• Transcribed: the saturation intensities of He, Ar and Kr in 500 fs pulses at 248.6 nm (Sec. VI, p. 399: 6.9 +- 0.8e14, 1.0 +- 0.15e14, 2.4 +- 0.6e13 W/cm2), from the plateau of the photoelectrons’ maximum ponderomotive shift, so independent of an intensity calibration; and Table I’s generalized cross sections sigma_(5) He, sigma_(4) Ar, sigma_(3) Kr and Xe (Xe from another paper’s ion yield curve with the intensity calibration). Table I prints the errors with the bounds’ signs swapped (+9/-0.4 for He); they are recorded as parameters, the schema having no asymmetric uncertainty. Neon has no value (a single rate does not describe it). The first multiphoton cross sections of the noble gases in optmat. Found by the triage of 2026-10-06’s library additions.

• New quantity: saturation_intensity (ionisation; W/cm2 or W/m2; against wavelength; required: the source’s definition and the pulse length), within the existing family: no OEP.

• Checked: the script reads Table I’s cells and Sec. VI’s sentence and reproduces the cross sections from the saturation intensities by their Eq. (9) with a sech^2 pulse of 500 fs: He 0.91e-152, Ar 1.58e-116 (printed 1.3e-116), Kr 1.22e-82.

• Finding: at the measured saturation intensities (Keldysh parameter 1.8, 3.7, 7.1) the integral of the default’s rate over the pulse is 3.4 (He), 4.3 (Ar) and 0.55 (Kr), against 1 for a match; the measurement’s 12 to 25 % in the intensity is a factor of 1.7 to 2 in the rate at these orders. With the static Coulomb factor it was 5.7, 32 and 13: the frequency-dependent factor removes most of the excess in the multiphoton regime, outside the range it was fitted in (and below the models’ 350 nm). Popruzhenko et al.’s factor: 1.6, 4.6, 0.53.

• Status: verified (2026-10-06); bears on TC-831 (the factor’s range) and TC-833 (hydrogen low above gamma = 2).

TC-854 lehmberg_1995 (Lehmberg et al., Opt. Commun. 121, 78 (1995)): xenon’s two-photon-resonant negative n2 and CO2’s n2 at 248.4 nm (2026-10-06)

• Where: src/optmat/data/sources/lehmberg_1995.toml, tools/extract/ lehmberg_1995.py, docs/nonlinear.md (Limitations).

• Transcribed: Table 1 (p. 87): n2 at 248.4 nm, 760 Torr and 300 K in 10^-14 esu, per <E^2> of the real field (their delta n = (1/2) n2 |E|^2 with the complex amplitude; nonlinear_index_field): Xe calculated -1.54 +- 0.30, Xe by self-defocusing -2.06 +- 0.14, Xe by CO2 compensation -1.82 +- 0.08, CO2 by self-focusing +0.160 +- 0.007. All use = check: xenon is 1 nm above the two-photon resonance with 6p[1/2]_0 at 249.6 nm, outside the below-resonance third-order model; CO2’s 10 ps value includes its rotational part. Air and fused silica rows are other papers’.

• Finding: nibbering_1997 reproduces xenon’s n2 as -963 +- 112 e-23 m2/W, 1.17 times the combined -1.97e-14 esu in intensity units (4 pi 10^7 n2(esu)/c = -8.25e-21 m2/W) and 1.12 times the self-defocusing value; its conversion is not stated. Fig. 12’s caption prints n2(Xe) where it means CO2.

• Status: verified (2026-10-06).

TC-855 masili_2003 (Masili & Starace, Phys. Rev. A 68, 012508 (2003)): helium’s dynamic polarizability through the 1s2p resonance (2026-10-06)

• Where: src/optmat/data/sources/masili_2003.toml, tools/extract/masili_2003.py.

• Transcribed: Table VI (p. 9), the column ‘This work’: alpha(omega) of helium in atomic units at 32 photon energies from 0.050 to 0.845 a.u., nonrelativistic, coupled-channel hyperspherical with logarithmic terms; through the 1s2p resonance (0.78 a.u.), where it changes sign. use = check.

• Erratum of the library, not of the paper: every minus glyph of the table was read as ‘2’ (in the CSV, the cells and the HTML alike); the ten negative values from 0.782 to 0.820 a.u. are restored by the script against the image, after checking each cell is ‘2’ followed by the printed magnitude (as hahn_1995).

• Finding: within 5e-5 of liu_1997 up to 0.55 a.u.; nearer the resonance lower, by 0.04 % at 0.65, 0.2 % at 0.70 and 2.5 % at 0.75 a.u., as the two calculations’ 1s2p energies differ. Not yet compared with optmat’s helium dispersion model.

• Status: verified (2026-10-06).

TC-856 mckenna_2004 (McKenna & van der Hart, J. Phys. B 37, 457 (2004)): R-matrix Floquet multiphoton cross sections of Ne and Ar; the sum over channels in the multiphoton regime (2026-10-06)

• Where: src/optmat/data/sources/mckenna_2004.toml, tools/extract/ mckenna_2004.py (vector figures), docs/ionisation_rates.md (Multiphoton saturation at 248.6 nm, Open questions), tests/test_ionisation_validation.py.

• Transcribed: the paper’s own all-electron R-matrix Floquet generalized cross sections (two ion target states, LS coupling, no spin-orbit), sigma^(N) = Gamma / Phi^N with Phi the photon flux in cm^-2 s^-1 (Eq. 3, as uiterwaal_1998), each at one intensity (1e12 W/cm2 for N = 2, 1e13 for N = 3): Ne two-photon 10.8-21.4 eV (Figs. 1, 2), Ne three-photon 7.2-10.7 eV (Fig. 3), Ar two-photon 7.9-14.6 eV (Figs. 5, 7), Ar three-photon 5.3-7.8 eV (Fig. 8 and inset). No table or printed curve exists; the vector drawings read by script (every tick within 0.12 pt; 2 % at a vertex, more on resonance flanks), all use = check. Curated by a delegated agent and reviewed.

• Checked: every value and position the text prints (Ar minimum 6.75e-84 read -0.2 %; Ar two-photon peak 3.6e-48 read +3.4 %; resonance positions to 0.003 eV; plateaus); each curve drawn twice agrees within 0.7 %. The figures’ Ne resonance labels use argon’s shells (slips, no effect on values). The rounded 3.5e16 in Eq. 3 makes sigma 0.5 to 0.8 % low.

• Finding: argon’s sigma_3 at 193 nm (6.4241 eV) is 6.43e-83 cm6 s2, on the rising wing of the calculated 4p two-photon resonance. The default’s effective sigma_3 = W / Phi^3 is 1.5, 4.3 and 11.6 times it at 1e13, 1e12 and 1e11 W/cm2 (gamma 15 to 150) with its integral over the channels (TC-654), but 0.74, 0.99 and 1.10 with the sum over them (channel_sum = “sum”): the integral gives the multiphoton yield a non-integer order (about 2.5 for this three-photon process), the sum the I^3 law, within 26 % of the all-electron calculation. The static Coulomb factor’s is 146 times at 1e13. With the sum, uiterwaal_1998’s saturation exponents become 4.0 (He), 2.3 (Ar), 1.2 (Kr), against 3.4, 4.3, 0.55 (TC-853). Both are below the models’ 350 nm.

• Decided (the maintainer, 2026-10-06): the default keeps the integral, chosen for its smoothness in the field (TC-654), which interpolation tables and quadratures over a beam need; the sum stays the documented option (channel_sum = "sum", on any model by dataclasses.replace), which the manual now recommends deep in the multiphoton regime.

• Status: verified (2026-10-06).

TC-857 lai_2017 (Lai et al., Phys. Rev. A 96, 063417 (2017)): ion yields of Ne, Ar, Kr and Xe from 0.4 to 3.9 um, linear and circular (2026-10-06)

• Where: src/optmat/data/sources/lai_2017.toml, tools/extract/lai_2017.py (vector figures), docs/ionisation_rates.md (Open questions).

• Transcribed: 16 ion-yield curves (435 points, arb. units, use = check) read from the vector Figs. 1-4: Xe 0.8 um linear and circular, 3.3 um linear; Ar 0.4, 0.8, 1.3 um linear and circular; Kr 0.8 um linear and circular, 3.3, 3.6, 3.9 um (polarisation not stated, displaced vertically by arbitrary amounts); Ne 0.8 um linear and circular. Circular at the same pulse energy (its field the linear one’s over sqrt 2). Intensity calibration about 20 % (Table I). Not taken: the metals (Na, K, Zn, Mg), the PPT and ADK curves, Figs. 10, 12, 14 (ratios to theory) and Fig. 13 (circular over linear at I_BSI; no quantity holds a ratio of one species’ two polarisations). Curated by a delegated agent and reviewed.

• Checked: every tick within 0.05 pt; every one of the page’s 504 marker paths accounted for (435 data, 57 duplicates, 12 legend); Fig. 9(a), a replot of Fig. 1(a), matches its 37 points within 0.3 % in intensity and 0.8 % in yield; Table I’s intensity ranges within 3 % (Ar 1.3 um 4.3 %).

• Caveats: ‘The experimental intensities in some cases are slightly scaled (<= 20 % from the calibration) to achieve best fit to the theoretical ion yield curves’ (p. 3), which sets unnamed, and the yields are ‘freely normalized to the theory’: these data test the shape of the yield, not the rate’s magnitude or intensity scale. Only ‘80- to 100-fs’ is printed for a duration (0.8 um; recorded as text, ‘not stated’ elsewhere). The circular-over-linear ratios the curves give at I_BSI are 4 to 39 % above the paper’s Fig. 13; the text says it evaluates them ‘approximately at’ I_BSI. The text’s ‘Figure 3 shows Xe’ means Fig. 1.

• Status: verified (2026-10-06); not yet compared with the models.

TC-858 travers_2026_trecx: one electron in the sin^2 pulses of published many-electron calculations (part M) (2026-10-06)

• Where: src/optmat/data/external/trecx/scan_sin2/results_*.csv, PROVENANCE.md there, travers_2026_trecx.toml (outside20_sin2_*, ionised_sin2_*), tools/extract/travers_2026_trecx.py (SIN2_TABLES, SIN2_FAMILIES, SIN2_MEASURES; six_fs_uncertainty: a family without convergence runs takes its own atom’s m = 0 changes, not argon’s), tests/test_extraction.py.

• Transcribed: J. C. Travers’s tRecX runs of 6 October 2026 (part M): one active electron, m = 0 and m = 1, in E(t) = E0 sin(omega t) sin^2(pi t / tau) on the field: Ar (Tong and Lin) at 1200 nm, 3 cycles, 1, 2, 4e14 W/cm2 (Pathak et al. 2020’s pulse), and m = 0 in their Muller-Kooiman potential (3p at -15.820 eV, as they state); Kr (part G’s) at 800 nm, 3 cycles, 1.6-2.5e14 (Pathak et al. 2022’s, envelope assumed); Ar at 800 nm, 3 cycles, 3-6e14 (Sato et al. 2018’s, envelope assumed); He at 800 nm, 6 cycles, 4-14e14 (Sato et al. 2016’s). Two measures: the probability outside 20 au at the end of the pulse (their measure, 1 - <chi[0,20]>, independent of the box) and the ionised fraction. Tier 3. Convergence 0.09 to 0.36 % (He 1.2 to 1.3 %).

• Checked: the pulses against the formula (2.9e-9 E0); no drift above 1.2e-8; the convergence by the runs’ rule, recomputed; the known warnings only (PROVENANCE.md).

• Finding: the Muller-Kooiman potential gives 0.77 to 0.84 of Tong and Lin’s yield at an ionisation energy 0.3 % higher. m = 1 is 2 to 13 % of m = 0, rising with intensity.

• Status: verified (2026-10-06).

TC-859 pathak_2020, pathak_2022, sato_2016, sato_2018: time-dependent many-electron calculations of Ar, Kr and He in short sin^2 pulses (2026-10-06)

• Where: src/optmat/data/sources/{pathak_2020,pathak_2022,sato_2016,sato_2018}.toml, tools/extract/{pathak_2020,pathak_2022,sato_2016,sato_2018}.py.

• Transcribed (read from the figures by script, TC-699; use = check; curated by delegated agents and reviewed):

  • pathak_2020 (J. Chem. Phys. 153, 034110), Fig. 2, vector (the library lost panel (a); read from the PDF): argon at 1200 nm, 3 cycles, 1, 2, 4e14 W/cm2, the probability outside 20 au at 3T for TDHF, TD-OMP2, TD-OCCD, TD-CASSCF and their single-electron calculation (Muller-Kooiman potential, from 3p0; its normalisation not stated). 0.5 %.

  • pathak_2022 (Front. Chem. 10, 982120), Fig. 2, raster: krypton at 800 nm, 3 cycles, 2e14 W/cm2, TDHF, TD-OCCD, TD-OCCD(T), TD-CASSCF at 3T; the envelope and phase not stated (the group’s sin^2 on the field assumed); the drawing’s zero 1.5 px above its tick (within the 1 %); the curves still rise at 3T (4 % over the last half cycle). The authors offer the raw data on request.

  • sato_2016 (Phys. Rev. A 94, 023405), Fig. 6, vector: helium at 800 nm, 6 cycles (Eq. 27), 4, 8, 14e14 W/cm2, the converged two-electron TD-CASSCF (MCTDHF) survival inside 20 au at 6T, stored as 1 - S. Their ADK and PPT curves (others’ formulas) not taken; the caption’s multipliers (ADK 2.55, 1.35, 0.96; PPT 1.24, 1.27, 1.24) reproduced from the drawn curves within 0.5 % (one 1.6 %); the formulas’ electron count is not stated.

  • sato_2018 (J. Chem. Phys. 148, 051101), Fig. 3, vector: argon at 800 nm, 3 cycles (envelope assumed), 6e14 W/cm2: single (Ar+) and double (Ar2+, charge = 2) probabilities outside 20 au at 3T for TDHF, TD-OCCD, TD-OCCDT, TD-CASSCF.

• Checked: every axis tick (residuals 0.02 to 0.05 pt); overlays; Sato 2016’s Fig. 4(c) agrees with its Fig. 6(b) to 1.4e-6; Pathak 2020’s curves at 3.3T within 0.4 % of 3T. Eq. 29 of Pathak 2020 prints ‘E(T) = 0 otherwise’ for E(t).

• Status: verified (2026-10-06).

TC-860 Finding: published many-electron calculations against one electron in their pulses (2026-10-06)

• Where: optmat.gas.ionisation_validation (PUBLISHED_ATOMS, published_atom_ratios), tools/ionisation_rate_tables.py (ionisation-rate-atoms), docs/ionisation_rates.md (The effective number of electrons), tests/test_ionisation_validation.py, tests/test_ionisation_rates_page.py.

• Finding: the published probability outside 20 au over one m = 0 electron’s (TC-858), same pulse, same measure:

  • argon at 1200 nm (Pathak et al. 2020, TD-CASSCF): 1.10, 0.95, 0.87 at 1, 2, 4e14;

  • argon at 800 nm, 6e14 (Sato et al. 2018): 0.80, near saturation;

  • krypton at 800 nm, 2e14 (Pathak et al. 2022): 0.91;

  • helium at 800 nm (Sato et al. 2016): 1.71, 1.60, 1.53 at 4, 8, 14e14. Argon about 0.9 of one electron, as haCC (0.76 to 0.87; TC-847) and the R-matrix at 390 nm (0.87; TC-842) find, now without Ar_qz; helium 1.5 to 1.7, as Parker et al. (1.47) and haCC (1.65). Krypton’s 0.91 is the first all-electron number for it, against Wallace et al.’s about 1.4 through the exact calculation (TC-846): an active space of the eight 4s4p electrons, no spin-orbit, against a measurement; not reconciled.

• Doubts: ‘one electron’ depends on the potential: Pathak et al.’s gives 0.77 to 0.84 of Tong and Lin’s yield, and their single-electron curve is 0.87 to 0.89 of tRecX’s in their potential, unexplained. The 800 nm pulses’ envelopes are assumed.

• Status: verified (2026-10-06); bears on TC-847, TC-848, TC-850 and TC-852.

TC-861 travers_2026_trecx: the argon atom in a 20 fs pulse (E3) and with mMax 1; one electron at the three-channel set-up’s ionisation energy (2026-10-06)

• Where: src/optmat/data/external/trecx/ar_hacc/results.csv (refreshed), ip_matched/results_c3_6fs.csv, results_c3_20fs.csv, PROVENANCE.md there, travers_2026_trecx.toml (hacc_normloss_gauss20_Ar_c3, hacc_normloss_gauss6_Ar_c3m1, normloss_ and ionised_ipmatched_c3_*, _c3_20fs_*), tools/extract/ travers_2026_trecx.py (HACC_PULSE, HACC_LMAX30, hacc_dataset, IP_MATCHED_CONVERGENCE, ip_matched_uncertainty), optmat.gas.ionisation_validation (HACC_YIELDS, HACC_REFERENCES, hacc_ratios), docs/ionisation_rates.md, tests/test_ionisation_validation.py, tests/test_extraction.py.

• Transcribed: haCC’s argon (Ar_qz, three ion channels, mMax 0, lMax 20; and its lMax 30 run) in a 20 fs Gaussian at 800 nm and 9.605215e13 W/cm2, the norm-loss at +1000 au: 8.4373e-3 (lMax 30: 8.1776e-3); the three-channel mMax 1 run at 6 fs, missing from TC-847’s table, now complete: 2.2203e-3. One electron at the three-channel set-up’s own 0.5626988 au (Tong and Lin scaled by beta 0.9939109898), m = 0 and m = 1, in A2’s 6 fs pulse and the 20 fs one: the norm-loss and the ionised fraction. Uncertainty: haCC’s by TC-847’s rule (7.3 %, the one-channel angular variations at 6 fs, and its own lMax 30 run); one electron’s by the runs’ rule, the 6 fs set taking the c3m1 set’s convergence (the same pulse and discretisation).

• Finding (hacc_ratios, now with one electron at exactly the set-up’s energy and pulse where it exists): the three-channel atom over one electron is 0.81 at 6 fs and 0.84 at 20 fs (lMax 30: 0.75 and 0.81): about 0.8, rising by 3 to 8 % with the pulse’s length; the angular correction (6.8 % at 6 fs, 3.1 % at 20 fs) does not cancel between the pulses, so the lMax 30 pair is the better estimate of the rise. With mMax 1 at 6 fs, 0.86 (TC-847’s interim reading confirmed). The interpolation between part J’s two energies gives 0.8088 at 6 fs against 0.8086 from the run at the exact energy.

• Status: verified (2026-10-06). Closes part E of the runs (E4 dropped). Krypton’s conflict (TC-860) is flagged in the manual’s Open questions and the paper’s plan, left as it is (the maintainer, 2026-10-06).

TC-862 nist_asd_2026: the levels of the neutral noble gases that bound the off-resonant third-order response (2026-10-07)

• Where: src/optmat/data/external/nist_asd/<He, Ne, Ar, Kr, Xe>_I_levels.tsv (PROVENANCE.md, with the query and sha256), src/optmat/data/sources/nist_asd_2026.toml (datasets level_<atom>_*), tests/test_nist_asd.py.

• Transcribed: the NIST ASD 5.12 levels form for He I, Ne I, Ar I, Kr I and Xe I (queried 2026-10-07, the ions’ query of TC-443 with the spectrum changed), kept as returned. Per atom: the lowest odd-parity J = 1 level (the one- and three-photon resonance) and the lowest even-parity levels of J = 0, 2 and 1 (two-photon); for helium, whose levels are LS-coupled, the singlets 1s.2p 1P1 (171134.894441 cm^-1), 1s.3p 1P1 and 1s.2s 1S0 (166277.437635 cm^-1), the triplets below them being spin-forbidden. The strings are NIST’s; every helium level is in square brackets (semi-empirical, the levels help page): those datasets are checks. NIST gives no uncertainty or bibliographic key for the Ar and Kr levels and no uncertainty for Xe’s: the cells are empty.

• Selection rules: in gamma’s sum over states the levels next to the ground level are dipole-coupled to it (odd J = 1: the one-photon limit, which the output’s three-photon resonance also reaches), and the middle level is two dipole steps away (even J = 0, 1 or 2). An even J = 1 level is reached only through the antisymmetric part of the two-photon tensor, which vanishes for two photons of the same frequency or of one linear polarisation; it is a separate dataset (the manual page Third-order nonlinearity, Resonance limits; TC-865).

• Checked: each dataset is the file’s row (tests/test_nist_asd.py); each atom’s one-photon level agrees within 0.01 cm^-1 with the upper level of the stored resonance line (<atom>_I_lines.tsv, TC-444’s files). The lowest even J = 0 level of xenon, 6p[1/2]0 at 80118.962 cm^-1, is the two-photon resonance at 249.63 nm that lehmberg_1995 (TC-854) names at 249.6 nm; its 6p[3/2]2 level (79212.465 cm^-1) is kramer_1985’s 252.5 nm.

• Cross-check (solprop SEP 12, section 4.4, which cites no source for them): the helium two-photon 1s2s 1S resonance, 20.616 eV, at a 120.28 nm fundamental; the three-photon 1s2p 1P (21.218 eV) and 1s3p 1P (23.087 eV) at 175.30 and 161.11 nm; the three-photon ionisation (24.587 eV, ie_He_I) below 151.28 nm. All four agree with SEP 12’s 20.62, 21.22, 23.09 and 24.59 eV and 120.3, 175, 161 and 151 nm.

• Status: verified (2026-10-07).

TC-863 nist_webbook_2026: the electronic states of H2, D2, N2, O2 and CO (Huber & Herzberg) (2026-10-07)

• Where: src/optmat/data/external/nist_webbook/<gas>_diatomic_constants.html.gz (PROVENANCE.md), src/optmat/data/sources/nist_webbook_2026.toml (datasets state_<gas>_<state>), the new quantity electronic_state_energy (docs/data.md), tests/test_nist_webbook_states.py.

• Transcribed: from the WebBook’s “Constants of diatomic molecules” (Huber & Herzberg’s compilation, data through February 1977; queried 2026-10-07 and stored as returned, unlike TC-444’s ion-energetics pages, which were read and not stored, so that the strings can be checked), Te of 20 states with the 0-0 band of the transition the page lists: H2 and D2 B 1Σu+, C 1Πu, E 1Σg+; N2 A 3Σu+, a’ 1Σu-, a 1Πg, a” 1Σg+, b 1Πu; O2 a 1Δg, b 1Σg+, A 3Σu+, B 3Σu-, C 3Πg; CO a 3Π, A 1Π, I 1Σ-, D 1Δ. use = reproduced (from Huber & Herzberg). Each dataset also states the curators’ reading of its selection rules from the ground state, from the state’s symmetry: one_photon and two_photon as allowed, forbidden (parity or Λ) or spin_forbidden.

• Doubt: H&H parenthesise or bracket some Te (N2 b, a”; O2 C): stated in the datasets. Two Trans. cells are garbled on the page: D2 C reads ‘CX ↔’ (C ↔ X), and D2 E reads ‘E → N’, which is E → B: B’s 0-0 band (90633.79) plus 8827.99 gives 99461.78 cm^-1, 0.33 cm^-1 above liu_2010’s EF(0,0)-X(0,0) interval (99461.449, their Table III, in the record’s notes).

• Checked: each value against the page (tests/test_nist_webbook_states.py); the 0-0 bands against the curated primaries’ lowest bands, to their 1 meV: H2 B-X 90203.35 cm^-1 (11.1838 eV) against Sakamoto’s Lyman 11.184 eV; CO A-X 64748.48 (8.0277 eV) against 8.028 eV; N2 b-X through b → a, a → a’, a’ ↔ X, 100817.3 cm^-1 (12.4997 eV), against chan_1993_n2’s first band, 12.500 eV. H2’s EF(0)-X(0), 90203.35 + 8961.23 = 99164.58 cm^-1, is shiner_1993’s Q(0) 99164.782 within 0.2 cm^-1.

• Status: verified (2026-10-07) for the strings and the cross-checks; the selection rules are the curators’ reading.

TC-864 Finding: the legs of the fitted third-order data (2026-10-07)

• Where: tools/fit/nonlinear_support.py (signed_legs, support), the manual page Third-order nonlinearity (Where the fits are supported, table nonlinear-support), tests/test_nonlinear_support_page.py.

• What: each fitted value and validator written as four signed leg wavenumbers (-nu_o; nu_1, nu_2, nu_3) by its process (Kerr, THG, ESHG, dc Kerr, CARS, pump-probe), their W2 and W4 identical to frequency_sums. For solprop’s SEP 6, which evaluates the fits leg by leg.

• Finding: the largest single leg among the fitted values is a harmonic leg, 1.6 to 1.7 times further out in wavenumber than the Kerr diagonal of the largest fitted W2 (374-401 nm): Shelton’s visible ESHG at 229.0-244.1 nm (Ne, Ar, Kr, Xe, H2, N2, O2, CH4, SF6; for Ne and N2 Hättig & Jørgensen’s ESHG at 457.9 nm), a calculated THG at 694.4-694.6 nm, 231.5 nm (D2, CO2, CO). Helium’s reaches 151.9 nm (Bishop & Pipin’s THG at 455.6 nm), N2O’s 580 nm (the probe of its single pump-probe value) and O3’s 694.6 nm. Between 1 and 7 fitted values per gas have their largest leg within 10 % of the largest. The validators reach no further except CH4’s (Hättig & Jørgensen’s THG, 158.8 nm). No quartet within a W2 has a leg beyond sqrt(3 W2 / 4) (the legs sum to zero; Cauchy-Schwarz), the third-harmonic output.

• Correction of the manual (not of data): Third-order nonlinearity said a calculated THG enters from 650 nm, “harmonic at 217 nm and longer”. The 650 nm window (TC-314) keeps 694.3 nm and longer, the calculations’ nearest fundamental above it for Ne, Ar, N2, H2 and D2: the harmonics that enter are at 231.4 nm and longer. Corrected; the fits are unchanged. Argon’s largest fitted leg is the 229.0 nm harmonic of Shelton’s 458.1 nm ESHG (shelton_1990/table3_Ar_literature), not a THG.

• Status: verified (2026-10-07).

TC-865 Finding: the resonance limits of the 15 gases (2026-10-07)

• Where: tools/fit/nonlinear_support.py (LIMITS, resonances), the manual page Third-order nonlinearity (Resonance limits, table nonlinear-resonances).

• Theory: in gamma’s sum over states (Orr & Ward; Shelton & Rice 1994, eq. 17) a single leg reaches the levels dipole-coupled to the ground state, E1 (the output’s denominator being the three-photon resonance of the inputs), and a pair sum |nu_a + nu_b| the levels two dipole steps away, E2 (two-photon, or electronic Raman for legs of opposite sign). For a scalar field of one linear polarisation the atoms’ even J = 1 levels (and CO’s Sigma- state) drop out; E2 of any polarisation keeps them. Ionisation lies above both.

• Values (cm^-1; nm of one leg at E1, of the degenerate fundamental at E2): He 171135 (58.4), 166277 (120.3); Ne 134459 (74.4), 149824 (133.5); Ar 93751 (106.7), 105617 (189.4); Kr 80917 (123.6), 92307 (216.7); Xe 68045 (147.0), 78120 (256.0), all from TC-862; H2 90203 (110.9), 99165 (201.7); D2 90634 (110.3), 99462 (201.1); N2 100817 (99.2), 68952 (290.1, the a 1Πg state); O2 49358 (202.6), 65670 (304.6, C 3Πg); CO 64748 (154.4) for both (no inversion centre), all T0 from TC-863. Polyatomic: N2O E1 from 5.70 eV (217.5 nm; chan_1994’s B band edge); CH4 and SF6 E1 a lower bound at 197.7 nm (no absorption down to there, ityaksov_2008); O3 absorbs throughout its range (Serdyuchenko et al. to 1046.8 nm; Chappuis continuum f about 2e-5, inn_1953_ozone); CO2’s onset not curated. No two-photon state of a polyatomic molecule is curated. Ionisation energies: those of optmat.gas.ionisation (O3: 12.66 eV, the lowest of mahla_2025’s measured thresholds).

• Doubt: the molecular states’ one- and two-photon labels are the curators’ reading of their symmetry. O2’s a 1Δg and b 1Σg+ states (7882 and 13121 cm^-1) are reached by pair differences inside the range but are spin-forbidden from X 3Σg- and are not counted. N2’s and O2’s two-photon limits are discrete vibronic band systems, narrower than the limits suggest.

• Not verified: CO2’s and SF6’s absorption onsets and every polyatomic two-photon state need primary sources (open, the roadmap).

• Status: open (2026-10-07) for CO2, SF6 and the polyatomic E2; verified for the rest. Qualified by TC-869 (absorption evidence, not levels; E2 of any polarisation the minimum of all eligible levels).

TC-866 Finding: the fits increase with each squared leg; the physical gamma in every curated case (2026-10-07)

• Where: tools/fit/nonlinear_support.py (slope_minimum), the manual page Third-order nonlinearity (Does gamma increase with each frequency?), tests/test_nonlinear_support_page.py.

• The fits: d(gamma/gamma0)/d(nu_j^2) = A + 2 B W2 + 2 B’ nu_j^2. Every one of the 15 fits has A > 0 (0.448 for He to 1.703 for Xe, 1e-10 cm^2), B >= 0 and B + B’ > 0, and nu_j^2 <= W2, so the slope is at least A at any W2, within the data and beyond; its minimum, A, is at the static limit (scanned to 4 W2,max as a check).

• The physical gamma: no theorem. Shelton & Rice (Chem. Rev. 94, 3 (1994), eq. 17, p. 10) note that the sum over states has a negative term, so a negative static gamma is possible in principle (a two-level system), though none had been reported. Every curated dispersion curve rises from the static limit toward the first resonance (their Fig. 1 for H; Bishop & Pipin’s He; Hättig & Jørgensen’s Ne, Ar, N2, CH4; Bishop et al.’s H2 and D2), and beyond the fitted data every calculation rises faster than the polynomial (TC-867). It fails above a two-photon resonance, where gamma can change sign (xenon’s n2 at 248.4 nm, TC-854).

• Status: verified (2026-10-07) for the fits; the physical statement is an empirical finding over the curated data. Qualified by TC-869 (not every point lies above the polynomial; no general lower bound).

TC-867 Finding and decision: per-leg bounds beyond the fitted data; the recommended rule (2026-10-07)

• Where: tools/fit/nonlinear_support.py (evaluate_cap, case, recommend), the manual pages Third-order nonlinearity (A rule for the legs beyond the support, table nonlinear-rule) and Third-order accuracy (Beyond the fitted data, tables nonlinear-caps, -carrier, -beyond, -cases).

• Caps nu_j -> min(|nu_j|, nu_c): (a) the Kerr diagonal sqrt(W2,max / 4); (b) the largest fitted leg (TC-864); (b’) sqrt(3 W2,max / 4); (c) min(E1, E2 / 2) (TC-865). 20 000 seeded random quartets per gas and test.

• Findings: (a) changes up to 27 fitted values of a gas, by up to -26 % (Xe), and in-support quartets by up to -30 %; against a 400 nm Kerr carrier it is worse for 11-16 % of the in-support quartets of the gases with ESHG or THG data, e.g. argon’s 400 + 400 - 800 -> 266.7 nm (W2 0.98 of the fitted) by -9.3 % against the carrier’s -4.3 %. (b) is exact on the data, up to -5.4 % in support (Xe). (b’) is exact on every fitted value and every in-support quartet, never worse than any carrier there, and beyond the data shown no worse (the carrier at or below the capped value, which is at or below the truth) for every quartet below resonance except 26 xenon and 37 CO quartets against a 400 nm carrier; none against 800 or 1030 nm. (c) is not a leg cap for the pair limit: capping single legs at E2/2 changes the data of Xe, N2, O2 and CO. The polynomial underestimates every calculation beyond the data (windowed-out and validator values): by 0.7-3.6 % at 1.8-2 W2,max (Ne, Ar, N2), 5 % (H2, D2) and 28 % for helium’s THG at 4 W2,max. Helium’s SPM at 120 nm is past the 1s2s 1S resonance (pair 1.002 E2).

• Decision (a recommendation; optmat’s interface does not yet carry it): refuse a field that reaches the band edge min(E1, E2 / 2) (E2 of any polarisation for a vector field), a check on the band and not a cap; below it, cap each leg at sqrt(3 W2,max / 4), read beyond the data as a lower bound. Where E2 is not curated (CO2, CH4, SF6, N2O) the band edge is the declared range’s; O3, which absorbs within its range, has no valid rule.

• Open questions for solprop’s SEP 6 (its Q2): whether a lower bound is acceptable as the extrapolated value; the mixed quartets that a 400 nm carrier cannot be shown to beat; whether the band check is solprop’s or optmat’s to publish; the helium VUV legs past 120.3 nm; N2O and O3; the weak spin-forbidden O2 states.

• Status: decided (2026-10-07), as a recommendation pending a public record. The recommendation is withdrawn by TC-868 (usage is the propagation code’s); the findings stand. Qualified by TC-869 (“shown no worse” rests on an assumption the calculations support but do not prove).

TC-868 Decision: optmat states the support facts; their use is the propagation code’s (2026-10-07)

• Where: the manual pages Third-order nonlinearity (Quantities derived from the facts, table nonlinear-derived, replacing A rule for the legs beyond the support) and Third-order accuracy (Beyond the fitted data, kept as evidence); tools/fit/nonlinear_support.py (derived, replacing recommend); OEP 5.

• Decision (the maintainer, John Travers, relayed by solprop’s SEP 6 review): optmat states material facts as well as it can; how they are used is a modelling decision and belongs to the propagation code. So optmat publishes, for each gas, the largest fitted W2 and leg with the values that set them, E1, E2 (one polarisation and any) and the ionisation energy with their sources (TC-864, TC-865), and, labelled as derived, sqrt(3 W2,max / 4) (the largest leg of any quartet within the fitted W2) and min(E1, E2 / 2) (the lowest frequency whose SPM quartet reaches a resonance; not defined where E1 or E2 is not curated). TC-867’s recommended rule (refuse a band reaching the edge, the declared range as the edge of the polyatomic molecules, no rule for O3) is withdrawn from the manual and from OEP 5; its cap comparison stays as evidence.

• solprop’s rule, for information (SEP 6, section 4.10): every leg capped at sqrt(3 W2,max / 4), the band labelled supported, bounded or best effort, nothing refused.

• Correction of the manual (not of data): the accuracy page’s table of solprop’s demonstration quartets (nonlinear-cases, TC-867) showed the rows of the rule table under its header (the tool reused the rows of the table built before it). Corrected; the values in TC-867’s text were right. A test now checks that each table’s rows are its own.

• Material judgement kept by optmat: O2’s spin-forbidden a 1Δg and b 1Σg+ states are not counted among the limits (TC-865); solprop agrees.

• Status: decided (2026-10-07). Qualified by TC-869 (the band edge is a sufficient bound, an SPM resonance only for one polarisation).

TC-869 Finding: OEP 5’s review qualifies TC-865 to TC-868 (2026-10-07)

• Where: the manual pages Third-order nonlinearity (Resonance limits, Does gamma increase with each frequency?, Quantities derived from the facts) and Third-order accuracy (Beyond the fitted data); tools/fit/nonlinear_support.py (E1_KIND, _values, the E2_any selections); OEP 5 (reviewed by John Travers and GPT-6, 2026-10-07).

• Corrections, each verified:

  • The band edge min(E1, E2/2) is a sufficient bound on all four legs (a pair sum is at most twice the largest leg), generated outputs included; a bound on the input band alone does not bound the outputs. For one linear polarisation the SPM quartet reaches the scalar E2 at the edge; for any polarisation it need not, since an atom’s even J = 1 level is not reached by two photons of equal frequency (TC-862’s own selection rule). TC-868 called it “the lowest frequency whose SPM quartet reaches a resonance” without that qualification.

  • No general lower bound. Just beyond the windows argon’s THG sits at model/value 1.001 and N2’s at 1.002 (the accuracy page’s table), so “every calculation rises faster than the polynomial” (TC-866, TC-867) holds for the trend farther out, not at every point. The comparisons include the fitted scales and cover particular processes and gases; they prove no lower bound for arbitrary mixed quartets. The accuracy page’s “shown no worse” count rests on that assumption, now stated.

  • Absorption evidence is not a level (TC-865): CH4 and SF6 show no absorption at Ityaksov et al.’s sampled wavelengths down to 197.7 nm, not a proven bound; 5.70 eV is the lower boundary of Chan et al.’s integration over N2O’s B band; 1046.8 nm is the end of the curated Serdyuchenko table (measured to 1100 nm), not O3’s onset. The tables now say so, and the derived band edge is not formed from evidence.

  • E2 of any polarisation is the minimum over all eligible levels (even J = 0, 1, 2; CO’s A and I states), not the J = 1 level by construction. Every value is unchanged: the J = 1 level (CO’s I state) is the lowest for every gas.

  • The analysis tool now fails on a fitted dataset it cannot read rather than skipping it; it skipped none (each gas’s fitted values and largest W2 equal the stored fit’s).

  • The sum over states: Shelton & Rice’s eq. 14 (p. 8) prints the dynamic expression with the denominators and permutations used here; eq. 17 (p. 10), which TC-865 cited, is its static limit. Orr & Ward’s paper, not checked, is no longer cited.

• Status: verified (2026-10-07).

TC-870 The hyperpolarizability support records (OEP 5, Phase 1) (2026-10-07)

• Where: data/gas/nonlinear_support.toml (the selection: each limit’s datasets and why), data/gas/models/nonlinear_support/<gas>.json (the records, written by tools/fit/nonlinear_support_record.py through optmat.gas._nonlinear_support), optmat.gas.nonlinear (HyperpolarizabilitySupport, SupportLimit, HyperpolarizabilityModel.support), the manual page Third-order nonlinearity (The support record).

• Decision (the limits): the selections of TC-865 as qualified by TC-869.

  • Atoms: NIST ASD levels (TC-862); E1 the lowest odd J = 1 level, E2 the smaller of the lowest even J = 0 and 2 levels, E2 of any polarisation the smallest of even J = 0, 1 and 2 (helium: 1s2p 1P1, 1s2s 1S0 for both).

  • Diatomic molecules: band origins T0 as sums of Huber & Herzberg’s 0-0 bands (TC-863): H2 and D2 B, and EF as E-B plus B-X; N2 b as b-a, a-a’, a’-X, and a as a-a’, a’-X; O2 B and C; CO A for E1 and E2, and the smaller of A and I (I) for any polarisation.

  • CH4 and SF6: absorption evidence, none detected at Ityaksov et al.’s sampled wavelengths, the shortest 197.7 nm. N2O: absorption detected above the 5.70 eV boundary of Chan et al.’s integration. O3: absorption detected throughout the curated 543.7-1046.8 nm. CO2’s E1, and every polyatomic E2, are missing, each with its reason. Evidence never forms the derived band edge.

  • Ionisation: the dataset optmat.gas.ionisation uses (a test keeps them equal); O3’s, the lower of Mahla et al.’s two thresholds (12.66 eV).

• Decision (the extents): the points the fit admits after its windows and row selections; validators and windowed-out values do not count. A point attaining the largest value to 1e-12 relative is a witness too (a tie differs only by rounding). The recomputed per-dataset counts and the largest W2 must equal the stored fit’s exactly, and do for all 15 gases.

• Uncertainty: NIST ASD states uncertainties for the helium and neon levels (level not stated); none for the argon, krypton and xenon levels or for any band origin, recorded as unstated, never as zero. The ionisation energies carry their datasets’.

• Checked:

  • against the analysis of the manual (tools/fit/nonlinear_support.py):

    • the largest W2, leg and pair sum, and the number of fitted points, to 1e-12;

    • every limit to 1e-9 (the tool converts eV with a 10-digit hc/e);

    • the band edges to the printed 0.1 nm;

  • every level is its printed NIST value times 100;

  • every band origin is the sum of its printed 0-0 bands;

  • helium against solprop’s SEP 12, section 4.4, and xenon’s 6p[1/2]0 at 249.6 nm against Lehmberg et al. (TC-854);

  • no model digest or golden value changed.

• Not verified: the molecular one- and two-photon assignments remain the curators’ reading of their symmetry (TC-865); CO2’s and SF6’s onsets and the polyatomic two-photon states are still open (TC-865).

• Status: decided (2026-10-07).

TC-871 The manual’s resonance tables read the support records (2026-10-07)

• Where: tools/fit/nonlinear_support.py (resonances), the manual page Third-order nonlinearity (table nonlinear-resonances); OEP 5’s Q11.

• Decision: the analysis tool takes each gas’s resonance limits from its support record (TC-870) instead of its own copy of the selections (LIMITS, NOBLE, E1_KIND, which TC-865 and TC-869 cite). data/gas/nonlinear_support.toml is now the one copy of the selections.

• Checked: every number of the manual’s tables is unchanged, and the accuracy page’s tables are identical. The resonance table now names E2 of any polarisation’s datasets for every gas; its cell for detected absorption reads “detected in a curated window ending at …” for N2O and O3 alike (it read “band integrated from” and “absorbs to the table’s end”); and it names O3’s ionisation row. Helium’s 1s3p level, the three-photon check against solprop’s SEP 12, is no longer a column of the table, being no limit; the page’s text names its dataset.

• Status: decided (2026-10-07).

TC-872 Vocabulary: four quantities for two-photon data (2026-10-08)

• Where: src/optmat/vocabulary.py (QUANTITIES), the data page’s quantities table (docs/data.md).

• Decision (the maintainer, 2026-10-08, before any data of these kinds; data rule 7):

  • two_photon_transition_strength: the rotationally averaged two-photon strength delta^TP of a bound transition from the ground state, in atomic units, with the rotational average’s convention (F, G, H), the polarisation and the frequencies stated (rotational_average, not the third-order convention). For the response-theory tables of Hattig et al. (1998) and Henriksson et al. (2005).

  • two_photon_excitation_cross_section: the frequency-integrated generalised cross section sigma_0^(2) of a bound two-photon line, W = sigma_0 g Phi^2, with the variable its line profile g is normalised in (angular or ordinary frequency: a factor 2 pi), the polarisation and the photon statistics (G2(0)) stated. For the measurements and calculations in cm4 or m4 (Kroll and Bischel 1990, Shekhtman et al. 2020, Drag et al. 2021, Dakka et al. 2018). A profile-dependent peak cross section in cm4 s is not this quantity.

  • excited_state_photoionization_cross_section: the one-photon photoionisation cross section of a named excited level, which sets the ionisation that follows a two-photon excitation; photoionization_cross_section is the ground state’s and is not bent to hold it.

  • multiphoton_ionization_polarization_ratio: sigma_circ / sigma_lin of N-photon ionisation (McGuire 1981’s R).

• Two-photon ionisation itself stays multiphoton_ionization_cross_section with photons = 2; its datasets state the polarisation, method, definition and energy axis in their parameters, as mckenna_2004’s do (TC-856). The coupling coefficients of the two-level helium 1s2s models (Kumar et al. 2026; Kapralova-Zdanska 2025) stay in their records’ notes (the maintainer, 2026-10-08).

• Status: decided (2026-10-08).

TC-873 saenz_1999 (Saenz & Lambropoulos, J. Phys. B 32, 5629 (1999)): two-, three- and four-photon partial ionisation cross sections of He, LOPT in a B-spline basis, on the authors’ shifted energy axes (2026-10-08)

• Where: src/optmat/data/sources/saenz_1999.toml, tools/extract/saenz_1999.py (vector figures), data/values/ionisation/He/saenz_1999__*.csv.

• Transcribed: the paper’s own generalised cross sections, W_N = sigma^(N) F^N with F the photon flux in cm^-2 s^-1 (Eq. 2), partial by the final symmetry, all use = check: two-photon 1S and 1D, 12.65-23.88 eV (Fig. 1); three-photon 1P and 1F, 8.50-11.95 eV (Fig. 2); four-photon 1S, 1D and 1G, 6.34-8.14 eV (Fig. 3); the 1D two-photon cross section in the velocity and length gauges (Fig. 4; the length gauge as the vertices of its 80 dashes). Every vertex of each drawn line (634 to 1832 per curve), 0.5 % digitising uncertainty; every tick within 0.019 pt. No total is drawn and none is taken. Six text values at 13.5 eV (p. 5634) as inline points: 1D 1.3e-51 (velocity), 1.35e-51 (length), 1S 0.2e-51 (velocity), 0.15e-51 (length), and the authors’ own complex-scaled CI calculation (length gauge), 1D 1.15e-51 and 1S 0.1e-51 cm4 s. The complex-scaling values are not reproduced from another paper: Froelich and Flores-Riveros (1986) is cited for the method (on hydrogen) only.

• Energy axes: recorded as drawn, not shifted. The authors’ ground state is about 0.69 eV off, and they moved the photon-energy axis of each order N ‘so as to reach the same energy above the ionization threshold. This is what has been done in figures 1-4. Needless to say, this scaling changes with the order N’ (p. 5632). The computed ground-state energy and the formula of the shift are not given. Each dataset says so in parameters.energy_axis.

• Checked: every number the text prints for these curves, at 13.5 eV: 1D velocity 1.3e-51 read 1.295e-51 (Fig. 4) and 1.294e-51 (Fig. 1(b)); 1D length 1.35e-51 read 1.340e-51 (Fig. 4, dashed); 1S velocity 0.2e-51 read 0.192e-51 (Fig. 1(a)). sigma^(4) ‘about 1e-118, or perhaps larger by a factor of about two’ at 7.5 eV (p. 5635): the three partial cross sections add to 2.65e-118. The text’s ‘sigma^(2) ~ 1e-51’ read from Fig. 1 at 13.5 eV: the drawn sum is 1.49e-51. The overlays of the extracted values on the rendered pages follow every drawn line.

• Finding: the gauge of Figs. 1-3 is not stated. Fig. 1 is the velocity gauge: Fig. 1(b) and Fig. 4’s velocity line agree within 0.32 % from 13 to 22 eV, and Fig. 1(a) at 13.5 eV gives the velocity value 0.2e-51 (-4 %), not the length value 0.15e-51 (+28 %). The gauges differ by up to 25 % at 20 eV (the length gauge is higher), and the complex-scaling 1D value is 12 % below the B-spline velocity value. The polarisation is not named; it is linear, since the 1S two-photon final state appears.

• Not taken: the ion-yield estimates for Kobayashi et al.’s experiment and for four-photon ionisation at 7.5 eV (no quantity holds them, and they rest on assumed densities and volumes). Copies of these curves in mihelic_2021 and nikolopoulos_2001 (Fig. 3 in each) are not taken.

• Status: verified (2026-10-08).

TC-874 mihelic_2021 (Mihelič & Horvat, Phys. Rev. A 103, 043108 (2021)): two-, three- and four-photon partial ionisation cross sections of He below and above the one-photon threshold, ECS (2026-10-08)

• Where: src/optmat/data/sources/mihelic_2021.toml, tools/extract/mihelic_2021.py (vector figures), data/values/ionisation/He/mihelic_2021__*.csv.

• Transcribed: the paper’s own generalised cross sections of He (driven Schrodinger equations with exterior complex scaling, amplitudes from Coulomb-wave fits; velocity form; linear polarisation; Eq. 31), all use = check, 25 curves: Fig. 3, the partial cross sections sigma_L by the final state’s total L, two photons (L = 0, 2), three (L = 1, 3) and four (L = 0, 2, 4), each from its N-photon threshold to the one-photon threshold, 24.6 eV (BTI), and from there to 43.5 eV (ATI: one-photon ionisation open, the last photons absorbed in the continuum, with the He+ n = 2 thresholds and the core-excited peak at 40.8 eV); Fig. 4, the total three-photon cross section from 25.25 to 27.35 eV with channels n_a <= 10 and n_a <= 5; Fig. 5, the two-photon partial cross sections of single channels near the lowest 1Po autoionising states, 59.05 to 64.30 eV (L = 0: total, 1s eps s, 2s eps s, 2p eps p; L = 2: total, 1s eps d, 2s eps d, 2p eps p, 2p eps f). Every vertex inside each frame (42 to 656 per curve; the drawing program simplified the paths), 0.5 % uncertainty; every tick within 0.001 pt. The right-hand axes of Fig. 3(b), (d), (f) carry no unit label and are taken in their row’s unit.

• Checked: the core-excited peak, printed 40.8 eV: read 40.803 (two photons), 40.808 (three), 40.824 eV (four); the jumps at the 2 l_a eps l thresholds, printed 32.7 and 21.8 eV: read 32.708 and 21.801 eV (at 16.35 eV, four photons, a clear step only for L = 2, 16.347 eV); Fig. 4’s dotted line at 1 a.u. reads 27.2114 eV; Fig. 4’s n_a <= 5 curve equals Fig. 3(d)’s L = 1 + 3 within 1.4 %. The paper prints no value of a He cross section. The overlays follow every drawn line.

• Finding: the dotted copies of Saenz and Lambropoulos’s curves in Fig. 3(a) agree with saenz_1999’s Fig. 1 within 1 % (2 % at 20.4 eV): they are its velocity gauge on its shifted axis, which confirms both readings. Mihelič and Horvat’s own cross sections are 0.75-1.06 (L = 0) and 0.89-1.19 (L = 2) times saenz_1999’s from 13 to 20.5 eV; at 13.5 eV 0.151e-51 and 1.16e-51 cm4 s, against saenz_1999’s 0.2 and 1.3e-51 (velocity), 0.15 and 1.35e-51 (length), 0.1 and 1.15e-51 (complex scaling). Four photons at 7.5 eV: 2.40e-118 cm8 s3 summed, against saenz_1999’s 2.65e-118; L = 0 is 0.27 to 0.78 times saenz_1999’s 1S from 6.5 to 7.5 eV (‘slightly larger differences’, p. 043108-6).

• Not taken: Fig. 2 (hydrogen): its lines are filled outlines of the strokes, not stroked paths, so the line’s centre is not in the file; the paper reports perfect agreement with Karule’s analytic tables (J. Phys. B 11, 441 (1978); J. Phys. B 21, 1997 (1988); not in the library), the primary numbers for hydrogen. The copies of saenz_1999’s curves (Fig. 3(a), (c), (e)); Figs. 1 and 6 (a radial function; the photoelectron asymmetry parameters, which no quantity holds).

• Status: verified (2026-10-08).

TC-875 nikolopoulos_2001 (Nikolopoulos & Lambropoulos, J. Phys. B 34, 545 (2001)): two-photon single and double ionisation of He, multichannel LOPT, 12-47 eV (2026-10-08)

• Where: src/optmat/data/sources/nikolopoulos_2001.toml, tools/extract/nikolopoulos_2001.py (vector figures), data/values/ionisation/He/nikolopoulos_2001__*.csv.

• Transcribed: the paper’s own generalised two-photon cross sections of He (LOPT, multichannel B-spline basis in a 40 au box; rate sigma F^2 with F the photon flux), linear polarisation, gauge not stated, all use = check: the partial cross sections to the S and D waves with the ion bound (single ionisation), 12.35-38.00 eV (Fig. 4; 236 and 225 vertices); the D wave again, 12.75-23.70 eV (Fig. 3; 100 vertices); the total single- and double-ionisation cross sections, 42.73-46.54 eV (Fig. 5; 17 markers each). 1 % digitising uncertainty; every tick within 0.085 pt. The text’s sigma_2(He+) ~ 1.2e-53 cm4 s at 45 eV as an inline point. All are the neutral atom’s (material He): ‘He+’ and ‘He++’ name the product ion.

• Checked: the text’s 1.2e-53 at 45 eV against Fig. 5: 1.267e-53 (the markers either side 1.271 and 1.264e-53); ‘about 10%’ double over single: 5.0 to 13.5 %. The overlays follow every drawn line and marker. The joining lines of Fig. 5 pass through every marker.

• Doubt: Fig. 4’s y axis reads ‘cm^2 s’; the values are cm4 s (the text’s definition, the labels of Figs. 3 and 5, and the same decades as Fig. 3). The record states cm4 s; no printed value is wrong, so there is no erratum.

• Finding: Fig. 3 is not Fig. 4’s D wave drawn again. Their energy grids differ, Fig. 3’s 1s2p peak is at 21.200 eV against Fig. 4’s 20.950 eV, and off resonance Fig. 4 is 0.74 to 1.30 times Fig. 3 (0.76 at 19 eV). The 0.25 eV is about half the 0.535 eV error of the computed ground state (p. 553), the shift saenz_1999 applies to its two-photon axis; the paper states no shift, and nothing is shifted here. Sato et al., J. Phys. B 44, 161001 (2011), Table 2, quote this calculation (‘Theory (LOPT)’) at 61.4, 58.4 and 56.0 nm as 8.0, 360 and 2.7e-52 cm4 s: Fig. 3’s D wave reads 1.04, 0.97 and 1.01 times them, Fig. 4’s S + D 0.96, 0.027 and 0.78 times. Sato et al.’s values are Fig. 3’s D wave, not Fig. 4’s total.

• Not taken: Saenz and Lambropoulos’s curve in Fig. 3 (saenz_1999 holds it); the points of Bachau, Lambropoulos and Tang, Phys. Rev. A 42, R5801 (1990) and Proulx and Shakeshaft, J. Phys. B 26, L7 (1993) in Fig. 4; Fig. 5’s pseudoresonance points, which the authors replaced by interpolation; the one-photon cross section and the yields (p. 558); the double-ionisation values the text quotes from Crance and Aymar, J. Phys. B 18, 3529 (1985) and Kornberg and Lambropoulos, J. Phys. B 32, L603 (1999), and the yields of Pindzola and Robicheaux, J. Phys. B 31, L823 (1998). None of these papers is in the library.

• Status: verified (2026-10-08).

TC-876 sato_2011 (Sato et al., J. Phys. B 44, 161001 (2011)): absolute two-photon ionisation cross section of He with an XUV free-electron laser, 53-61 nm (2026-10-08)

• Where: src/optmat/data/sources/sato_2011.toml, tools/extract/sato_2011.py.

• Transcribed: Table 2 (p. 3; cells checked against the table image): the measured two-photon ionisation cross section of He at 1e13 W/cm2, 2.6 (6), 23 (7), 0.9 and 7 (5) x 10^-52 cm4 s at 61.4, 58.4 (on the 1s2p resonance), 56.0 and 53.4 nm (on the 1s3p tail); the parenthesised errors per point, their level not stated, none for 56.0 nm. Sigma is the rate coefficient (Eq. 3, Gamma = sigma Phi^2) and depends on the intensity (sigma ~ I^(n1 - n2 - 1), Table 1’s exponents); absolute through the one-photon H2+ yield of 3 % H2 in the beam and H2’s literature cross section (Chung et al. 1993), with a pulse length assumed, not measured (300 fs; sigma scales as 1/tau) and a 10 um focus. The photon statistics of the SASE pulses are not discussed and no G^(2) correction is stated. Table 2’s two theory columns as reproduced values: van der Hart and Bingham’s R-matrix Floquet at 1e13 W/cm2 (2005; not in the library) and Nikolopoulos and Lambropoulos’s LOPT (nikolopoulos_2001). The text’s values extrapolated to 1e10 W/cm2 (5.1, 550, 2.2 x 10^-52 at 61.4, 58.4, 56.0 nm, p. 5) inline. All use = check, the house convention for the gases’ multiphoton cross sections (as uiterwaal_1998): none is fitted. Not taken: Table 2’s H2 row (Chung et al.’s measurement), Table 1 (no quantity holds a yield’s exponent), Figs. 1-3 (images; Fig. 3’s values at 2e13 and 5e13 W/cm2 exist only there).

• Checked: the inline values against the sentence of the text layer; the text’s LOPT values against Table 2’s column; Eq. 5 with Table 1’s exponents extrapolates Table 2 to 1e10 W/cm2 as 5.19 (61.4 nm; printed 5.1) and 2.06 (56.0 nm; 2.2); the LOPT column against nikolopoulos_2001’s figure files: its Fig. 3 (the D wave) gives 8.35, 349 and 2.73 x 10^-52, within 4 % of 8.0, 360, 2.7, and its Fig. 4 S + D total 7.7, 9.8 and 2.1.

• Doubt: at 58.4 nm Eq. 5 with Table 1’s exponents (n1 = 1.1, n2 = 0.78) gives 2520 x 10^-52 at 1e10 W/cm2, against the printed 550 (the slope -0.68 against an implied -0.46; Table 1’s stated errors allow 1100 to 5800): Table 1’s n1 at 58.4 nm, the text’s value, or both are in error; Figs. 2-3 (images) could decide. A flat-top intensity from the stated pulse energies, the 10 um spot and 300 fs is 0.42 to 0.71 of the central intensities the text gives; how the paper obtains its intensity is not stated. The text cites Ref. 12 for H2’s cross section before Eq. 5, Table 2 Ref. 14 (a slip).

• Status: verified (2026-10-08).

TC-877 petrov_2016 (Petrov et al., Phys. Rev. A 93, 033408 (2016)): correlated two-photon 3p ionisation cross sections of Ar with core polarisation, totals and partials (2026-10-08)

• Where: src/optmat/data/sources/petrov_2016.toml, tools/extract/ petrov_2016.py (vector figures).

• Transcribed: the paper’s own generalised two-photon ionisation cross sections (G2PICS, Eqs. 19-20, cm4 s; Gamma = sigma Phi^2 as in Starace and Jiang 1987, whose Eq. 23 is Eq. 20 with alpha = 1/c; LOPT with the correlation-function technique, LS coupling, no intermediate-state widths, so infinite at every resonance), linear polarisation, against the photon energy, 8 to 15 eV: Fig. 10’s four totals (corr and corr + CP, length and velocity forms, log scale) and the partials on the same footing, Fig. 6 ep(1S) (the same four), Fig. 7 ep(1D) and Fig. 8 ef(1D) (corr and corr + CP, length form): 12 datasets, each with photons, polarization, gauge, method, definition (and channel for the partials). The energy denominators use the experimental E(3p) = 1.158 Ry; the LS-coupled resonances sit where the calculation puts them (no shift of the taken curves by the authors). No table or supplement: the drawings read by script, every vertex and dash end inside the frame, clipped vertices not taken; every tick within 0.03 pt; 2 % at a vertex (Fig. 10), 2e-53 cm4 s (linear partials); all use = check. Not taken: the LOPT curves, the overlaid curves of Pindzola and Kelly (1975), Starace and Jiang (1987) and Pan, Gao and Starace (1990), Figs. 11-12 (beta parameters), Tables I-VII (geometric and angular coefficients of the method) and Table VIII (one correlation process’s amplitude at 8 eV, not a cross section: its square, 2.1e-52 cm4 s in the length form, cannot check Fig. 10’s total, which interferes all amplitudes, Eq. 21).

• Checked: core polarisation’s increase of the total at 9.5 eV, read 1.184 (L) and 1.151 (V) against the printed 18 % and 15 %; the corr L/V difference, 3.9 to 9.2

  11 %; ef(1D) +14 to +16.5 % at 8-10 eV against 16 %; ep(1D)’s minimum moved 0.13 eV by core polarisation against 0.2 (a flat minimum); the sum of the three partials equals the total (Eq. 19) within 0.05 % at 8-10.5 eV, corr and corr + CP; Fig. 10 over Fig. 9 (the same four curves, log and linear) within 0.5 %; Fig. 10’s five vertical lines at the NIST ASD levels of Ar I 3p5(2P3/2) nl [3/2] J = 1 (4s, 5s, 3d, 6s, 4d; nist_asd_2026) within 0.0009 eV. The 4s resonance leaves the frame at 11.639 eV (corr + CP, L) and 11.630 (V), against the experimental 11.624, and at 11.91 eV without core polarisation (the paper’s 11.90). The overlays of the extracted values on the rendered pages follow every drawn curve.

• Doubt: the conclusions’ 17 % increase ‘at the threshold’ (p. 10) is not the drawn total’s (1.128 L, 1.130 V at 8 eV, the lowest energy drawn) but matches the ep(1S) partial’s (1.167); the abstract’s ‘approximately 15%’ over 8-10 eV spans 1.13 to 1.22 (L) and 1.13 to 1.17 (V). Fig. 2(b)’s caption and the text (p. 5) disagree on whether the experimental or the Hartree-Fock E(3p) was used (a figure not taken).

• Finding: against mckenna_2004’s R-matrix Floquet total (TC-856, its Fig. 5 at 1e12 W/cm2), petrov_2016’s corr + CP length form is 0.909, 0.918, 0.915 and 1.044 times it at 8, 9, 10 and 11 eV, the velocity form 0.995, 0.956, 0.928 and 0.941; at 11 eV petrov_2016 is on the wing of its 4s resonance (11.63 eV) and McKenna’s (11.97 eV, LS coupling without core polarisation) is still flat. Without core polarisation (corr L) the ratio is 0.81, 0.79, 0.75, 0.71. The two all-electron calculations agree within 9 % off resonance between 8 and 10 eV.

• Status: verified (2026-10-08).

TC-878 starace_1987 (Starace & Jiang, Phys. Rev. A 36, 1705 (1987)): transition-matrix two-photon cross sections of Ar 3p, partial and total, linear and circular (2026-10-08)

• Where: src/optmat/data/sources/starace_1987.toml, tools/extract/ starace_1987.py (raster figures of a scanned PDF).

• Transcribed: 17 datasets (549 points, cm4 s against photon energy, all multiphoton_ionization_cross_section, photons = 2, gauge = length, use = check), lowest-order transition-matrix theory (Dalgarno-Lewis sum, particle-hole correlations) of Ar 3p two-photon ionisation below the one-photon threshold: the linear partial cross sections of the f 1D, p 1D and p 1S channels (Figs. 2-4) at the HF, + GSC, + IIC and + ESI levels (11 datasets; no GSC in Fig. 3), the shifted f 1D IIC and ESI (Fig. 5), and the circular (Fig. 6) and linear (Fig. 7) totals, IIC and ESI. 8.1 to 14.0 eV every 0.1 eV where the line is clear of the other curves; nothing near the 4s, 5s and 3d 1P resonances (the paper gives none). Read from the 600 dpi page images: ticks found and checked (residuals within 3.5 pixels), the 0.2-degree rotation interpolated out, each curve traced and its line style (solid, dashed, dash-dot, dash-double-dot) checked by script; samples within about a line width of another curve left out and listed in the script. Digitising uncertainty 4 pixels: 0.01e-50 cm4 s (Figs. 6, 7), 0.04e-51 (Figs. 2, 4, 5), 0.012e-51 (Fig. 3). The energy axis is the photon energy; the calculation uses HF energies except the experimental 3p threshold, 0.579 a.u., in the photoelectron energy k^2/2 = 2 omega - 0.579 a.u. (p. 1715), and only Fig. 5 is shifted to the experimental resonance energies. Not taken: McGuire’s (mcguire_1981), Pindzola and Kelly’s (Phys. Rev. A 11, 1543 (1975)) and Moccia, Rahman and Rizzo’s (J. Phys. B 16, 2737 (1983)) curves in Figs. 5-7; Table III’s resonance energies (Moore’s levels rounded, and HF model energies), used only to check the drawn lines. Curated by a delegated agent.

• Checked: Fig. 6 against 3/2 times Figs. 2 + 3 (the paper’s p. 1716 rule, Table II’s f_q): IIC 0.997-1.010, ESI 0.990-1.006; Fig. 7 against Figs. 2 + 3 + 4: IIC 0.998-1.010, ESI 0.981-1.010 (four independently read figures). The drawn resonance lines A, B, C, a, b, c lie at Table III’s energies within 0.045 eV (Fig. 2’s A 0.071) on the calibrated axes. Eq. 24’s 1.8967e-50 cm4 s is a0^4 t0 (CODATA 1.89679e-50). The text’s ‘about 15%’ reduction by GSC + IIC below the 4s resonance: the linear total’s IIC/HF is 0.88-0.90; ESI ‘approximately a factor of 2’: ESI/IIC down to 0.53 (p 1S), 0.59 (f 1D). Table III checked cell by cell against the image. Overlays inspected.

• Finding: against McKenna and van der Hart’s R-matrix Floquet linear total (mckenna_2004, TC-856) below 10.4 eV, this paper’s IIC total is 1.02 to 1.19 times it and its ESI total 0.82 to 0.87 times: the all-electron result lies between the two approximations. The curves’ rises into the 4s resonance begin some 0.3 to 1 eV below the experimental 4s position (11.62 eV) in Figs. 3, 4, 6 and 7, so their values above about 10.5 eV are resonance wings of this calculation. Text slips without effect on values: ‘Table II’ for Table III (p. 1716); Ref. 51’s factor 6.7734e-34 is a0^2 t0 in cm2 s, not the factor per printed unit of Pindzola and Kelly.

• Status: verified (2026-10-08).

TC-879 mcguire_1981 (McGuire, Phys. Rev. A 24, 835 (1981)): central-potential two-photon cross sections and circular/linear ratios of Ne, Ar, Kr and Xe, read from the scanned figures (2026-10-08)

• Where: src/optmat/data/sources/mcguire_1981.toml, tools/extract/mcguire_1981.py (raster figures, 1-bit page scans at about 600 dpi).

• Transcribed: the paper’s own lowest-order sigma_2^C (circular polarisation; cm4 s, W = sigma Phi^2, Eq. 1) and R = sigma_2^C / sigma_2^L of Figs. 1-4, against the photon wavelength in angstrom: Ne 593-1120, Ar 829-1390, Kr 960-1600, Xe 1120-1940 angstrom (sigma, 75-105 points each), R over 594-1100, 830-1390, 946-1560, 1152-1860 angstrom (50-98 points each); all use = check. The method: an approximate Hermann-Skillman central potential with an exact characteristic Green’s function, jl coupling, dipole-length matrix elements; each Green’s function’s ionisation energy adjusted so that the nearest resonance of each series lies at its experimental (Moore) level, the higher members moving with it, and the ‘differences of as much as twenty-five percent’ at the boundaries of the spectral ranges smoothed over (p. 835). Xe’s step at 1843 angstrom is the 2P1/2 channel closing; the Beutler autoionising structure above it is neglected (p. 844). sigma_2^L is not stored: it is sigma_2^C / R. Not taken: the three-photon Figs. 5-8 (not read in this curation), Fig. 1’s dashed 3d’’ enlargement (and the solid line from 611 to 617 angstrom that it crosses), Fig. 2’s LS-coupling circles and its triangles (Pindzola and Kelly’s sigma_L converted with McGuire’s R), Tables I-IV (binding energies below the ion limits, experimental and model; not level_energy), V (algebra) and VI (Xe lifetimes).

• Checked: the wavelength axis is piecewise linear (expanded at resonances): each segment calibrated from its own ticks, worst residual 0.3-2.9 pixels; segments of a single unchecked division left out (Ar 950-1000; Kr 1100-1160, 1240-1250; Xe 1400-1460, 1480-1500 angstrom). Log axes calibrated decade by decade (residuals within 4.0 pixels; 265-335 pixels per decade). Xe’s drawn step reads 1843.1 angstrom against the printed 1843. McCown et al.’s quotation of this Xe value at 193 nm (mccown_1982, 8e-32 cm4 W-1, circular) times hbar omega is 8.23e-50 cm4 s; the curve reads 8.36e-50 at 1930 angstrom (+1.5 %), and R there (1.15-1.20 at 1840-1860 angstrom) puts sigma_L 13-17 % lower, against their ‘~20 % lower’. Overlays of the values mapped back through the calibration on the page images inspected. Digitising uncertainty 5 % (sigma).

• Finding: the drawn ‘R = 1.5’ line reads 1.57 (Ne), 1.62-1.65 (Ar), 1.67-1.71 (Kr) and 1.50-1.52 (Xe) on the figures’ right axes, and Kr’s curve reads up to 1.58 where it meets the line although R <= 3/2 by Eqs. 3a-3b: the R values of Ne, Ar and Kr may be high by up to 5, 10 and 14 % (their stated uncertainties). Whether the sigma curves share the offset cannot be told from the figures; for Xe the McCown check holds to 1.5 %.

• Doubt: the text puts Fig. 1 ‘at 1 A per division near the 3d resonances’ (p. 837); the axis is 5 angstrom per division there and 1 angstrom per division only from 592 to 604 (4d, 5s); the figure is followed. The top axes’ ticks lie up to 12 pixels (median 2-5.5) right of the bottom ones carried along the frame: a drawing offset, part of the wavelength uncertainty (at most 0.1 angstrom in the 1-angstrom segments, 6 angstrom in the 50-angstrom ones). No values at the resonance peaks or steep flanks (the trace’s run-height rule), nor of R where it touches the R = 1.5 line.

• Status: verified (2026-10-08).

TC-880 lagutin_2017 (Lagutin et al., Phys. Rev. A 95, 063414 (2017)): relativistic, correlated two-photon ionisation cross sections of Xe 5p, linear and circular (2026-10-08)

• Where: src/optmat/data/sources/lagutin_2017.toml, tools/extract/ lagutin_2017.py (vector figures).

• Transcribed: the paper’s own generalised two-photon ionisation cross sections (G2PICS, Eq. 3, cm4 s; LOPT with no intermediate-state widths, so infinite at every resonance) of the Xe 5p shell in jj coupling, against the energy of one photon, 6.72 to 11.5 eV (the 5p1/2 two-photon threshold up: nothing is computed between the 5p3/2 and 5p1/2 thresholds, 6.065 to 6.718 eV): Fig. 3 (HF, PF, PFCP, length form, both panels), Fig. 4 (PF and CIPFCP, length and velocity forms), Fig. 6 (CIPFCP less shake-up, with and without nonlinear screening), Fig. 7 (the partial 5p3/2^5 ep3/2 (J = 0) channel, CIPF with and without shake-up, both forms; linear axis) and Fig. 8 (CIPFCP, length form, linear and circular polarisation): 18 datasets, each with photons, polarization, method, gauge, definition (and channel for Fig. 7). The energy denominators use the experimental ionisation energies 0.8915 and 0.9875 Ry; the resonances sit where the computed Rydberg energies put them (no shift by the authors). No table or supplement: the vector drawings read by script, every vertex inside the frame (dash ends for dashed lines), vertices clipped by the frame not taken; every tick within 0.03 pt; 2 % at a vertex, 8 % for CIPFCP (with the paper’s 7.7 % ‘measure of accuracy’); all use = check. Not taken: Table I (geometric factors), Fig. 1 (raster; an LS-coupled LOPT illustration for Ar and Xe), Figs. 2, 5 and 9 (one-photon cross sections, amplitudes, angular-distribution parameters), and the other papers’ curves drawn in Figs. 6 and 8 (L’Huillier and Wendin 1987, Fink and Johnson 1990, Gangopadhyay et al. 1986, McGuire 1981).

• Checked: the threshold L/V difference 7.4 % read for CIPFCP (7.7 % printed) and 80.1 % for PF (80 %); the first CIPFCP point at 6.7215 eV against 0.9875 Ry / 2 = 6.7178 eV; Fig. 3’s resonance shifts, 6s relativistic -0.112 eV (printed -0.11), 6s core polarisation -0.375 (-0.36), 5d core polarisation -0.073 (-0.08); Fig. 6’s WO / W at 8 eV 1.93 (printed ‘only … 2’); McCown et al.’s point, drawn as a star in Figs. 4 and 8, at 6.4238 eV and 4.1175e-50 cm4 s against mccown_1982’s 4e-32 cm4 W-1 times the 193 nm photon energy, 4.117e-50 (0.01 %); the 21 experimental-energy marks (Figs. 3, 4 bars, Fig. 8 dotted lines) each within 0.0018 eV of a NIST odd J = 1 level of nist_asd_2026; one calculation drawn twice agrees off resonance within 0.8 % (Figs. 4 and 8), 1.4 % (Figs. 3 and 4, PF) and 2.5 % (Fig. 3’s panels). The overlays of the extracted values on the rendered pages follow every drawn curve.

• Doubt: the drawn 5d resonances of Fig. 3’s HF and PF calculations coincide (10.595 and 10.596 eV), where the text gives a relativistic shift of -0.02 eV; the check passes only at its 0.02 eV margin. The computed resonance positions differ from experiment by up to 0.13 eV (6s’ at 9.70 eV against 9.570): values near a resonance are not to be compared at the experimental energy.

• Finding: the circular-to-linear ratio of the CIPFCP calculation (Fig. 8, not recorded as data) is 1.01 at 6.8 eV, 1.05 at 7.0, 1.08 at 7.5, 0.92 at 8.0, 1.15 at 9.0 and 0.69 at 10.0 eV. Off resonance the CIPFCP cross section is 4.5e-50 cm4 s at the threshold, 3.4e-50 at 8 eV and 7.7e-51 at 10 eV; karamatskou_2017’s TDCIS values are 20 to 200 times larger at the same photon energies.

• Status: verified (2026-10-08).

TC-881 karamatskou_2017 (Karamatskou & Santra, Phys. Rev. A 95, 013415 (2017)): TDCIS two-photon ionisation cross sections of the Xe 5p subshell (2026-10-08)

• Where: src/optmat/data/sources/karamatskou_2017.toml, tools/extract/ karamatskou_2017.py (vector figures).

• Transcribed: from the arXiv preprint (arXiv:1701.04789v1, the library’s copy; the arXiv page links the journal DOI 10.1103/PhysRevA.95.013415, which Crossref gives as Phys. Rev. A 95, 013415 (2017); the journal version is not in the library) the paper’s own TDCIS generalised two-photon cross sections, sigma^(2) = P_2 / int dt [I(t)/omega]^2 (Eq. 7, atomic units, plotted in 10^-48 cm4 s), velocity form, linear polarisation, nonrelativistic (no spin-orbit), each point a propagation with a 3000 a.u. Gaussian pulse at a perturbative, unstated intensity: Fig. 1 (interchannel and intrachannel, 9.0 to 12.56 eV), Fig. 2 (interchannel again) and Fig. 3 (interchannel, energies moved by the authors), 4 datasets with method telling the coupling schemes apart. No table or supplement: the gnuplot drawings read by script, each vertex a computed point (gnuplot’s clip vertices on the frame dropped), every tick within 0.043 pt; digitising 5e-50 and 4e-50 cm4 s on the linear axes, 1 % on the log axis; all use = check. Peak heights and widths are set by the pulse (‘limited by the Gaussian pulse duration used’, p. 6), not by the atom. Not taken: Fig. 2’s one-photon excitation spectrum (lines broadened by the 5e4 a.u. window) and Fig. 3’s RPAE curve of Wendin, Jonsson and L’Huillier (J. Opt. Soc. Am. B 4, 833 (1987), not in the library).

• Checked: the paper prints no value of the cross section. Every point of Fig. 2 and of Fig. 3 pairs with one of Fig. 1 at a constant energy offset (spread 0.0005 eV) and the same value (within 0.1e-48 cm4 s or 3 %); Fig. 3’s offset is -0.3264 eV against the text’s ‘about 0.3 eV’. The overlays of the extracted values on the rendered pages follow every drawn line.

• Finding: Fig. 3’s curve is Fig. 1’s with the photon energies moved by -0.3264 eV (0.0120 hartree), the values unchanged: the authors shifted the plotted axis, not the calculation, though the text speaks of ‘shifting the 5p binding energy’. The dataset keeps the drawn energies (energy_shift_ev = -0.3264); its photon energies are Fig. 1’s.

• Finding: Fig. 2’s interchannel points lie 0.0135 eV (about 0.0005 hartree) below Fig. 1’s, values equal, beyond the drawings’ 0.0006 eV resolution; the paper does not say which is right. Fig. 1 is taken as the reference; Fig. 2 is kept as drawn.

• Doubt: off resonance the TDCIS cross section (interchannel 1.0 to 2.0e-48 cm4 s from 9.25 to 11 eV, intrachannel 3 to 8e-48) is 20 to 200 times lagutin_2017’s CIPFCP and PF values at the same photon energies, and above the RPAE curve drawn in Fig. 3, which falls below 0.05e-48 between the resonances. The paper compares only resonance positions and does not discuss the magnitude. For the reconciliation.

• Status: verified (2026-10-08).

TC-882 lhuillier_1989 (L’Huillier, Tang & Lambropoulos, Phys. Rev. A 39, 1112 (1989)): MQDT two-photon cross sections of Kr and Xe between and above the fine-structure limits (2026-10-08)

• Where: src/optmat/data/sources/lhuillier_1989.toml, tools/extract/ lhuillier_1989.py (raster figures; the PDF is a 600 dpi 1-bit scan).

• Transcribed: the paper’s own MQDT generalised two-photon cross sections (Eq. 29; rate sigma_2 F^2, F the photon flux; linear polarisation; length form, epsilon . r; intermediate sum truncated to about 25 discrete Rydberg states), all use = check, read from the page images at native resolution: Fig. 6, between the 2P3/2 and 2P1/2 limits, the total (J = 0 and 2 final states) and the J = 0 partial of Kr (115.01- 116.49e3 cm^-1 total energy; 122 and 68 points) and Xe (103.02-105.98; 119 and 42), 1e-50 cm4 s on linear axes; Fig. 10, above the 2P1/2 limit, this paper’s solid line only, Xe 110.5-129.5 and Kr 120.5-139.5e3 cm^-1 (38 and 39 points, log axes). This is the only near-threshold krypton two-photon curve held. The text’s sigma_3 = 6e-82 cm6 s2 at 266 nm, inline (photons = 3; the sentence names no gas: Xe, since 3 x 266 nm = 112.8e3 cm^-1 lies above Xe’s second limit, below 110e3 by Fig. 10(a), and below Kr’s, above 116.5e3 by Fig. 6(a)). Uncertainty 0.1 and 0.15e-50 (totals), 0.05 and 0.08e-50 (J = 0), 3 % (Fig. 10): line half-width, pixel, calibration; the paper states none. Not taken: Tables I-III (MQDT parameters; no quantity), Figs. 4-5 (one- and three-photon spectra), 7-9; Fig. 10’s overlays (Gangopadhyay et al. 1986, McGuire 1981, L’Huillier and Wendin’s RPAE); the text’s sigma_3 of McGuire (5e- 82), Perry and Landen (1.2e-82, unpublished) and Kulander (2.5e-82).

• Decided: the figures’ x axis is the TOTAL two-photon energy (the ranges of p. 1118 and p. 1120 lie between and above the limits); the data files hold the PHOTON wavenumber, half of it, with the total energy and the pixel in each printed cell. No axis was shifted; the resonance positions are the MQDT fit’s, J-resolved.

• Checked: every frame line fitted and the scan’s shear corrected (up to 0.013 pixel per row); every tick found where the script writes it and on the fitted scale: Fig. 6 within 3.8 pixels in x and 2.4 in y (its inner x ticks sit 2-5 pixels off the line through the frame lines: about 5 cm^-1 of total energy in Kr, 10 in Xe), Fig. 10 within 6.2 pixels (hand-placed minor ticks; 0.43 % per pixel; panel (a)’s labels 10^-49 and 10^-50 are centred on the ticks at rows 3576.5 and 4122.5, a dash of McGuire’s line meeting the frame 33 pixels higher). Steep flanks, narrow peaks and the off-scale f’ resonances are not read (a value needs a single run of ink at most 12 pixels tall). The overlays of all values on the page images were inspected: all on their lines.

• Finding: McCown et al.’s cross in Fig. 6(b) lies on the Xe total (5.70 against 5.67e-50) at 103.62e3 cm^-1, twice the photon wavenumber of 193 nm (not twice their ArF line centre, 103 466); its height is 1.39 times their printed alpha = 4e-32 cm4 W-1 as sigma = alpha hbar omega (4.12e-50, mccown_1982). lhuillier_1987’s Fig. 6 draws the same point at 0.99 times it. The conversion used here is not stated.

• Doubt: the text (p. 1118) puts ‘the cross in Fig. 6(a)’; it is in Fig. 6(b), the Xe panel (a misprint; no value affected), and the caption spells ‘McCowen’. The printed Fig. 2 (p. 1117) carries the caption of an unrelated paper (‘Three stages of the plasma-vacuum interface development …’) under the Kr Lu-Fano plot; the library copies it. Nothing taken depends on Fig. 2.

• Status: verified (2026-10-08).

TC-883 lhuillier_1987 (L’Huillier & Wendin, Phys. Rev. A 36, 4747 (1987)): HF, RPAE and LDRPA two-photon cross sections of the Xe 5p shell, threshold and ATI regions (2026-10-08)

• Where: src/optmat/data/sources/lhuillier_1987.toml, tools/extract/ lhuillier_1987.py (raster figures; the PDF is a 600 dpi 1-bit scan).

• Transcribed: the generalised two-photon cross section of the Xe 5p shell (Eq. 8; rate sigma_2 F^2, F the photon flux; linear polarisation; length form, r or the screened r(omega)), 1e-49 cm4 s on log axes against the PHOTON energy in Ry, each approximation its own dataset (method): Fig. 6, 0.462-0.762 Ry, Hartree-Fock (solid, 127 points), RPAE with nonlinear screening (dashed, 117) and LDRPA with nonlinear screening (dotted, 0.464-0.844 Ry, 154); Fig. 7 (above-threshold region), 0.985-1.395 Ry, the same three (83, 76, 61). All use = check, from the page image at native resolution. Uncertainty 5 % (HF), 8 % (dashed, dotted: line half-width, pixel, calibration, and the stretches where the two lines run together). The paper states none. Not taken: the overlays of Fig. 6 (McGuire’s squares, Gangopadhyay et al.’s circles, McCown et al.’s cross); Figs. 9-11 (5p + 5s totals; linear screening, TDAE and 2 omega screening), left for a later round; Fig. 12 (sigma_2 F / sigma_1), Fig. 5, Table I.

• Energy axis: as printed and as calculated: nonrelativistic, spin-orbit-averaged, from the two-photon HF threshold (0.46 Ry); the LD 5p ionisation energy is 0.62 Ry. The resonances are the calculation’s: the HF 6s spike at 0.660 Ry and the RPAE 6s resonance at 0.675 Ry (read), against the experimental 5p5(2P3/2)6s 1P1 at 0.62 Ry (p. 4754). Nothing shifted.

• Checked: every tick (x every 0.05 Ry, y every decade) found where the script writes it and on the fitted scale within 2 pixels (1.33 % per pixel); the unlabelled frame lines at the text’s 0.46, 0.86 and 0.98 Ry within 0.001 Ry. Lettering, the cross and the 13 filled markers erased (counted); dots, dashes and the solid line sorted by the size of their connected pieces; steep flanks and peaks, and the overlapping 5d-8s resonances above 0.79 Ry (HF) and 0.765 Ry (RPAE), not read; a value kept only if its neighbour agrees. The overlays were inspected: all values on their lines. McCown et al.’s cross lies at 0.4719 Ry (193 nm: 0.4722) and 0.408e-49 cm4 s, 0.99 times their alpha = 4e-32 cm4 W-1 as alpha hbar omega (mccown_1982).

• Finding: the text’s ‘enhanced compared to the independent-electron result, by more than one order of magnitude’ above threshold (p. 4753) holds below about 1.1 Ry: RPAE / HF reads 34 at 0.985 Ry, 23 at 1.0, 9 at 1.1 and 7-7.5 from 1.2 to 1.4 Ry. lhuillier_1989 draws McCown et al.’s point 1.39 times as high (its entry).

• Status: verified (2026-10-08).

TC-884 mccown_1982 (McCown, Ediger & Eden, Phys. Rev. A 26, 3318 (1982)): the two-photon ionisation coefficient of Xe at 193 nm (2026-10-08)

• Where: src/optmat/data/sources/mccown_1982.toml, tools/extract/mccown_1982.py (Table I, tbl_0641e78d7d33, JSON cells).

• Transcribed: Table I’s xenon row, cm4 W-1 as printed, abscissa 193 nm: the measurement alpha = 4 x 10^-32 (alpha_Xe, use primary; ArF, 140 cm-1 FWHM, 13 ns FWHM, randomly polarised (polarization = "natural"), ~20-146 MW/cm2 at the focus, 10-300 Torr; absolute electron density by microwave bridge; no uncertainty printed), and, use = check with reproduced_from, Bischel et al.’s estimate 1 x 10^-34 (IEEE JQE 15, 380 (1979), not in the library), Hodges, Lee & Moseley’s lower limit 5 x 10^-34 (Int. J. Mass Spectrom. Ion Phys. 39, 133 (1981), not in the library; limit = "lower") and McGuire’s circular-polarisation calculation 8 x 10^-32 (mcguire_1981; linear ~20 % lower, p. 3322). The definition, verbatim: ‘dn/dt = alpha [Xe] I^2 / hbar omega … alpha is the two-photon ionization coefficient and has the units of cm^4 W^-1’ (Eq. 9, p. 3322); n = (alpha [Xe] / hbar omega) int I^2 dt (Eq. 10). Propane’s row is not taken (not a curated material).

• Checked: every cell against the table image and the page; identity on the first page.

• Finding: alpha is the ionisation rate per atom times hbar omega / I^2, so the generalised cross section on the photon flux (Gamma = sigma_2 Phi^2, Phi = I / hbar omega; uiterwaal_1998, mckenna_2004) is sigma_2 = alpha hbar omega = 4.11 x 10^-50 cm4 s at the line centre (two photons 103 466 cm-1, hbar omega = 6.414 eV). Santra and Greene quote this measurement as ‘about 4 x 10^-50 cm^4 s’ (santra_2004), the same conversion; the script checks it. Not stored as data.

• Finding: two 193 nm photons (12.83 eV) lie between the Xe+ 2P3/2 and 2P1/2 limits, in the autoionising region; the authors attribute the size of alpha to the 7d’[1 1/2] (J = 2) autoionising state within the 140 cm-1 linewidth (pp. 3322-3323). alpha is a bandwidth average across a resonance, not a smooth continuum value. Independent-particle theory without the 2P1/2 limit (santra_2004, 6.2 x 10^-50 cm4 s) lacks this structure.

• Doubt: Eq. (10) with the printed int I^2 dt (9.7 x 10^7 W2 s cm-4 at 84 MW/cm2) and the slope-2 lines of Fig. 2 (read on the library image: n = (I/12.2)^2 x 10^12 cm-3 at 300 Torr, (I/21.15)^2 x 10^12 at 100 Torr) gives 5.1 x 10^-32 cm4 W-1 at both pressures with the gas at 296 K (fill temperature not stated): 1.3 times the printed value, whose reduction the paper does not describe. The published value is kept.

• Status: verified (2026-10-08).

TC-885 santra_2004 (Santra & Greene, arXiv:physics/0407010; Phys. Rev. A 70, 053401 (2004)): independent-particle multiphoton cross sections of Xe and Xe+ (2026-10-08)

• Where: src/optmat/data/sources/santra_2004.toml (inline points; no script).

• Transcribed: from the library’s arXiv preprint v2 (the journal version, doi 10.1103/PhysRevA.70.053401, is not in the library and was not checked; pages are the preprint’s): sigma_2 of Xe+ at 12.7 eV, 4.5 x 10^-49 cm4 s (Eq. 17, 5p only) and 4.6 x 10^-49 (Eq. 27, with the crude 5s-mediated estimate); sigma_2 of neutral Xe at 6.42 eV, 6.2 x 10^-50 cm4 s (p. 7); the one-photon cross section of Xe at 12.7 eV, 119 Mb (p. 7). All use = check: Hartree-Fock-Slater potential tuned to the 5p binding energy, CAP-Floquet, length gauge, linear polarisation, rate dn/dt = sigma_N (I / omega)^N n (Eq. 24; the photon-flux convention). No uncertainty stated.

• Checked: every number against the rendered pages; identity on the first page. Eq. 15’s m-averaged rate 2.35 x 10^-5 a.u. at 10^11 W/cm2, times 6 electrons (Eq. 16), over the photon flux at 12.7 eV, gives 118.6 Mb: the printed 119 Mb.

• Doubt: the model has one ionisation limit per charge state (no spin-orbit, no multiplets): neutral Xe’s two-photon sigma at 6.42 eV has none of the autoionising structure between the 2P3/2 and 2P1/2 limits that dominates the measurement it is compared with (mccown_1982; ‘about 4 x 10^-50’ quoted). The same model’s one-photon cross section is ‘a little more than a factor of 2’ from experiment (p. 7).

• Not taken: sigma_3 to sigma_6 of Xe2+ to Xe5+ (Eqs. 18-21, 28-31): no such materials in the registry; Table I’s ionisation potentials and X-alpha parameters (model inputs, mostly quoted); the quoted experimental 4 x 10^-50 (mccown_1982 holds the original); Figs. 4 and 6 (a model of one FEL experiment).

• Status: verified (2026-10-08) against the preprint; the journal version open.

TC-886 geohegan_1986 (Geohegan, McCown & Eden, Phys. Rev. A 33, 269 (1986)): Kr (2+1) ionisation at 193 nm; the 6p[3/2]2 photoionisation bound (2026-10-08)

• Where: src/optmat/data/sources/geohegan_1986.toml (inline points; no script).

• Transcribed: the upper-limit estimate of the photoionisation cross section of Kr 4p5 6p[3/2]2 at 193 nm, ~6 x 10^-19 cm2 (Eq. 16, p. 273; limit = "upper", excited_state_photoionization_cross_section, use = check), from sigma_PI I_min Delta t / hbar omega ~ 1 with I_min ~ 60 MW/cm2 and Delta t ~ 25 ns; and footnote 2’s upper limit of Kr’s nonresonant three-photon ionisation cross section at 248 nm, 3 x 10^-45 cm6 W-2 (multiphoton_ionization_cross_section, photons = 3, the source’s Eq. 3 definition n_e = [Kr] sigma int I^N dt / hbar omega; use = check).

• Checked: the numbers against the rendered pages; identity on the first page. hbar omega / (I_min Delta t) = 6.85 x 10^-19 cm2 (printed ‘~6’). Eq. (15) with the quadratic lines of Fig. 4 (read on the library image; tau = 30 ns, 296 K assumed) gives 2.25, 2.05 and 2.05 x 10^-32 cm4 W-1 at 10, 20 and 50 Torr: the printed effective 2 x 10^-32. The printed line-shape factor (sqrt(2) Delta / delta) exp[((2 omega_L - omega_0)/Delta)^2] = 24 840 takes it to 4.97 x 10^-28, the printed 5 x 10^-28. In the photon-flux convention the 248 nm bound is sigma_3 = 1.9 x 10^-81 cm6 s2; uiterwaal_1998’s Kr sigma_3 (1.2 x 10^-82 at 248.6 nm) is 16 times below it.

• Decided: the effective two-photon cross section, 2 x 10^-32 cm4 W-1 (p. 273, ‘for an ArF laser with a bandwidth (FWHM) of 140 cm-1’, p. 275), is not taken. Kr is not ionisable by two 193 nm photons: the value is the bandwidth-averaged rate of the two-photon excitation of 6p[3/2]2 (2.1 THz off the laser’s centre) with the ionisation step saturated. It is not a multiphoton ionisation cross section, and not the frequency-integrated cm4 quantity two_photon_excitation_cross_section holds (TC-872); converting it needs a line shape. Nor is the line-centre 5 x 10^-28 cm4 W-1 (peak-normalised Gaussian, an estimated 300 MHz atomic width). The conclusions print it ‘5 x 20^-28’ (p. 275), a misprint of Sec. V B’s 5 x 10^-28 (not data, no erratum). The quoted values (Bokor/Bischel TPA (1-2.3) x 10^-31 cm4 W-1 for 100 cm-1; Chang & Kim 8.0 x 10^-19 and Bokor et al. 3.2 x 10^-19 cm2 for 6p[3/2]2, photon energies not stated) are not taken.

• Doubt: the text says the effective value comes ‘From Fig. 3 and Eq. (15)’; the densities are in Fig. 4 (Fig. 3 shows waveforms): a slip of the figure number.

• Status: verified (2026-10-08).

TC-887 hattig_1998b (Hättig, Christiansen & Jørgensen, J. Chem. Phys. 108, 8355 (1998)): coupled-cluster two-photon transition strengths of He, Ne and Ar; the tables’ S^0f and K (2026-10-08)

• Where: src/optmat/data/sources/hattig_1998b.toml, tools/extract/hattig_1998b.py (Tables II-V, from the library’s cells).

• Transcribed: the CCS, CC2 and CCSD two-photon transition strengths (a.u.) of the 1Se levels, He 1s2s, Ne 2p5 3p, Ar 3p5 4p, for omega_1 = omega_2 = omega_f0/2 and for omega_2 = 10.49 eV (18 one-row datasets, two_photon_transition_strength, TC-872; polarization linear_parallel, F = G = H = 2, as Eqs. 16-19 and p. 8356 state); the CCS, CC2 and CCSD oscillator strengths of the ground state to the lowest 1Po level (9 datasets). t-aug-cc-pV5Z, valence electrons correlated for Ne and Ar; no spin-orbit. All use = check; no uncertainty stated. Every cell checked against the table images.

• Checked: all 36 rate constants K of Tables III-V (1Se and 1De, both frequency pairs, CC and the reproduced SCF/MCSCF rows) reproduced from S^0f with each method’s own Table I excitation energy and omega_2 = 0.3855 au, within the printing (worst 0.26 %); Table II’s CCSD values within the experimental uncertainties the text cites (He 0.2766 vs 0.280 +- 0.007, Ne 0.1650 vs 0.171 +- 0.008, Ar 0.3219 vs 0.331 +- 0.016); the text’s 1.83e-51 and 2.05e-51 cm4 s and 10.49 eV = 0.3855 au.

• Finding: Eq. (15), K = a0^4 t0 (2 pi)^2 alpha^2 omega_1 omega_2 delta^TP, gives every tabulated K 2 pi too small (ratio 6.278-6.300); the tables follow (2 pi)^3.

• Finding: for a 1De level the printed S^0f is not delta^TP but the square of the one tensor element S_xy of the level’s xy component: argon’s SCF 90.23 and MCSCF 108.66 and neon’s SCF 8.799 are the squares of the S_xy of Sundholm et al. (1994) and Hettema et al. (1992) as henriksson_2005 quotes them (9.499, 10.424, 2.9663), and the 1De K follow from (4/15) S^0f, the F = G = H = 2 average of that one component (the K is one of the five components’). Summed over the level it is (4/3) S^0f, henriksson_2005’s convention. The 1De rows are not taken (no quantity holds S_xy^2). Neon’s MCSCF 11.289 is not 3.3450^2 (the SD RAS of Hettema et al. that henriksson_2005 quotes, at 19.170 against 18.874 eV here): a different calculation.

• Errata: Table V labels argon’s levels ‘2p5 3p1’ (neon’s shells), corrected to 3p5 4p1 (6 errata); Table II’s heading prints the level as 1Pe, corrected to 1Po (a dipole transition from the ground state; the text’s ‘ground state to 1Po transitions’; 9 errata). Table V’s K ‘1.19 x 20^-51’ (Ar, SCF, 10.49 eV), printed so in the PDF, is 1.19e-51 (reproduced 1.1875e-51); not held, so recorded in the notes.

• Not taken: the 1De rows; the K columns; the experimental argon 1De K, 2.05e-51 cm4 s (a rate constant, from Payne et al. 1981 and McCann, Chen & Payne 1989, not in the library); Table I’s computed excitation energies; Table II’s experimental rows (chan_1991, chan_1992_neon, chan_1992) and SCF/CAS rows (Sundholm et al. 1994).

• Status: verified (2026-10-08).

TC-888 henriksson_2005 (Henriksson, Norman & Jensen, J. Chem. Phys. 122, 114106 (2005)): TDHF and relativistic TDDHF one- and two-photon strengths of He to Xe (2026-10-08)

• Where: src/optmat/data/sources/henriksson_2005.toml, tools/extract/henriksson_2005.py (Tables I-V, from the library’s cells).

• Transcribed: per gas (He, Ne, Ar, Kr, Xe), non-relativistic TDHF and relativistic four-component TDDHF: the two-photon strengths delta_TPA of the even levels (two_photon_transition_strength, TC-872; degenerate photons; summed over M_J) and the oscillator strengths delta_OPA (Eq. 2) of the odd ones, 20 datasets, all rows with the selection-rule zeros; TDHF rows named by configuration and LS term, TDDHF rows by their printed J and energy (the TDDHF columns are sorted by computed energy and do not line up with the LS terms; for Xe their J do not even match the block’s terms). Also the text’s TDDHF He 2 1S0 with qaug-cc-pV5Z, 1.4737 au. All use = check. Stated accuracy: within 5 % of the Hartree-Fock limit for He, Ne, Ar (He 2 1S0 excepted); nothing for Kr, Xe. Not taken: Rn (no material), the experimental energies (Moore), Figs. 1-4.

• Checked: the neon table, merged by the library into one cell per column and configuration, split from the table image and checked to rejoin exactly; every row of Tables I-V (78) found in the PDF’s text layer; parity against the term marks; the text’s numbers: Ne and Ar 1D2 delta = (4/3) S_xy^2 from the quoted tensor elements (11.060, 5.6086, 113.40, to 2e-4), He 2 1S0 1.6002, Ne oscillator strengths 0.0043, 0.1608, 0.1645, argon’s 9 % leakage (0.089); the TDDHF strengths summed over each J within 1.4 % of TDHF (Ne, Ar), as the text says.

• Decision: polarization = linear_parallel, inferred: F, G, H and the polarisation are not stated (Eq. 6); the non-zero J = 0 strengths exclude circular, and the (4/3) S_xy^2 relation is the parallel-linear average (F = G = H = 1 with Eq. 6’s 1/15; hattig_1998b’s F = G = H = 2 with 1/30).

• Finding: the text misquotes hattig_1998b for neon: ‘1D2 … DE = 18.532 eV and delta_TPA = 19.915’ and ‘1S0 … DE = 18.855 eV and delta_TPA = 12.559’ pair the CCSD energies with Hättig’s CCSD (19.915) and CCS (12.559) strengths of the 1Se level; Hättig’s CCSD 1De strength is 12.024. The ‘50 %’ underestimate of 1D2 and the ‘fortuitous’ 1S0 agreement rest on it: TDHF 1S0 is 35 % below CCSD (12.850 vs 19.915). For 1D2 the papers’ conventions also differ (hattig_1998b prints S_xy^2, here (4/3) S_xy^2): Hättig’s CCSD is 16.03 (Ne) and 139.45 (Ar) here, against TDHF 11.060 and 113.40. He TDHF 10.426 against Hättig’s CCS 10.824: different methods, same convention.

• Doubt: Table II prints neon’s 2p5 4s 3P0 experimental energy as 16.761 eV, out of sequence (19.664-19.780 eV); not taken, not corrected.

• Status: verified (2026-10-08).

TC-889 shekhtman_2020 (Shekhtman, Mustafa & Parziale, Appl. Opt. 59, 10826 (2020)): calculated two-photon excitation cross sections of eight Kr 5p, 5p’ and 6p levels; four printed inconsistencies (2026-10-08)

• Where: src/optmat/data/sources/shekhtman_2020.toml, tools/extract/shekhtman_2020.py.

• Transcribed: sigma_o^(2) (cm4, two_photon_excitation_cross_section, TC-872) of Tables 5, 6 and 7 (basis sets 1-3), quantum-defect and quantum-defect with NIST oscillator strengths, and Table 9 (single path): seven datasets of eight lines, 192.749-216.667 nm. Row: the final level (Racah notation, from Table 3); abscissa: the laser’s vacuum wavelength as printed. Linear polarisation; a calculation (photon statistics: corrected); no uncertainty stated. Basis set 3 with oscillator strengths, the authors’ result, is primary; the others are checks. Version of record; tables read from their JSON cells and checked against the table images.

• Checked: the profile-dependent column sigma^(2) (cm4 s), divided by sigma_o^(2), is Eq. (9)’s Gaussian peak with Delta omega_L = 2 pi x 1350 MHz and Kr’s Doppler width at 2 omega_L and 298 K, both angular: 1.0045-1.0125 (mean 1.008; 1.000 at 292 K) in all 52 regular cells, against 2 pi times less with ordinary frequency: the line profile is normalised in the two-photon angular frequency (frequency_variable = angular, as kroll_1990 and drag_2021). Each normalised column agrees with sigma^(2) / max to its rounding. Table 3’s lambda_L equal 2 h c / (E - E_G) from its own energies to 0.0005 nm (vacuum; air would be 0.07 nm shorter). The text’s 4.18e-35 cm4 at 214.769 nm is Table 7’s.

• Errata: Table 6, QD, 193.494 nm (6p[3/2]2): sigma_o^(2) printed 9.85 x 10^-35, the 204.196 nm cell repeated; the row’s sigma^(2) 7.42e-46 and ratio 0.084 give 2.26 x 10^-35 (+-0.01 from the spread of the regular cells’ ratios), corrected. Table 9, 214.769 nm (5p[3/2]2): sigma_o^(2) printed 8.54 x 10^-35; sigma^(2) 3.05e-46 and ratio 0.318 give 8.54 x 10^-36 (ratio 1.010), corrected. Table images and the PDF text layer agree with the printed values.

• Finding: two misprints in columns not taken: Table 5, QD, sigma^(2) at 214.769 and 216.667 nm, 1.98 x 10^-46 and 2.24 x 10^-46 for 1.98 and 2.24 x 10^-45 (their sigma_o^(2) g and printed ratios 0.404, 0.455); Table 7, QD, the normalised ratio at 193.494 nm, 0.198 for 0.169. The text quotes dakka_2018 as 5.2 +- 2.2 x 10^-35 cm4; the library’s (submitted) copy prints 5.2 +- 2.1.

• Doubt: the bases differ by up to three orders of magnitude for the 6p lines (192-194 nm), which the paper calls predictions; the QD Einstein coefficients (Table 4) differ from NIST’s by 2-541 %. Basis set 3 with OS gives 4.18e-35 cm4 for 5p[3/2]2, 0.80 times dakka_2018’s 5.2e-35, and 5.08e-35 cm4 for 6p[3/2]2, about 94 times Khambatta et al.’s 5.4e-37 cm4 as reproduced by drag_2021.

• Status: verified (2026-10-08).

TC-890 kroll_1990 (Kröll & Bischel, Phys. Rev. A 41, 1340 (1990)): Xe 2p5, 2p6, 2p9 two-photon excitation and 2p5, 2p6 photoionisation cross sections (2026-10-08)

• Where: src/optmat/data/sources/kroll_1990.toml, tools/extract/kroll_1990.py.

• Transcribed: Table I’s ‘This work’ rows (10^-35 cm4, two_photon_excitation_cross_section, TC-872, label abscissa 2p5, 2p6, 2p9 = 6p[1/2]0, 6p[3/2]2, 6p[5/2]2): the measured product sigma_tot G2(0), 7.0, 2.4, 4.0 (use = check), and sigma_tot = the same over an assumed G2(0) = 1.4, 5.0, 1.7, 2.9 (use = primary); 30 % (2p9 50 %), one standard deviation of 15 (7) independent measurements; linear polarisation; the line profile normalised in the two-photon angular frequency (Eq. 4). Table II’s measured photoionisation cross sections (10^-18 cm2, excited_state_photoionization_cross_section): 2p5 4.3 +- 0.7 (248 nm) and 1.9 +- 0.7 (193 nm), 2p6 3.7 +- 0.7 and 1.8 +- 0.5 (fluorescence depletion; the level of the +- not stated). Scanned PDF: every cell checked against the table images and the rendered pages.

• Decided: both two-photon rows are kept: the measurement is the product, the correction rests on G2(0) = 1.4, measured for the second anti-Stokes line of the same laser (Bamford et al., JOSA B 5, 1369 (1988)) and assumed for the first, with no stated uncertainty; sigma_tot is primary, the product a check, never used beside it.

• Checked: sigma_tot G2(0) / 1.4 rounds to every printed sigma_tot. Sec. V’s sigma^(2) = 4.0 x 10^-45 cm4 s for 2p5 is 7.0e-35 cm4 times the peak of a Gaussian of the stated 0.086 cm-1 Doppler width normalised in angular frequency (5.80e-11 s): 4.06e-45 (sigma_tot would give 2.9e-45). So Eq. (4)’s integral is over the two-photon angular frequency, and Sec. V’s fractional-ionisation estimate (Fig. 8) uses the as-measured product. The 0.086 cm-1 is xenon’s Doppler FWHM at 80 119 cm-1 and 295 K (0.0860).

• Finding: dakka_2018 compares with this paper’s 2p6 value as 2.4 +- 0.8 x 10^-35 cm4, the G2-uncorrected product; drag_2021 quotes the corrected 5.0, 1.7, 2.9 x 10^-43 m4 without saying they assume G2(0) = 1.4.

• Not taken: Table I’s other experiments (Chen, Hurst & Payne, Chem. Phys. Lett. 75, 473 (1980); Gornik et al., J. Chem. Phys. 75, 68 (1981); Raymond et al., Phys. Rev. A 29, 721 (1984)): the paper does not say how they were brought to its definition; Pindzola, Payne & Garrett’s range 4-13 (Phys. Rev. A 24, 3115 (1981)); Table II’s theory (Pindzola, Phys. Rev. A 23, 201 (1981), ranges; Chang & Kim, Phys. Rev. A 26, 2728 (1982), a configuration average). None is in the library.

• Status: verified (2026-10-08).

TC-891 drag_2021 (Drag, Marmuse & Blondel, Plasma Sources Sci. Technol. 30, 075026 (2021)): Xe 6p’[3/2]2 and 6p’[1/2]0 integrated two-photon cross sections by absorption (2026-10-08)

• Where: src/optmat/data/sources/drag_2021.toml, tools/extract/drag_2021.py.

• Transcribed: the paper’s results, sigma-bar^(2) = 1.36 (+0.46 -0.34) x 10^-43 m4 (6p’[3/2]2, 224.3 nm) and 1.88 (+0.75 -0.54) x 10^-43 m4 (6p’[1/2]0, 222.6 nm), text (p. 25 and abstract), inline points, two_photon_excitation_cross_section (TC-872), primary; the asymmetric errors as parameters error_plus and error_minus (as uiterwaal_1998); no stated confidence level. Single-mode laser, G2(0) = 1; linear polarisation implied (Brewster-angle windows), not stated; the profile normalised on the 2 omega scale (Eq. 8). Table 1’s absolute values of other authors as reproduced datasets (m4): Khambatta et al. (J. Appl. Phys. 64, 4809 (1988), not in the library) Kr 6p[3/2]2 5.4e-45 +- 50 %; dakka_2018 Kr 5p[3/2]2 5.2e-43 +- 40 %; kroll_1990 Xe 6p[1/2]0, 6p[3/2]2, 6p[5/2]2 5.0, 1.7, 2.9e-43 +- 30, 30, 50 %. The library holds the accepted manuscript (HAL); its text layer has line-number debris and a garbled abstract, so every number was read on the rendered pages.

• Checked: the wavelengths are half the level energies the text gives (224.310, 222.568 nm, vacuum). The errors are the value times (F - 1) and (1 - 1/F), F = 1.334 and 1.396 the products of Table 3’s (1 + u), to 0.4 % (the printed relative -26 % is a point more than -0.34 gives). The ratio 1.88/1.36 = 1.382 (printed 1.38 +0.21 -0.18). Table 2: D(0) of Eq. (32) at 300 K 5.13e-11 s (5.1e-11), sigma-bar D(0) 9.18e-54 (9.2e-54), sigma-bar / (pi beta) 3.82e-51 (3.9e-51), sqrt(2 sigma-bar / pi) Phi_0 5.75e7 (5.9e7). Table 1 against the curated records: kroll_1990’s sigma_tot and dakka_2018’s sigma_0^(2), converted 10^-35 cm4 = 10^-43 m4, with their uncertainties: exact.

• Finding: Table 1 quotes kroll_1990’s G2-corrected values (G2(0) = 1.4 assumed) without saying so; the 6p’[3/2]2 result is 0.38 times the 3.6 x 10^-43 m4 deduced from Niemi et al. (2005) and Bamford et al. (1987) (p. 26). Khambatta et al.’s Kr 6p[3/2]2, 5.4e-45 m4, is about 94 times below shekhtman_2020’s calculation for that level (5.1e-43 m4).

• Not taken: Table 1’s ratios to H, N and O (Niemi et al. 2001, 2005; Goehlich et al. 1998; Elliott et al. 2016) and the ratio 1.38 of the two levels: no quantity; Table 3 (the budget, described); Table 4’s partial two-photon amplitudes (a.u., without signs, from Aymar & Coulombe and Salah & Hassouneh’s dipole elements); the pressure shift and broadening of the 6p’[1/2]0 line; Fig. 5’s caption units (‘m4 s-1’, ‘m2’) are slips, no value taken.

• Status: verified (2026-10-08).

TC-892 dakka_2018 (Dakka et al., Phys. Rev. Lett. 121, 093201 (2018)): Kr ground-2p6 two-photon cross section and 2p6 photoionisation cross section (2026-10-08)

• Where: src/optmat/data/sources/dakka_2018.toml, tools/extract/dakka_2018.py.

• Transcribed: Table I, ‘This work’ (the library holds the submitted version, arXiv:1805.05669v1): sigma_0^(2) = 5.2 +- 2.1 x 10^-35 cm4 for 4p6 1S0 -> 2p6 (5p[3/2]2), near 215 nm (two_photon_excitation_cross_section, TC-872, label abscissa, primary); sigma_ei = 3.8 +- 1.7 x 10^-18 cm2 for the 2p6 level at 215 nm (excited_state_photoionization_cross_section, check). Both fitted with a four-level density-matrix model to the 760 nm fluorescence of 5 ns, 200 GHz-wide OPO pulses (phase-diffusion model, so G2(0) = 1 in the model; not measured); polarisation not stated; the errors’ level not stated. Table image checked.

• Checked: sigma_0^(2) is defined through Eq. (2), Omega = sqrt(2 sigma_0 / pi) I / hbar omega_0, which is drag_2021’s Eq. (11) derived from the cross section integrated over the two-photon angular frequency: frequency_variable = angular. Table I’s ‘Literature’ 2.4 +- 0.8 is kroll_1990’s xenon 2p6 product sigma_tot G2(0), not its G2-corrected 1.7 (script, against the record).

• Doubt: Eq. (3) writes the ionisation rate as sigma_ei I / (2 hbar omega_0) with omega_0 the laser frequency; with the photon flux I / hbar omega_0 the printed sigma_ei would be twice the usual one-photon cross section, or Eq. (3) is misprinted; kept as a check. The published version is not in the library: shekhtman_2020 quotes sigma_0^(2) as 5.2 +- 2.2 (this copy: 2.1; drag_2021’s +- 40 % fits 2.1).

• Not taken: the branching ratio 75 +- 4 % to 1s5 (and the literature average 76 +- 3 %): no quantity. The ‘Literature’ sigma_ei, 3.3 x 10^-18 cm2, ‘calculated from’ H. Hyman, Appl. Phys. Lett. 31, 14 (1977) (not in the library; the calculation not given).

• Status: verified (2026-10-08).

TC-893 andrade_2025 (Andrade et al., Nat. Photon. 19, 1240 (2025)): eFROG of few-fs VUV pulses by two-photon photoionisation of Xe and Kr; no values taken (2026-10-08)

• Where: src/optmat/data/sources/andrade_2025.toml (notes only).

• Transcribed: nothing. Two-photon ionisation enters only through the measured traces and a fitted, delay-independent response function; no cross section is printed. The TD-CIS method (HF reference, small-core relativistic ECP, 164 spin-angular partial waves, surface-flux spectra) is recorded in the notes.

• Checked: Extended Data Tables 1 and 2 against their images and against nist_asd_2026 (TC-862): the half ionisation energies agree to the printed digits except He (12.30 printed, 12.2937 eV) and Xe (6.07, 6.0649 eV); the ‘lowest Rydberg state’ is the lowest odd J = 1 level for Ne-Xe (to 0.004 eV) but the spin-forbidden 1s.2s 3S1 level (19.82 eV) for He. Table 2’s experimental Xe ionisation potentials (5p3/2, 5p1/2, 5s1/2: 12.130, 13.436, 23.397 eV) agree with NIST to the printed digits; its ‘Rel. Delta’ column is in per cent though headed ‘(eV)’.

• Doubt: the text says the ECP gives the ‘correct spin-orbit splitting’; the table’s TD-CIS splitting is 1.457 eV against the experimental 1.306 eV.

• Status: verified (2026-10-08).

TC-894 pini_2026 (Pini et al., Nat. Commun. 17, 9912 (2026)): UV-XUV photoelectron spectroscopy with 3 fs resolution; no two-photon values (2026-10-08)

• Where: src/optmat/data/sources/pini_2026.toml (notes only).

• Transcribed: nothing: no Kr or Xe (or other) two-photon number is printed. The instrument response, 3.2 +- 0.2 fs, comes from XUV + UV sideband cross-correlation in argon; two-photon ionisation of noble gases is cited only as andrade_2025’s method.

• Status: verified (2026-10-08).

TC-895 bergeson_1998 (Bergeson et al., Phys. Rev. Lett. 80, 3475 (1998)): the He 1 1S-2 1S two-photon frequency; not held, compared with NIST (2026-10-08)

• Where: src/optmat/data/sources/bergeson_1998.toml (notes only).

• Transcribed: nothing. The result, 4 984 872 315(48) MHz (1 sigma), is a frequency; level_energy holds cm^-1 or eV, and a hand conversion is not data.

• Checked: the binding energies against the page image (the library’s text has lost their minus signs and parentheses). Converted for comparison only: 166 277.44234 (160) cm^-1, 0.00471 cm^-1 (141 MHz, 2.9 sigma of Bergeson) above nist_asd_2026’s level_He_1s2s_1S0, 166 277.437635(63) cm^-1; the derived ground-state binding energy, 5 945 204 356(48) MHz = 24.5873896 eV, is 144 MHz (3.0 sigma) above ie_He_I, 24.587389011 eV.

• Finding: the 1998 two-photon value lies about 3 of its own standard uncertainties above NIST’s current evaluation of both the 1s.2s 1S0 level and the ionisation energy; NIST’s evaluation is the one the package uses.

• Status: verified (2026-10-08).

TC-896 pan_1990 (Pan, Taylor & Clark, J. Opt. Soc. Am. B 7, 509 (1990)): perturbative harmonic generation in hydrogen; not the ‘Pan et al.’ of argon’s two-photon cross section (2026-10-08)

• Where: src/optmat/data/sources/pan_1990.toml (notes only).

• Transcribed: nothing. Hydrogen’s harmonic-generation susceptibilities (Table 1) are in the paper’s own normalisation, and hydrogen’s third-order response is not curated; Table 2’s noble-gas values are reproduced from Li et al. (1989).

• Checked: Table 1 against its image. The argon two-photon cross section McKenna and van der Hart attribute to ‘Pan et al (1990)’ (0.85e-50 cm4 s within 20 %; TC-856) is C. Pan, B. Gao and A. F. Starace, Phys. Rev. A 41, 6271 (1990), by McKenna’s reference list: a different paper by different authors, not in the library.

• Doubt: the text’s I_c(31) = 2.77e14 W/cm^2 is 3.77 (14) in Table 1, and its ‘I_c(19) = 1.66e11’ is I_c’(21) in the table (I_c’(19) = 1.79e11); nothing taken.

• Status: verified (2026-10-08).

TC-897 dorr_1990 (Dörr, Potvliege & Shakeshaft, J. Opt. Soc. Am. B 7, 433 (1990)): Sturmian-Floquet multiphoton rates of hydrogen; methods only (2026-10-08)

• Where: src/optmat/data/sources/dorr_1990.toml (notes only).

• Transcribed: nothing. The perturbative integrated rates of Tables 1-3 (harmonic generation, 1s -> 2s Raman scattering, N-photon ionisation of H(1s) at 1e13 W/cm^2, 265-1064 nm) are three-photon and higher (N_0 = 3, 4, 6, 12) and are rates at one nominal intensity; the nonperturbative results are figures. No two-photon quantity.

• Status: verified (2026-10-08).

TC-898 kumar_2026 (Kumar et al., Phys. Rev. Research 8, 013009 (2026)): two-photon excitation of He 1s2s 1S0 by femtosecond pulses; coefficients in the notes (2026-10-08)

• Where: src/optmat/data/sources/kumar_2026.toml (notes only, the maintainer’s decision of TC-872).

• Transcribed: nothing. Table I’s coefficients of the two-level model at 120.27 nm (S_g, S_e, Omega_ge^P = 0.886278 E_0^2, delta E_e/hbar, Gamma_e = 0.869215 E_0^2 a.u.) and Table II’s two-colour ones are in the notes, checked against the table images; the 10 TW/cm^2 columns are reproduced (their E_0^2 is 0.02 % below CODATA’s). The journal is Phys. Rev. Research, not Phys. Rev. A.

• Finding: in Eq. 7 the off-diagonal is Omega_ge^P/2 and the 1s2s diagonal carries -(i/2) Gamma_e, so Gamma_e is the population ionisation rate (as Eq. 11, the golden rule, also gives). With Phi = I_0/(hbar omega), Gamma_e/Phi is the 1s2s 1S0 photoionisation cross section at 10.31 eV: 1.691e-18 cm^2 (1.69 Mb); at 19.06 eV (Table II) 0.46 Mb. Not data: no curated value of this cross section exists to compare with (excited_state_photoionization_cross_section, TC-872, holds none for He). See the next entry for kapralova_zdanska_2025.

• Status: verified (2026-10-08).

TC-899 kapralova_zdanska_2025 (Kaprálová-Žďánská, Phys. Rev. A 111, 043105 (2025)): non-Hermitian Floquet coupling of He 1s2 and 1s2s at 120.3 nm; coefficients in the notes; agreement with kumar_2026 (2026-10-08)

• Where: src/optmat/data/sources/kapralova_zdanska_2025.toml (notes only, the maintainer’s decision of TC-872).

• Transcribed: nothing. Table I (|mu_0| = 2.03 a.u., gamma = 25.5, delta_omega = 58, gamma_1s2s = 25.3 microE_h/(TW cm^-2), with the other fits’ values) is in the notes, checked against the table image. The library copy is the author’s manuscript with its supplementary material (99 PDF pages), not the version of record.

• Checked: gamma I_0 is a full width (quasi-energies carry I_0 (delta - i gamma/2), Eqs. 25-28; Eq. 109 calls gamma I_0/2 hbar the cycle-averaged ionisation rate), so the 1s2s population decays at gamma_1s2s I_0/hbar. Appendix F’s intensity conversion is printed the wrong way round; read as I_0[a.u.] = 2.84937923e-5 I_0[TW/cm^2], it reproduces the paper’s a = 0.52 (Eq. 111).

• Finding: the implied 1s2s 1S0 photoionisation cross section at 120.3 nm is 1.727e-18 cm^2 (1.72-1.73 for gamma_1s2s = 25.2-25.4), 2.1 % above kumar_2026’s 1.691e-18 cm^2 at 120.27 nm: no factor 2, the two calculations (complex-scaled Gaussian Floquet; finite-volume R-matrix) agree. In the same units the two-photon couplings agree too: Omega = |mu_0| sqrt(2/(c eps_0)) I_0 = 0.8694 E_0^2 against kumar_2026’s Omega_ge^P = 0.886278 E_0^2 (1.9 %), both with Omega/2 off the diagonal.

• Doubt: crosswise the coefficients match more closely (Kumar’s Gamma_e 0.869215 against this Omega 0.8694, 0.02 %; Kumar’s Omega_ge^P 0.886278 against this gamma_1s2s 0.8879 E_0^2, 0.2 %): either chance within Table I’s three figures or Kumar’s Table I rows Omega_ge^P and Gamma_e interchanged. Neither paper decides it; the cross section would change by 2 % (1.73 Mb). Also: the text’s gamma_1s2s = 25.2 +- 0.2 (p. 44) against Table I’s 25.4* for the same fit.

• Status: open (the possible interchange).

TC-900 rupper_2004 (Rupper & Merkt, Rev. Sci. Instrum. 75, 613 (2004)): argon two-photon resonances for VUV four-wave mixing; the first adiabatic ionisation energy of CO2 (2026-10-08)

• Where: src/optmat/data/sources/rupper_2004.toml (inline text points, no script).

• Transcribed: the first adiabatic ionisation energy of CO2 (X 2Pi_3/2g (0,0,0) J+ = 3/2 from the neutral’s J’’ = 0), cm^-1, as printed: the abstract’s 111 112.3 +- 0.8 (p. 613; adiabatic_CO2, primary) and the text’s two derivations, 111 112.0 +- 0.8 via the PFI-ZEKE A-state ionisation energy and the A-X interval of Johnson and Rostas (p. 621), and 111 112.7 +- 1.0 via the B state and the B-X band system of Watson et al. (p. 622) (adiabatic_CO2_routes, check). Levels of the uncertainties not stated.

• Checked: each value against the page text (PDF pp. 2, 10, 11); Table I against its image. Minnhagen’s argon two-photon term values reproduced in Table I are NIST’s strings (nist_asd_2026 level_Ar_even_J2 105617.2700, level_Ar_even_J0 107054.2720 cm^-1; the other three identical to rows of Ar_I_levels.tsv); the paper’s own nu_1 + nu_Ex agree within its uncertainties (differences 0.01-0.27 cm^-1, 0.17 with the second F2 line).

• Doubt: the paper prints three values of one quantity and does not say how the abstract’s is formed; the inverse-variance mean of the two derivations is 111 112.27 cm^-1 (+-0.62), consistent with it, but the abstract keeps the A route’s +-0.8. Both routes rest on others’ optical spectroscopy of CO2+ for the interval to the X state.

• Not taken: Table I’s argon 3p5 4p two-photon resonance positions, widths (laser bandwidths) and relative four-wave-mixing efficiencies (1.2, 1, 4.0, 1.0, 7.5 for 4p[5/2]2, [3/2]2, [1/2]0, 4p’[3/2]2, [1/2]0; +-30 %): not cross sections. The F2 lines, 63 439.322(40) and 63 482.257(40) cm^-1 (157.6308 and 157.5242 nm), lie below argon’s two-photon ionisation threshold (157.344 nm, half of ie_Ar_I): two main-line photons fall 231 cm^-1 short. The acetylene ionisation energy (C2H2 not registered) and the CO2+ A- and B-state ionisation energies (Table IV, text) are not taken.

• Status: verified (2026-10-08).

TC-901 parker_2007, parker_2009, lehmberg_1995: notes amended for the two-photon curation (2026-10-08)

• Where: src/optmat/data/sources/parker_2009.toml and src/optmat/data/sources/lehmberg_1995.toml (notes only; no dataset changed). parker_2007.toml unchanged.

• Checked: parker_2007 holds helium rates at 390 and 780 nm only (two text points, ionization_rate, check; 8 and more photons); parker_2009 holds only the static-field rates of its Table 1, and its notes already say the 195 nm rates are in figures only and not taken. At 195 nm (omega = 0.23366 au) single ionisation of He needs four photons (Ip/omega = 3.87 at zero intensity, with parker_2007’s Ip = 0.903724 au): not two-photon ionisation. No ultraviolet He rate is held as ionization_rate beyond parker_2007’s 390 nm text point.

• Decision: parker_2009’s notes now say so in one sentence. lehmberg_1995’s notes gain a paragraph pointing to kroll_1990 (Kröll and Bischel, Phys. Rev. A 41, 1340 (1990), Lehmberg’s Ref. [5]) for the 6p[1/2]_0 two-photon cross section, and recording as not taken the Appendix’s upper limit on the Xe2 dimer’s two-photon excitation rate (W < 3.7e5 I^2 s^-1, I in GW/cm^2) and the dimer photoionisation cross section quoted from Ref. [22] (printed ‘4 x 10^-18 cm^-1’, meaning cm^2; checked on the page image, p. 88).

• Status: decided (2026-10-08).

TC-902 The two-photon data on one footing: thresholds, coverage and comparison; what is missing (2026-10-08)

• Where: tools/two_photon_tables.py, the manual page Two-photon ionisation and absorption: the data (docs/two_photon.md), tests/test_two_photon_page.py; the roadmap’s Papers and data we are looking for.

• Transcribed: nothing new. The tables are computed from the records of TC-873 to TC-901, TC-856 (mckenna_2004) and nist_asd_2026 (TC-443, TC-862). The thresholds are half the ionisation energy, and half of it plus the ion’s 2P1/2 level. E1 and E2/2 are the levels OEP 5’s support records select. Values are on one footing:

  • cm4 s, with Gamma = sigma Phi^2;

  • McCown’s alpha times hbar omega, by its Eq. 9 (TC-884);

  • against photon energy, each curve on its own source’s axis, none shifted;

  • interpolated in log sigma between a curve’s own vertices, never extrapolated;

  • partials summed where only partials are drawn.

• Finding, the window of direct two-photon ionisation without a one-photon resonance, [I_p/2, E1):

  • He 100.85 to 58.43 nm;

  • Ne 114.99 to 74.37 nm;

  • Ar 157.34 to 106.67 nm;

  • Kr 177.13 to 123.58 nm;

  • Xe 204.43 to 146.96 nm.

  The 2P1/2 thresholds are at Ne 114.48, Ar 155.59, Kr 169.08 and Xe 184.55 nm. Argon at the F2 laser lines (157.52, 157.63 nm; TC-900), Kr at 193 nm and Xe at 248 nm are below their thresholds. Xe at 193 nm is between its two.

• Finding, per gas (ratios to the first-named calculation, off resonance):

  • He: Saenz & Lambropoulos (S + D, velocity), Mihelic & Horvat (0.89 to 1.13) and Nikolopoulos & Lambropoulos (Fig. 4, 0.85 to 1.01) agree within about 15 % from 13 to 20 eV. Sato et al.’s one measured point in the window (61.4 nm, 2.6(6)e-52 cm4 s at 1e13 W/cm2) is about a third of them. Sato’s LOPT column is Nikolopoulos’s Fig. 3 D wave alone (TC-875, TC-876).

  • Ne: a single calculation (McKenna & van der Hart). McGuire’s circular values are 0.59 to 0.96 of its linear ones.

  • Ar: McKenna & van der Hart, and Petrov et al. with core polarisation in both gauges, agree within 10 % from 8 to 11 eV. Without core polarisation Petrov’s is 0.71 to 0.81. Starace & Jiang’s IIC and ESI (raster) bracket them, 0.72 to 1.27. McGuire’s circular values are 1.2 to 1.9 times the linear calculations.

  • Kr: only raster curves, L’Huillier, Tang & Lambropoulos’s MQDT and McGuire’s circular. No vector or tabulated cross section and no measurement exists in the library: the data do not support a model of krypton.

  • Xe: above the 2P1/2 threshold, L’Huillier & Wendin’s RPAE and L’Huillier et al.’s MQDT (raster) are 0.27 to 0.61 of Lagutin et al.’s CIPFCP. Karamatskou & Santra’s TDCIS starts above the window and is 20 to 200 times Lagutin’s there (TC-881). Lagutin computes nothing between the thresholds, where the only measurement lies: McCown’s 4.1e-50 cm4 s at 193 nm (natural polarisation, averaged over a 140 cm-1 band across an autoionising resonance). Santra & Greene’s single-threshold 6.2e-50 and the MQDT curve’s 5.7e-50 are drawn near it. Lagutin’s circular/linear ratio is 0.92 to 1.08 in the window; McGuire’s circular values are 2.8 to 4 times Lagutin’s linear.

• Finding, the drawings of McCown’s point disagree: Lagutin et al. and L’Huillier & Wendin draw it at its printed value (within 1 %); L’Huillier, Tang & Lambropoulos 1.39 times higher (TC-882).

• Missing:

  • any Kr cross section from a vector or tabulated source;

  • any measured Ar or Ne cross section;

  • calculations of Xe between its thresholds other than the raster MQDT;

  • Fink & Johnson’s relativistic Ne to Xe;

  • measured bound two-photon strengths of He, Ne and Ar, and their excited levels’ photoionisation;

  • the higher members of every two-photon series below I_p/2.

  The requests are on the roadmap.

• Decided: the manual’s comparison names the comparator of each gas only for the ratios; no source is preferred or fitted (data rule 8: every figure value is use = check). A model and its references are OEP 6’s.

• Status: decided (2026-10-08).

TC-903 OEP 6: evaluation on propagation grids, and the time-resolved loss current as a documented gap (2026-10-08)

• Where: OEP 6 (accepted 2026-10-08), section 6 (Warnings and refusals) and section 4 (Broadband fields, Q9); the roadmap’s OEP 6 entry. Part I is frozen; these are the author’s decisions for the implementation, to be reported as deviations in Phase 1’s Part II report.

• Decided (the author, 2026-10-08, on the review’s revisions):

  1. No raising on propagation grids. Section 6 as accepted raises when an input array contains a frequency outside the reference coverage (a data gap, at or above E1). A propagation grid always contains such points. Phase 1 therefore:

     • adds a read-only availability query (for example available(omega), a boolean mask from the support record);

     • evaluates arrays without raising at unavailable points.

     The value returned there is settled in Phase 1, recommended NaN with the mask defining it. It is never a zero or an extrapolation: optmat still manufactures no value. Scalar requests outside coverage may still raise.

  2. The time-resolved loss current is a documented gap. The review withdrew the causal-filter loss current, because the spectral factor’s phase, and with it the time dependence, is not fixed by sigma^(2). optmat supplies:

     • the cross section;

     • the pair-spectral-density yield and its energy, which are integral identities in the stated approximation.

     It does not supply how the loss is distributed within a pulse. That needs the nondegenerate amplitudes of Q9. It is recorded as a gap on the roadmap and in the manual, open for OEP 6 Phase 2 or for the propagation code. A band-centroid rate (the paired solprop proposal’s first phase) is unaffected.

• Status: decided (2026-10-08).

TC-904 vanderhart_2005 (van der Hart & Bingham, J. Phys. B 38, 207 (2005)): R-matrix Floquet two- and three-photon ionisation cross sections of He at 1e13 W/cm2 (2026-10-09)

• Where: src/optmat/data/sources/vanderhart_2005.toml, tools/extract/ vanderhart_2005.py (vector figures).

• Transcribed: the generalised two-photon (Fig. 2, 0.453-0.840 au) and three-photon (Fig. 9, 0.302-0.420 au) cross sections of ground-state He, transformed by the authors from the R-matrix Floquet total ionisation rate at 1e13 W/cm2 (intensity_w_cm2 = 1e13; higher orders included; the three-photon autoionising spikes near 1s2p are in the two-photon line, ‘absent in the true generalized two-photon cross sections’); abscissa the photon energy in hartree, the ground state shifted by the authors to its experimental energy. With them, reproduced_from = saenz_1999 (TC-873), the dashed lines: Saenz and Lambropoulos’s perturbative totals (1S + 1D, 1P + 1F), supplied in numerical form, on those authors’ scaled axis. Every vertex of each drawn line (every tick within 0.06 pt; 1 % (Fig. 2) and 1.5 % (Fig. 9) at a vertex). All use = check. Linear polarisation inferred (not named); gauge not stated. No table holds a cross section: Tables 1-3 (energies and widths of the autoionising states, field-free and dressed) and Figs. 1, 4-8 (rates against frequency at 1, 2, 5, 10 x 10^13 W/cm2) are not taken (no quantity).

• Checked: the transformation, which the paper does not print, is Gamma = sigma^(N) Phi^N with Phi = I / (hbar omega): Fig. 1’s 1e13 rate so converted is 0.3 to 0.8 % above Fig. 2, Fig. 7’s 0.9 to 2.4 % above Fig. 9 (two readings of 0.7 to 1.1 % each). The text: RMF within 10 % of perturbation theory off resonance (read 9.1 %), within 15 % in the three-photon regime (read 15.8 %); resonance strengths 30 and 5.6 times (read 29.6 and 5.75); ‘three orders of magnitude’ at 1s2p (drawn peaks 1230 times); ‘a factor of 10’ at 1s2s (drawn 7.5); I^2 scaling of Fig. 1’s curves (within 0.7 %, 2.3 % and 4.0 % at 2, 5, 10 x 10^13 W/cm2, which also confirms the dash-to-intensity assignment). The ground state’s rate at the 2p3d 1Po resonance, 4.3e-7 and 1.1e-5 au at 1e13 and 1e14 W/cm2 (p. 216): Fig. 1 reads 4.8e-7 and 1.0e-5 at 0.7856 au, where Fig. 6 draws it. The dashed lines equal saenz_1999’s partial curves summed, at frequency x 27.2114 eV, within 0.6 % at 16 frequencies. Overlays of the extracted values on the rendered figures inspected.

• Finding: sato_2011’s ‘Theory (R-matrix Floquet)’ column (TC-876), supplied by van der Hart: 8.5, 63 and 3.5 x 10^-52 cm4 s at 61.4, 58.4 and 56.0 nm are 0.97, 1.05 and 0.99 times Fig. 2 (8.74, 60.0, 3.54; 58.4 nm on the 1s2p peak, where the line runs from 5.1 to 6.4e-51 within 0.001 au); 6.9 at 53.4 nm (0.8532 au, beyond Fig. 2’s 0.840 au) is 1.30 times the 5.29 from Fig. 1’s 1e13 rate converted. 53.4 nm lies on the steep flank of the 1s3p resonance (drawn peak 0.8485 au): the line reaches 6.9e-52 0.0012 au (0.07 nm) lower, five times the drawing’s frequency quantum. Not resolved. sato_2011 names this paper by a citation string in reproduced_from; it can now be vanderhart_2005.

• Status: verified (2026-10-09).

TC-905 bachau_1990 (Bachau, Lambropoulos & Tang, Phys. Rev. A 42, 5801 (1990)): L^2-basis two-photon (and ATI) cross sections of He (2026-10-09)

• Where: src/optmat/data/sources/bachau_1990.toml, tools/extract/bachau_1990.py (table, raster figure, text).

• Transcribed: Table I, sigma_2 of He (x 10^-53 cm4 s) at hbar omega = 0.5 (below the one-photon threshold) and 1.0-1.3 au (two-photon ATI): the authors’ L^2 column (130.69, 29.46, 17.89, 11.77, 7.72) and Rudolph’s single-channel quantum-defect Green’s-function column; every cell checked against the scanned table image. Fig. 1(a)’s long-dashed line (the authors’ W / I^2, 10^-16 s^-1 W^-2 cm^4, against the photon energy in Ry): 28 samples on its first three dashes, 0.902-1.100 Ry, read from the page image (raster, about 600 dpi; ticks from the frame, the scan’s shear removed, x within 8.9 pixels (0.011 Ry), y within 4.3 (0.03); 4 %), where the dashes stand clear of the other authors’ curves. The text’s three- and four-photon ATI rates at 14.38 eV, W^(3) = 500 I^3 and W^(4) = 5.083e3 I^4 ‘a.u.’ (1skp, 1sks), inline, unit au (which atomic unit of intensity is not stated). Linear polarisation (M = 0, final L = 0, 2); velocity gauge (stated for ATI). All use = check. Not taken: the four-photon Rabi frequencies (no quantity), the other authors’ curves of Fig. 1(a), Fig. 1(b) (Mg).

• Checked: the text’s ‘factor of 3.6’ between the columns (29.46 / 8.12 = 3.63). Fig. 1(a) at 1 Ry, interpolated under Kulander’s ‘+’ by a quadratic through the three dashes, 2.806, is 1.020 times Table I’s 0.5 au entry as sigma_2 / (hbar omega)^2 (2.750): the unit’s implied definition W = sigma_2 Phi^2 holds. The sample overlay on the image inspected.

• Finding: nikolopoulos_2001’s Fig. 4 squares (‘Bachau et al (1990)’, TC-875, not taken there) are Table I’s L^2 column at 1.0-1.3 au: 0.996 to 0.999 times it, at the photon energies x 27.2114 eV within 0.01 eV. proulx_1993’s Table 2 ‘Bachau et al’ column equals Table I’s, cell for cell.

• Status: verified (2026-10-09).

TC-906 proulx_1993 (Proulx & Shakeshaft, J. Phys. B 26, L7 (1993)): two- and excess-photon ionisation of He, Sturmian perturbation theory (2026-10-09)

• Where: src/optmat/data/sources/proulx_1993.toml, tools/extract/proulx_1993.py (tables).

• Transcribed: Table 1, Gamma_a / I^2 of ground-state He in atomic units below the one-photon threshold (0.23170 to 0.02685) at photoelectron energies epsilon = 0.15 to 0.75 au; Table 2 ‘Present’, sigma_2 = 26.7, 750, 16.2, 10.5 x 10^-53 cm4 s at omega = 1.0-1.3 au (750 on a 1De resonance). Every cell checked against the scanned table images. Velocity gauge, linear polarisation, final-state correlation included, He+ left in 1s. All use = check. Decided (this curation): Table 1’s abscissa is converted from the photoelectron energy to the photon energy, (epsilon + I_p) / 2, with the calculation’s own I_p = 0.902995 au (binding energy 2.90283-2.90316 au less 2; +-0.00008 au in hbar omega); epsilon is kept as printed. Table 2’s ‘Bachau et al’ column is bachau_1990’s Table I and is not taken. Not taken: Figs. 1-6 (raster; Gamma / I^2 from the ground and 1s2s states against the photoelectron energy, not read), Tables 3-4 (resonance positions and widths, no quantity).

• Checked: Gamma_b (induced width) within 0.04-0.13 % of Gamma_a. The atomic unit of intensity, not named: the text’s ‘about 10^11 s^-1’ for ‘1 x I^2 au’ at 1e13 W/cm2 holds with E_h / (hbar a_0^2) = 6.436e15 W/cm2 (1.0e11; 3.51e16 W/cm2 would give 3.4e9). In that unit Table 1 as sigma_2 (1.22e-51 to 3.48e-52 cm4 s) is 0.88, 0.95, 1.02, 1.12, 1.10 times saenz_1999’s 1S + 1D summed (TC-873; the same through vanderhart_2005’s dashed line within 0.2 %).

• Finding: nikolopoulos_2001’s Fig. 4 circles (‘Proulx and Shakesaft,1993’, TC-875, not taken there) are Table 2’s ‘Present’ column: 0.997 to 1.005 times it.

• Status: verified (2026-10-09).

TC-907 kobayashi_1998 (Kobayashi et al., Opt. Lett. 23, 64 (1998)): XUV autocorrelation by two-photon ionisation of He, nothing taken (2026-10-09)

• Where: src/optmat/data/sources/kobayashi_1998.toml (notes only).

• Transcribed: nothing. The ninth harmonic of a Ti:sapphire laser (photon energy not stated) autocorrelated by two-photon ionisation of He: 27 fs (sech^2). The paper prints and uses no two-photon cross section, its own or another’s: the He+ signal is relative (Figs. 2-4, raster), and the one absolute comparison is a Keldysh-Faisal-Reiss estimate of the ion number (60 per pulse expected at 155 GW/cm2 and 1 Torr against ~20 detected), with no rate or focal volume given.

• Checked: the record’s numbers against the text layer and the figures.

• Status: verified (2026-10-09).

TC-908 pan_1990b (Pan, Gao & Starace, Phys. Rev. A 41, 6271 (1990)): correlated two-photon cross sections of Ar 3p, partial and total, length and velocity, linear and circular, read from the scanned figures (2026-10-09)

• Where: src/optmat/data/sources/pan_1990b.toml, tools/extract/pan_1990b.py (raster figures of a scanned PDF). The id pan_1990 is Pan, Taylor and Clark’s harmonic-generation paper.

• Transcribed: 16 datasets (521 points, cm4 s against photon energy, all multiphoton_ionization_cross_section, photons = 2, use = check): variationally stable perturbation theory of Ar 3p two-photon ionisation below the one-photon threshold, with correlations added process by process (Table I). Fig. 1(b): the linear p 1S channel, length and velocity, with all processes and without the intermediate-state shake-up (4); Figs. 2 and 3: the linear p 1D and f 1D channels, length, all processes; Fig. 4: the linear total, length and velocity, HF, without the shake-up and with all processes; Fig. 5: the circular total, length and velocity, HF and all processes. 8.1 to 14.0 eV every 0.1 eV where the line is clear of the other curves; nothing on the rises into or the peaks of the 4s, 3d/5s and 4d/6s 1P resonances. Read from the 595 dpi page images: ticks found and checked (residuals within 3.9 pixels), the scan’s 0.2-degree rotation interpolated out, each curve traced and its line style checked by script; samples within about a line width of another curve left out, and where two curves of one figure are read within 7 pixels of each other (Fig. 5 at 9.2 and 10.5-10.8 eV) left out of both; both lists in the script. Digitising uncertainty 5 pixels: 0.05e-51 cm4 s (Figs. 1-3), 0.010e-50 (Fig. 4), 0.017e-50 (Fig. 5). The energy axis is the photon energy; the experimental 3p binding energy, 15.76 eV, replaces the HF 16.08 eV in the intermediate-state Green’s functions and in the photoelectron energy k^2/2 = 2 omega - 15.76 eV, half the experimental double-ionisation energy (43.4 eV) in process (6); the resonances stand at the calculation’s own positions, unshifted (p. 6278). Not taken: the F- detachment cross sections (no material); Fig. 1(a), the HF and processes (1)-(3) curves of Figs. 2-4 (intermediate approximations); the other authors’ curves in Fig. 6 (Starace and Jiang, starace_1987; Moccia et al., moccia_1983; Pindzola and Kelly, pindzola_1975; McGuire, mcguire_1981); Tables I and II (no quantity). Curated by a delegated agent.

• Checked: Fig. 4(c) length against Figs. 1(b) + 2 + 3 (Eq. 49): 0.983-0.997 (8.4-9.3 eV); Fig. 5’s all-process length against 3/2 times Figs. 2 + 3 (Table II’s f_q): 1.000-1.003 (8.4-9.1 eV); Fig. 6(a)’s solid curve against Fig. 4(c): 0.981-1.015 (8.4-13.8 eV, 32 samples): three independently read figures. Eq. 54’s 1.8967e-50 cm4 s is a0^4 t0 (CODATA 1.89679e-50). Table II gives the 3/2 and no circular 1S. The text’s shake-up reduction of the total, ‘approximately 0.1 x 10^-50 cm^4 sec’ (p. 6282): the length total falls by 0.13e-50 to 0.30e-50 (Fig. 4(b) - 4(c), 8.4-11.1 eV), the length p 1S channel by 0.14e-50 to 0.25e-50; length over velocity of the total below the 4s rise is 2.05-2.83 (HF), 1.52-2.04 (without the shake-up) and 0.93-1.11 (all processes), the agreement the text claims. Overlays inspected.

• Finding: the paper’s final linear length total (Fig. 4(c)) against McKenna and van der Hart’s R-matrix Floquet total (mckenna_2004, TC-856): 0.78 at 8.4 eV, 0.74 at 9.0, 0.69 at 10.1, 0.63 at 11.0 (0.62-0.78 over 8.4-11.1 eV); the velocity total 0.69, 0.71, 0.71, 0.67 at 8.1, 9.0, 10.1, 11.0 eV. Against Petrov et al.’s final corr + CP length total (petrov_2016, TC-877): 0.85, 0.81, 0.75, 0.60; against their corr length total without core polarisation: 0.96, 0.94, 0.92, 0.88. Against Starace and Jiang’s ESI total (starace_1987, TC-878): 0.90, 0.89, 0.86, 0.84. What the citing records quote: McKenna and van der Hart’s ‘within 20% of 0.85 x 10^-50 cm4 s’ holds (0.98e-50 at 8.4 eV to 0.71e-50 at 11.0 eV, within 16 %), and ‘about 30 % below’ the R-matrix Floquet curve holds (22-38 %); Petrov et al.’s ‘approximately 12% smaller than our G2PICS’ (length, 8-11.5 eV) matches their corr curve (4-12 % below) and not their final corr + CP curve (15-45 % below), as read here. No value of the curves is printed, so the figures are the only source.

• Status: verified (2026-10-09).

TC-909 pindzola_1975 (Pindzola & Kelly, Phys. Rev. A 11, 1543 (1975)): many-body perturbation theory partial two-photon cross sections of Ar 3p, length and velocity, read from the scanned figures at the computed points (2026-10-09)

• Where: src/optmat/data/sources/pindzola_1975.toml, tools/extract/ pindzola_1975.py (raster figures of a scanned PDF, about 580 dpi; the reading machinery is imported from tools/extract/pan_1990b.py).

• Transcribed: 8 datasets (62 points, multiphoton_ionization_cross_section, photons = 2, linear polarisation, use = check): the second-order partial cross sections of the kp 1D (Fig. 2), kp 1S (Fig. 3) and kf 1D (Fig. 4) channels, length and velocity, and the kf 1D channel with third-order intrashell ground-state and intermediate-state correlations, LGI and VGI (Fig. 6). The figures plot sigma/F in 10^-18 cm^2 per atomic unit of flux (sigma of Eq. 24 is proportional to the flux F); the values are kept as printed with scale = 1e-18 cm^2 a0^2 t0 = 6.7736e-52 to cm4 s (CODATA; the paper prints no factor; its ‘flux of 10^32 photons/cm2 sec (0.07 a.u.)’ agrees). Read only at the computed points, every 0.5 eV from 8.0 eV (‘Points were calculated … at intervals of 0.5 eV’, p. 1547), where the line is clear. The energies are the photon energy; Moore’s experimental bound-state energies and 3p ionisation energy (15.755 eV) are used, so the resonances stand at 11.62, 14.09 and 14.15 eV. Digitising uncertainty 4 pixels: 0.05 (Figs. 2, 3) and 0.1 (Figs. 4, 6) printed units. Not taken: Fig. 4’s LG and VG (dashed, within a few pixels of each other and crossing twice: their identities cannot be told reliably), AHF and AHY (Bebb-Gold-type approximations), Table I (a sum-rule test of radial matrix elements). Curated by a delegated agent.

• Checked: the drawn vertical lines against the energies the text prints: 4s 1P within 0.007 eV of 11.62, 5s 1P within 0.002 of 14.09, 3d 1P within 0.015 of 14.15, the single-photon threshold within 0.008 of 15.755, the threshold A 7.876 (7.88); Fig. 6’s line C (13.82 eV) is the 3d 1D autoionising resonance, whose energy is not printed. Fig. 6’s L and V (Fig. 4’s curves drawn again) against Fig. 4’s: 0.998-1.009 and 0.993-1.012. Ticks on one linear scale per side within 3.1 pixels. Overlays inspected.

• Finding: the second-order totals, Figs. 2 + 3 + 4 where all three are read (8.0-9.0 and 12.5-13.0 eV): length 1.24e-50 cm4 s at 8.0 eV and 1.17e-50 at 9.0, 0.98 and 0.94 times McKenna and van der Hart’s R-matrix Floquet total (mckenna_2004, TC-856); velocity 7.3e-51 and 6.6e-51, 0.57 and 0.53 times it. Against Pan, Gao and Starace’s final length total (pan_1990b): 1.27 at 9.0 eV; against Moccia, Rahman and Rizzo’s length total (moccia_1983): 1.07 at 9.0 eV. Fig. 3’s last x tick is labelled ‘18’ for 16 eV (a slip in the axis label; the ticks are evenly spaced).

• Status: verified (2026-10-09).

TC-910 moccia_1983 (Moccia, Rahman & Rizzo, J. Phys. B 16, 2737 (1983)): RPA two-photon cross sections and circular/linear ratios of Ne and Ar, length and velocity, read from the scanned figures (2026-10-09)

• Where: src/optmat/data/sources/moccia_1983.toml, tools/extract/moccia_1983.py (raster figures of a scanned PDF, about 250 dpi, 1-bit).

• Transcribed: 8 datasets (418 points, all use = check, photons = 2, abscissa the photon energy in hartree): the total generalised two-photon cross section for linear polarisation, velocity (full curve) and length (chain curve), of Ne (Fig. 1, cm4 s, 0.41-0.756 hartree) and Ar (Fig. 2, 0.29-0.562 hartree), as multiphoton_ionization_cross_section; and sigma^C/sigma^L in both forms for Ne (Fig. 4) and Ar (Fig. 5) as multiphoton_ionization_polarization_ratio. Lowest-order perturbation theory with an RPA sum over intermediate states whose first excitation energies are replaced by Table 1’s LS-weighted experimental ones, and a static-exchange continuum. Samples every 0.005 hartree left of the axis break and 0.001 right of it (the scale is enlarged after the second resonance), where the line is clear of the other curve, the resonance lines and the drawn R = 1.5 line; nothing on the resonances’ flanks and peaks. Uncertainty 4 pixels in y: 1e-53 cm4 s (Ne), 2e-52 (Ar), 0.015-0.02 in the ratio; in x up to 0.003 hartree (Ne) and 0.005 (Ar) on the left scales (below). Not taken: Figs. 3 and 6 (matrix-element contributions, phase shifts), Figs. 7 and 8 (differential cross sections; no quantity), Table 1 (model and averaged level energies). Curated by a delegated agent.

• Checked: every tick found in the image; each x scale’s ticks on one line within 1.6 pixels, except Ne’s 0.70 tick (5.6 pixels, 0.003 hartree, off the line of the others in both Figs. 1 and 4); the y ticks within 1.6 pixels; the drawn R = 1.5 line reads 1.485-1.504 on the y scales. The vertical broken lines found against the thresholds (IP/2) and Table 1 on the tick scales: Ne within 0.0014 hartree; Ar right of the break within 0.0005, but on Ar’s left scale the threshold line stands at 0.2847-0.2851 against 0.2896 and the 4s line at 0.4366 against 0.4347: the drawing’s lines and curves sit up to 0.005 hartree (0.13 eV) from the ticks there. The energies are recorded as the ticks give them; that offset is stated as the x uncertainty. Length over velocity: Ne 0.10-0.50, Ar 0.58-1.68. No number of the curves is printed. Overlays inspected.

• Finding: Ne against McKenna and van der Hart’s R-matrix Floquet cross section (mckenna_2004, TC-856): velocity 0.75 (11.2 eV), 0.62 (12.0), 0.48 (13.1), 0.36 (14.0), 0.26 (15.0), 0.13 (16.1); length 0.20 (12.0) down to 0.02 (15.8). Their description of this paper, ‘up to a factor of 4’ below and ‘strongly gauge dependent’, fits the velocity form to 15 eV; the length form is 5 to 50 times below. Ar against McKenna: velocity 0.61 (8.0 eV) to 0.81 (11.0), length 1.03 to 0.75; against Pan, Gao and Starace’s final length total (pan_1990b): velocity 0.93-1.29, length 1.14-1.20 (9.0-11.0 eV); against Starace and Jiang’s ESI total (starace_1987, TC-878): velocity 0.82-1.09, length 1.00-1.05. Table 1’s Ar ‘3p->6s’ experimental energy, printed 0.5221 hartree (below 5s’s 0.5239, though its RPA value is above), has no drawn line; Figs. 2 and 5 draw one at 0.5522: the printed value is very likely a misprint of 0.5521 (Table 1 is not taken; no erratum entered).

• Status: verified (2026-10-09).

TC-911 xenakis_1996 (Xenakis, Faucher, Charalambidis & Fotakis, J. Phys. B 29, L457 (1996)): two-XUV-photon ionisation of Ar at 82.9 nm observed, no cross section (2026-10-09)

• Where: src/optmat/data/sources/xenakis_1996.toml (no datasets, no script).

• Transcribed: nothing into data. The record states what the letter measured: Ar+ from two photons of the third harmonic (82.9 nm, 14.96 eV) of a 248.6 nm, about 450 fs KrF pulse, made in a Xe jet and imaged into an Ar jet; the first photon between the 6s’[1/2]1 and 6s[3/2]1 levels (detunings 485.6 and -915.5 cm-1); the Ar+ yield rises with slope 3 in the fundamental’s energy, not 6, which the authors ascribe to saturation of the near-resonant first step. Not taken: the harmonic’s intensity, ‘estimated to be in the range of 10^5-10^8 W cm^-2’ from Xe and Kr one-photon ion signals, the He two-photon cross section, the extraction volume and the pressure (no absolute photon number was measured; a condition, not a property of Ar); the estimated resonant absorption cross section of the first step, ~7e-11 cm2 (Lorentzian, g ratio 3) reduced to ~7e-12 cm2 for the detunings and bandwidth (assumed line shapes; ‘the absorption cross section to these states is not known to us’); the ion yields (arbitrary units) and time-of-flight spectra of Figs. 3 and 4. Curated by a delegated agent.

• Checked: identity on PDF p. 2 (J. Phys. B 29, L457-L463); every quoted number against the page’s text layer (pp. L458-L462).

• Finding: no two-photon cross section of Ar is measured or deduced, absolute or relative. The He two-photon cross section used to bound the harmonic’s intensity is cited to ‘Starace et al 1987’ = Starace and Jiang, Phys. Rev. A 36, 1705 (1987) (starace_1987, TC-878), which computes argon only (it says its approach ‘is … applicable with minor modifications to He’), and to a private communication (Cormier 1995): the He value behind the intensity range cannot be traced.

• Status: verified (2026-10-09).

TC-912 fink_1990 (Fink & Johnson, Phys. Rev. A 42, 3801 (1990)): relativistic TDDF two-photon ionisation cross sections of Ar, Kr and Xe, linear and circular, from raster figures (2026-10-09)

• Where: src/optmat/data/sources/fink_1990.toml, tools/extract/fink_1990.py (raster figures of a scanned PDF).

• Transcribed: the total generalised two-photon cross sections (J_tot = F^2 sigma^(2), F the photon flux, Eq. 4.1), length form, relativistic time-dependent Dirac-Fock (second order in the field, J = 0 and 2 final channels, Dirac-Fock thresholds), linear and circular: Ar (Fig. 3, 0.294-0.505 a.u., 26 + 26 markers), Kr (Fig. 4, 0.270-0.437 a.u., 31 + 35), Xe (Fig. 5, 0.250-0.342 a.u., 18 + 23), and Xe’s partials to the 2P3/2 and 2P1/2 cores (Fig. 6, 14, 26, 11 and 16 markers). Abscissa the photon energy in hartree, unshifted (the calculation’s own thresholds and resonances, J-resolved). The paper prints no table of cross sections; each computed value is a marker, seeded by inspection and centred by the script on its shape’s template in the native 600-dpi page image (ticks within 1 pixel in x, 3 in y), each value’s pixel in its printed cell; markers merged in clusters (Kr 0.317-0.345, Xe 0.293-0.302 a.u.) and off scale are not read. Uncertainty: the paper’s ‘numerically more accurate than 5%’ with the reading (0.015e-50 Fig. 3, 0.03e-50 Fig. 4, 4 % on the log axes). All use = check. Not taken: Figs. 1 (He) and 2 (Ne, against n_eff), raster line curves; the Lu-Fano plots; Table I (model and unattributed thresholds, used in the checks).

• Checked: Table I against its image cell by cell; its splittings are the differences of its energies within 0.01 eV. Fig. 6’s partials add up to Fig. 5’s totals: 0.989-1.055 (linear, 7 frequencies), 0.989-1.023 (circular, 9). Fig. 5 against Lagutin et al.’s vector redrawing of these curves (lagutin_2017 Fig. 8, TC-880, not taken there): 0.84-0.99 (linear) and 0.93-1.03 (circular) at 6.80-8.10 and 8.70-9.28 eV; the redrawing starts at 6.803 eV, Fig. 5’s first frequency 0.2500 a.u. Fig. 3 against Starace and Jiang’s ESI totals (starace_1987, TC-878; ‘within drawing accuracy’, p. 3812): 0.986-1.010 (linear), 0.954-0.971 (circular) at 8.1-9.4 eV. The value overlays on the page images were inspected.

• Finding: the first computed frequency of each curve lies at or just above half the experimental 2P1/2 binding energy of Table I (Ar 0.2940 against 0.2929, Kr 0.2700 against 0.2696, Xe 0.2500 against 0.2470 a.u.) and, for Ar and Kr, below half the Dirac-Fock 2P1/2 energy that the text names as the calculation’s threshold (0.2977, 0.2708), although the text says only final states above both thresholds were computed (pp. 3801, 3812). No values lie between the fine-structure thresholds: Kr’s begin at 7.347 eV (two-photon thresholds 7.000 and 7.333 eV), Xe’s at 6.803 eV (6.065-6.718 eV).

• Finding: krypton (OEP 6 Q2) is given only as a raster figure: no table and no vector drawing. Its smooth part runs from 7.35 to 9.79 eV, below the first resonance (the calculation’s between 9.95 and 10.33 eV; experimentally 10.03 eV): linear 2.03e-50 cm4 s at 7.6 eV falling to 1.22e-50 at 9.55 eV, circular 1.57e-50 to 1.20e-50. Against McGuire’s Kr (mcguire_1981, TC-879, circular) these are 0.22-0.39 times (7.9-9.8 eV). Fig. 3’s Ar linear is 0.78-0.89 times McKenna and van der Hart’s R-matrix Floquet (mckenna_2004, TC-856) at 8.0-10.0 eV.

• Status: verified (2026-10-09).

TC-913 fink_1989 (Fink & Zoller, Phys. Rev. A 39, 2933 (1989)): MQDT parametrisation of two-photon ionisation; hydrogen 1s cross sections, and no noble-gas values (2026-10-09)

• Where: src/optmat/data/sources/fink_1989.toml, tools/extract/fink_1989.py.

• Transcribed: Table I’s sigma^(2) (cm4 s) of atomic hydrogen 1s, circular polarisation, at nine wavelengths from 924.06 to 300 angstrom (the first just below the one-photon threshold, the others above it: two-photon above-threshold ionisation), printed ‘5.530[-52]’ and written 5.530e-52; use = check. The wavelengths are 2 pi c / omega with omega in hartree for an infinite nuclear mass. Not taken: the amplitude parameters t^s, t^o, t_3 (no quantity), Ref. 13’s comparison column, Tables II and III (2PI from the excited 2s and 3s states, which multiphoton_ionization_cross_ section does not hold), Figs. 2-5 (raster: H near threshold, a hypothetical two-channel model).

• Checked: Tables I-III against their images cell by cell (all agree). Every row is reproduced from its printed parameters by Eqs. 2.1, 3.2 and 3.9 (Omega^2 = 2/15): within 2e-4, 1.2e-3 and 2.0e-3 above the one-photon threshold (Tables I, II, III) and 0.6 % at each table’s first row (nu = 8.50, below it). This paper’s sigma^(2) agrees with Ref. 13’s (Aymar and Crance; Klarsfeld and Maquet) within 0.9 %.

• Finding: the paper gives no values for any noble gas, in table, figure or text: for Kr and Xe it offers a formula (Eqs. 4.21-4.24; two channels, Eqs. 5.5-5.7) whose parameters (reaction matrices and smooth dipole matrices) it does not give; a cross section can be reproduced from such parameters, as the hydrogen tables show, but they would have to come from elsewhere (energy levels, one-photon data, or a fit to ab initio amplitudes, p. 2945).

• Status: verified (2026-10-09).

TC-914 gangopadhyay_1986 (Gangopadhyay, Tang, Lambropoulos & Shakeshaft, Phys. Rev. A 34, 2998 (1986)): MQDT two- and three-photon cross sections of Xe between and above the fine-structure thresholds (2026-10-09)

• Where: src/optmat/data/sources/gangopadhyay_1986.toml, tools/extract/ gangopadhyay_1986.py (two tables; one raster figure of a scanned page).

• Transcribed: Table I, the two-photon GCS in the open continuum with the core left in J = 3/2 and in J = 1/2 (two partial cross sections, cm4 s; total energies 14 to 16.871 eV), and Table II, the three-photon GCS likewise (cm6 s2; 14 to 14.506 eV), every cell with its own power of ten as printed; Fig. 1, the two-photon GCS between the 2P3/2 and 2P1/2 limits (1e-50 cm4 s, linear axis), 415 values every 0.002 eV of total energy from 12.206 to 13.196 eV where the line is one short run (peaks and steep flanks not read; 0.02e-50 absolute, energy to 0.002 eV total). All use = check (validators, OEP 6). Definition: W^(N) = sigma^(N) F^N (Eq. 1), F the photon flux; length form; linear polarisation (not stated in words; Fig. 3 draws its direction). The paper’s accuracy: truncation error ‘not expected to be more than a factor of 2’.

• Decided: every energy the paper prints or draws is the total energy above the ground state; the data files’ x is the photon energy, the total divided by 2 or 3 (exact for the tables), with the printed total energy kept as the row id and in the printed cell. No axis is shifted. The thresholds and J-resolved resonance positions are those of the MQDT fitted to experimental levels.

• Checked: the table cells against the table images; Fig. 1’s ticks (all, within 2 pixels; the spacing varies by 7 %, so the scale is piecewise linear between ticks); Fig. 1’s arrows point at Fig. 3’s printed resonance energies (12.6023 for ‘E = 12.602’, 12.9463 for ‘E = 12.95’); the overlay of every value on the page image. Table I as later papers draw it, the sum of the two cores at half the total energy: lagutin_2017’s (TC-880) six vector squares 0.9997-1.0031 of the sums; lhuillier_1987’s (TC-883) six circles 0.979-1.043; lhuillier_1989’s (TC-882) four crosses 0.94-1.04 (drawn 0.1-0.4e3 cm^-1 above Table I’s energies), the fifth on its solid line, which is 0.89 of the sum at 16.001 eV; lhuillier_1987b’s six squares 0.978-1.069.

• Finding: every later drawing of ‘Gangopadhyay et al.’ is Table I’s open-continuum total, above the 2P1/2 limit; none draws the region between the thresholds. There, Fig. 1 gives 0.458e-50 cm4 s at McCown et al.’s ArF line centre (two photons 103 466 cm^-1) and 0.50e-50 at twice the 193 nm photon: 0.11-0.12 of mccown_1982’s alpha hbar omega (4.11e-50). The background between the resonances is 0.3-0.64e-50.

• Doubt: Fig. 1 labels the dip at 12.60 eV ‘J = 2’, Fig. 3(a) gives ‘E = 12.602’ as ‘J = 0’. Fig. 2’s second x label ‘12.6’ must be 12.4 (Fig. 2 not read).

• OEP 6, Q3: between the Xe thresholds this is a raster figure on a linear axis of total energy, linear polarisation; no table or vector drawing exists for that region.

• Status: verified (2026-10-09).

TC-915 wendin_1987 (Wendin, Jonsson & L’Huillier, J. Opt. Soc. Am. B 4, 833 (1987)): the RPAE two-photon cross section of Xe that karamatskou_2017 overlays; nothing extracted (2026-10-09)

• Where: src/optmat/data/sources/wendin_1987.toml (no datasets).

• Transcribed: nothing. The two-photon cross sections (Figs. 3 and 4, p. 837) are lhuillier_1987b’s Figs. 2 and 4 redrawn (‘closely following Ref. 15’, p. 836): holding them again would count one calculation twice (data rule 5). The definition (Eq. 14) is written with (1 / F F0)^2 and the intensity carried in the amplitude t; lhuillier_1987b’s Eq. (1) with (omega / F0)^2: the same generalised cross section, rate sigma_2 F^2.

• Checked: lhuillier_1987b’s readings of all five lines, mapped onto this paper’s Figs. 3 and 4 through calibrations from their own ticks, lie on the drawn lines (overlays inspected). The text’s comparisons (McGuire slightly below the independent-electron result; Gangopadhyay et al.’s squares in agreement in 0.5-0.6 Ry; McCown et al.’s point at 0.47 Ry closer to RPAE and LDRPA) are the letter’s.

• Finding: karamatskou_2017 (TC-881) overlays ‘the RPAE curve of Wendin et al.’ (this paper, digitised by its authors) and moves its TDCIS curve 0.3264 eV down onto it. That curve, read from karamatskou_2017’s vector drawing, peaks at 9.176 eV (0.6744 Ry, the 6s), is clipped at 10.81-10.83 and 11.00-11.02 eV (5d, 7s), and peaks at 11.535 and 11.636 eV (6d, 8s): this paper’s RPAE resonances (lhuillier_1987 reads the 6s at 0.675 Ry, 9.184 eV). karamatskou_2017’s shifted 6s, 9.159 eV, lies 0.017 eV below it. Off resonance the RPAE falls below that figure’s frame (5e-50 cm4 s), so no magnitudes are compared there.

• Status: verified (2026-10-09).

TC-916 lhuillier_1987b (L’Huillier & Wendin, J. Phys. B 20, L37 (1987)): RPAE and LDRPA two-photon cross sections of Xe, the letter before lhuillier_1987 (2026-10-09)

• Where: src/optmat/data/sources/lhuillier_1987b.toml, tools/extract/ lhuillier_1987b.py (raster figures of a 300 dpi scan).

• Transcribed: sigma_2 of the Xe 5p shell against the photon energy (Ry, as printed; the calculation’s own nonrelativistic thresholds and resonances, not shifted), linear polarisation, length form, Eq. (1): sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum |t|^2, F0 = 3.22e34 photons/cm2 s. Fig. 2 (LDA basis, linear axis, 0.34-1.39 Ry): independent-electron, LDRPA fully screened and with only the first interaction screened (0.015e-49 cm4 s absolute); Fig. 3 (HF basis): the RPAE with only the first interaction screened, 0.464-0.782 Ry (6 %); Fig. 4: RPAE (0.462-0.790 and 0.976-1.374 Ry, 5 %) and LDRPA (0.344-1.380 Ry, 6 %) fully screened. All use = check.

• Not taken: Fig. 3’s HF and RPAE lines (lhuillier_1987, TC-883, holds them); the squares (gangopadhyay_1986’s Table I) and crosses (mccown_1982).

• Checked: every tick (within 2 pixels, 1.5 on the fitted scale); Fig. 3’s frame at the text’s 0.46 and 0.86 Ry; overlays of every value on the page images. Fig. 4’s cross at 0.4719 Ry (193 nm: 0.4722), 1.00 times mccown_1982’s alpha hbar omega. Fig. 4’s squares are gangopadhyay_1986’s Table I sums (0.978-1.069), drawn 0.001-0.0055 Ry right of Table I’s photon energies. The same calculation drawn twice agrees: Fig. 4’s LDRPA over Fig. 2’s, median 1.016 (0.992-1.053); Fig. 3’s HF and RPAE over lhuillier_1987’s Fig. 6, medians 0.991 and 0.993 (0.93-1.04); Fig. 4’s RPAE and LDRPA over lhuillier_1987’s Figs. 6-7, medians 1.006 and 1.001.

• Finding: what is new against lhuillier_1987: the LDA-basis curves (Fig. 2) from the LDA two-photon threshold 0.31 Ry, the HF-basis first-screened RPAE (Fig. 3), and the RPAE and LDRPA over 0.31-1.40 Ry in one figure (the LDRPA below 0.46 Ry and in 0.86-0.98 Ry are not in the PRA’s figures). Fig. 3 draws McCown et al.’s cross at 0.4846 Ry, 0.0124 Ry above 193 nm (Fig. 4 at 193 nm); Fig. 4’s hatched one-photon threshold stands at 0.907 Ry where the caption says 0.92 (the two-photon one at 0.457, caption 0.46). wendin_1987’s Figs. 3 and 4 are this letter’s Figs. 2 and 4 redrawn.

• Status: verified (2026-10-09).

TC-917 bischel_1979 (Bischel, Bokor, Kligler & Rhodes, IEEE J. Quantum Electron. QE-15, 380 (1979)): estimated Xe two-photon ionisation coefficient at 193 nm (2026-10-09)

• Where: src/optmat/data/sources/bischel_1979.toml, tools/extract/bischel_1979.py (Table I, JSON cells).

• Transcribed: Table I’s xenon row at 193 nm with excited product Xe+: alpha = 1 x 10^-34 cm4/watt (multiphoton_ionization_cross_section, photons = 2, unit as printed, use = check), an estimate from second-order perturbation theory with one intermediate state (energy denominator 16 x 10^3 cm^-1, mu^2 = 1 debye^2) and a width of ~10^9 MHz, footnote (g) ‘Estimated for photoionization continuum’. The definition, quoted: ‘sigma(nu_2) = alpha I_1’ (Eq. 1) and ‘W_fg = alpha I^2 / hbar omega’ (p. 382): mccown_1982’s (TC-884) and hodges_1981’s definition; sigma_2 = alpha hbar omega = 1.03e-52 cm4 s (not printed). The text: autoionising resonances ‘could enhance the value of alpha given in Table I by a factor of ~10^2’ (p. 386).

• Not taken: the bound two-photon excitation estimates of Table I (H2, CO, N2, Kr, I2 at 193 nm; Xe 5p5 6p and N2O at 248 nm), the H2 measurement (~10^-32 cm4/W) and the N2O upper limit: linewidth-dependent peak coefficients that no quantity holds (two_photon_excitation_cross_section is frequency-integrated; converting would need the assumed line shape). Krypton (OEP 6, Q2): no two-photon ionisation value in any form; Table I’s Kr row is a bound excitation estimate, 1 x 10^-31 cm4/watt for a 100 cm^-1 laser.

• Checked: the cell against the table image; the script requires the table’s value to equal the text’s ‘sigma / I ~ 10^-34 cm4/W (see Table I)’ (p. 388) and mccown_1982’s reproduction (1 x 10^-34), and footnote (a)’s 3 x 10^6 MHz to be the text’s 100 cm^-1 (100.07). The p. 388 ion-density estimate (Xe 3 x 10^17 cm^-3, 10^9 W/cm2, 20 ns pulse) follows from alpha as 5.8e11 cm^-3 against the printed ~3 x 10^11 (2.9e11 for 10 ns): an order-of-magnitude estimate.

• Finding: mccown_1982 describes this value as an estimate ‘assuming a laser linewidth of 100 cm-1’; Table I gives the Xe+ row the photoionisation-continuum width of footnote (g), ~10^9 MHz, not the 100 cm^-1 of the bound rows. geohegan_1986’s (TC-886) ‘(1-2.3) x 10^-31 cm4 W-1’ for Kr 6p[3/2]2 ‘assuming a 100-cm-1-bandwidth’ laser: this paper’s 1 x 10^-31 is the lower end; 2.3 x 10^-31 is not in it (the bokor_1980 record: 2.34 x 10^-31 for a 25 cm^-1 laser).

• Doubt: Table I prints the Kr 4p5 6p level at ‘103,762 cm^-1’; the text (p. 386) puts 6p(1 1/2)2 at 103 363 cm^-1, inside the ArF two-photon range it gives (103 300-103 560 cm^-1): probably a misprint in the table (no value of it is taken).

• Status: verified (2026-10-09).

TC-918 hodges_1981 (Hodges, Lee & Moseley, Int. J. Mass Spectrom. Ion Phys. 39, 133 (1981)): Xe two-photon ionisation lower limit at 193 nm (2026-10-09)

• Where: src/optmat/data/sources/hodges_1981.toml (text value only).

• Transcribed: the two-photon coefficient of Xe at 193 nm, alpha = 5 x 10^-34 cm4 W^-1 (p. 138), ‘a lower limit, since eqn. (1) does not include the mass-spectrometer detection efficiency’ (multiphoton_ionization_cross_section, photons = 2, unit as printed, use = check, parameters.limit = lower). The source’s own definition, quoted: ‘n+/n0 = alpha I^2 tau / h nu’ (Eq. 1), n+ the ions detected per pulse, n0 the Xe atoms in the sampled volume (~0.004 cm3), I the laser flux, tau the pulse duration: the rate per atom is alpha I^2 / h nu, the definition of mccown_1982 (TC-884) and of bischel_1979 (this paper’s Ref. 3); sigma_2 = alpha h nu = 5.1e-52 cm4 s (not printed). Power density 0.8 MW/cm2 from the measured beam and the manufacturer’s 10-15 ns (p. 137).

• Not taken: the relative ionisation rates of Tables 1 and 2 (ion counts per pulse and mtorr, uncorrected for the mass filter; no quantity), including Xe’s three-photon rate at 248 nm; Fig. 2 (power dependence, relative).

• Checked: Eq. (1) with Table 2’s 0.4 counts/(pulse mtorr), 0.004 cm3, 0.8 MW/cm2 and Xe at 296 K (the temperature is not stated) gives 4.9e-34 for tau = 10 ns and 3.3e-34 for 15 ns: the printed value is the 10 ns end. mccown_1982’s reproduction (5 x 10^-34, a lower limit) and this paper’s quotation of bischel_1979 (1 x 10^-34; autoionising states ‘could increase this value by a factor of ~10^2’) match their originals.

• Status: verified (2026-10-09).

TC-919 mccann_1988 (McCann, Chen & Payne, J. Chem. Phys. 89, 5429 (1988)): Xe two-colour two-photon ionisation rate constant; Ar, Kr, H2 two-photon rate constants not taken (2026-10-09)

• Where: src/optmat/data/sources/mccann_1988.toml (text values only).

• Transcribed: the two-photon ionisation rate constant of xenon for one 118 nm and one 355 nm photon, 3.5 x 10^-45 cm4 s (p. 5436), as multiphoton_ionization_cross_section with photons = 2, non-degenerate (x the 118 nm photon, the 355 nm in parameters), linear (vertical) polarisation, use = check: the VUV photon lies just above a one-photon transition of xenon, so the value is near-resonant; no uncertainty is stated. Identity checked on the article’s first page (the library’s file is named 1989; the year is 1988).

• Not taken: Table II (Ar 3p5 4p, 4p’, Kr 4p5 4f) and Table III (H2 E,F): K2, the line-centre rate constant per product of the two photon fluxes (Eqs. 7, 25), depends on the lasers’ bandwidths; T2 = K2 (Delta1^2 + Delta2^2)^(1/2) (Eq. 28, ‘cm4’, the header’s ‘cm4 s2’ a slip) equals the frequency-integrated cross section only up to the unstated line shape (g(0) Delta = 0.939 Gaussian, 0.637 Lorentzian), and the widths behind it are inconsistent: T2/K2 = 3.79-4.05 x 10^11 rad/s (2.0-2.15 cm-1) for every Ar and Kr row, not the 1.74 x 10^12 of Sec. IV’s Delta1 and Delta2, and 2.6-5.4 x 10^11 varying row to row for H2. All pairs are non-degenerate (118 nm + visible).

• Checked: Table II against its image (every cell). Eq. (7) with M2 = 1.7 and the printed widths: 2.32 x 10^-11 s cm4 J-2 (printed 2.3), times a 118 nm and a 443.6 nm photon energy 1.75 x 10^-47 cm4 s (printed 1.7, against Table II’s measured 1.3 for 4p’[3/2]2). Eq. (28) refers K2 to ‘Eq. (16)’, a slip for Eqs. (7) and (25).

• Finding: hattig_1998b’s (TC-887) experimental 2.05 x 10^-51 cm4 s for argon’s 1De is sundholm_1994’s sum 1.4 + 0.53 + 0.12 x 10^-51, which are this paper’s T2 of 4p[5/2]2, 4p[3/2]2, 4p’[3/2]2 (6.2, 2.2, 0.51 x 10^-35 cm4) times the atomic unit of time: 1.500, 0.532, 0.123, sum 2.16. The first term is 7 % low as quoted; the quantity is T2, with its line-shape ambiguity, for a non-degenerate pair. payne_1981 and payne_1982 print no argon rate constant.

• Status: verified (2026-10-09).

TC-920 khambatta_1988 (Khambatta et al., J. Appl. Phys. 64, 4809 (1988)): Kr 6p[3/2]2 two-photon excitation and photoionisation cross sections at 193.41 nm (2026-10-09)

• Where: src/optmat/data/sources/khambatta_1988.toml (text values only).

• Transcribed: sigma_0^(2) of 4p6 1S0 -> 4p5 6p[3/2]2, 5.4 x 10^-37 cm4 (two_photon_excitation_cross_section, primary), adjusted so that rate equations reproduce the absolutely calibrated 427.4 nm fluorescence densities (Table III); the profile has unit area in the two-photon angular frequency (Eq. 3, Gaussian laser), photon statistics corrected with an assumed G^(2) = 2, linear polarisation (> 80 %). No uncertainty is printed for it (the measured densities carry +-50 %). The adjusted 6p[3/2]2 photoionisation cross section at 193.41 nm, 4.39 x 10^-19 cm2 (excited_state_photoionization_cross_section, primary; ion densities +-25 %, no uncertainty for sigma_pi). As checks: the single-path sigma_0^(2), 8.7 x 10^-37 cm4, and the quantum-defect sigma_pi, 1.696 x 10^-19 cm2. Krypton two-photon ionisation: none (193 nm ionisation of Kr is 2+1).

• Checked: on the rendered pages: g = 3.298 x 10^-14 s (printed 3.3); Delta omega_L = 2.014 x 10^13 s-1 is Table II’s 0.40 nm at 193.41 nm (the text’s ‘0.04 nm’ is a slip); Delta omega_D = 1.313 x 10^10 s-1 is Kr’s one-photon Doppler width at 297 K (half the two-photon width the text names; negligible); Eqs. (14), (15) give 8.68 x 10^-37 cm4; alpha = sigma g G / h nu gives 5.59 and 3.47 x 10^-32 cm4/W (printed 5.6, 3.5); Eq. (4) gives 1.6961 x 10^-19 cm2.

• Finding: drag_2021 (TC-891) reproduces the value correctly (5.4 x 10^-45 m4, angular); its ‘not stated’ polarisation and photon statistics are linear and G^(2) = 2 assumed; its +-50 % is the uncertainty of the measured densities, not one printed for sigma_0^(2); its 193.5 nm is the laser’s 193.41 nm. The quoted alphas of bokor_1980 (2.34 x 10^-31, a 25 cm-1 laser) and geohegan_1986 (TC-886, 2 x 10^-32 cm4/W, an off-line average for 140 cm-1) match their originals as printed.

• Status: verified (2026-10-09).

TC-921 bokor_1980 (Bokor, Zavelovich & Rhodes, Phys. Rev. A 21, 1453 (1980)): Kr 6p[3/2]2 photoionisation cross section at 193 nm (2026-10-09)

• Where: src/optmat/data/sources/bokor_1980.toml (text values only).

• Transcribed: the photoionisation cross section of Kr 4p5 6p[3/2]2 at its two-photon line centre (Table I: 193.49 nm), (3.2 +- 2.0) x 10^-19 cm2 (excited_state_photoionization_cross_section, primary; the +- without a level, mostly the focal intensity of a multimode beam; a 10-20 % pulse-shape correction included), from the saturation of the 427.4 nm fluorescence (Eqs. 11, 12, Fig. 4), independent of the two-photon rate. As a check: the quantum-defect estimate 1.8 x 10^-19 cm2 at 193.5 nm (Eq. 13). Krypton two-photon ionisation: none.

• Not taken: Table I’s alpha (2.62 and 2.34 x 10^-31 cm4/W for 6p[1/2]0 and 6p[3/2]2): single-path estimates of a line-centre coefficient for this 25 cm-1 laser, including the factor 2! of chaotic light (Eqs. 1, 5); the lifetimes and quenching rates (no quantity).

• Checked: Eqs. (1), (5) with the table’s dipoles and 29 000 cm-1 give 2.73 and 2.44 x 10^-31, both 4.1 % above the printed values (a detuning near 29 600 cm-1 fits). In khambatta_1988’s convention the 6p[3/2]2 alpha corresponds to sigma_0^(2) = 8.5 x 10^-37 cm4 (derived, not data), as khambatta_1988’s own single-path 8.7.

• Finding: geohegan_1986 (TC-886) quotes this paper’s 3.2 x 10^-19 cm2 correctly; its alpha range ‘(1-2.3) x 10^-31 cm4 W-1’ ‘assuming a 100-cm-1-bandwidth ArF laser’ mixes bischel_1979’s 1 x 10^-31 (100 cm-1) with this paper’s 2.34 (25 cm-1). khambatta_1988’s quotations (2.34 x 10^-31, 3.2 +- 2.0) match.

• Status: verified (2026-10-09).

TC-922 gornik_1981 (Gornik, Kindt, Matthias & Schmidt, J. Chem. Phys. 75, 68 (1981)): Xe 5p5 6p two-photon transition rates, not taken (2026-10-09)

• Where: src/optmat/data/sources/gornik_1981.toml (notes only, no datasets).

• Not taken: the measured two-photon transition rates of 6p[1/2]0, 6p[3/2]2, 6p[5/2]2 (Table I, 3.2 x 10^4, 3.5 x 10^3, 1.8 x 10^4 s-1 at I0 = 1.8 MW/cm2 and Delta omega / 2 pi = 4 GHz; the absolute one ‘accurate within a factor of 3’, the ratios 9 : 5 : 1 to about 20 %) and the single-path estimates: a rate at one estimated intensity and bandwidth is not a quantity; the paper prints no cross section. In the paper’s own line shape (unit area in the two-photon angular frequency, factor 2 for chaotic light) they correspond to sigma G2 = 16.7, 1.79, 8.95 x 10^-35 cm4 (derived, in the notes only).

• Checked: Table I against its image; 4 GHz is sqrt(2) x the 2.8 GHz laser of the absolute measurement.

• Finding: kroll_1990’s (TC-890) row for this paper, sigma_tot G2(0) = 6.8, 0.74, 3.7 x 10^-35 cm4, is raymond_1984’s Table I (108, 12, 61 cm4/J2) times (hbar omega)^2, not taken from this paper; Raymond et al.’s conversion corresponds to g = 9.1 x 10^-11 s for all three levels, 2.4 times this paper’s 3.74 x 10^-11 s, so the row is 2.4 times below this paper’s rates in its own line shape (ratios agree). geohegan_1986’s (TC-886) ‘alpha ~ 1.2 x 10^-27 cm4 W-1’ for 6p[3/2]2 is the single-path estimate (5.1 x 10^3 s-1 gives 1.24 x 10^-27), not the measurement (8.5 x 10^-28).

• Status: verified (2026-10-09).

TC-923 raymond_1984 (Raymond, Böwering, Kuo & Keto, Phys. Rev. A 29, 721 (1984)): Xe 6p two-photon coefficients alpha, not taken (2026-10-09)

• Where: src/optmat/data/sources/raymond_1984.toml (notes only, no datasets).

• Not taken: Table I’s alpha (cm4/J2) for 6p[1/2]0, 6p[3/2]2, 6p[5/2]2: this work 43 +- 20, 4.5 +- 2, 22 +- 11 (VUV detection at 1000-2800 Torr against Rayleigh scattering, +-50 %; infrared detection ‘an order of magnitude smaller’), single-path estimates, and others’ values. The unit is not one that two_photon_excitation_cross_section (TC-872) holds, and alpha is defined through R(0) = 6 alpha I^2 g(0) with a g(0) (Eq. 1b) that is not a unit-area profile in either frequency variable and weights the Doppler-free and Doppler-broadened parts equally; photon statistics are not discussed.

• Checked: Table I against its image. The Dirac-Fock 210 and 58.9 are Pindzola, Payne & Garrett’s 2.10 x 10^-12 and 5.89 x 10^-13 cm4/erg2 (pindzola_1981b, table image checked), whose alpha uses G = (8 ln 2/pi)^(1/2) / Delta_L: another convention.

• Finding: kroll_1990’s (TC-890) rows for refs. 8, 9, 10 are this table’s experimental rows times (hbar omega)^2 (6.84, 0.743, 3.67; 2.72, 0.279, 1.32; 6.08 x 10^-35 cm4) and its ‘4-13’ is the Dirac-Fock pair converted (3.73, 13.3): right as arithmetic, not in a stated convention. The Chen row (96, under 6p[1/2]0, laser width ‘assumed to be 0.01 A’) is reproduced within 1.5 % from R/I^2 = 2 x 10^-9 with a 0.01 A Gaussian and the Doppler width in a unit-area angular profile, at either level; see chen_1980 for the conflicting level and width in the original accounts. The printed ratio ‘8:4:1’ is 9.6 : 4.9 : 1 in the table.

• Status: verified (2026-10-09).

TC-924 chen_1980 (Chen, Hurst & Payne, Chem. Phys. Lett. 75, 473 (1980)): Xe (2+1) resonance-ionisation rates, not taken (2026-10-09)

• Where: src/optmat/data/sources/chen_1980.toml (notes only, no datasets).

• Not taken: the fitted rates ‘Gamma_I = 3I and R ~ 2 x 10^-9 I^2’ (I in W/cm2, p. 476): a line-centre two-photon rate for a 0.4 A laser of unstated line shape, and an ionisation rate (sigma_I = 3 hbar omega = 2.4 x 10^-18 cm2 at 252.6 nm if Gamma_I = sigma_I I / hbar omega; derived, not data). The theoretical R ~ 3.1 x 10^-9 I^2 is reproduced from Eqs. (2), (3).

• Finding: the measurement’s level, laser width and coefficient differ between its authors’ accounts: here 252.6 nm (6p[3/2]2), 0.4 A, 2 x 10^-9; Pindzola, Payne & Garrett (pindzola_1981b) 2496 A (6p[1/2]0), ‘between 0.05 and 0.01 A’ (their table uses 0.05 and 0.10), 2.4 x 10^-9; Payne et al. (payne_1982, pp. 246-247) 2496 A, 0.05-0.1 A, K = 2 x 10^-9, sigma_1 = 3 x 10^-18 cm2. Pages checked in both. raymond_1984’s 96 cm4/J2 and kroll_1990’s (TC-890) 6.1 x 10^-35 cm4 for 6p[1/2]0 rest on an assumed 0.01 A width that no account states; with 0.08 A the same conversion gives 4.6 x 10^-34 cm4, with 0.4 A about 2 x 10^-33.

• Status: verified (2026-10-09).

TC-925 sundholm_1994 (Sundholm, Rizzo & Jørgensen, J. Chem. Phys. 101, 4931 (1994)): MCSCF two-photon transition moments and rate constants of argon 1Se -> 1De; their convention, and the experimental comparison (2026-10-09)

• Where: src/optmat/data/sources/sundholm_1994.toml (inline text points, no script).

• Transcribed: the HF and CAS oscillator strengths of argon’s 1Se -> 1Po (lowest, 3p5 4s) transition, 0.3154 and 0.3358 (p. 4933, text; two inline datasets, oscillator_strength, use = check). Not taken: Table III (the element S_xy of one component of 3p5 4p 1De: HF 9.499 and 20.467, CAS 10.424 and 27.367 au at omega_1 = omega_f/2 and 0.3855 au), Table IV (K in cm4 s), Tables I-II: no quantity holds them (two_photon_transition_strength holds the level’s delta^TP, TC-872).

• Checked: the convention by reproduction: every K of Table IV is Eq. (2), K = a0^4 t0 (2 pi)^3 alpha^2 omega_1 omega_2 delta^TP, with delta^TP = (4/15) S^2 (the F = G = H = 2 average of the xy component alone) and omega_2 from the method’s Table I energy (0.3701, 1.1873, 0.4261, 1.9107 x 10^-51 against 0.370, 1.19, 0.426, 1.91). The level’s delta^TP (all five components, henriksson_2005’s convention, TC-888) is (4/3) S^2 = 5 x (4/15) S^2. Table III’s columns sum to their totals; the CAS oscillator strength is 2 omega mu^2 from Tables I-II (the HF one gives 0.3172, not 0.3154); hattig_1998b’s argon SCF/MCSCF 1De S^0f and K are this paper’s (TC-887); the text’s ratios (10 %, 45 %, 2.6 times, 33 %, 7 %) and closure estimate (10.40; 14.72 against ‘14.8’).

• Finding: Table IV quotes Moccia and Rizzo’s 1De K (moccia_1984: 2.16 x 10^-51 cm4 s, reproduced from its amplitude) as 0.216 x 10^-51, and Lebedev and Yakovleva’s (2.88 x 10^-51 from their amplitude 14.0 by the same formula) as 0.288 x 10^-51: both ten times too small, and the text’s ‘good agreement with previously calculated rate constants’ rests on them.

• Finding: the computed K are one component’s; the experiment (2.05 x 10^-51 cm4 s, the sum over the three J = 2 levels with 1De character) is the level’s. Per level the CAS K at 0.3855 au is 9.55 x 10^-51, a factor 4.7 above experiment, not the ‘excellent agreement’ (7 %) the paper reports (as for hattig_1998b’s CCSD 1.83, TC-887).

• Finding: the experimental parts 1.4, 0.53 and 0.12 x 10^-51 cm4 s are McCann et al.’s T2 (mccann_1988, Table II: 6.2, 2.2, 0.51 x 10^-35 cm4) times t0 (Eq. 4): the second and third reproduce (0.532, 0.123), the first does not (1.500 against 1.4); the sum is 2.16, not 2.05. T2 uses G = 1/Delta, not a normalised line shape (mccann_1988).

• Doubt: Table II’s 1Po contributions S_1Po do not follow from its mu and Table I’s energies (implied factors 0.83-0.97); the text’s ‘13%-16%’ is 14.6-19.3 % by Tables II-III. ‘Less than 5%’ uncertainty (CAS) is the authors’ judgement.

• Status: verified (2026-10-09).

TC-926 hettema_1992 (Hettema, Jensen, Jørgensen & Olsen, J. Chem. Phys. 97, 1174 (1992)): MCSCF quadratic response; Ne two-photon tensor elements, not taken (2026-10-09)

• Where: src/optmat/data/sources/hettema_1992.toml (notes only).

• Transcribed: nothing. Table VII prints, for Ne 1Se -> 2p5 3p 1De, the single element S_xy (A = x, B = y carrying the frequency) at four frequencies, HF, CAS three shell, SD RAS three and four shell, with each method’s excitation energy (0.738 881 to 0.704 482 au); at 0.3425 au 2.9663, 3.3265, 3.2665, 3.3450. A one-component element is not delta^TP (TC-872; (4/3) S_xy^2 per level, sundholm_1994’s notes). The H2 X -> E,F zz elements (Tables II-IV), at one internuclear distance, and the Ne polarisability and gamma (Tables IX-XII, another family) are not taken.

• Checked: Table VIII sums to Table VII’s last row (images checked); the text’s 0.07 au, ‘about 60%’ (0.638) and ‘10%-15%’ (1.128); the RPA energy is moccia_1984’s. The text’s ‘0.3452 a.u.’ for Table VIII is the caption’s 0.3425 (transposed digits).

• Finding: Eq. (102) applied to Table VII’s excitation energies gives 0.697 63 +- 0.006 85 au; the text prints 0.6936 +- 0.0068: the uncertainty reproduces, the value does not (0.0040 au lower). hattig_1998b’s Ne 1De ‘MCSCF’ 18.874 eV is the printed 0.6936 (TC-887).

• Finding: hattig_1998b’s Ne SCF 1De entry 8.799 is 2.9663^2, computed at omega_B = 0.3425 with omega_2 = 0.3964 au, not the degenerate pair of its column. Its MCSCF 11.289 (sqrt 3.3599) is not reproduced by any cell of Table VII or by Eq. (102) (3.3450^2 = 11.189; Eq. 102 11.86; with the extended basis 12.10; squares 11.84): not resolved. henriksson_2005’s quotations (2.9663, 3.3450 at 20.106, 19.170 eV) are this paper’s (TC-888).

• Finding: the text compares Moccia and Rizzo’s 3.84 (moccia_1984) with its S_xy 2.9663 directly; Moccia’s M is the zz element of the M = 0 component, (2/sqrt 3) S_xy, so S_xy = 3.322, 12 % above, and Moccia used experimental energies in the denominators; the basis (the text’s explanation) is not needed for most of the gap.

• Status: verified (2026-10-09).

TC-927 moccia_1984 (Moccia & Rizzo, Mol. Phys. 51, 1095 (1984)): RPA two-photon amplitudes and rate parameters of Ne and Ar, not taken; their convention (2026-10-09)

• Where: src/optmat/data/sources/moccia_1984.toml (notes only).

• Transcribed: nothing. The paper prints amplitudes M (Tables 2-3; LG Ne 2p5 3p 1Se 4.514, 1De 3.836, Ar 3p5 4p 1Se 14.907, 1De 12.149 au) and rate parameters K in cm4 s (Table 4; Figs. 1-5, scanned images, K against omega_1), for parallel linear polarisation, with experimental (LS-averaged) energies for the final and first 1Po levels. M is an amplitude (delta^TP = |M|^2 would be a derived value), K no quantity.

• Checked: every EMM K of Table 4 (Ne and Ar, 1Se and 1De, LG and VG) from Table 3’s M by Eq. (6), K = (2 pi)^3 alpha^2 omega_1^g omega_2^g |M|^2 x 1.8967e-50 cm4 s, with omega = half of Table 1’s experimental energy (worst 0.32 %); M = M^d + M^c in every column; Table 2’s ‘This work’ is Table 3 rounded (table images checked).

• Finding (convention): M is the zz amplitude of the final level’s M = 0 component for parallel linear polarisation, so |M|^2 is the level’s strength: for 1Se, S_zz^2 = delta^TP (F = G = H = 2); for 1De, (4/3) S_xy^2, henriksson_2005’s per-level convention (TC-888), five times the one-component values of sundholm_1994 and hattig_1998b (TC-887). Against henriksson_2005’s TDHF strengths, |M|^2 is 1.30-1.59 times larger (experimental energies in the denominators).

• Finding: sundholm_1994 quotes the argon 1De K as 0.216 x 10^-51 cm4 s; Table 4 prints 2.16(-51). hettema_1992 compares the Ne 1De 3.84 with its S_xy without the factor 2/sqrt 3.

• Status: verified (2026-10-09).

TC-928 moccia_1985 (Moccia & Rizzo, J. Phys. B 18, 3319 (1985)): two-photon transitions of H2O; the rotational average’s F, G, H, a methods reference (2026-10-09)

• Where: src/optmat/data/sources/moccia_1985.toml (notes only).

• Transcribed: nothing: the values (Table 2’s K, Figs. 1-7’s K and polarisation ratios) are for water, not a registry material. Recorded as the reference that hattig_1998b and sundholm_1994 cite for the polarisation factors.

• Checked: the appendix’s F_J (Eq. A6) and the map to Monson and McClain’s F, G, H (Eq. A8), evaluated: parallel linear polarisation (M1 = M2 = 0, beta_12 = 0) F = G = H = 1/15, i.e. 2, 2, 2 in the 1/30 normalisation of hattig_1998b and sundholm_1994 and 1, 1, 1 in henriksson_2005’s 1/15 (TC-887, TC-888); co-rotating circular (M1 = M2 =

  1. F, G, H = -1/15, 1/10, 1/10 = -2, 3, 3. The rate, Eq. (8), is moccia_1984’s Eq. (6) with the rotational average.

• Status: verified (2026-10-09).

TC-929 pindzola_1981b (Pindzola, Payne & Garrett, Phys. Rev. A 24, 3115 (1981)): Dirac-Fock two-photon excitation parameter of Xe 6p[1/2]0, not taken; the conversion behind kroll_1990’s ‘4-13’ (2026-10-09)

• Where: src/optmat/data/sources/pindzola_1981b.toml (notes only).

• Transcribed: nothing. Table II prints the ‘two-photon excitation parameter’ alpha (W = alpha I^2 G(omega), I in erg cm-2 s-1) in cm4/erg2 for Xe 5p6 -> 5p5 6p 2P3/2 (J = 0): Dirac-Fock length 2.10e-12, velocity 5.89e-13, Hartree-Fock 1.04e-12 and 4.61e-13, four closure values, two ‘inferred from experiment’; best estimate 1.4e-12 (factor 3.5). two_photon_excitation_cross_section holds cm4 or m4; no krypton.

• Checked: the four closure rows from Eqs. (12)-(13) with the printed r^2 elements, 9.9308/2 eV and the 6s[3/2]1 level of nist_asd_2026, in units a0^4/E_h^2 = 4.1255e-13 cm4/erg2 (worst -0.2 %); rows 9-10 from W = 2.4e-23 I^2 and Eq. (14) at 0.05 and 0.10 A (exact); the length/velocity ratio 3.57.

• Finding: alpha (hbar omega)^2, with hbar omega = 4.9654 eV, gives 1.33e-34 and 3.73e-35 cm4 for Dirac-Fock length and velocity: kroll_1990’s quotation ‘4-13 x 10^-35 cm4’ (TC-890). Whether that is the coherent-light cross section in the two-photon angular frequency depends on Eq. (14)’s G, (8 ln 2/pi)^(1/2)/Delta_L: twice the normalised two-photon Gaussian peak (the factor 2 being Payne et al.’s chaotic G2(0), Payne_1981_ResonanceIonizationSpectroscopy Eqs. 7-8), or the normalised peak in the laser frequency (then the cross section is twice alpha (hbar omega)^2). Not decided; no conversion made.

• Finding: the text’s linewidth range ‘0.05 and 0.01 A’ is 0.05 and 0.10 A (Table II); ‘Table I’ for the experimental spread is Table II; the ‘average’ of 2.10 and 0.589 is 1.34, printed 1.4; the quoted W = 2.4e-23 I^2 of Chen et al. is not in that paper (Chen_1980_DirectCountingXe: fit R ~ 2e-9 I^2 in W/cm2 = 2e-23 in erg units; estimate 3.1e-9).

• Status: verified (2026-10-09); the line-shape question decided (2026-10-09): see TC-952.

TC-930 bassi_2000 (Bassi & Baluja, Pramana 54, 377 (2000)): partial-closure two-photon decay of H(2s) and He(2 1S), not taken; hydrogen’s Table 1 not reproduced (2026-10-09)

• Where: src/optmat/data/sources/bassi_2000.toml (notes only).

• Transcribed: nothing. The paper prints spontaneous two-photon decay rates W (s-1, Table 1, five choices of the mean excitation energy Delta), helium’s photon energy distribution A(y) (Table 3) and hydrogen’s 1s-2s amplitude D(omega) (Table 2): no quantity holds a two-photon decay rate or its spectrum, and D(omega) is a radial amplitude with Rydberg denominators, not delta^TP (TC-872).

• Checked: Table 2’s nine rows from Eqs. (5)-(6) (within 3e-7); helium’s Table 1 rows Delta_2-Delta_5 by numerical integration of Eqs. (21)-(23) (within 0.04 %); hydrogen’s Delta_2 (-0.1 %); Table 3’s 21 rows of A(y) and its integral (53.65 s-1 = Delta_3), except y = 0.200 (110.86, printed 110); Table 3’s ‘Exact’ column and 51.3 s-1 are Drake, Victor and Dalgarno 1969’s He I values (Drake_1969_TwoPhotonDecay, all 21 rows); Eq. (23)’s 18.415 is twice Eq. (7)’s prefactor (CODATA: 18.399).

• Finding: hydrogen’s Delta_3, Delta_4, Delta_5 rows (7.3240, 8.2260, 5.3918 s-1) do not follow from Eqs. (7)-(9) (7.873, 8.344, 6.878); the ‘tuned’ Delta reproducing 8.226 s-1 is 0.9787 Ryd, not 0.988118. Delta_1 rows: hydrogen’s integral is elementary, 3.229 s-1, not 0.0888; helium’s diverges (a pole at y = 0.0278).

• Finding: S_zz = (4/3) D(omega) in atomic units for H 1s -> 2s, so at the degenerate frequency delta^TP = 252.7 au (partial closure) and 246.7 au (Table 2’s ‘Exact’, source unnamed): derived, not taken.

• Status: verified (2026-10-09).

TC-931 chang_1982 (Chang & Kim, Phys. Rev. A 26, 2728 (1982)): photoionisation cross sections of the excited np5 mp (1S) states of Ne, Ar, Kr and Xe (2026-10-09)

• Where: src/optmat/data/sources/chang_1982.toml, tools/extract/chang_1982.py (Table II, text, raster figures).

• Transcribed: a single-configuration calculation (hole-corrected Hartree-Fock effective Hamiltonian), LS-coupled J = 0 states, as excited_state_photoionization_cross_section (TC-872), all use = check except as noted. Table II (p. 2731), the length form (p. 2732): Ne 3p 2.0 and Xe 6p 6.9 Mb at 308 nm, Ar 4p 4.8 and Kr 5p 4.5 Mb at 248 nm; its Duzy and Hyman column (Phys. Rev. A 22, 1978 (1980), not in the library) as use = reproduced. The text’s Kr 6p, 7.4e-19 cm2 at 193.5 nm (velocity), inline. Figs. 1-4 (raster scans, velocity form, against the photoelectron energy, log-log): Ne 3p, Ar 4p, Kr 5p, Kr 6p and Xe 6p, read by the script from the page images (per-side decade calibration, decades within 5 pixels, every minor tick within 10; the curves taken by rank where four runs are resolved), from 0.6-0.9 eV (Ar, Kr, Xe; below, the curves merge) or 2.6 eV (Ne; they cross near 1 eV) to 52-60 eV, 8 % uncertainty. The photon energy is the photoelectron energy plus the calculation’s binding energy Ry / n*^2 from Table I (a conversion the record states; not shifted to experimental thresholds). Tables checked against the images; overlays (points and the calibrated decade grid on the page images) inspected.

• Checked: Table II (length) against the figures (velocity) at the same wavelength: Ar 4p 0.97, Kr 5p 0.99 (the paper’s 10 % between the forms), Xe 6p 0.89 (‘larger’ for Xe); Ne 3p lies in the crossing region, not read.

• Finding: Fig. 3’s Kr 6p curve at 193.5 nm reads 8.2e-19 cm2, 1.10 times the text’s 7.4e-19 (both velocity); the experimental J = 0 threshold changes the reading by 1.8 % only. Unresolved; both kept. geohegan_1986 (TC-886) quotes ‘Chang and Kim’ as 8.0e-19 (within 2 % of the figure, not the text) and cites page 2278 for 2728. kroll_1990 (TC-890) quotes this paper for Xe 6p as 3.7 (248 nm) and 1.8e-18 (193 nm), values the paper does not print: Fig. 4 gives 3.47 and 1.74 Mb (velocity), the length form about 13 % more; consistent with this calculation (figure or the authors’ tabulation). pindzola_1981 is cited with a wrong initial and page (‘M. A. Pindzola, 23, 20’).

• Not taken: Table I’s n* (no quantity; used for the thresholds); the other curves of Figs. 1-4; Fig. 5 (wave functions), Fig. 6 (beta, no quantity).

• Status: verified (2026-10-09).

TC-932 pindzola_1981 (Pindzola, Phys. Rev. A 23, 201 (1981)): Hartree-Fock and Dirac-Fock photoionisation cross sections of Xe 6p[1/2]0, partial and total, length and velocity (2026-10-09)

• Where: src/optmat/data/sources/pindzola_1981.toml, tools/extract/ pindzola_1981.py.

• Transcribed: Table I (p. 204), all four parts (the 2P3/2 es, ed-bar (j = 3/2) and ed (j = 5/2) partial cross sections (J = 1) and the total) in four forms (HF length and velocity, DF length and velocity), at seven photon energies 2.70-18.20 eV, 16 datasets of excited_state_photoionization_cross_section (TC-872) with gauge and channel; initial level 5p5 2P3/2 6p (J = 0) = 6p[1/2]0, Paschen 2p5 (threshold 2.1958 eV, p. 201). Frozen-core calculations with no correlation; the forms differ by up to 75 % and the paper prefers none: all use = check. Powers of ten printed as superscripts (note b); two cells carry footnote marks (a, b), kept in printed. All 112 cells checked against the rendered page (a scan).

• Checked: the partials sum to the printed total within the rounding of the four numbers in 27 of 28 cells.

• Doubt: DFV at 6.20 eV: the partials add to 8.7386e-19 against the printed 8.735e-19 (3.6 units of the last figure where rounding allows 1.1); every cell is as printed; which one slipped cannot be told; nothing corrected.

• Finding: kroll_1990 (TC-890) quotes this paper for 2p5 as 1.3-3.0e-18 (248 nm) and 0.7-1.8e-18 cm2 (193 nm), ‘HF velocity to DF length’: the 4.97 eV totals are HFV 1.321, DFL 3.049 (agree); at 193 nm (6.424 eV) log-log interpolation gives HFV 0.71, DFL 1.67, so the upper 1.8 is the 6.20 eV row’s 1.845. chang_1982 cites this paper as ‘M. A. Pindzola, Phys. Rev. A 23, 20 (1981)’ and finds its own Xe 6p value ‘higher … by a factor of two or more’: at 308 nm (4.03 eV) the HF length total is 3.6e-18, 0.52 of chang_1982’s 6.9 Mb.

• Not taken: Fig. 1 (raster), the four totals from threshold to 15 eV; it draws Table I’s values, only the steep 2.20-2.70 eV stretch is not printed.

• Status: verified (2026-10-09).

TC-933 hyman_1977 (Hyman, Appl. Phys. Lett. 31, 14 (1977)): photoionisation cross sections of the excited Ar(4s, 4p) and Kr(5s, 5p) configuration averages at 2486 A (2026-10-09)

• Where: src/optmat/data/sources/hyman_1977.toml, tools/extract/hyman_1977.py.

• Transcribed: Table I (p. 15), one value each, at ‘lambda = 2486 A’ (KrF; air or vacuum not said): Ar(4s) 2.1e-20, Ar(4p) 4.3e-18, Kr(5s) 1.3e-19, Kr(5p) 4.5e-18 cm2, as excited_state_photoionization_cross_section (TC-872), all use = check. A central-field model (Hartree-Fock ion potential plus a polarisation potential, no spin-orbit) of levels averaged over J and over the two core states; the s states include the 3P0,2 metastables and ‘the two 3P1 levels’ (p. 14, as printed). The library’s cells are an OCR of the scan (‘4. 3x 10-18’), kept in printed; checked against the table image. No uncertainty stated; the s-state values are ‘very sensitive to the details of the model’ (p. 15).

• Checked: the text’s repetitions (Ar 4p 4.3e-18, the abstract’s ~4.5e-18). Figs. 2 and 3 (raster, sigma against the excess energy epsilon) read by the script from the page images (per-side tick calibration, every tick within 3 pixels): Table I lies on the 4p and 5p curves at epsilon = 0.167 and 0.170 Ry, implying binding energies of 2.72 (Ar 4p) and 2.68 eV (Kr 5p) (+-0.03 eV) with the paper’s 1 Ry = 13.6 eV; overlays inspected.

• Finding: dakka_2018 (TC-892) quotes 3.3e-18 cm2 for Kr 2p6 at 215 nm ‘Calculated from’ this paper: Fig. 3’s 5p curve 0.0573 Ry above Table I’s point gives 3.39e-18 (dakka/read 0.97), so the quotation is this configuration average carried along Fig. 3, within the reading. chang_1982’s Table II reproduces the later Duzy and Hyman values (5.4, 5.2 Mb at 248 nm), 26 and 16 % above this paper’s.

• Not taken: Figs. 2-3 as data (no threshold of the averaged levels is printed, so no photon energy); Dunning and Stebbings’s threshold bounds (Phys. Rev. A 9, 2378 (1974), not in the library); the renormalised Ar(4s) ~1.5e-19.

• Status: verified (2026-10-09).

TC-934 hummer_1998 (Hummer & Storey, Mon. Not. R. Astron. Soc. 297, 1073 (1998)): R-matrix photoionisation cross sections of He 1s2 and the 1sns 1S and 1snd 1D levels (2026-10-09)

• Where: src/optmat/data/sources/hummer_1998.toml, tools/extract/ hummer_1998.py (Table 1, raster figure).

• Transcribed: Table 1 (p. 1074), threshold cross sections (Mb), the rows two photons reach from the ground state and the ground state: 1 1S (photoionization_cross_section), 2-4 1S and 3-4 1D (excited_state_photoionization_cross_section, TC-872), in the This Work (R-matrix, seven-orbital He+ target) and Extrapolated (from Drake’s oscillator strengths by Eq. 1, with the printed fitting error, +-0.000 to +-0.053) columns; one point each at the level’s NIST ionisation energy (nist_asd_2026, He_I_levels.tsv; the paper prints no level energies), in cm-1. Fig. 1 (p. 1076, an embedded image), the n = 1 and n = 2 1S curves from 0.08 to 2.45 Ryd above threshold, read by the script (per-side linear calibration, ticks within 2 pixels, minor ticks within 3), 4 % uncertainty; photon energy = electron energy + the calculation’s binding energy 1/(n - delta)^2 Ryd from Table 2’s This Work quantum defects (a conversion the record states; the calculated thresholds are 0.33 % (1 1S) and 0.14 % (2 1S) below NIST’s and are not shifted). All use = check. Table 1 checked against its image; the overlay inspected.

• Checked: the n = 1 curve carried to threshold gives 0.996 of Table 1’s 7.394 Mb.

• Finding: at the photon energy of kumar_2026 (TC-898) and kapralova_zdanska_2025 (TC-899), 10.31 eV (0.466 Ryd above the 1s2s threshold), Fig. 1’s 1s2s 1S curve reads 1.733 Mb: their implied 1.691 and 1.727 Mb are 0.976 and 0.997 of it; at 19.06 eV (65.05 nm) 0.461 Mb against kumar_2026’s 0.459. Three independent calculations agree within the reading.

• Not taken: Table 1’s 1P and triplet rows (not two-photon levels; their thresholds would need J averages), the Coulomb and OP columns (older methods; OP from TOPBASE), Fig. 1’s n = 5-25 curves and Fig. 2 (1P series), Table 2 (quantum defects, no quantity), Tables 3-6 (recombination). No fit coefficients are printed; the full cross sections were to go to TOPBASE.

• Status: verified (2026-10-09); the threshold cross sections’ energies corrected (2026-10-09): see TC-951.

TC-935 drake_1969 (Drake, Victor & Dalgarno, Phys. Rev. 180, 25 (1969)): two-photon decay rates of the 2 1S0 and 2 3S1 levels of He-like ions; no values taken (2026-10-09)

• Where: src/optmat/data/sources/drake_1969.toml (notes only, no datasets).

• Transcribed: nothing. The paper gives spontaneous two-photon emission rates (s^-1) and their photon-energy distributions, He I to Ne IX (variational, nonrelativistic, infinite nuclear mass); no quantity of the vocabulary (TC-872) holds a decay rate, and the rates are not converted into a two-photon strength or cross section. The helium values are recorded in the notes: 2 1S0 A = 5.13 x 10^1 s^-1, lambda_max 771 A (Table I, p. 29); 2 3S1 A = 4.02 x 10^-9 s^-1, lambda_max 699 and 2400 A (Table III, p. 30); both checked against the table images.

• Checked: Simpson’s rule over the He columns of the distributions (Tables II, IV, y = 0-0.5) gives 51.15 s^-1 (Table I 51.3, -0.3 %) and 4.04 x 10^-9 s^-1 (Table III 4.02 x 10^-9, +0.5 %): the tables give the rate per unit y counting each photon of a pair, the total being the integral over half the range (Eq. 2). The wavelength peaks from the distributions and NIST’s level energies: 761 A (printed 771; the peak is flat to 0.1 % over that interval) and 700, 2344 A (printed 699, 2400).

• Finding: see bondy_2020: 51.3 s^-1 is 0.54 % above bondy_2020’s infinite-mass 51.0233 s^-1, and the other ions’ rates differ from bondy_2020’s by -0.39 to +0.49 %, more than the paper’s ‘converged to the number of figures quoted’.

• Status: verified (2026-10-09).

TC-936 bondy_2020 (Bondy, Morton & Drake, Phys. Rev. A 102, 052807 (2020)): two-photon decay rate of He 2 1S0 with finite nuclear mass; no values taken; comparison with drake_1969 (2026-10-09)

• Where: src/optmat/data/sources/bondy_2020.toml (notes only, no datasets).

• Transcribed: nothing; no quantity holds a decay rate (TC-872). Recorded in the notes, for 4He 2 1S0 -> 1 1S0 (Tables II, IV, V, VI, images checked): w_inf = 51.023 3210(5) s^-1 (nonrelativistic, infinite mass), the finite-mass correction -0.015 617 48, the relativistic estimate -0.08(7), total 50.93(7) s^-1 (Derevianko and Johnson 51.02); w/alpha^6 = 8.170 693 021 30(21) x 10^-3 au (velocity), length form equal to 1.2 x 10^-8; peak rate 72.562 3228 s^-1 per unit y at 120.2628 nm.

• Checked: w_inf/alpha^6 x 6242.763420 s^-1 reproduces Table VI’s w_inf (51.023 321) and the finite-mass corrections of 4He and 3He (-0.015 617 5, -0.020 725 9); the peak wavelength is 2 / Delta.

• Finding: drake_1969 (same approximation) gives 51.3 s^-1 for He, 0.54 % above w_inf = 51.0233; its Li II to Ne IX rates differ from Table VI’s w_inf by +0.49, -0.39, +0.48, +0.23, -0.26, -0.14, +0.23, -0.36 %, errors of a few units of the third figure where drake_1969 says its results converged to the figures quoted. drake_1969’s He distribution peak, 1.45 x 10^2 s^-1, is twice this paper’s 72.562 within its rounding, as the text says (drake_1969’s table counts both photons). The paper gives no 2 3S1 rate (drake_1969: 4.02 x 10^-9 s^-1); it quotes a triplet-to-singlet ratio of 6.2 x 10^-11 (Derevianko and Johnson) without saying which rates it divides (drake_1969’s ratio is 7.8 x 10^-11).

• Doubt: three misprints in the text, none affecting a value: ‘total rate of 50.093 s^-1’ for Table VI’s 50.93; Sec. V’s wavelengths in ‘um’ are nm or angstrom (‘601.40 um’ is 601.40 A, 1e8 / 166 277.44 cm^-1); the lifetimes 5.178(45) x 10^-4 s and 1.9634(28) x 10^-2 s are attributed to He and 7Li+ respectively, the reverse of 1/w (1/50.93 s^-1 = 1.9635 x 10^-2 s for He, 1/1938.8 s^-1 = 5.158 x 10^-4 s for 7Li+); 5.178(45) is not 1/1938.8(17) (5.158(5)): unexplained.

• Status: verified (2026-10-09).

TC-937 payne_1981 (Payne et al., Chem. Phys. Lett. 79, 142 (1981)): photoionisation cross sections of two-photon-excited np5 n’p[1/2]0 levels of Ar, Kr, Xe (estimates) (2026-10-09)

• Where: src/optmat/data/sources/payne_1981.toml (inline text points, no script).

• Transcribed: four one-figure estimates of excited_state_photoionization_cross_section (cm2) quoted in the text (pp. 145-146, rendered pages read): Ar 3p5 4p[1/2]0 at 1576 A, ~1 x 10^-18; Kr 4p5 6p[1/2]0 at 1927.48 A, ~5 x 10^-19 (Ref. 9, Pindzola, unpublished); Kr 4p5 5p[1/2]0 at 3262 A, 10^-18; Xe 5p5 6p[1/2]0 at 2496 A, ~3 x 10^-18 (Ref. 9). All use = check; the two Ref. 9 values reproduced_from Pindzola (unpublished); no uncertainty stated. Wavelengths in vacuum (2 x 1e8 / 1927.48 A = 103 762.4 cm^-1 against NIST’s Kr 6p[1/2]0, 103 761.63; air would be 1926.9 A).

• Checked: Xe against pindzola_1981 (Table I at 4.97 eV): 1.32 (HF velocity) to 3.05 x 10^-18 cm2 (DF length); the 3 x 10^-18 here is the largest form. Kr 6p against bokor_1980: (3.2 +- 2.0) x 10^-19 cm2, but for 6p[3/2]2 at 193.49 nm.

• Finding: hattig_1998b (TC-887) cites this paper among four sources for an ‘experimental value of 2.05 x 10^-51 cm4 s’ for argon’s 4p J = 2 levels. The paper has no argon measurement: it treats only the J = 0 level 4p[1/2]0, in theory (R_2 = 1.7 e^2 a0^2, k’ ~ 1.0 x 10^-9 s^-1 W^-2 cm^4 for 1576.3 + 2292.8 A). mccann_1988’s notes ascribe ‘two-photon and three-photon schemes’ to it: the three-photon (He, Ne) estimates are in payne_1982, not here.

• Not taken: the radial integrals R_2 and the bandwidth-dependent rate coefficients k, k’ (s^-1 W^-2 cm^4): no quantity (not two_photon_excitation_cross_section, which is frequency-integrated); Table 1 (effective volumes). Ref. 9/10 numbering slip noted.

• Status: verified (2026-10-09).

TC-938 payne_1982 (Payne, Chen, Hurst & Foltz, Adv. At. Mol. Phys. 17, 229 (1981/1982)): review of resonance ionisation spectroscopy; no values taken (2026-10-09)

• Where: src/optmat/data/sources/payne_1982.toml (notes only, no datasets).

• Transcribed: nothing. Dated 1981 on the volume page (‘Copyright 1981’, p. 229) and by the papers that cite it (hattig_1998b, mccann_1988), 1982 by the publisher’s registry; the citation gives both, the id follows the library.

• Checked: what the review prints, against the rendered pages and table images. The Xe 6p[1/2]0 fit (K = 2 x 10^-9 s^-1 W^-2 cm^4, sigma_1 = 3 x 10^-18 cm2) is Chen, Hurst and Payne’s 1980 measurement (chen_1980), reproduced; the excited-state photoionisation cross sections of Figs. 5-7 are Duzy and Hyman’s (1980), reproduced and raster; the closure formula and R_2 values repeat payne_1981; Sec. III.E’s three-photon He and Ne estimates carry an unknown factor L_3 (1-100); Table I is a mathematical function, Table II CO isotopologue rovibronic levels (no quantity; 12C18O A v = 1, J = 1 prints 67 759.75 for evidently 67 259.75).

• Finding: the review’s theoretical K for Xe with R_2 = 7 e^2 a0^2 and 0.08 A, ‘1 x 10^-9’, differs from payne_1981’s 1.3 x 10^-9 for the same inputs. It reports no measured two-photon rate of argon (‘Very little experimental information exists’, p. 246): hattig_1998b’s 2.05 x 10^-51 cm4 s (TC-887), which cites it, is not here. The text cites ‘Payne et al., 1980’ for the schemes; the reference list holds only the 1981 Chem. Phys. Lett. paper (payne_1981).

• Status: verified (2026-10-09).

TC-939 palm_1998 (Palm & Merkt, Appl. Phys. Lett. 73, 157 (1998)): resonant four-wave mixing in Ar beyond 19 eV via the 4p[5/2]2 two-photon resonance; no values taken (2026-10-09)

• Where: src/optmat/data/sources/palm_1998.toml (notes only, no datasets).

• Transcribed: nothing: the paper reports XUV output (photons per pulse, ~10^-6 conversion, 0.1 cm^-1 bandwidth) and relative signals. The Ar 3p5 4p[5/2]2 resonance (2 nu = 105 617.3 cm^-1) is Moore’s (1949), reproduced.

• Checked: the resonance positions named (Ar 189.3, 186.8, 184.0 nm; Kr 212.5, 202.3, 192.7 nm) are NIST’s levels as vacuum wavelengths (2/105 617.27 … 2/103 761.63 cm^-1); the XUV energies 18.32, 18.76, 19.64 and ‘up to 19.66’ eV follow from 105 617.3 cm^-1 and the stated second-laser wavelengths. Not reproduced: the Kr 192.7 nm resonance’s limit ‘155 700 cm^-1 (19.3 eV)’; with the same 189 nm limit it would be 156 672 cm^-1 (19.42 eV). The page prints ‘10-20 uJ’ where the text layer has ‘mJ’.

• Finding: compared with rupper_2004 (TC-900), the same group’s later laser: there the J = 0 argon resonances 4p[1/2]0 and 4p’[1/2]0, which this paper expected to improve the conversion, give 3.3 and 6.3 times the four-wave-mixing output of the 4p[5/2]2 resonance used here (rupper_2004 Table I, 4.0(12) and 7.5(24) against 1.2(2)), much less than the factor of about 100 between krypton’s J = 2 and J = 0 resonances quoted here, and the Kr 6p[1/2]0 resonance gave 45 times the XUV signal of Ar 4p[5/2]2. Neither paper gives a two-photon cross section.

• Status: verified (2026-10-09).

TC-940 li_1989 (Li et al., Phys. Rev. A 39, 5751 (1989)): saturation intensities at 1064 nm and THG chi(3) of the rare gases from harmonic generation (2026-10-09)

• Where: src/optmat/data/sources/li_1989.toml, tools/extract/li_1989.py.

• Transcribed: Table I (p. 5752), saturation_intensity of Xe, Kr, Ar, Ne, He at 1064 nm with 36 ps pulses, 1.2 x 10^13 to 2.8 x 10^14 W cm^-2, +-50 % (level not stated), defined as the intensity at which the single-ionisation probability reaches one; reproduced_from L’Huillier et al., J. Phys. B 16, 1363 (1983) (not in the library), whose He and Ne values the reference note says were overestimated by a factor of 2. Table II (p. 5754), the chi^(3) row, hyperpolarizability (esu, convention ward_1969: 4 x Lehmeier’s gamma(3), per the caption’s factor of 4) of Kr, Ar, Ne and He from the third-harmonic yields, normalised to Lehmeier et al.’s Xe; +-50 %. Xe’s chi^(3) is the normalisation and is not taken. All use = check. The library CSV mislabels the chi^(3) and chi^(5) rows ‘chi_0’; taken by position (image checked).

• Checked: the script tests Table II’s chi_0^(3) row against lehmeier_1985’s esu values times 4 (6.88, 2.336, 0.856, 0.0656, 0.03656 x 10^-37 against the printed 6.9, 2.3, 0.86, 0.065, 0.036): within one unit of the last figure, Ne and He truncated rather than rounded. This paper’s chi^(3) is 0.98 (Kr), 1.07 (Ar), 0.70 (Ne) and 0.63 (He) times Lehmeier’s, inside its +-50 %.

• Not taken: chi^(5) (Table II) and Ar’s chi^(7) = 2 x 10^-60 esu (no quantity); Delta k_3, Delta k_5 (from Leonard’s indices, at one density); the harmonic yields and slopes (Figs. 4-13, raster). No two-photon data.

• Status: verified (2026-10-09).

TC-941 yoshino_1985 (Yoshino & Freeman, J. Opt. Soc. Am. B 2, 1268 (1985)): the odd J = 1 Rydberg levels and series limits of Xe from VUV absorption (2026-10-09)

• Where: src/optmat/data/sources/yoshino_1985.toml, tools/extract/yoshino_1985.py.

• Transcribed: Tables 1-5 (pp. 1270-1272), the five series from 5p6 1S0, nd[3/2]1 (n = 5-66), nd[1/2]1 (5-34), ns[3/2]1 (7-47), nd’[3/2]1 (5-65) and ns’[1/2]1 (6-39): the printed wave number of each absorption line (vacuum, cm^-1) as level_energy of its upper level, one dataset per series, 223 measured rows; the five rows printed in parentheses (quantum-defect estimates: ns 22, nd’ 6, 7, ns’ 8, 9) excluded. Uncertainty 0.2 cm^-1, the paper’s absolute accuracy (level not stated); the diffuse nd’ n = 8-13 rows print only whole cm^-1. The series limits (p. 1271) as ionization_energy: 97 833.75 +- 0.05 cm^-1 (to Xe+ 2P3/2) and 108 370.8 +- 0.2 cm^-1 (to 2P1/2). The nd’ and ns’ levels above the first limit are the autoionising resonances between 12.13 and 13.44 eV (two photons of 184.6-204.4 nm reach that region; these odd J = 1 levels are one-photon levels). No cross section, oscillator strength or absolute absorption is printed (Figs. 1, 2: plates and relative densitometer traces).

• Checked: every row’s wave number against 1e8 over its wavelength and its n* against the Rydberg formula with the paper’s limits (R(Xe) = 109 736.857 cm^-1), within the printed rounding; the 28 levels NIST cites to this paper (key L6449) equal it to every digit; NIST’s other levels (n <= 20) differ by -0.26 to +0.23 cm^-1. The limits’ eV values follow with 8065.479 cm^-1/eV; NIST’s first ionisation energy is 97 833.787 cm^-1 (+0.037). Misprinted cells checked on the table images and rendered pages.

• Errata: six wave numbers (each fails both checks; the correction passes both): nd[1/2] n = 10, 95 912.98 -> 95 912.87 (NIST 95 912.880, another source); nd[1/2] n = 31, 97 798.4 -> 97 698.4; ns[3/2] n = 10, 94 487.09 -> 94 787.09 (NIST 94 787.084); ns[3/2] n = 23, 97 350.0 -> 97 530.0; nd’[3/2] n = 11, 107 209. -> 106 929. (the next row’s value repeated; NIST’s L6449 entry is 106 929.); ns’[1/2] n = 11, ‘106 120 8’ -> 106 120.8 (point missing; NIST L6449 106 120.8). Also misprinted, not in a value column: Table 1 n = 14 wavelength 1030.453 (1030.435), Table 5 n = 12 ‘3937.650’ (937.650), Table 4 n = 23 n* 20.74 (20.72).

• Doubt: the text says 224 lines are identified; the tables hold 223 measured rows.

• Status: corrected (2026-10-09).

TC-942 The two-photon follow-up literature on one footing: krypton and xenon unchanged, the bound-strength conventions, the quoted values traced (2026-10-09)

• Where: tools/two_photon_tables.py, the manual page Two-photon ionisation and absorption: the data (docs/two_photon.md), tests/test_two_photon_page.py; the records of TC-904 to TC-941.

• Decided, axes (each recorded in its record; a change of variable using the source’s own numbers, never a shift to match experiment, data rule 4). Where a source plots against something other than one photon’s energy, the abscissa is converted to photon energy:

  • total two-photon energy halved (gangopadhyay_1986, TC-914, as lhuillier_1989, TC-882);

  • photoelectron energy plus the calculation’s own threshold or binding energy, halved for two photons (proulx_1993 Table 1, TC-906; chang_1982 figures, TC-931).

  The printed value of the original variable is kept in each row. hummer_1998’s threshold cross sections print no energy and are placed at NIST’s threshold of each level (from the held NIST level lists); the calculation’s own thresholds are 0.07 to 0.33 % lower (TC-934).

• Finding, two-photon ionisation (ratios off resonance, as tabulated on the page):

  • He: van der Hart & Bingham’s R-matrix Floquet (1e13 W/cm2) is 0.92 to 1.07 of saenz_1999 from 13 to 20 eV. Sato et al.’s quoted R-matrix Floquet values are this paper’s within 5 % at three wavelengths and 1.30 times at 53.4 nm, unresolved (TC-904).

  • Ne: the only independent calculation, Moccia, Rahman & Rizzo (raster), is strongly gauge dependent: velocity 0.62 to 0.14, length 0.19 to 0.02 of mckenna_2004 from 12 to 16 eV (TC-910).

  • Ar: the older many-body calculations (all raster) lie mostly below the two all-electron ones:

    • Pan, Gao & Starace 0.63 to 0.74;

    • Moccia et al. 0.61 to 0.87;

    • Fink & Johnson 0.66 to 0.83;

    • Pindzola & Kelly’s second order 0.94 to 1.02.

    McKenna’s quotation of Pan et al. holds (TC-908). Petrov’s “about 12 % smaller” matches its uncorrected curve. No measured Ar cross section: Xenakis et al. measured none (TC-911).

  • Kr: Fink & Johnson’s relativistic calculation (TC-912) is a scanned (raster) figure, as is every other Kr curve. Above 2P1/2 it differs from L’Huillier et al.’s MQDT by up to a factor of 6 (8 eV). OEP 6 Q2 is unchanged: no eligible krypton reference.

  • Xe:

    • Fink & Johnson’s curve is 0.75 to 0.99 of lagutin_2017 (which redraws it).

    • Gangopadhyay et al.’s Table I is 0.37 to 0.69; every later drawing of “Gangopadhyay” is this table, above 2P1/2.

    • Gangopadhyay’s raster curve between the thresholds reads 0.11 of McCown’s measurement at its line centre. No vector or tabulated source covers the region: OEP 6 Q3 is unchanged.

    • Bischel et al.’s estimate and Hodges et al.’s lower limit at 193 nm (McCown’s definition) are 400 and 80 times below McCown.

• Finding, bound strengths: a 1D (J = 2) level’s strength is printed in two conventions: one tensor component’s S_xy^2 (hattig_1998b, sundholm_1994, hettema_1992), and the level’s, five times larger (henriksson_2005). On the per-level basis sundholm_1994’s argon value is 4.7 times the measured constant it claims to match within 7 % (TC-925). OEP 6 Phase 2 must fix this convention before reconciling delta^TP with sigma_0^(2).

• Finding, quoted values:

  • hattig_1998b’s “measured” Ar 1D 2.05e-51 cm4 s is sundholm_1994’s sum of mccann_1988’s three J = 2 terms, the first quoted 7 % low. The sum is 2.16e-51 (TC-919, TC-925); neither Payne paper holds an argon measurement (TC-937, TC-938).

  • kroll_1990’s literature rows for Gornik, Raymond and Chen are raymond_1984’s coefficients times (hbar omega)^2, in no stated convention (TC-922 to TC-924).

  • Its “4-13” is pindzola_1981b converted the same way. That conversion is right only if Pindzola’s line-shape factor includes chaotic light’s factor 2, which the paper does not state (open; TC-929).

  • geohegan_1986’s Kr values trace to:

    • chang_1982’s figure, not its text;

    • bischel_1979 (100 cm-1);

    • bokor_1980 (25 cm-1), which it mixes in one range.

  • drag_2021’s Khambatta quote is right; its “not stated” polarisation and photon statistics are linear and G2 = 2 assumed (TC-920).

  • dakka_2018’s 3.3 is hyman_1977’s curve carried to 215 nm (TC-933).

• Finding, the He 1s2s photoionisation: hummer_1998 reads 1.733 Mb at 10.31 eV; kumar_2026 is 0.976 and kapralova_zdanska_2025 0.997 of it (TC-934).

• Status: decided (2026-10-09). The Pindzola line-shape factor is open (TC-929).

TC-943 OEP 6 Phase 1: the reference curves approved under data rule 8, and evaluation on grids (2026-10-09)

• Where: src/optmat/data/gas/two_photon.toml; OEP 6, Q1 (the references) and section 6 (Warnings and refusals), with TC-903.

• Decided (the author, John Travers, 2026-10-09; data rule 8, TC-699): these vector drawings may be the models’ references. Their datasets stay use = "check"; the model interpolates the drawn vertices and fits nothing.

  • He, linear: mihelic_2021/fig3a_sigma2_L0 + fig3a_sigma2_L2, velocity form (TC-874). It covers the window from the threshold, where saenz_1999 starts at 12.65 eV (98.0 nm). The paper prints no value of its own; its redrawing of Saenz and Lambropoulos’s curves matches saenz_1999 within 1 to 2 %.

  • Ne, linear: mckenna_2004/fig1_sigma2_Ne (TC-856), the only vector source. A single source: status untested.

  • Ar, linear: mckenna_2004/fig5_sigma2_Ar (TC-856). It starts at 7.91 eV (156.7 nm), petrov_2016 at 8.00 eV (155.0 nm), which matters for resonant dispersive waves near 155 nm. Petrov et al.’s two gauges with core polarisation are its validators.

  • Xe, linear and circular: lagutin_2017/fig8_cipfcp_linear and fig8_cipfcp_circular, length form, from one figure (TC-880). The source’s own accuracy is its 7.7 % length-velocity difference; its velocity form (fig4_cipfcp_velocity) is a gauge diagnostic, not an independent calculation.

  • Kr: none (OEP 6, Q2; TC-942).

• Decided (the author, 2026-10-09, after TC-903): evaluation returns NaN where the model is unavailable, with an availability mask, for scalars and arrays alike. It never raises on a frequency grid. It raises only for arguments outside their domain: a frequency not finite and positive, an intensity or density not finite and non-negative.

• Status: decided (2026-10-09).

TC-944 OEP 6 Phase 1: the two-photon ionisation models (2026-10-09)

• Where:

  • src/optmat/gas/two_photon.py (the model, its loader and registry);

  • src/optmat/gas/_two_photon_derivation.py (the derivation);

  • src/optmat/data/gas/two_photon.toml (the selection);

  • src/optmat/data/gas/models/two_photon/<gas>_<polarization>.json (the stored models), written by tools/fit/two_photon_record.py;

  • src/optmat/exceptions.py (ArgumentError, UnavailableModelError);

  • tests/test_two_photon.py, tests/data/golden_models.json;

  • the manual page Two-photon ionisation and absorption, Propagation, Ionisation rates;

  • the gallery example Two-photon ionisation of the noble gases.

• Decided, the derivation:

  • Thresholds: half the neutral’s ionisation energy, and half of it plus the ion’s 2P1/2 level (nist_asd_2026, as TC-902). E1 is OEP 5’s level.

  • Vertices: a vector drawing’s staircase puts several vertices at one photon energy (its 0.13 pt quantum: 143 of McKenna’s Ne vertices in the window, 100 of Ar’s, 106 of Lagutin’s linear Xe). Each such group is one point at its geometric mean, so the curve is a function of frequency.

  • Partial cross sections (He) are each interpolated linearly in log sigma on the union of their vertices over their common coverage, and summed.

  • Kept vertices: those from the lowest threshold to E1 only.

• Decided, the regions (OEP 6, section 6):

  • below_threshold: zero.

  • unavailable: from the threshold to the first vertex, from the last vertex to E1, and at and above E1 (NaN).

  • unsupported_detail: values with ModelRangeWarning. For an LS-coupled reference (Ne, Ar), the band between the two thresholds. For every gas, the 0.6 eV below E1: there the independent calculations depart from the references. Within 0.3 eV of E1 they would enter the spread as resonance placements, not cross sections:

    • Petrov et al. reach 1.58 times McKenna at 11.3 eV;

    • Nikolopoulos and Lambropoulos’s displaced 1s2p resonance reaches 8.4 times Mihelič;

    • Fink and Johnson depart from 8.0 eV.

    0.6 eV is uniform, chosen on those numbers.

  • supported: the rest of the reference.

• Finding, the models (bands in nm; spreads over the supported band, of the validators to the reference):

  • He: supported 100.80 to 60.13. Saenz 0.85 to 1.14; Nikolopoulos 0.75 to 1.19; van der Hart 0.87 to 1.04.

  • Ne: supported 114.48 to 77.15; no validator.

  • Ar: supported 155.59 to 112.47; unavailable 157.34 to 156.71. Petrov length 0.91 to 0.99, velocity 0.92 to 0.99.

  • Xe, linear: supported 184.47 to 158.21; unavailable 204.43 to 184.47 (between the thresholds). Fink and Johnson (raster) 0.65 to 0.87; the reference’s velocity form 1.08 to 1.15.

  • Xe, circular: Fink and Johnson (raster) 0.62 to 0.71.

  At 155 nm in argon at 1 bar and 293.15 K the loss coefficient is 4.9e-15 m/W (sigma 1.27e-58 m4 s).

• Checked:

  • the stored models equal a fresh derivation;

  • every stored vertex reproduces its dataset (to rounding);

  • mckenna_2004’s printed plateaus: Ar within 8 % of 1.2e-50 cm4 s from 8.0 to 11.0 eV; Ne within 11 % of 1.65e-51 from 11 to 16 eV;

  • the thresholds against the manual’s table to 0.01 nm, and argon’s against the printed NIST values;

  • beta against dI/dz = -2 hbar omega N W and a fourth-order integration of the loss law;

  • NaN, zero and finite values by region on a 300 to 60 nm grid, without error;

  • the manual’s table against the models;

  • golden digests and values;

  • the full gate, poe test-library and poe test-release.

• Deviations from OEP 6, section 6:

  • uncertainty is a property, not a function of frequency: the spreads are over the supported band;

  • evaluation returns NaN and never raises on a grid (TC-943);

  • added available (the mask), region (the labels) and two_photon_ionisation_models() (the registry);

  • two exceptions added to the core, ArgumentError and UnavailableModelError.

• Status: decided (2026-10-09).

TC-945 OEP 6 after Phase 1: the author’s decisions on Phase 2, xenon between its thresholds, and the confirmations (2026-10-09)

• Where: OEP 6 (Part III, history), the roadmap’s OEP 6 entry; TC-929, TC-934, TC-942, TC-944.

• Decided (the author, John Travers, 2026-10-09, accepting the recommendations):

  • Phase 2 is restricted to curation (2a).

    • It will give the even J = 0, 2 levels below I_p/2 from the held NIST level lists, and their two-photon strengths in one stated convention. One tensor component’s S_xy^2 (hattig_1998b, sundholm_1994, hettema_1992) is a fifth of a J = 2 level’s strength (henriksson_2005; TC-942); the convention is to be settled first.

    • Beside them, the measured strengths (kroll_1990, drag_2021, dakka_2018, khambatta_1988) with their photon-statistics and line-shape conventions, and the levels’ photoionisation cross sections.

    • The complex evaluator is Phase 2b, deferred until a derivation answering Q9 exists and is reviewed: OEP 6’s own fallback. TC-929 (Pindzola’s line-shape factor) and Dakka’s rate factor (Q7) are settled in 2a.

  • Xenon between its thresholds (Q3) stays unavailable (204.43 to 184.47 nm). Its only calculation there, gangopadhyay_1986’s raster curve, reads 0.11 of McCown’s measurement (TC-914, TC-942).

  • TC-944’s implementation choices are confirmed:

    • the 0.6 eV resonance wing;

    • the geometric mean of a drawing’s repeated vertices;

    • region, available and the registry;

    • uncertainty as a property;

    • ArgumentError and UnavailableModelError.

  • TC-942’s axis conversions are confirmed (photoelectron energy to photon energy with the calculation’s own threshold; total energy halved). hummer_1998’s threshold values move to the calculation’s own thresholds (TC-951).

  • Release: v0.5.0 tagged locally on main, after Phase 1.

  • Krypton: the five papers the curated records cite as its likeliest further sources were requested and are curated below.

• Status: decided (2026-10-09).

TC-946 ritchie_1977 (Ritchie, Phys. Rev. A 16, 2080 (1977)): tabulated two-photon ionisation cross sections of He, Hartree-Fock independent-particle model; no krypton (2026-10-09)

• Where: src/optmat/data/sources/ritchie_1977.toml, tools/extract/ ritchie_1977.py (Tables I and II, CSV).

• Transcribed: Tables I and II (p. 2083), ‘Values of sigma^(2) x I_0/2I in a_0^2’ for two-photon ionisation of He 1 1S, linear polarisation, dipole-velocity form: Table I (Hartree-Fock ground state, 22 photon energies 0.456-0.868 au) and Table II (one-parameter variational ground state, 10 energies 0.456-0.799 au), each in exchange (E) and nonexchange (NE) columns, each cell a value and a parenthesised value without the final-state orthogonalisation: eight datasets, unit a0^2 as printed, abscissa E_p in hartree as printed. The dipole-length value at 1000 angstrom, 1.403 (p. 2084), inline. Uncertainty: the author’s numerical ‘within about 5 %’ (p. 2088); no model error stated. All use = check. Helium only: no krypton, xenon, argon or neon numbers of any kind (OEP 6 Q2: nothing for Kr here).

• Checked: every cell of both tables against the table images and the page image at native resolution (all agree; the specks over five decimal points of Table II’s E column are dust). Every Table I wavelength against its E_p (hc / E_h = 455.634 angstrom au, within both roundings). The text’s numbers: unshifted first resonance |epsilon^(0)| - 1/8 = 0.793 and 0.771 au; epsilon^(0) = -0.8965 for zeta = 27/16; the accurate V_I 0.904 au and 2 1P position 0.780 au against nist_asd_2026 (0.90357, 0.77975 au); the nonexchange model’s ‘about 20 %’ dynamical error, 1 - E / 2 NE = 0.199 (Table I), 0.200 (Table II) at threshold.

• Finding: the definition. sigma^(2) of Eq. 1 is an intensity-dependent cross section (rate sigma^(2) Phi), so a printed v is sigma_2 = 2 v a_0^2 E_p E_h / I_0 (I_0 = 14.038e16 W/cm2) for Gamma = sigma_2 Phi^2; 1.267 at 0.456 au is 1.005e-51 cm4 s. Confirmed by lhuillier_1986’s Fig. 13, which draws Table I’s E column as p / I^2: the drawn line is 0.93, 0.95 and 1.01 times the converted values at 0.506, 0.570 and 0.651 au. The values are not converted in the data.

• Finding: below the 1s2p resonance (12.4-19.1 eV) the Hartree-Fock values are 0.77-0.89 times mihelic_2021 (and OEP 6’s He model, TC-943), 0.71-0.96 times saenz_1999, 0.62-1.18 times nikolopoulos_2001, and 0.79 times bachau_1990’s L^2 value at 0.5 au. The resonances sit at the model’s orbital energy (first near 0.79 au against the real 0.780 au); no shift applied.

• Status: verified (2026-10-09).

TC-947 lhuillier_1986 (L’Huillier, Jonsson & Wendin, Phys. Rev. A 33, 3938 (1986)): LDA one-electron and RPA two-photon ionisation of He, raster Fig. 11; no krypton (2026-10-09)

• Where: src/optmat/data/sources/lhuillier_1986.toml, tools/extract/ lhuillier_1986.py (Fig. 11 from the page image).

• Transcribed: Fig. 11 (p. 3948), p / I^2 of He in 10^-16 s^-1 W^-2 cm^4 against the photon energy in Ry, linear polarisation, length form, local-density basis: the RPA (screened) line and the one-electron line, read from the scan at native pixels (data rule 8, TC-699): 0.67-1.02, 1.20-1.28/1.39 and 1.55-1.78 Ry, 139 and 151 samples, where each line stands clear of the others. Unit s-1 cm4/W2, scale 1e-16, as bachau_1990’s Fig. 1(a). Digitising uncertainty 0.05 (10^-16 units) absolute; the paper states none and says its purpose ‘is not to obtain any accurate results’. The axis is the LDA’s, unshifted (two-photon threshold 0.57 Ry, one-photon 1.13 Ry); below 0.90 Ry the curve is not real ionisation (the authors’ region (i)). All use = check. The PDF is a scan; every figure is raster. Helium only: no krypton numbers (one sentence on Kr needing three photons at 193 nm) and no xenon two-photon cross section (OEP 6 Q2: nothing for Kr here).

• Checked: the ticks found in the image (x within 3.7 pixels, 0.004 Ry; y within 5.1, 0.03), the scale interpolated between the two edges (a slightly rotated page); the overlay inspected. The text’s ‘lowered by a factor of 1.4’ at 1 Ry: 3.541 / 2.513 = 1.409; the reversal ‘around 1.5 Ry’ / ‘above 1.45 Ry’: the one-electron line above the RPA line at 1.20-1.24 Ry and below it from 1.55 Ry. Fig. 13’s Ritchie line against ritchie_1977’s Table I converted: 0.93-1.01 (the record’s notes).

• Finding: the frame’s left edge, labelled ‘0.57’ (Fig. 11) and ‘0.6’ (Fig. 13), lies at 0.62 Ry on the tick scale; the dotted threshold lines labelled 1.13 and 1.81 lie at 1.12 and 1.80. Fig. 13’s caption cites Victor as Ref. 35 (Pindzola and Kelly); the text’s Ref. 33 is Victor. No number affected.

• Finding: the RPA line as sigma_2 = (p / I^2)(hbar omega)^2 at 0.92-1.00 Ry is 1.16-1.19e-51 cm4 s: 0.88-0.92 times mihelic_2021 (OEP 6’s He model, TC-943), 0.80-0.81 times saenz_1999, 0.74-0.85 times nikolopoulos_2001, 0.91 times bachau_1990 at 0.5 au.

• Status: verified (2026-10-09).

TC-948 kulander_1987 (Kulander, Phys. Rev. A 36, 2726 (1987)): time-dependent Hartree-Fock ionisation rates and one- and two-photon cross sections of He (2026-10-09)

• Where: src/optmat/data/sources/kulander_1987.toml, tools/extract/ kulander_1987.py (Table I).

• Transcribed: Table I (p. 2732; every cell checked against the table image), all use = check. (a) He ionisation rates (s^-1) at 1.064 and 0.532 um (5e14, 1e15, 2e15 W/cm2) and at 9.0 eV photons (1e15), each in the columns ‘1s^2’ and “1s1s’”, read as the time-dependent Hartree-Fock rate extrapolated to the static orbital energy and the frozen one-electron model (the table does not name them; the text compares the two there), ionization_rate, linear polarisation, 20 % (the paper’s sensitivity to the grid and time step, p. 2728). The 9.0 eV rows carry wavelength_nm = 137.76 (hc / 9.0 eV, the record’s conversion) and photon_energy_ev = 9.0. (b) the TDHF two-photon generalised cross sections, 3e-16 at 13.6 eV and 1e-16 cm4/W2 s at 17.7 eV (multiphoton_ionization_cross_section, unit ‘s-1 cm4/W2’ as printed: W / I^2, photons = 2, length form), and the one-photon 4e-18 cm2 at 30.0 eV (photoionization_cross_section). Photon energies as printed; the calculation’s threshold is its grid orbital energy, 24.28 eV (two-photon 12.14 eV), not shifted.

• Checked: as sigma_2 = (W / I^2)(hbar omega)^2 (the script’s report) the TDHF values are 1.424e-51 cm4 s at 13.6 eV and 8.04e-52 at 17.7 eV: 1.10 and 0.91 of mihelic_2021 (TC-874, L = 0 + 2), 1.06 and 0.92 of vanderhart_2005 (TC-904), 0.96 and 0.94 of saenz_1999 (TC-873, 1S + 1D), each on its record’s own axis; within the one printed figure. bachau_1990 (TC-905) draws this value as a ‘+’ at 1.0 Ry, where its own line reads 2.81e-16 s^-1 W^-2 cm^4. The one-photon 4 Mb at 30 eV is 0.74 of samson_1994 (TC-85), 5.38 Mb.

• Doubt: the column reading of Table I(a). The text calls the long-wavelength agreement of the two models ‘excellent’; the table’s frozen/TDHF ratios are 1.4 to 2.2. At 9 eV the TDHF decay is not exponential at late times, and how the ‘1s^2’ value was taken there is not stated. The rates at the longest wavelength and highest intensity ‘are expected to be upper bounds’ (the grid lies inside the ponderomotive barrier; 15 % lower at 532 nm, 1e15 W/cm2, on a grid twice as long, p. 2732).

• Not taken: Table I(b)’s PT column (2.5e-16 and 1.1e-16 cm4/W2 s, ‘Refs. 25-27’: Victor 1967, Ritchie 1977, L’Huillier, Jonsson and Wendin 1986, unassigned; 5e-18 cm2, Cooper 1962): other papers’ values. As sigma_2 the PT values are 0.91, 0.88, 0.80 (13.6 eV) and 1.01, 1.01, 1.03 (17.7 eV) of mihelic_2021, vanderhart_2005, saenz_1999. Figs. 1-20 (expectation values, norms, rates against orbital energy, densities): no quantity; their rates are Table I’s.

• Status: verified (2026-10-09).

TC-949 kulander_1988 (Kulander, Phys. Rev. A 38, 778 (1988)): single-active-electron one-, two- and three-photon cross sections and ionisation rates of Xe; Gangopadhyay et al.’s three-photon values in error (2026-10-09)

• Where: src/optmat/data/sources/kulander_1988.toml, tools/extract/ kulander_1988.py (raster figures).

• Transcribed: from the text (inline points, read on the page images, pp. 780-781): the total photoionisation cross section, 46 Mb at 14.4 eV and 29 Mb at 15.63 eV; the two-photon generalised cross section, 4e-50 cm4 s at 193 nm; the three-photon ones, 1e-82 cm6 s2 at 293 nm (an I^3 fit to the rates) and 2.5e-82 at 266 nm. From the figures (p. 781, scanned; no table or vector figure exists): the p shell’s rate (the 5p_0 and 5p_+-1 rates summed) against peak intensity at 293 nm (Fig. 1’s total, 1e13-2e14 W/cm2, eight markers), 586 nm (Fig. 2, 1e13-7.5e13, seven) and 1064 nm (Fig. 2, 2e13-8e13, seven), ionization_rate, linear polarisation, digitised = raster, 5 %. The model: one active electron, the others frozen in a Hartree-Slater potential fitted to 12.13 eV, no spin-orbit (one continuum), length form. Axes as printed; nothing shifted. All use = check.

• Checked: the reading against the text: Fig. 2’s open square (Perry et al.) reads 3.99e11 s^-1 at 1e13 W/cm2 (printed 4e11); the open circle and the 1064 nm open triangle read 4.18e13 and 2.78e13 W/cm2 (printed 4.2e13, 2.8e13); Fig. 1’s dashed I^3 line has slope 2.97 and gives sigma_3 = 1.05e-82 cm6 s2 at 293 nm (printed 1e-82). Internally: Fig. 1’s total is 0.96-1.02 of its 5p_0 plus 5p_1 markers at seven intensities, Fig. 2’s 293 nm squares 0.93-1.03 of Fig. 1’s total at six, every marker within 2 % of a round intensity, the right frame lines at 2.00 and 2.04e14 W/cm2. The decades of the drawing are uneven (264-288 pixels in Fig. 2), so the scale is piecewise between the ticks. Overlays inspected. Kulander’s quotations at 193 nm against the curated originals: lhuillier_1987 (TC-883) HF 1.49e-49 (quoted 1.5e-49), RPAE 2.58e-50 and lhuillier_1987b (TC-916) 2.61e-50 (quoted 2e-50, 0.77 of the curves; no number printed in either), mcguire_1981 (TC-879) 8.36e-50 (quoted 8e-50), gangopadhyay_1986 (TC-914) Fig. 1 5.03e-51 (quoted 5e-51), mccown_1982 (TC-884) 4.12e-50 as alpha hbar omega (quoted 4e-50). Kulander’s own 4e-50 is 0.97 of McCown et al.’s. lagutin_2017 (TC-880) starts at 6.72 eV and has no value at 193 nm. The 2.5e-82 at 266 nm that lhuillier_1989 (TC-882) quotes is this paper’s.

• Finding: Kulander reports (p. 781, citing P. Lambropoulos, private communication) ‘an error in a conversion factor’ in Gangopadhyay et al.’s three-photon calculations, after which ‘they now obtain results which are in good agreement with our result’. gangopadhyay_1986’s Table II (TC-914) holds 2.02e-76 + 3.15e-76 = 5.17e-76 cm6 s2 at 265.7 nm, the 5e-76 quoted here, about 1e6 times this paper’s 2.5e-82 and lhuillier_1989’s 6e-82: Table II’s three-photon values are in error by about six orders of magnitude (no published correction is in the library). Its two-photon Table I and Fig. 1 are not affected by this statement.

• Finding: lhuillier_1989 sets ‘Perry and Landen have measured sigma_3 = 1.2 x 10^-82’ beside its 266 nm values; here 1.2e-82 is Perry et al.’s 293 nm rate (4e11 s^-1 at 1e13 W/cm2, unpublished) converted: a 293 nm value.

• Doubt: the paper: the 293 nm rates above 1e14 W/cm2 come from non-exponential decay (‘probably no more than a factor of 2’), and rates below 1e10 s^-1 suffer from numerical instabilities (586 nm at 1e13, 1064 nm at 2e13). The one-photon values are 0.74 and 0.50 of chan_1992’s (TC-68) measured; the model has no 2P1/2 continuum, and 266 nm lies above that limit.

• Not taken: Fig. 2’s 586 and 1064 nm markers from 1e14 W/cm2 (drawn on top of one another) and its 293 nm squares (the same calculation as Fig. 1’s total); Fig. 1’s 5p_0 and 5p_1 rates (no quantity holds an orbital’s partial rate); Fig. 2’s open symbols (other papers’ saturation intensities turned into rates by this paper’s rule); the 5s cross section (4.5e-20 cm2 at 24 eV, one subshell) and 5s rate bound; the resonance-state decay rates; other papers’ quoted values.

• Status: verified (2026-10-09).

TC-950 crance_1985 (Crance & Aymar, J. Phys. B 18, 3529 (1985)): two-photon detachment of H-, a method reference; no values taken; nikolopoulos_2001’s helium quotation is not in it (2026-10-09)

• Where: src/optmat/data/sources/crance_1985.toml (notes only, no datasets).

• Transcribed: nothing. The paper calculates the one- and two-photon detachment cross sections of H- (a dressed-atom calculation in a complex square-integrable two-electron basis, lowest order in the field; two-photon in s^-1 (W cm^-2)^-2, between the three- and one-photon thresholds, Fig. 2, raster). The material registry holds no anion (‘ion’ is a gas-phase cation, TC-440), so nothing can be recorded. Table 1’s ground-state expectation values (E_g = -0.5273 au against Pekeris’s -0.5277) were checked against the table image and are in the notes.

• Why it is curated: pan_1990b (TC-908, its Ref. 16) and starace_1987 (TC-878, its Ref. 19) cite it among the two-photon calculations, for H-; bachau_1990 (TC-905) does not cite it. Its method (complex basis functions only for the continua that carry a pole) is recorded in the technique.

• Finding: nikolopoulos_2001 (TC-875) quotes ‘Crance and Aymar, J. Phys. B 18, 3529 (1985)’ for two-photon double-ionisation cross sections of helium (2.05, 1.74, 1.73 x 10^-55 cm4 s at 43.5, 45, 46.25 eV), as Nikolopoulos and Lambropoulos’s paper prints the reference. The paper at that reference holds no helium values and no double ionisation; the quoted values’ source is not identified.

• Status: verified (2026-10-09).

TC-951 Correction of TC-934: hummer_1998’s Table 1 threshold cross sections at the calculation’s own thresholds (2026-10-09)

• Where: src/optmat/data/sources/hummer_1998.toml (notes, The thresholds of Table 1; the twelve table1_ datasets), tools/extract/hummer_1998.py.

• The inconsistency: TC-934 placed Table 1’s threshold cross sections (1 1S to 4 1S, 3 1D, 4 1D; This Work and Extrapolated) at NIST’s ionisation energy of each level (nist_asd_2026), in cm-1, while the same record places Fig. 1’s curves with the calculation’s own binding energies from Table 2’s quantum defects. The paper prints no level energies; NIST’s are not the source’s. TC-942 repeats TC-934’s placement. TC-934 stays as written; this entry supersedes its placement of the Table 1 points (approved by the maintainer, 2026-10-09).

• Corrected: the 1S rows, both columns, now stand at the calculation’s threshold, 1/(n - delta)^2 Ryd (R_infinity hc) with Table 2’s This Work quantum defects (0.2549, 0.1478, 0.1419, 0.1401): 1.801237, 0.291490, 0.122418 and 0.067119 Ryd, the abscissa of Fig. 1’s photon energies, so the record uses the source’s own energies throughout. Each point’s printed adds the quantum defect used. The script checks the calculated thresholds against NIST’s: 0.99673 (1 1S), 0.99857 (2 1S), 0.99911 (3 1S), 0.99933 (4 1S), the 0.07-0.33 % TC-934 stated. Table 2 prints no D quantum defects (‘the results for the other symmetries are essentially unchanged’, p. 1075), so the two 1D rows’ threshold is not stated (NIST: 12205.70227 and 6864.21323 cm-1, in the notes only). The Extrapolated values (from Drake’s oscillator strengths, which refer to the true threshold) share the calculation’s point with This Work. The cross sections themselves are unchanged.

• Also corrected: the record’s 2 1S binding energy, written 0.291492 Ryd in its notes, is 0.291490 (1/1.8522^2); the data files always used the exact value.

• Status: corrected (2026-10-09).

TC-952 The two-photon strength of a bound level: one convention, the conversions, and the checks (2026-10-09)

• Where: src/optmat/gas/two_photon_bound.py (sigma0_from_delta, SIGMA0_PER_DELTA), src/optmat/data/gas/two_photon_bound.toml, the manual page Two-photon ionisation and absorption (Bound two-photon excitation); OEP 6, Phase 2a.

• Derived (from the curated papers’ own equations, in SI, golden rule). For coherent light, a line profile g normalised in the two-photon angular frequency, linear polarisation and equal photons:

  • sigma_0^(2) = pi omega^2 |S_zz|^2 / (8 eps0^2 c^2) = 2 pi^3 alpha^2 a0^4 omega_au^2 delta^TP, i.e. 2.58949e-44 m4 times omega_au^2 delta;

  • W = sigma_0 g(2 omega) Phi^2.

  It is identical to drag_2021 Eq. 9, shekhtman_2020 Eq. 8, khambatta_1988 Eq. 1 and pindzola_1981b Eq. 2, whose sums take one photon ordering (S/2). The Rabi frequency Omega_R = (E0^2/4)|S_zz| (a.u.) = sqrt(2 sigma_0/pi) Phi is drag_2021 Eq. 11 and dakka_2018 Eq. 2.

• Decided (the author, 2026-10-09):

  • The canonical strength is delta^TP per level: summed over M_J, equal to |S_zz(M_J = 0)|^2 from J = 0 with linear light. It is for parallel linear polarisation and equal photons, in atomic units, at the source’s own energy.

    • henriksson_2005 and moccia_1984 print it.

    • hattig_1998b, sundholm_1994 and hettema_1992 print one tensor component’s S_xy^2. For a J = 2 level that is a fifth of the level’s (4/15 S^2 against 4/3 S^2; the sum is rotation-invariant). Such a value is converted by 4/3 as a derived value. J = 0 levels are the same in both conventions.

  • Measured cross sections are held as printed, corrected for the photon statistics their source used: kroll_1990 G2(0) = 1.4 assumed; khambatta_1988 2 assumed; drag_2021 1 (single-mode); dakka_2018 1, assumed.

  • Placement: each level’s sigma_0 is evaluated at its NIST photon frequency.

  • The rate constant K of hattig_1998b (Eq. 15 printed with (2 pi)^2; the tables follow (2 pi)^3: a misprint, as TC-887 found), moccia_1984 Eq. 6 and sundholm_1994 Eq. 2 is a two-beam constant. For two beams sigma_12 = K/t0; for one beam with equal photons, sigma_0 = K/(4 t0).

  • TC-929 is decided: pindzola_1981b’s alpha gives sigma_0 = alpha (hbar omega)^2. His G (Eq. 14) is 2 (4 pi s^2)^(-1/2), the chaotic-light line-centre factor of Payne et al.’s Eq. 8, so the factor 2 sits in G and kroll_1990’s “4-13e-35 cm4” is a correct conversion.

• Checked:

  • Xenon: henriksson_2005’s TDDHF per level is 1.30, 0.83 and 0.98 of kroll_1990’s corrected sigma_tot at 6p[1/2]0, 6p[3/2]2 and 6p[5/2]2. It is 1.17 and 1.19 of drag_2021’s at 6p’[3/2]2 and 6p’[1/2]0; that rests on assigning the cluster’s highest TDDHF row of each J to 6p’, other assignments giving 0.17 to 0.60.

  • The convention test: within one experiment calibration and photon statistics cancel. drag_2021’s J = 0/J = 2 ratio is 1.38 (+0.21 -0.18), against 1.41 per level and 7.0 per component. kroll_1990’s 2p6/2p5 and 2p9/2p5 are 0.34 and 0.58, against 0.22 and 0.44 per level and 0.044 and 0.088 per component.

  • Helium: hattig_1998b’s CCSD 1s2s delta of 12.306 is compared with:

    • Drake’s exact A(1/2) = 145 s^-1, through bassi_2000 and A(1/2) = 12.01 delta s^-1: 12.22;

    • kumar_2026’s Rabi coupling: 12.57;

    • kapralova_zdanska_2025’s: 12.09;

    • bassi_2000’s partial closure: 12.81.

    These agree within 1 to 4 %.

  • Krypton: shekhtman_2020 (a per-level calculation) is 94 times khambatta_1988 at 6p[3/2]2. henriksson_2005 is 0.16 of dakka_2018 at 5p[3/2]2, and 0.12 to 0.35 of shekhtman_2020 for J = 0 and 2 alike, so the gap is the method, not the factor 5.

  • Argon: mccann_1988’s printed T2/K2 implies widths 4.5 times smaller than those it states, and it sees J = 1 lines that parallel beams forbid. So its three J = 2 terms are 0.85 or 4.25 of the per-level calculations depending on the reading: they do not decide the convention.

• Doubt: dakka_2018’s Eq. 3 makes its photoionisation cross section twice the usual one or is misprinted (OEP 6 Q7); held as a check. The TDDHF assignments in the Xe 6p’ and 7p cluster are the curators’.

• Status: decided (2026-10-09).

TC-953 OEP 6 Phase 2a: the bound two-photon level records (2026-10-09)

• Where:

  • src/optmat/gas/two_photon_bound.py (two_photon_bound_levels, TwoPhotonBoundLevels, BoundLevel, BoundStrength, BoundPhotoionisation, sigma0_from_delta);

  • src/optmat/gas/_two_photon_bound_derivation.py;

  • src/optmat/data/gas/two_photon_bound.toml;

  • src/optmat/data/gas/models/two_photon_bound/<gas>.json, written by tools/fit/two_photon_bound_record.py;

  • tests/test_two_photon_bound.py, tests/data/golden_models.json;

  • the manual page Two-photon ionisation and absorption.

• Decided:

  • The levels: every even level with J = 0, 1 or 2 below the ionisation energy in data/external/nist_asd/<gas>_I_levels.tsv (term not starred), helium’s singlets only: He 67, Ne 85, Ar 116, Kr 140, Xe 117. J = 1 levels are marked reachable only with unequal photons or another polarisation.

  • The assignments (each with its reason in the selection):

    • henriksson_2005’s TDDHF rows by order within J in their configuration;

    • measured and Racah-labelled values by their printed level;

    • LS-coupled 1S strengths (hattig_1998b Ne, Ar) and J-averaged or LS cross sections (chang_1982, hyman_1977) held unassigned.

  • Assessments: He and Xe checked; Ne, Ar and Kr unresolved (TC-952).

  • No evaluator (TC-945).

• Checked:

  • the records against a fresh derivation;

  • the convention constant against scipy’s CODATA alpha and a0;

  • Xe 6p[1/2]0’s 249.63 nm;

  • the xenon, krypton and helium numbers of TC-952;

  • SI conversion of the photoionisation cross sections;

  • every refusal;

  • golden digests;

  • the full gate, poe test-library and poe test-release.

• Status: decided (2026-10-09).

TC-954 Vocabulary and materials for strong-field dissociation data (2026-10-09)

• Where:

  • src/optmat/vocabulary.py (QUANTITIES) and the data page’s quantities table (docs/data.md).

  • src/optmat/data/materials.toml.

• Decision (the maintainer, 2026-10-09, before any data of these kinds; data rule 7):

  • No OEP for the quantities. Quantities for the dissociation of molecules in and after an intense pulse are added before an OEP, as for the two-photon data (TC-872). A model built on them needs its own OEP.

  • Scope boundary. optmat is to give the products a pulse leaves in each molecule. The plasma kinetics that follows stays outside optmat, and its rate data are curated as data only.

• The quantities:

  • In the ionisation family:

    • dissociation_energy: a dissociation limit of a neutral or an ion. It states the products and the kind: D0, De, or a threshold measured from a stated reference state, e.g. a dication’s limit above the neutral.

    • ionic_state_population: the population of an electronic state of the molecular ion after a pulse, as a fraction of the ions or of the molecules. For measured state populations such as N2+ X/A/B, and for the density-matrix calculations.

    • fragmentation_branching_ratio: one channel’s yield over a stated reference (the parent ion, all ions, or another channel), under photoionisation or a strong-field pulse.

    • kinetic_energy_release: the energy released into a channel’s fragments.

    • dissociation_time: a lifetime or appearance time, with its pressure when it is collisional.

    • dissociative_recombination_rate_coefficient: k for e + AB+ -> A + B, as a value at the abscissa’s electron temperature, or as a printed power law in (T_ref/T_e).

  • In the absorption family:

    • photodissociation_quantum_yield: per absorbed photon, against wavelength.

    • transition_dipole_moment: between two electronic states, at a stated geometry.

• What existing quantities hold, rather than bent ones:

  • ionization_energy with final_state: the vertical ionisation energies of individual ionic states.

  • tunnelling_structure_coefficient: the structure coefficients of inner orbitals.

  • appearance_energy: the appearance energies of fragment ions.

  • absorption_cross_section: one-photon absorption.

  • ionization_yield_ratio: the yield ratio of a molecule’s ions to a companion gas’s ions. A ratio between a molecule’s own fragmentation channels is fragmentation_branching_ratio, not this.

• Materials registered by reference only (no models; as atomic hydrogen):

  • the gases NO2, N2O5 and NO;

  • the ions NO2+ and NO+;

  • the dications N2++ and O2++, for the transition dipoles between dication states. A dication channel’s kinetic energy release stays with the neutral molecule the pulse ionises, with the dication state named in its channel.

• Status: decided (2026-10-09).

TC-955 yuen_2022 (Yuen & Lin, Phys. Rev. A 106, 023120 (2022)): N2^2+ vertical energies and KER of the density-matrix SDI model; the N2+ couplings (2026-10-09)

• Where: src/optmat/data/sources/yuen_2022.toml, tools/extract/yuen_2022.py (Table I, PDF p. 5 of the accepted manuscript; text pp. 3-4).

• Transcribed:

  • Table I (every cell checked against the table image; read from the library’s cells, the table has no CSV):

    • the vertical I_p of N2 to the eleven N2^2+ states with two valence holes, 42.7 to 57.4 eV, at R = 1.09 angstrom, reproduced from Bhattacharya et al. 2021 (ionization_energy, kind vertical, the dication state per row; material N2);

    • the KER of the dissociating states, kinetic_energy_release kind calculated: states 5-9 to N+(3P) + N+(3P) (5 rows) and states 10-11 to N+(1D) + N+(1D) (2 rows). States 1-4 are metastable.

  • Text, as points:

    • the I_p used for N2 to X, A and B, 15.58, 16.93 and 18.75 eV (p. 4; no reference, kind not stated);

    • the N2+ transition dipoles X-A d_x = 0.25 a0 and X-B d_z = 0.75 a0 (p. 3), reproduced from Langhoff et al. 1987 and 1988 (transition_dipole_moment, material N2+).

  • All theory, no uncertainty stated; use = check or reproduced.

• Checked:

  • I_p - KER is 38.96 eV for all five 3P + 3P rows and 42.76 eV for both 1D + 1D rows (the script raises otherwise). The limits are only named in the table, so these implied limits above the neutral are the only dissociation energies, and no dissociation_energy dataset is made.

  • The text’s 29.49 and 27.67 eV (state 6 from A and from B) are 46.42 - 16.93 and 46.42 - 18.75.

  • The dipoles against jia_2024’s Table III from the same references: about 0.265 and 0.74 au at 2.06 a0 (interpolated). The X-A value 0.25 is 6 % lower; the X-B value agrees.

• Doubt:

  • State 10 is printed ‘m.s. / N+(1D) + N+(1D)’ with a KER. It is filed with the 1D + 1D limit.

  • 15.58 and 18.75 eV are not the vertical values zhao_2010 prints for these orbitals (15.6, 17.2, 18.7). The paper does not say which kind it used.

  • The KER are filed under N2, with the dication state in the channel (the convention of TC-954).

• Not taken:

  • The structure parameters: the paper uses zhao_2010’s.

  • The figures, not digitised (vector except Fig. 1). Worth digitising later:

    • Fig. 2 bottom: angle-averaged yields of the dissociative states 5-11 with and without the cation couplings, 800 nm, 8 fs, 1.2e15 W/cm^2.

    • Fig. 5: the yields of states 1-9 against peak intensity.

    • Fig. 3: the X, A, B populations against time.

• Status: open (the figures).

TC-956 yuen_2023 (Yuen et al., Phys. Rev. A 107, 013112 (2023)): O2 in the density-matrix SDI model; structure coefficients that are not zhao_2010’s (2026-10-09)

• Where: src/optmat/data/sources/yuen_2023.toml, tools/extract/yuen_2023.py (Tables I-III, pp. 2-3; text pp. 4-5 and footnote 41, p. 10).

• Transcribed (every cell checked against the table images; the CSV loses the Pi of the Table I state labels, and the rows are named from the image):

  • Table I: O2 to O2+ X, a, b, the experimental vertical I_p 12.3, 16.7, 18.2 eV, reproduced from Baltzer et al. 1992 (ionization_energy). Also the C_lm of the HOMO, HOMO-1 and HOMO-2 of O2 (three tunnelling_structure_coefficient datasets, moadk, m = 1, 1, 0).

  • Table II: the calculated vertical I_p of O2 to eight O2^2+ states, 37.19 to 45.42 eV, from the zero-point level, shifted as a whole to put B 3Pi_g at 43.46 eV. Also their KER, calculated: four states to O+(4S) + O+(2D) and three to O+(4S) + O+(4S).

  • Table III: for O2+ X, the effective binding energies of the spin-up 1pi_g, 1pi_u and 3sigma_g orbitals, 24.88, 30.60 and 32.86 eV (ionization_model_parameter, E_b: multiplicity-weighted model inputs, as guo_1998’s effective I_p). Also their C_lm (material O2+).

  • Text, as points:

    • the O2+ a-b dipole, 0.29 au along x;

    • the quintet I_p, 45.5 and 46.9 eV, and their KER, 13.2 and 11.2 eV;

    • footnote 41: E_b 26.2 and 25.3 eV and C_lm of the 1pi_g of O2+ a and b.

  • Table IV (p. 4): the calculated transition dipoles between O2^2+ states at R = 1.21 angstrom, 4 rows: W 3Delta_u, B 3Sigma_u- and A 3Sigma_u+ to B 3Pi_g, 0.318, 0.123 and 0.234 au; 1 1Sigma_u- to 1 1Pi_g, 0.126 au. All are printed along x (perpendicular). transition_dipole_moment, material O2++ (registered in TC-954), use = check. The CSV loses the Greek letters of the labels, so the script names the pairs from the image. The W-B value is ‘double counted since both states are doubly degenerate’ (caption): it is the model’s coupling, not one component.

• Checked:

  • I_p - KER is 35.68 eV for every 4S + 2D row and 32.35 eV for every 4S + 4S row (the script raises otherwise). The caption says KER = I_p - limit, and the quintet KER follow from the same limits.

  • Table I’s I_p equal zhao_2010’s table4_expt_O2 (both from Baltzer et al.). They are a copy and are not to be fitted beside it.

• Finding: Table I’s C_lm are captioned with ref. 37 (Zhao et al. 2010) but are not zhao_2010’s printed values:

  Orbital	Table I	zhao_2010	zhao_2017
  HOMO 1pi_g	{0.69, 0.06}	{0.52, 0.03}	{0.64, 0.04}
  HOMO-1 1pi_u	{1.86, 0.36, 0.02}	{2.04, 0.33, 0.01}
  HOMO-2 3sigma_g	{3.49, 2.06, 0.25}	{3.05, 1.59, 0.08}

  The ratios differ by orbital and by l, so this is not a change of normalisation. They seem to be a new calculation by Zhao’s method (S.-F. Zhao is a co-author), at R = 1.21 angstrom against zhao_2010’s 1.208. Kept as this paper’s (use = check).

• Doubt:

  • Fig. 1’s caption: states 2 and 4-7 reach Table II’s limits only through spin-orbit coupling.

  • Table II’s absolute energies rest on the one shift. Only its spacings are the CASPT2’s.

  • The quintet energies’ shift is not stated.

• Figures for later (all vector): Fig. 3 (the O2^2+ state populations left by 800 nm, 8 fs, 1.2e15 W/cm^2), Fig. 9 (the yields of states 0-3 and 6 against intensity), Fig. 7 (the yields at 564 and 1675 nm).

• Status: open (the figures).

TC-957 jia_2024 (Jia et al., Phys. Rev. A 110, 023112 (2024)): N2 SDI against bond length; N2^2+ energies, LB-alpha structure coefficients, N2+ dipoles (2026-10-09)

• Where: src/optmat/data/sources/jia_2024.toml, tools/extract/jia_2024.py (Tables I-III, PDF pp. 4-5 of the accepted manuscript).

• Transcribed (every cell checked against the table images; Tables I and II read from the library’s cells):

  • Table I: the vertical I_p of N2 to the eleven N2^2+ states at R = 1.00, 1.05, 1.10, 1.15 and 1.20 angstrom (55 values), reproduced from Pandey et al. 2014. One dataset with the column internuclear_distance.

  • Table II, per orbital (3sigma_g, 1pi_u, 2sigma_u) and R:

    • the LB-alpha binding energy (kind not stated, check);

    • the CASSCF+MRCI ionisation energy, reproduced from Bhattacharya et al. 2021 (vertical);

    • the C_l, as 15 tunnelling_structure_coefficient datasets, one per orbital and R (the C_l reader takes rows l at one geometry);

    • alpha stays in the printed cells.

  • Table III: the N2+ X-A (x) and X-B (z) transition dipoles at R = 1.80-2.40 a0, reproduced from Langhoff et al. 1987 and 1988. Two datasets, R as the row and as the column internuclear_distance (bohr).

  • Table IV (p. 6): this paper’s transition dipoles between N2^2+ states (Table I’s indices) at R = 1.00-1.20 angstrom, 10 pairs x 5 R. Material N2++ (registered in TC-954), use = check. One dataset per pair, as Table III, with R in the column internuclear_distance (angstrom). The pairs: d(1-4), d(2-5), d(3-6), d(4-7), d(4-8) and d(9-10) along x; d(1-10), d(2-6), d(4-9) and d(8-10) along z.

• Checked:

  • Against yuen_2022 (Bhattacharya et al., R = 1.09 angstrom), Table I at 1.10 angstrom is 0.13 to 0.21 eV lower for states 1-10 and 0.85 eV lower for state 11.

  • Table IV: each pair’s axis is the same at every R (checked by the script), and it is the one the states’ symmetries allow: Sigma-Pi and Pi-Delta along x; Sigma_g-Sigma_u and Pi_g-Pi_u along z.

  • The text’s KER peaks at 1.10 angstrom are Table I’s I_p less yuen_2022’s implied 3P + 3P limit, 38.96 eV: 6.54 eV (state 5) and 10.03 eV (state 9).

• Finding: at R = 1.10 angstrom the C_l differ from zhao_2010’s (LDA + LB) and zhao_2017’s (LB-alpha, alpha = 1.12), both at 1.098 angstrom, with the same convention:

  Orbital	Table II	zhao_2010	zhao_2017
  3sigma_g	{2.99, 1.48, 0.12}	{2.68, 1.10, 0.06}	{3.39, 1.40, 0.05}
  1pi_u	{2.15, 0.37, 0.00}	{1.89, 0.22, 0.01}
  2sigma_u	{4.22, 0.55, 0.04}	{3.72, 0.34, 0.01}

  • alpha is set anew at each R (1.15, 1.08, 1.13, 1.14, 1.11), and the C_l and LB-alpha energies are not smooth in R (3sigma_g C_0m 3.11, 3.25, 2.99, 2.56, 2.89).

  • Use the R dependence with care: the C_l change by up to 15 % between neighbouring R.

• Doubt: in Table IV, d(4-9) falls from 0.787 au at 1.15 angstrom to 0.530 at 1.20. Its other steps are at most 0.03, so this may be a state crossing or a misprint. The paper does not comment, and the value is kept as printed. d(8-10) falls steeply over the whole range (0.832 to 0.263).

• Figures for later (vector, except Fig. 1):

  • Fig. 2: the alignment-averaged yields of the dissociative states, with and without the dication couplings, 800 nm, 8 fs, 1.2e15 W/cm^2.

  • Fig. 3: the N2^2+ populations against time.

  • Fig. 4: the R-averaged KER spectra.

• Status: open (the figures).

TC-958 kleine_2022 (Kleine et al., Phys. Rev. Lett. 129, 123002 (2022)): N2+ X, A and B populations after an 800 nm pulse, and the collisional N + N+ appearance time (2026-10-09)

• Where: src/optmat/data/sources/kleine_2022.toml.

• Transcribed: from the text (p. 4), ionic_state_population of N2 (abscissa none, normalisation ions): X 2Sigma_g+ 0.47 +- 0.02, A 2Pi_u 0.07 +- 0.01, B 2Sigma_u+ 0.46 +- 0.07, the fractions of the N2+ ions in X, A and B together after the pulse (Eq. 1, normalised over delays 160-300 fs); 800 nm, 4.5 x 10^14 W cm^-2; level not stated. dissociation_time of N2+ -> N + N+ (kind appearance, pp. 4-5): 19.8 +- 1.5 ps at 4 bar backing pressure (abscissa pressure), use primary; the authors’ Eq. (2) estimate, ~28 ps (kind calculated, use check).

• Checked: every number against the rendered pdf text (pp. 2, 4, 5); the three populations sum to 1.00.

• Doubt:

  • The pump’s duration and polarisation are not in the Letter (only in its Supplemental Material, not held): pulse_fs and polarization are “not stated”; the alignment model implies linear polarisation.

  • The populations rest on relative oscillator strengths 0.8 : 1.0 : 0.15 (X : A : B) from x-ray emission (Glans et al. 1996); B’s weak line is scaled by 1/0.15.

  • The 19.8 ps is collisional (dissociative excitation by plasma electrons, as the authors assign it) and falls as 1/p with backing pressure (Fig. 4(d)); the pressure in the focus is not stated. Not a prompt optical dissociation time.

  • The estimate’s definition, tau = 1/(k ln 2), is kept as printed.

• Not taken: the ionised fraction. The 401 eV bleach is ~61 +- 4 % of the N2 absorbance (p. 2), and the rate estimate assumes 60 % ionisation; neither is a focal-volume probability that ionization_yield holds (which also needs a numeric pulse length).

• Open: figures for later digitising (vector, pdf pp. 3-4): Fig. 3(b), the X, A, B populations against delay; Fig. 4(d), the dissociation time against backing pressure with its 1/p fit; Fig. 4(c), the N and N+ rise to 80 ps. The Supplemental Material is needed for the pulse duration.

• Status: open (2026-10-09): the pulse duration.

TC-959 wu_2006 (Wu et al., Phys. Rev. A 73, 051402(R) (2006)): KERs of the N2 3+ and O2 3+ (2,1) channels at 800 nm, 60 fs (2026-10-09)

• Where: src/optmat/data/sources/wu_2006.toml.

• Transcribed: from the text, kinetic_energy_release (kind peak, 800 nm, 60 fs, linear): N2 3+ -> N2+ + N+, 15.0 eV (p. 2), use primary; O2 3+ -> O2+ + O+, 13.8 eV (p. 3), use check. Filed under N2 and O2, the irradiated gases, since N2 3+ and O2 3+ are not registered materials. No uncertainty stated. The intensities quoted in the text (2.8 and 4.0 x 10^14 W/cm^2, positions on Figs. 2-4; calibration not described) are in the notes.

• Checked: against the rendered pdf text (pp. 2-3).

• Doubt: the O2 value is followed by a citation of Normand et al. 1991 (not in the library), so it may be that paper’s.

• Not taken, no quantity: the thresholds 11.14 and 11.43 eV of N2+(4P) + N+(1S) and N2+(2Po) + N+(3Do) above the ground limit N2+(2Po) + N+(3P), and 35.12 eV of O(2,1) above O(1,1): measured from another limit, not from a species’ ground state, as dissociation_energy (kind threshold) requires. The “ionization potentials” 46.6 (N+ + N+) and 40.1 eV (O+ + O+) above the neutral include the measured KER, so they are not dissociation limits.

• Open: Fig. 4 (raster), the ratio curves N(2,1)/N(1,1) and O(2,1)/O(1,1) against intensity, fragmentation_branching_ratio (reference: another channel), to digitise; Figs. 2-3 (raster), the channel yields against intensity.

• Status: open (2026-10-09): Fig. 4.

TC-960 song_2010 (Song et al., J. Phys. Chem. A 114, 3087 (2010)): neutral dissociation of superexcited O2, predissociation and depletion times (2026-10-09)

• Where: src/optmat/data/sources/song_2010.toml (library folder dated 2009, the online date; the id takes the journal year).

• Transcribed: from the text, dissociation_time of O2 (all use check, no uncertainty): the 777.5 nm fluorescence depletion ‘lasts for 150 fs’, the ‘measured lifetime of 150 fs for the intermediate’ (kind lifetime, p. 3094; 800 nm, 42 fs, about 2 x 10^14 W/cm^2, probe 1338 nm); quasi-classical trajectories, about 100 fs to the crossing of the predissociating curve and about 600 fs for a direct dissociation (kind calculated, p. 3093).

• Checked: against the rendered pdf text (pp. 3088-3094).

• Doubt: the 150 fs is the width of a depletion curve, not a fitted constant; the fluorescence counts excited O atoms only, not a calibrated yield.

• Not taken, no quantity: the photon-order slopes 8.9, 11.1 and 11.3 of the 615.9, 777.5 and 845.0 nm lines against intensity (p. 3089), an intensity exponent. Table 1 (tbl_70f4477290cb, tbl_a2059a5c3c11), a mapping of excitation bands to superexcited states, products O(3P) + O* and atomic O emission lines: an assignment, with O not a registered material; quoted in the notes.

• Open: Fig. 4(a) (raster), fluorescence against intensity; Fig. 8(b) (raster), the depletion against delay.

• Status: decided (2026-10-09).

TC-961 talebpour_1996 (Talebpour et al., J. Phys. B 29, L677 (1996)): O2+ suppression attributed to dissociative recombination; recorded as a claim only (2026-10-09)

• Where: src/optmat/data/sources/talebpour_1996.toml (no datasets).

• Transcribed: nothing. The one measured number, the O2+ appearance intensity 1.3 x 10^13 W cm^-2 at 800 nm, 220 fs (p. L679), is defined by the apparatus’s detection limit and has no quantity; the 5.0 eV release of O2+ + e -> O(3P) + O(1D) is quoted from Bates 1994 (not in the library).

• Finding: the proposed mechanism (recollision-driven dissociative recombination) is contradicted by guo_1998, which finds the same O2+ suppression relative to Xe+ with circular polarisation, where recollision is suppressed; talebpour_1999 (same group) models the suppression with an effective charge instead. optmat takes no rate or yield from this Letter.

• Open: Fig. 1 (raster): O2+, O+ and Xe+ yields against intensity.

• Status: decided (2026-10-09).

TC-962 de_2011 (De et al., Phys. Rev. A 84, 043410 (2011)): calculated KERs of O2+ a 4Pi_u by one-photon promotion; few-cycle pump-probe of N2, O2, CO (2026-10-09)

• Where: src/optmat/data/sources/de_2011.toml, tools/extract/de_2011.py.

• Transcribed: Table II (p. 6, tbl_a5247d8a13ea), the O2+ a 4Pi_u block, v = 0-15: kinetic_energy_release of O2+ (kind calculated, label v), the KER of O+ + O after one 800 nm photon, from Marian et al.’s levels (ref. 38); rows v = 0-10 are negative (below the limit) and excluded; use check. From the text (p. 3), the asymptotic KER of 1 eV of dissociating O2+ -> O+ + O, the adjustable parameter of the authors’ Coulomb model (use check).

• Checked: the table against its image; the script checks every KER step v -> v + 1 against h times the mean of the two printed beat frequencies (largest misfit 0.9 meV, tolerance 1.5 meV). Against h nu_v alone the steps are 0.9-2.4 meV short: the printed frequency of row v is not exactly the v -> v + 1 spacing.

• Not taken: the CO+ and CO++ blocks (materials not registered); Table I’s spectroscopic constants (omega_0, x; reproduced from Langhoff 1987, Dawber 1994, Huber-Herzberg, Wannberg 1988, Lundqvist 1995; no quantity); the dication KERs of 7.5 eV, quoted from Voss et al. 2004 (not in the library).

• Open: none for digitising: the results are KER-delay density maps; Fig. 5(b) (raster), the low-KER O+ spectrum, is the only curve.

• Status: verified (2026-10-09).

TC-963 bocharova_2011 (Bocharova et al., Phys. Rev. A 83, 013417 (2011)): Coulomb-explosion imaging of N2, O2 and CO; the O2 2+ asymptotic KER (2026-10-09)

• Where: src/optmat/data/sources/bocharova_2011.toml.

• Transcribed: from the text (pp. 10-11), kinetic_energy_release of O2 2+ -> O+

  • O+, about 11 eV, the asymptote of the (2,2) KER-delay trace, assigned to bound-then- dissociating O2 2+ states (kind asymptotic, use check; 800 nm, 8 fs pump at 8 x 10^14 W/cm^2). Filed under O2, since O2 2+ is not a registered material.

• Checked: against the rendered pdf text.

• Not taken: the other energies are trace readings at stated delays, not channel KERs (O2+ 5-7 eV, a range; the zero-delay starts for N2 of 25, 45 and 65 eV; the (3,1) traces 36 -> 17 eV in N2 and 40 -> 18 eV in O2, which vanish after 20 fs). No asymptotic energy is printed for N2.

• Open: none for digitising (all results are density maps).

• Status: decided (2026-10-09).

TC-964 alnaser_2005 (Alnaser et al., Phys. Rev. A 72, 041402(R) (2005)): resonant production of O2 2+ B 3Pi_g; context only (2026-10-09)

• Where: src/optmat/data/sources/alnaser_2005.toml (no datasets).

• Transcribed: nothing: no KER or ratio is printed in the text. The band assignment is from Voss et al. 2004 (not in the library); the B 3Pi_g band is the integration window 10.5-12.7 eV of Fig. 2’s axis label. The finding: the B 3Pi_g / all ratio of O2 2+ -> O+ + O+ peaks at a photon energy of 1.4 eV (about 890 nm).

• Doubt: the intensities differ between wavelengths (1.0-2.8 x 10^14 W/cm^2), with no calibration described.

• Open: Fig. 2, lower panel (raster): the ratio against photon energy at eight wavelengths with error bars, a fragmentation_branching_ratio to digitise.

• Status: open (2026-10-09): Fig. 2.

TC-965 berkowitz_1977 (Berkowitz & Eland, J. Chem. Phys. 67, 2740 (1977)): fragment appearance energies and branching ratios of N2O photoionisation; extends TC-503 (2026-10-09)

• Where: src/optmat/data/sources/berkowitz_1977.toml, tools/extract/ berkowitz_1977.py (Tables IV and VII, CSV); the ionisation energies of TC-503 are unchanged.

• Transcribed:

  • Table IV (p. 2745): O+ and NO+ (‘15NO+ + 14NO+’) per N2O+ = 100 at ~798.3, ~792 and ~782 angstrom (A-state autoionisation), two datasets of 3 rows, scale 0.01, primary.

  • Table VII (p. 2748): the rows without an asterisk (ion intensities at 600, 660 and 668.3 A), NO+, N2+, O+ (3 rows each) and N+ (600 A only), primary; the rows with an asterisk (resonance amplitudes, ‘peak heights or step heights’, footnote a) at 5 C-state Rydberg resonances, NO+ and N2+ (5 rows) and O+ (4), use = check. Every row on N2O+ = 100; quantity fragmentation_branching_ratio, material N2O, photoionisation at the abscissa’s vacuum wavelength.

  • Text: appearance energies of NO+ (14.77 eV first seen, 14.97 eV threshold, pp. 2742-2743) and N+ (20.075 eV, p. 2748); O+/NO+ ‘essentially constant value of 3 below 780 A’ (p. 2745, check); the 4A’’ survival time ~3e-7 s (dissociation_time, check; a deduction, not a measured decay).

  • No uncertainty is stated for any of them.

• Not taken: Table VII’s three rows with a dash for N2O+ (B 2Pi 705-685 and 685-640 A, C 2Sigma+ 618 A), which have no stated reference; the 15NO+/14NO+ column (a ratio within 14N15NO); Table VIII’s branching of the C-state Rydbergs to the ionic states X, A, B and 4A’’ (no quantity holds a resonance’s branching to ionic states); the O+ threshold ‘~813 A’ (no energy printed). All are in the record’s notes, with the paper’s state-to-fragment assignments (4A’’ to NO+ + N below 15.25 eV and O+ + N2 above; A (100) to NO+ + N only; B to NO+ + N(2D) and N2+ + O(3P); C to all four).

• Checked: both tables cell by cell against their images (agree; the 666.7 A row’s ‘nso’ is ns sigma on the page). The C-state ratio of the text against the page image at 2.5x.

• Finding: the text (p. 2749) gives the C-state branching ‘to NO+, N+, N2+, and O+ as ~5.7:2.0:2.1:0.2’, and Table VII’s C row prints NO+ 57*, N2+ 20*, N+ 21*, O+ 2.2*: N+ and N2+ are exchanged between them. Which is right cannot be told from the paper; the row is not taken.

• Doubt: Table IV’s O+/NO+ is 2.5, 1.9 and 4.4 at 798.3, 792 and 782 A, while the text gives a ratio that ‘rises fairly smoothly’ to a constant 3 below 780 A. Table IV’s NO+ is labelled ‘15NO+ + 14NO+’, probably measured on 14N15NO with the other apparatus (0.7 A); not stated. No detector-efficiency correction is described.

• Status: verified (2026-10-09).

TC-966 kubel_2014 (Kübel et al., New J. Phys. 16, 065017 (2014)): the denitrogenation/deoxygenation ratio of N2O2+ and its KERs, 4 fs, 750 nm (2026-10-09)

• Where: src/optmat/data/sources/kubel_2014.toml (text values only).

• Transcribed (p. 9, p. 10; all text, no uncertainty printed):

  • coincident N+ + NO+ over O+ + N2+: 6.2 ‘for the conditions of our experiment’ and 6.7 ‘at about twice the intensity’ (linear), 13 (circular, intensity not stated), primary;

  • the non-coincident N-N over N-O bond breaking, 3.5, ‘likely dominated by the dissociation of the N2O cation’, check;

  • KERs: denitrogenation 6.8 eV (3Sigma-), deoxygenation peak 5.8 eV (3Sigma-) and shoulder 7.2 eV (3Pi), linear, 1.5e14 W/cm2 (Fig. 5).

• Checked: every number against the PDF’s text layer (pdf pp. 10-11 = pp. 9-10): all agree.

• Doubt: the only experimental intensity printed is Fig. 5’s 1.5e14 W/cm2, with no calibration; the 6.2 is assigned to it by our reading of ‘the conditions of our experiment’. The 3.0e14 W/cm2 of p. 7 is a model parameter. How the non-coincident fragments were summed for the 3.5 is not stated.

• Not taken: Table 1 (CEP asymmetry amplitudes and phases; no quantity, and not relevant to phase-averaged products); the KERs expected from Taylor et al.’s (2006) potentials and the dication limits of Fig. 1 (reproduced); the metastable lifetime ‘a few 100 ns’ (no number).

• Open: figures for later, all vector: Fig. 5(a) (KER spectra of both channels), Fig. 4 (kinetic energy spectra of the four fragments, the low-energy parts from the cation’s dissociation), Fig. 7(a) (angular distributions).

• Status: verified (2026-10-09).

TC-967 zhu_2006 (Zhu et al., Chin. Sci. Bull. 51, 1185 (2006)): NO2+/NO+ of NO2 at 810 and 405 nm from the text; Fig. 3 for later (2026-10-09)

• Where: src/optmat/data/sources/zhu_2006.toml (text values only).

• Transcribed: NO2+ over NO+ ‘about three times’ at 810 nm (~60 fs), and NO+ over NO2+ ‘about threefold’ at 405 nm (pp. 1186-1187), each one point, material NO2, use = check, no uncertainty; the ratio is stated to be independent of intensity over the estimated ranges 1.12-2.48e15 (810 nm) and 1.43-3.86e15 W/cm2 (405 nm). The 270 nm ratio is ‘almost equal’ (no number; not taken).

• Checked: the quoted sentences, intensity ranges and both polarisation statements against the PDF’s text layer (pp. 1186-1189): all agree.

• Not taken: the log-log slopes (810 nm: NO2+ 5.0, NO+ 4.8, N+ and O+ about 11; 405 nm: 3.5, 3.2; 270 nm: 1), in notes; the quoted ionisation and appearance potentials.

• Doubt: the intensities are ‘estimated’, with no method or uncertainty; the 405 and 270 nm pulse durations are not stated. The polarisation is ‘perpendicular to the detector’ on p. 1186 and ‘parallel to the time of flight axis’ on p. 1189.

• Open: figures for later, raster: Fig. 3 (NO2+/NO+ against the Keldysh parameter at the three wavelengths, the paper’s main result) and Fig. 2 (ion yields against intensity).

• Status: verified (2026-10-09).

TC-968 singhal_1998 (Singhal et al., Chem. Phys. Lett. 292, 643 (1998)): identity established; context only, NO2+/NO+ in figures (2026-10-09)

• Where: src/optmat/data/sources/singhal_1998.toml (no datasets); library key Unverified_30706154dbb1.

• Checked: the identity, on pdf page 1: title, nine authors, Chem. Phys. Lett. 292 (1998) 643-646, and ‘PII: S0009-2614(98)00718-0’, the suffix of the DOI 10.1016/S0009-2614(98)00718-0. Recorded VALIDATED_WITH_WARNINGS: the library’s own metadata remain unverified and should be corrected there.

• Decision: nothing taken. The NO2+/NO+ ratios (Fig. 1 against intensity at 750 and 375 nm, 90 fs; Fig. 2 against pulse duration at 750 nm) are raster figures. The text’s ‘about 10 times larger’ parent-ion yield at 750 than 375 nm does not say whether it is the ratio or the yield; the slopes (3.0-3.5 at 750 nm, 2.2-2.9 at 375 nm) fit no quantity. The intensity is ‘up to 2.3 x 10^14’ in the abstract and ‘up to 2.5 x 10^14 W cm^-2’ in the text.

• Open: figures for later, raster: Figs. 1 and 2. The commented paper, Vijayalakshmi et al., Chem. Phys. Lett. 270, 37 (1997), is not in the library.

• Status: decided (2026-10-09).

TC-969 wang_2019 (Wang et al., Chin. Phys. B 28, 053301 (2019)): context only; appearance intensities of N2O’s multiply charged fragments have no quantity (2026-10-09)

• Where: src/optmat/data/sources/wang_2019.toml (no datasets).

• Decision: nothing taken; every yield is in a vector figure (Figs. 1-5, 800 nm, 50 fs, 2e13-3.6e14 W/cm2, calibration not stated). The text’s numbers are in the notes:

  • the intensities at which O^2+ and N^2+ (7.0e13 W/cm2) and N^3+ (1.2e14 W/cm2) first appear: no quantity holds an appearance intensity (reported);

  • the CP/LP ratio of each singly charged fragment’s ratio to N2O+, ‘about 15%-25%’ at 1.4e14 W/cm2: a ratio of two branching ratios, neither printed;

  • the N2O2+ metastable lifetime 660 +- 70 ns, quoted from their Ref. 32 (not in the library).

• Checked: the quoted intensities, the 15%-25% and the 660 +- 70 ns against the PDF’s text layer (pp. 053301-2 and -3): all agree.

• Open: figures for later, vector: Fig. 1 (yields of N2O+ and the fragments against intensity, linear) and Fig. 3 (fragment/N2O+ against ellipticity).

• Status: decided (2026-10-09).

TC-970 zhao_2020 (Zhao et al., Phys. Rev. A 101, 013416 (2020)): context only; the KERs are of the probe’s three-body Coulomb explosion (2026-10-09)

• Where: src/optmat/data/sources/zhao_2020.toml (no datasets).

• Decision: nothing taken. Every KER printed is of N2O3+ -> N+ + N+ + O+ made by the probe (bands 1.5-7, 7-16 and 17-25 eV; fragment energies of 0.5-5 eV), which images the geometry at the delay and is not the energy a dissociation releases. No time constant is fitted. The lifetimes of N2O+ A (tens to hundreds of ns), B (30 fs) and C (~2 ps) are quoted from other papers (not in the library). The assignments (N2O+ B 2Pi bends and dissociates; the dication’s two-body and three-body channels) are in the notes.

• Open: figure for later: Fig. 2(a), KER against delay (raster map), if a time constant for the B 2Pi dissociation is wanted.

• Status: decided (2026-10-09).

TC-971 zhao_2023 (Zhao et al., Commun. Phys. 6, 124 (2023)): KERs of N2O+ B 2Pi -> NO+ + N and N2+ + O, and their ~1 ps completion (2026-10-09)

• Where: src/optmat/data/sources/zhao_2023.toml (text values only).

• Transcribed (pp. 3-4): the asymptotes at 6 ps of the delay-dependent probe KER, 0.6 eV (NO+ + N+) and 0.4 eV (N2+ + O+), primary, taken by the paper as the KER of the B 2Pi dissociation; the simulated 1.1 and 0.5 eV (check); the completion ‘at around 1 ps’ for both channels (dissociation_time, check). Pump 800 nm, ~35 fs, linear, 1.0e14 W/cm2. No uncertainty is printed.

• Checked: the numbers against the PDF’s text layer (pp. 3, 4, 6): all agree.

• Doubt: the asymptotes still contain the Coulomb energy 1/R at the probe (0.19 eV at the R = 140 a.u. the paper gives for 1500 fs; R at 6 ps not stated), so they are upper bounds to the dissociation’s KER. The experiment-theory difference (0.6 against 1.1 eV) is ascribed to the fragments’ internal energy, neglected in the simulation. The supplement (rise times of the channels) is not in the library.

• Open: figure for later: Fig. 3(a, c), measured KER against delay (raster maps).

• Status: verified (2026-10-09).

TC-972 el_helou_2005 (El Helou et al., J. Chem. Phys. 122, 244311 (2005)): O3 absolute cross sections in the Chappuis and Wulf bands from 293 to 144 K; agreement with optmat’s O3 spectrum (2026-10-09)

• Where: src/optmat/data/sources/el_helou_2005.toml, tools/extract/ el_helou_2005.py (Tables I-VIII, cells only, pp. 4-9).

• Transcribed: absorption_cross_section of O3 in 10^-23 cm^2 (scale), abscissa FTS wavenumber in cm^-1 (vacuum), the bracketed uncertainty as sigma, level not stated, parameters.temperature_k per dataset:

  • Chappuis band at the five He-Ne lines (15798.01-18393.61 cm^-1 = 632.99-543.67 nm), 5 rows each: the LASIM cell at 293, 223, 175 and 144 K and the Reims cell at 291 and 225 K (use primary); Anderson & Mauersberger 1992 (+-1 SD), Orphal 2003 (a review average) and Brion et al.’s monochromator values (= brion_1998/present) as reproduced datasets.

  • Wulf bands, eight band maxima 9553.23-13356.11 cm^-1 (1046.8-748.7 nm): the LASIM cell at 294, 222 and 150 K (8 rows each, primary), Anderson et al. 1993 at 293 K (4 rows, reproduced).

• Checked:

  • Every table against its image. Tables I, II (FTS row), III and VI repeat rows of Table IV, and Table VIII repeats Table VII’s 294 and 150 K columns: the extraction checks them equal and raises otherwise.

  • The paper’s own percentages from the transcribed values: Tables I, III, V, VI (all 25 Chappuis d sigma / sigma) and Table VIII (all 8) reproduce to the printed digit (e.g. 317.2 / 340.1 - 1 = -6.7 %, 1.28 / 0.67 - 1 = +91 %).

  • The bracketed values are 0.79-0.81 % of the LASIM Chappuis values (the stated +-0.82 %) and 0.90-0.92 % of the Reims values (labelled +-0.71 %).

  • Against reproductions already in optmat: gorshelev_2014’s el_helou_2005_vis and _nir (293-294 K) and serdyuchenko_2014’s el_helou_2005_223 equal these values in every row; brion_1998/present equals the Table II monochromator row.

• Finding (agreement with optmat’s O3 spectrum; nothing changed): the O3 model’s measured spectrum (data/gas/absorption/O3.toml: Serdyuchenko et al. 293 K, 50 cm^-1 Gaussian smoothing) against lasim_293 / lasim_wulf_294:

  • Chappuis maximum, 604.78 nm: 5.099 x 10^-21 (smoothed) and 5.104 x 10^-21 cm^2 (native) against 5.125 x 10^-21 cm^2: -0.5 % and -0.4 %. Over the five He-Ne lines, -1.2 % (632.99 nm) to +1.0 % (543.67 nm), a slope in wavelength; the Reims 291 K values give -1.0 to +0.3 %.

  • 800 nm (12 500 cm^-1) lies between two Wulf maxima and is not tabulated. The model gives 1.501 x 10^-22 cm^2 (smoothed), 1.475 x 10^-22 (native). At the neighbouring maxima, 817.22 and 779.42 nm, the model is +0.4 % and -0.3 % (smoothed), and Serdyuchenko’s native values averaged over +-2 cm^-1 are +2.1 % and +0.8 %.

  • Wulf maxima 748.7-944.3 nm: Serdyuchenko (+-2 cm^-1) is +0.8 % to +5.0 % above El Helou; at the (1,0) band, 991.8 nm, +2.2 %; at the weak (0,0) origin, 1046.8 nm (6.7 x 10^-24 cm^2), +22 %. The 50 cm^-1 smoothing lowers the narrow (1,0) peak by 39 % against the tabulated maximum, as the decision of TC-218 implies; this is not a disagreement between the data.

  • Temperature: the Chappuis cross section falls by 4.2-6.7 % from 293 to 144 K, while the Wulf maxima rise (by up to +91 % at the origin). The O3 model’s T243 variant covers the Chappuis band only to its own data; El Helou’s low-temperature sets are candidates for checking it (open).

• Finding (erratum candidate in another record): serdyuchenko_2014’s Table 4 prints El Helou’s 150 K value at 898.247 nm as 0.667 x 10^-22 cm^2; El Helou print 6.97 x 10^-23 (Tables VII and VIII), confirmed by their own +12 % from 294 K (6.21). The reproduction (serdyuchenko_2014__el_helou_2005_150.csv, row 898.247) is 4.3 % low. The image of Serdyuchenko’s table shows 0.667, so it is the paper’s misprint, not the extraction’s. Not corrected here (not this group’s record).

• Doubt:

  • Table III labels both rows ‘T=225 K’; the first is the 291 K row (Table IV and the table’s ‘(291-225 K)’ line). Table II gives the same Reims row as 295 K. 291 K is recorded.

  • Table II’s reference numbers do not match the reference list (its ‘Ref. 14’ row is Brion et al., Ref. 8).

  • The Wulf assignments ‘12830.12 Y ?’ and ‘13356.11 (3,0) ?’ are the authors’ uncertain ones; Table VII’s head prints lambda for sigma.

  • Uncertainty level not stated; Anderson’s are 1 SD.

• Not taken: the spectra (Figs. 5, 6, 8-11), all raster images. Worth digitising later: Fig. 10 (Wulf bands 10 000-13 700 cm^-1 at three temperatures) and Fig. 9 (12 500-16 000 cm^-1 at 293, 223, 144 K), which hold the temperature dependence around 800 nm between the tabulated maxima; raster, at 4 cm^-1 resolution.

• Status: open (the O3 model’s temperature variant against these data; gorshelev_2014’s and serdyuchenko_2014’s El Helou reproductions could name el_helou_2005 in reproduced_from, and serdyuchenko_2014’s 898.247 nm row needs an erratum, both for the maintainer).

TC-973 grebenshchikov_2007 (Grebenshchikov et al., Phys. Chem. Chem. Phys. 9, 2044 (2007)): O3 dissociation thresholds and transition moments, theory and quoted experiment (2026-10-09)

• Where: src/optmat/data/sources/grebenshchikov_2007.toml, tools/extract/ grebenshchikov_2007.py (Table 1, CSV, p. 2047; eqns (1)-(5), p. 2045; p. 2062).

• Transcribed:

  • dissociation_energy of O3, kind D0 (from the X~ ground vibrational level, as Fig. 1 defines E = 0), eV, use check:

    • calculated (Table 1, MRCI+Q/aug-cc-pVQZ): channel (1) O(3P) + O2(X 3Sigma_g-) 1.01, channel (2) O(3P) + O2(a 1Delta_g) 2.00, channel (5) O(1D) + O2(a 1Delta_g) 3.95;

    • experimental, quoted without a reference (eqns (1)-(5); footnote b): 1.051, 2.026, 2.678 (O(3P) + O2(b)), 3.016 (O(1D) + O2(X)), 3.999 eV; and 4.651 eV for O(1D) + O2(b 1Sigma_g+) (p. 2062). Inline points, one dataset per channel.

  • transition_dipole_moment of O3 at the Franck-Condon point, D (Table 1 row mu, “4.6 (-4)” written 4.6e-4): this work’s 1 3A’ 4.6e-4, 1 3A’’ 2.5e-3, 2 3A’’ 8.9e-3, 1 1A’’ 0 (use check); 2 1A’’ 0.06 and 3 1A’ 2.13 from the authors’ earlier papers (refs. 43, 49; reproduced).

• Checked: Table 1 against its image (every cell). The repeated D0 cells of each channel are equal (the extraction raises otherwise). Calculated minus quoted experiment: -0.04 eV (1), -0.03 eV (2), -0.05 eV (5).

• Doubt:

  • The experimental thresholds have no reference in the paper (use check, not reproduced: their origin cannot be named).

  • Footnote o assigns the 2 1A’’ and 3 1A’ moments to refs. 43 and 49 ‘respectively’, but the same table attaches ref. 49 to the Chappuis state (2 1A’’) and ref. 43 to the Huggins band (3 1A’): the order is probably reversed. Both are kept.

• Not taken:

  • The Hartley quantum yields: ‘as high as 85-90 %’ for O(1D) + O2(a) and ‘About 10-15

    quoted from Houston’s review (ref. 13). Data rule 6: notes only.

  • The band origins T0 (calculated and experimental, the latter from refs. 20, 38, 51, 52), the vertical energies T_v, the geometries and frequencies. They fit electronic_state_energy only per state; T_v is a vertical energy, which that quantity’s kinds (Te, T0, onset) do not hold. Recorded in the notes.

  • Figures (theory; raster): none worth digitising for the dissociation model.

• Status: verified (2026-10-09).

TC-974 harwood_1998 (Harwood, Burkholder & Ravishankara, J. Phys. Chem. A 102, 1309 (1998)): N2O5 cross sections 208-398 nm and NO3 quantum yields at 248, 308, 352.5 nm (2026-10-09)

• Where: src/optmat/data/sources/harwood_1998.toml, tools/extract/ harwood_1998.py (Table 2, CSV, p. 1312; Table 3, cells, p. 1313; abstract).

• Transcribed:

  • absorption_cross_section of N2O5, Table 2: 96 wavelengths, 208-398 nm every 2 nm, 10^-20 cm^2, about 298 K, use primary. Uncertainty not stated. The absolute scale is Harwood et al. 1993’s at 280 nm, to which the spectrum is normalised. Wavelengths recorded as standard air (mercury calibration, medium not stated; 0.07 nm against the 1 nm resolution).

  • photodissociation_quantum_yield of N2O5, product NO3, use primary: 0.64 +- 0.10, 0.96 +- 0.15 and 1.03 +- 0.15 at 248, 308 and 352.5 nm. These are the abstract’s values (inline points), 2 sigma including systematic errors, independent of pressure (150-600 Torr N2 or O2).

  • The same yield by actinometric method, Table 3 (6 rows; +- 2 sigma of the precision only), use check.

• Checked:

  • Tables 1-3 against their images. Table 2 is read in wavelength order and falls monotonically (checked by the extraction).

  • Table 2 at 248 and 308 nm equals Table 1’s ‘this work’ values (41.9, 2.40).

  • The averages against Table 3: 248 nm, weighted mean of 0.67 +- 0.14 and 0.64 +- 0.08 = 0.65 (printed 0.64); 308 nm, (0.88 + 1.03)/2 = 0.955 (0.96).

  • The abstract’s +-0.10 and +-0.15 are Table 3’s ‘+-15 % of the measured value’.

• Doubt:

  • 352.5 nm: the two methods (0.91 +- 0.04, 1.21 +- 0.04) average to 1.06, not the printed 1.03. The paper does not say how the average was formed.

  • p. 1316 gives the 248 nm yield as 0.64 +- 0.20 (2 sigma), twice the abstract’s. The abstract’s is recorded; it is consistent with the stated 15 %.

  • Table 1’s N2O5 cross section at 352.5 nm, 1.89 x 10^-20 cm^2, is ten times Table 2’s (0.188 at 352 nm), and equals its 312 nm value within rounding. A misprint in Table 1: the BrONO2 yields, ratioed to N2O5, would be ten times smaller with it. Table 1 is not extracted, so no erratum is needed.

• Finding: the 248 nm NO3 yield disagrees with ravishankara_1986 (TC-975).

• Not taken: the BrONO2 yields and the Br, Cl + BrONO2 rate coefficients (species not registered). Figures: Fig. 1 (N2O5 spectrum against DeMore et al. and Harwood et al. 1993) is raster and repeats Table 2. None to digitise.

• Status: verified (2026-10-09).

TC-975 ravishankara_1986 (Ravishankara et al., J. Geophys. Res. 91, 5355 (1986)): N2O5 quantum yields of O(3P) at 248-289 nm and of NO3 at 248 nm; the 248 nm NO3 disagreement with harwood_1998 (2026-10-09)

• Where: src/optmat/data/sources/ravishankara_1986.toml, tools/extract/ ravishankara_1986.py (Table 1, p. 5356; Table 2, p. 5359; both cells only; the PDF is a page scan).

• Transcribed: photodissociation_quantum_yield of N2O5, 298 K, N2 buffer, use primary:

  • O(3P) at 248, 266, 286.9 and 288.9 nm (Table 1, ‘Phi +- Accuracy’): 0.72 +- 0.17, 0.38 +- 0.10, 0.21 +- 0.05, 0.15 +- 0.05. The accuracy includes the ~20 % systematic error; level not stated. The 286.9 and 288.9 nm values are corrected for O(3P) from NO2 photolysis.

  • NO3 at 248 nm (Table 2, footnote d): 0.96 +- 0.13, random and systematic errors combined; level not stated.

• Checked:

  • Both tables against their images, and Table 2’s footnotes against the page image (‘Uncorrected average’). The 266 nm final value sits on a row without the wavelength (two run sets, footnote g); the extraction carries the wavelength down.

  • The averages: 248 nm, mean of 0.786, 0.687, 0.680, 0.719 = 0.718 (printed 0.72).

• Doubt:

  • The N2O5 density is measured at 213.9 nm with a printed cross section of 4.00 x 10^-19 cm^2 (page image checked). This is smaller than the paper’s own 248 nm value (4.45 x 10^-19), while N2O5 absorbs about seven times more strongly at 214 than at 248 nm (harwood_1998: 2.85 x 10^-18 and 4.19 x 10^-19). It is probably a misprint for 4.00 x 10^-18; with the printed value the yields could not come out near one. An inference: the yields are recorded as printed.

• Finding (the 248 nm NO3 yield):

  • Ravishankara et al. 0.96 +- 0.13 (level not stated) against harwood_1998 0.64 +- 0.10 (2 sigma). Taken as 2 sigma both, the difference, 0.32, is 3.9 combined sigma. Swanson et al. (1984), quoted in both papers: 0.89 +- 0.15.

  • Harwood et al. re-evaluated Ravishankara’s value with Yokelson et al.’s (1994) NO3 cross section: 0.77 +- 0.13 (2 sigma), 1.6 combined sigma from 0.64.

  • The yield scales as sigma(213.9) / sigma(248), which the two groups take from different spectra. Harwood’s spectrum gives 285 / 41.9 = 6.80. Ravishankara’s printed values give 0.90, or 8.99 if 4.00 x 10^-18 was meant. Rescaled to Harwood’s spectrum, 0.96 becomes 0.73 (an inference resting on that reading).

  • Ravishankara’s O(3P) yield at 248 nm (0.72 +- 0.17) plus a unit NO3 yield exceeds one. The authors propose N2O5 -> NO3 + NO + O(3P) (threshold 298.5 nm); Harwood et al. note that their lower NO3 yield leaves room for other products.

  • Neither value is preferred here. A model of N2O5 photolysis must choose, with this spread (0.64 to 0.96) as its uncertainty.

• Not taken: the quoted yields of Swanson, Magnotta and Margitan (no primaries in the library; notes); the cross sections assumed (DeMore et al. 1983; notes). Figures: none.

• Status: open (which 248 nm NO3 yield a model uses; the 213.9 nm cross section’s reading, to be checked against DeMore et al. 1983 when in hand).

TC-976 kossyi_1992 (Kossyi et al., Plasma Sources Sci. Technol. 1, 207 (1992)): dissociative recombination coefficients of N2+, O2+, NO+, NO2+ and N2O+ in an air-plasma kinetic scheme (2026-10-09)

• Where: src/optmat/data/sources/kossyi_1992.toml (text, reactions (35)-(42), pp. 209-210; no script).

• Transcribed: dissociative_recombination_rate_coefficient, cm^3/s, law power_law, T_ref = 300 K, exponent as printed (T_e = 2 epsilon_e / 3k). Inline points, one per channel:

  • N2+ -> N + N, 2.8 x 10^-7, n = 1/2 [22];

  • N2+ -> N + N(2D), 2 x 10^-7, n = 1/2 [20];

  • O2+ -> O + O, 2 x 10^-7, n = 1 [24];

  • NO+ -> N + O, 4 x 10^-7, n = 1.5 [24];

  • NO+ -> N(2D) + O, 3 x 10^-7, n = 1 [20];

  • NO2+ -> NO + O, 2 x 10^-7, n = 1/2 [22].

  All are reproduced: the scheme takes each from a cited compilation, none of which is in the library ([20] the DNA Reaction Rate Handbook 1978; [22] Smith & Thomson 1978; [24] Kozlov et al. 1988). N2O+ -> N2 + O is set equal to NO2+’s (k36 -> k35), with no source: kept with use excluded.

• Checked: every coefficient, exponent and reference against the page images of pp. 209-210 (220 dpi). The text extraction misplaces the equation numbers.

• Doubt: no uncertainty and no T_e range is given. The products’ electronic states are given only for the N(2D) channels.

• Not taken (notes): the cluster ions N4+, O4+, NO+.NO (2 x 10^-6, 1.4 x 10^-6, 1.3 x 10^-6 (300/T_e)^1/2, from Smirnov 1983) and those set equal to them; N3+ (set equal to NO2+’s); three-body recombination (k43, k44); the rest of the scheme.

• Status: verified (2026-10-09).

TC-977 peters_2019 (Peters, Shneider & Miles, J. Appl. Phys. 125, 243301 (2019)): a FLEET kinetics model of femtosecond-ionised nitrogen; the N2+ recombination coefficient, and which coefficients were tuned (2026-10-09)

• Where: src/optmat/data/sources/peters_2019.toml, tools/extract/ peters_2019.py (Table I, cells only, p. 243301-3).

• Transcribed: dissociative_recombination_rate_coefficient of N2+, R12, e- + N2+ -> 2N: 2.8 x 10^-7 (300/T_e)^1/2 cm^3/s. Form power_law; reproduced from kossyi_1992 (ref. 23) and Popov 2001 (ref. 40); not tuned.

• Checked: Table I against its image. The printed form is checked by the extraction. The value and law equal kossyi_1992/dr_N2+_N_N.

• Doubt: none for R12.

• Not taken: R7-R9 (e- + N4+ -> N2(A, B, C) + N2) were tuned by a random search to the measured emission (Table I footnote a, Table IV, Sec. III A): 2.5 %, 87 % and 11 % of 2.4 x 10^-6 (300/T_e)^1/2. A tuned constant of a model is not a property, and N4+ is not registered: notes only. Also in the notes: R5 and R23-R25 (tuned); R11 (N3+, not registered); the initial conditions (model assumptions). Figures: model results, none to digitise.

• Status: verified (2026-10-09).

TC-978 decleva_2016 (Decleva et al., arXiv:1610.06913 (2016)): vertical ionisation energies of O3 to 19 cation states from X and from the Hartley state, MRCI-SD(Q) (2026-10-09)

• Where: src/optmat/data/sources/decleva_2016.toml, tools/extract/ decleva_2016.py (Table 1, CSV, PDF p. 18 of the preprint).

• Transcribed: ionization_energy of O3, kind vertical, eV, at the Franck-Condon point, rows labelled by the O3+ state (C2v, numbered as Ohtsuka et al. 2007), use check. Two datasets of 19 rows: from X 1A1 (E_j - E_X, 12.38-19.94 eV), and from the B (Hartley) state (E_j - E_B, 6.59-14.16 eV; initial_state). The squared Dyson norms, I(X) and I(B), are in the notes: no quantity holds them.

• Checked: Table 1 against its image (every cell). The two columns differ by 5.77-5.79 eV in every row, the caption’s 5.78 eV (checked by the extraction). Against the photoelectron values in mahla_2025 (12.73, 13.00, 13.54 eV), the three lowest calculated energies are 0.35, 0.49 and 0.34 eV lower.

• Doubt: the library copy is the arXiv v1 preprint. A journal version, if any, is not in hand.

• Not taken: the time-resolved and angle-resolved photoelectron spectra (Figs. 2-6), model results. None to digitise.

• Status: verified (2026-10-09).

TC-979 hooshyar_2025 (Hooshyar & Dumitrache, J. Phys. D 58, 325204 (2025)): femtosecond-filament post-discharge model; the N2+, O2+ and NO+ recombination coefficients it reprints (2026-10-09)

• Where: src/optmat/data/sources/hooshyar_2025.toml, tools/extract/ hooshyar_2025.py (Table 2, CSV, PDF p. 8).

• Transcribed: dissociative_recombination_rate_coefficient in m^3/s (as printed), form power_law, T_ref 300 K: N2+ -> N + N, 2.8 x 10^-13, n = 1/2 (R12); O2+ -> O + O, 2 x 10^-13, n = 1 (R13); NO+ -> N + O, 4 x 10^-13, n = 1.5 (R14). Reproduced from Shneider, Zheltikov & Miles 2011 (the table is ‘Reprinted from [28]’).

• Checked: Table 2 against its image. The extraction checks the printed form, the exponent and the unit. The values are kossyi_1992’s k38, k40 and k41 in SI.

• Doubt: a copy of a copy; it adds no independent value, and records only the values a 2025 filament model uses. The N(2D) channels of kossyi_1992 are absent.

• Not taken: the cluster-ion recombinations R10-R11 (not registered). Table 1, the model’s end-of-pulse state at 1 bar: T_e 1.2 eV, n(N2+) 8.7 x 10^21, n(O2+) 4.9 x 10^22, n_e 5.7 x 10^22 m^-3, at 5 x 10^13 W/cm^2, 100 fs, wavelength not stated. These are model outputs, and no quantity holds ion number densities: notes only. Figures: model results.

• Status: verified (2026-10-09).

TC-980 kuze_2008 (Kuze et al., Chem. Phys. Lett. 455, 156 (2008)): isotope-selective one-photon predissociation of O3 in the Wulf band near 1 um; context only (2026-10-09)

• Where: src/optmat/data/sources/kuze_2008.toml (no datasets).

• Transcribed: nothing. The record states what the paper shows: narrow-band irradiation of single rotational lines of the Wulf band 3A2 <- 1A1 (v2 = 1-0) near 10 080 cm^-1 decomposes the irradiated isotopologue. The decomposition is nearly proportional to laser power with no threshold, so the process is one-photon predissociation.

• Checked: the text and figure captions against the PDF (pp. 156-158).

• Doubt: none.

• Not taken: decomposition volumes and peak-height decays (Figs. 2-4, raster), which depend on the cell; line positions and isotopologue fractions (no quantity). The paper gives no cross section or quantum yield. Its ‘10^-23 cm^2’ is an order of magnitude; el_helou_2005 has 3.80 x 10^-23 cm^2 at the (1,0) maximum. Nothing worth digitising.

• Status: verified (2026-10-09).

TC-981 burns_2018 (Burns, Peters & Danehy, Meas. Sci. Technol. 29, 115302 (2018)): FLEET velocimetry in a cryogenic nitrogen tunnel; the signal lifetimes’ density fit; context only (2026-10-09)

• Where: src/optmat/data/sources/burns_2018.toml (no datasets).

• Transcribed: nothing. The notes keep Table 1 (PDF p. 9), the empirical fit of the two FLEET-signal lifetimes, tau / tau_ref = C1 (rho/rho_ref + C2)^C3: tau_ref 21.6 and 69.1 us at rho_ref = 1.15 kg m^-3 (800 nm, about 0.6 mJ at the flow; pulse duration not stated).

• Checked: Table 1 and the laser description against the PDF.

• Doubt: the lifetimes are those of the tagged spot’s emission in a flowing, laser-heated gas. The authors give them no physical attribution; they are not a dissociation time or a rate coefficient of a molecule.

• Not taken: the lifetimes and signal intensities against pressure, temperature and density (Figs. 5-6, 8, raster) and the velocimetry results. They fit no quantity. peters_2019 models the same signal.

• Status: verified (2026-10-09).

TC-982 OEP 7 decisions: the total ionisation and the structure coefficients of the inner orbitals (2026-10-09)

• Where: OEP 7 (docs/oeps/oep-0007-strong-field-dissociation.md), Q1 and Q2; for the fragmentation model of its Phase 1.

• Decision (the maintainer, 2026-10-09, accepting the draft’s recommendations):

  • Q1. The model’s total ionisation is the HOMO channel plus the inner-orbital channels, not renormalised to molecular_rate_model’s total. The HOMO channel is molecular_rate_model’s default unchanged, so no recommended value changes.

  • Q2. The HOMO keeps the default model’s structure coefficients (zhao_2010 or zhao_2017 as now; TC-446, TC-675). The inner orbitals take the coefficients of the paper that defines them: yuen_2023 for O2’s HOMO-1 and HOMO-2 (TC-956), and jia_2024 for N2’s at R = 1.10 A, the tabulated distance nearest equilibrium (TC-957). The other sets are comparison models.

• Reason: these sets disagree with Zhao’s, and not by a common normalisation: O2’s HOMO leading coefficient is 0.69 in yuen_2023 against 0.52 (zhao_2010) and 0.64 (zhao_2017), and the small coefficients differ more; N2’s 3sigma_g is 2.99 in jia_2024 against 2.68 and 3.39 (TC-956, TC-957). Keeping the HOMO on the default leaves every existing result unchanged. Taking the inner orbitals from the papers that define their states keeps each state’s energy and coefficients from one calculation.

• Status: decided (2026-10-09).

TC-983 nist_asd_2026: the near-infrared lines of Ne, Ar, Kr and Xe (2026-10-09)

• Where: src/optmat/data/external/nist_asd/<Ne, Ar, Kr, Xe>_I_lines_nir.tsv, PROVENANCE.md there, the record’s notes, tests/test_nist_asd.py.

• Transcribed: the NIST ASD lines form (version 5.12, queried 2026-10-09), kept as returned, with the query, the windows and each file’s sha256 in PROVENANCE.md.

  • What they hold: the transitions among the excited levels, with their transition probabilities, oscillator strengths and accuracy grades.

  • Windows: from the end of each resonance-line window to 5000 nm (Ne 76, Ar 110, Kr 125 and Xe 150 nm up).

  • Wavelengths: vacuum throughout. The resonance lines’ query used the default show_av=2, which gives air wavelengths from 200 nm; this one uses show_av=1.

  • Coverage of the ns-np lines: NIST gives transition probabilities for 30 of 30 (Ne 3s-3p), 29 of 29 (Ar 4s-4p), 29 of 30 (Kr 5s-5p) and 22 of 26 (Xe 6s-6p).

  • Use: inputs to the sums over intermediate states of two-photon amplitudes (OEP 6, Q9). No dataset holds them yet.

• Checked: each file’s sha256 against PROVENANCE.md; its wavelengths are vacuum and inside its window. NIST repeats its header line inside long outputs; the files keep it.

• Status: verified (2026-10-09).

TC-984 OEP 8 decisions: the real part, the background, the split rule, the integrator, photon statistics and the continuum (2026-10-09)

• Where: OEP 8 (docs/oeps/oep-0008-bound-two-photon-response.md), Q1 to Q6; for the bound-level response record of its Phase 1.

• Decision (the maintainer, 2026-10-09, accepting the draft’s recommendations):

  • Q1. gamma_resonant publishes its dispersive part, labelled as failing lehmberg_1995’s xenon n2 by 2.2-2.8; the absorptive and dispersive parts are qualified separately. The earlier xenon n2 literature goes to the papers wanted.

  • Q2. No subtracted background gamma until Phase 4 (OEP 6, Q8). The resonant tail is 63 % of OEP 5’s xenon gamma at 1064 nm with fixed residues and 15 % with falling ones, so the subtraction stays undecided.

  • Q3. D_eff = 0.75 D_1 (D_1 = E_1 - hbar Omega_f / 2) is adopted as a labelled bound from the curated cases (He 1s2s, Ne and Ar 1S/1D, Kr and Xe single paths); the Kr and Xe cases assume the sign of the second path.

  • Q4. The reference integrator stays in tools/; its fixtures are stored with digests for solprop parity. No public integrator.

  • Q5. The residues are for coherent light; photon statistics are the propagation code’s.

  • Q6. The continuum’s time-resolved loss is not a phase of OEP 8; it stays OEP 6’s documented gap (TC-903) for a new OEP once a small-split continuum amplitude is curated.

• Reason: as the OEP’s section 13 recommended. No recommended value or default changes; OEP 5’s gamma is untouched.

• Status: decided (2026-10-09).

TC-985 Correction of TC-983: the near-infrared NIST lines re-queried with vacuum wavelengths at every wavelength (2026-10-09)

• Where: src/optmat/data/external/nist_asd/<Ne, Ar, Kr, Xe>_I_lines_nir.tsv, PROVENANCE.md there, nist_asd_2026’s notes, tests/test_nist_asd.py.

• Error: TC-983’s query used show_av=1, which the lines form defines as vacuum below 1000 nm and wavenumber above. In the tab-separated output NIST writes those wavenumbers into the nm columns as minus the wavenumber in cm⁻¹ times 1e-9 (for example “-0.000009548433” for 9548.433 cm⁻¹), after a second header line. So 579 (Ne), 109 (Ar), 213 (Kr) and 374 (Xe) rows had no wavelength. TC-983’s statement that the wavelengths are vacuum and inside the window did not hold above 1000 nm. Its test skipped the negative cells. Found by the curation of wiese_1989, dzierzega_2000 and sabbagh_1977, which matched lines on level energies instead.

• Corrected: re-queried on 2026-10-09 with show_av=3 (vacuum at all wavelengths), otherwise the same query; the files replaced as returned, with new sha256 in PROVENANCE.md.

• Checked:

  • Every column other than the wavelengths and their uncertainties is identical, row for row, as a multiset. The old files’ only extra row is the second header line.

  • Every row with a positive wavelength in the old files has the same wavelength cells.

  • Every converted row’s new vacuum wavelength equals 10⁷ over the old wavenumber, to the printed precision.

  • No wavelength is negative. Every printed observed or Ritz wavelength lies inside its window. The test now checks both columns of every row.

  • The ns-np coverage stated in TC-983 is unchanged (Ne 30/30, Ar 29/29, Kr 29/30, Xe 22/26 with Aki).

• Effect: no dataset or model used the files.

• Status: verified (2026-10-09).

TC-986 meshulach_1998 (Meshulach & Silberberg, Nature 396, 239 (1998)): phase-shaped two-photon excitation of Cs 6S-8S, dark pulses; the pair spectrum in the frequency domain; context only (2026-10-09)

• Where: src/optmat/data/sources/meshulach_1998.toml (no datasets).

• Transcribed: nothing. The notes keep the transition (Cs 6S1/2-8S1/2, 411 nm, photons at 822 nm; 31 fs sech^2, 23 nm FWHM = 42.2 meV), the paper’s Eq. (1), S_2 = |integral E(omega_0/2 + Omega) E(omega_0/2 - Omega) dOmega|^2, and the three tests of Fig. 3: dark pulses of a cosine phase near alpha = 1.2 (alpha_0 = 1.2024 for a square spectrum), the antisymmetric sine phase, and the modulation-phase scan (contrast better than 1 in 200).

• Checked: Eq. (1), the text and the captions against the PDF (pp. 239-242). Eq. (1) is the squared modulus of OEP 8’s pair spectrum S_2(Omega_f) (section 4.1, Check 2) in the frequency domain, the same within conventions (2 pi and the change of variable dropped; proportionality only). No intermediate level or detuning is printed.

• Doubt: under the antisymmetric phase the measured signal falls slowly (to about 0.4 at alpha = 6, by eye), where Eq. (1) is constant; the authors blame loss and the discrete modulator. A split-dependent kernel (OEP 8 Eqs. (3)-(5)) would also break the invariance; the paper gives nothing to estimate it. Text slips (not values): Theta for Omega on p. 241; ref. 17’s year printed 1997.

• Not taken: the normalised fluorescence of Fig. 3 (raster; caesium is not a material).

• Status: verified (2026-10-09).

TC-987 meshulach_1999 (Meshulach & Silberberg, Phys. Rev. A 60, 1287 (1999)): the closure-approximated two-photon amplitude, pi phase steps on Cs 6S-8S and the broad-line limit; context only (2026-10-09)

• Where: src/optmat/data/sources/meshulach_1999.toml (no datasets).

• Transcribed: nothing. The notes keep the derivation (Eqs. (2)-(6), (9)-(11)) and the tests: a pi spectral phase step on Cs 6S1/2-8S1/2 (Fig. 6, dark pulses at delta / Delta omega = +-0.31; delta = 0 almost reproduces the transform limit) and on Coumarin 6H, whose broad line gives integral I^2 dt (Fig. 7).

• Checked: the equations and captions against the PDF (pp. 1287-1292). Eq. (4), P = hbar^-4 |<f|mu^2|g>/omega_bar|^2 |integral eps^2 exp(i omega_0 t) dt|^2, is OEP 8’s pair form with the same hbar^-4 once sum_n d_fn d_ng / D_n is replaced by the closure <f|mu^2|g>/omega_bar, i.e. kappa = 0 in OEP 8 Eq. (4); the time integral is OEP 8’s S_2(omega_0). Eqs. (9)-(11) are OEP 8’s Check 2 (OEP 6 section 4) with K constant. Meshulach’s S_2 is OEP 8’s |S_2|^2.

• Doubt: in Fig. 6 (by eye) the measured signal stays at 1 out to |delta / Delta omega| about 1 where the calculation falls from about 1.5, and the minima are 0.1 and 0.02; the paper does not comment. No intermediate detuning is printed.

• Not taken: Figs. 2, 6, 7 (raster, normalised; caesium and the dye are not materials). Bebb and Gold, Phys. Rev. 143, 1 (1966), cited for the closure, is in the library without a record.

• Status: verified (2026-10-09).

TC-988 dudovich_2001 (Dudovich et al., Phys. Rev. Lett. 86, 47 (2001)): resonant two-photon excitation of Rb 5S-5D through 5P beats the transform limit; the pair form’s failure at an intermediate resonance; context only (2026-10-09)

• Where: src/optmat/data/sources/dudovich_2001.toml (no datasets).

• Transcribed: nothing. The notes keep the transition and printed wavelengths (omega_fg/2 778.1 nm, 5S-5P 780.2 nm, 5P-5D 776.0 nm, 18 nm FWHM), the amplitudes Eqs. (2)-(3), and the two tests: a symmetric slit doubles the signal at 71 % power loss and peak intensity / 38 (Fig. 2); a 4 nm pi/2 phase window centred on 778.1 nm raises it by a factor 7 (Fig. 3).

• Checked: equations, text and captions against the PDF (pp. 47-50). Computed from the printed wavelengths: D = E_5P/hbar - Omega_f/2 = -4.29 meV (-34.6 cm^-1) against a 36.9 meV FWHM. Eq. (2) is OEP 8’s pair form at nu = 0 (same prefactor i/hbar^2 and D_n; the 1/(2 pi) sits in the unstated Fourier normalisation); Eq. (3) is OEP 8 Eqs. (1)-(2) for one intermediate level with the causal pole, P/(omega_ig - omega) + i pi delta. Same within conventions.

• Finding: under the pair form no phase-only shaping exceeds the transform limit and no blocking raises the signal; the factor 7 and the factor 2 measure its failure with the pole inside the spectrum (2 kappa sigma^2 about 27). OEP 8 Eq. (2) does not state the -i0 (or width) a pole inside the spectrum needs; its section 4.3 excludes that regime, so nothing in OEP 8 changes. The abstract’s ‘factor of 40’ is the figure’s 38 rounded.

• Not taken: Figs. 2-3 (normalised fluorescence; rubidium is not a material).

• Status: verified (2026-10-09).

TC-989 knight_1990 (Knight, Lauder & Dalton, Phys. Rep. 190, 1 (1990)): laser-induced continuum structure; ionisation widths, continuum light shifts, complex two-photon coupling; notes only (2026-10-09)

• Where: src/optmat/data/sources/knight_1990.toml (notes only; a review of model calculations).

• Transcribed: nothing. The notes hold Eqs. 2.10-2.12 (read from the page images, pp. 12-13), Eqs. 2.59-2.65, 3.9-3.10 and 3.28-3.35. The only noble-gas item is Hutchinson and Ness’s xenon LICS figure (Fig. 5.4), with intensities only.

• Finding: kumar_2026’s Eqs. 10-11 (TC-898) are Eqs. 2.10 and 2.12 term for term: the continuum shift there is the resonant term only. Eq. 3.29 adds the counter-rotating continuum term; its size for He 1s2s is unknown, and it bears on OEP 8’s Re alpha_f taken from kumar_2026. Gamma = (pi/2) hbar |Omega|^2 is a population rate, sigma^PI Phi, and gives OEP 8’s Im alpha_f = eps_0 c sigma/omega.

• Finding: two levels ionised into one continuum acquire a complex coupling of size about sqrt(Gamma_0 Gamma_1) (Eqs. 2.61-2.63). OEP 8’s (2+1) and direct three-photon channels share final energies at two-photon resonance, but OEP 8 section 4.4 adds them. Laser phase diffusion adds pure dephasing (Eq. 3.10); for one laser driving a two-photon ladder it is 4 Delta_laser (derived).

• Status: verified (2026-10-09).

TC-990 kaufman_2020 (Kaufman et al., Phys. Rev. A 102, 063117 (2020)): adiabatic elimination for two-photon coupling; its error scales with intensity; notes only (2026-10-09)

• Where: src/optmat/data/sources/kaufman_2020.toml (notes only; a three-level model, Table II).

• Transcribed: nothing. The notes hold the eliminated equations (Eqs. 11, A5-A6), the validity condition (Eq. 9), Table II’s parameters and the printed 2.5 % error.

• Finding: Eqs. 11/A5 are OEP 8’s Eq. 6 for one intermediate: the off-diagonal (1/4) chi chi/(omega_gi + omega_0) equals -(1/2) M_f (E^+)^2 with M_f = 2 d d/D, and the Stark shifts are -alpha |E^+|^2 with the full polarisability. Kaufman et al.’s “two-photon Rabi frequency” is the off-diagonal element, half of OEP 8’s Omega_R and of kumar_2026’s Omega_ge^P (TC-898). kumar_2026’s Eqs. 7-9 follow this form. kumar_2026’s numbers do not appear in this paper.

• Finding: integrating Table II’s model, full and eliminated, reproduces Fig. 1 (P_e 0.843 against 0.869; 3.1 %, printed 2.5 %). The error scales with peak intensity (0.64, 2.2 and 3.1 % at 0.0667, 0.2 and 0.6667 TW/cm^2, 30 fs; 15 % at 0.6667 TW/cm^2 and 100 fs). In weak field it equals 2 (mu E_0/(2 hbar D))^2, the intermediate admixture, where OEP 8’s spectral bound (Eq. 5) gives 0.20 %. The paper’s constant-area series confounds the two errors. OEP 8 section 4.3 needs the field-strength condition |d E_0|/(2 hbar D) << 1 besides its spectral one.

• Status: verified (2026-10-09).

TC-991 toth_2023 (Tóth et al., Phys. Rev. A 107, 053101 (2023)): two- and three-state models with dynamic Stark shifts for Na and Li; notes only (2026-10-09)

• Where: src/optmat/data/sources/toth_2023.toml (notes only: Na and Li, no material in optmat).

• Transcribed: nothing. The library copy is the APS author proof (Phys. Rev. A 00, 003100, dated 26 April 2023), not the version of record; Eqs. 5-7 and 12 were read from the page image (PDF p. 6).

• Finding: Eq. 6 (Omega_2 = -sum mu mu E_0^2/(4 (omega_mI - omega)), the off-diagonal itself, pi-pulse at integral Omega_2 dt = pi/2) and Eq. 7 (the Stark shifts) are kumar_2026’s Eq. 9 halved and Eq. 8 (TC-898) and OEP 8’s Eq. 6 term for term. Gamma_0 = 2 pi |mu E_0/2|^2 (Eq. 12) is kumar_2026’s Eq. 11 and knight_1990’s Eq. 2.12: a population rate, sigma^PI Phi. kumar_2026’s coefficients are not in this paper; its continuum shift (Eq. 10) is not either (Tóth et al. include the continuum in the sum-integral of Eq. 7).

• Finding: for a transform-limited Gaussian pulse the best two-photon detuning is 0.76 of the peak relative Stark shift. OEP 8’s Bloch model carries the time-dependent shift; a rate model with a fixed line centre would need such a factor.

• Status: verified (2026-10-09).

TC-992 ackerhalt_1977 (Ackerhalt & Shore, Phys. Rev. A 16, 277 (1977)): rate equations against Bloch equations (Wilcox-Lamb); notes only (2026-10-09)

• Where: src/optmat/data/sources/ackerhalt_1977.toml (notes only; a model study, no atom named).

• Transcribed: nothing. The notes hold the two-level Bloch equations with ionisation R and collisional phase destruction 1/T_I (Eqs. 4-6), the Wilcox-Lamb rate R_s = (1/4) Omega^2 (R + 1/T_I)/[(R/2 + 1/(2 T_I))^2 + Delta^2] (Eq. 10) and the cross section (Eq. 12), read from the scanned page image (p. 278), and the three-level comparisons of Figs. 1-9 as stated in the text.

• Finding: Eq. 10 is OEP 8 section 4.5’s rate in one-photon form: with Omega_R = sqrt(2 sigma_0/pi) Phi it gives W = sigma_0 g Phi^2 exactly, so OEP 8’s Omega_R, Gamma^coh and W are mutually consistent. Ackerhalt and Shore’s 1/T_I enters the coherence as 1/(2 T_I): it is twice OEP 8’s gamma^phi.

• Finding: rate and Bloch solutions agree after the transients once the dephasing is comparable with the Rabi frequency, and fail (no ionisation against about 20 %) for a detuning equal to the Rabi frequency without dephasing. Only constant fields are tested. This supports OEP 8’s added requirement that Gamma^coh exceed the rates of change of the envelope and the light shift.

• Doubt: Eqs. 1 and 2 print the same sign (not population-conserving; Eq. 5 is right), Eq. 3 has +i Delta where Eq. 6 has -i Delta, and Eqs. 11-12 omit hbar (consistent with each other for hbar = 1). Nothing is taken, so there are no errata.

• Status: verified (2026-10-09).

TC-993 manakov_1986 (Manakov, Ovsiannikov & Rapoport, Phys. Rep. 141, 319 (1986)): He and Xe dynamic polarizability and hyperpolarizability at 1060 and 695 nm; the two-photon formulas (2026-10-09)

• Where: src/optmat/data/sources/manakov_1986.toml, tools/extract/ manakov_1986.py, data/values/refractive/{He,Xe}/manakov_1986__alpha.csv, data/values/third_order/{He,Xe}/manakov_1986__gamma_{linear,circular}.csv.

• Transcribed: Table 5.3 (p. 381), the He and Xe rows: the ground state’s scalar polarizability alpha^S(omega) and the hyperpolarizability components gamma_0^l (linear) and gamma_0^c (circular), in atomic units, at omega_N = 0.043 and omega_R = 0.0656 a.u. (1059.6 and 694.6 nm). The review quotes them from the authors’ Zh. Eksp. Teor. Fiz. 70, 1697 (1976) (Ref. [78], not in the library), so all six datasets are use = reproduced. The method is not stated for the table (the review lists [78] among its Fues model-potential calculations). No uncertainty is given. gamma_0^l is gamma_T(-w; w, -w, w) (process kerr, component parallel). The paper’s own definitions establish this: epsilon^(4) = -gamma_0 F^4/64 with F the amplitude, the static limit -gamma E^4/4!, and chi_xxxx = gamma_0^l/6. gamma_0^c = 12 chi_xxyy (component circular). It is not the mean gamma, and the fitting code refuses it. The H and alkali rows are described in the notes only. Identity checked on PDF pages 1-2.

• Checked: every taken cell against the table image and the rendered page. The header frequencies are checked against the text’s 1.17 and 1.78 eV (p. 376) by the script. gamma_0^c/gamma_0^l = 0.6667 for He at omega_N (the Kleinman 2/3); Xe 0.656 and 0.650.

• Finding: compared with optmat’s fits at the same wavelengths, the table is high for gamma and for He’s alpha:

  Quantity	Table 5.3 / fit at omega_N	at omega_R
  He alpha^S	1.074 (1.49 / 1.387)	1.072
  He gamma_0^l	1.307 (57.3 / 43.85, OEP 5’s fit)	1.308
  Xe alpha^S	1.003 (27.4 / 27.32)	1.009
  Xe gamma_0^l	1.763 (12900 / 7317)	1.809

  The dispersion between the two frequencies agrees for He: +2.3 % against +2.2 % in the fit. It does not for Xe: +14.4 % against +11.5 %. The xenon value is 1.76 times the gamma_fit = 7312 au that OEP 8 (section 4.6) uses at 1064 nm. It is a 1976 model calculation and does not bear on OEP 8’s Q1.

• Finding: the review prints no noble-gas two-photon ionisation cross section and no two-photon bound strength. It prints no oscillator strength or transition probability either, and has no figure of any of them. Nothing compares with TC-943’s references or with TC-983’s NIST lines. For krypton (OEP 6, Q2) there is no table, no vector figure and no raster figure.

• Finding (OEP 8 conventions):

  • The light shift -(1/4) alpha F^2 (Eq. 5.7) is OEP 8’s -alpha |E^+|^2.

  • The optical theorem sigma = 4 pi (omega/c) Im alpha (p. 377) is OEP 8’s Im alpha = eps0 c sigma/omega.

  • The total two-photon ionisation rate is W^(2) = Im gamma_0^(l,c) F^4/(32 hbar) (Eq. 5.21), so it depends on polarization.

  • The general two-photon rates for an S state are Eqs. 6.6-6.11. With them, W^c/W^l is at most 3/2 (Eq. 6.14), and beta_2^c = -10/7 and beta_4^c = 3/7 (p. 398).

  • The (2+1) Breit-Wigner and two-level formulas are Eqs. 6.16-6.23. The two-level solution with an ionisation-broadened upper level is the reduction of OEP 8’s Eq. 7.

  • A J = 2 level’s light shift depends on M through the tensor polarizability (Eqs. 5.7-5.8), which OEP 8’s scalar alpha_f omits.

• Not taken (awaiting vocabulary): He 2 3S1, from text p. 376. These are the measured alpha^T(0) = 3.53(14) x 10^-2 au (Player and Sandars 1969) and the calculated alpha^a(omega_N) = -12.1 and alpha^T(omega_N) = 4.04 au (Manakov and Ovsiannikov 1978), both quoted. This needs the candidate quantity level_polarizability (with werbowy_2026’s).

• Not taken (not two-photon data or no material):

  • Tables 5.1 and 5.2 (alkalis).

  • The p. 412 N2+/N+ table for the noble gases, from L’Huillier et al. 1983.

  • Figs. 6.1-7.4.

• Status: verified (2026-10-09).

TC-994 lambropoulos_1976 (Lambropoulos, Adv. At. Mol. Phys. 12, 87 (1976)): review of multiphoton processes; cross-section definition, photon statistics, resonance shifts and polarisation; notes only (2026-10-09)

• Where: src/optmat/data/sources/lambropoulos_1976.toml (kind compilation; no datasets).

• Transcribed: nothing. The notes keep:

  • the generalised cross section, W = sigma_N I^N, sigma_N = (2 pi alpha)^N / (4 pi^2) (m K / hbar) omega^N int |M^(N)|^2 dOmega, I in photons cm^-2 s^-1, sigma_N in cm^2N s^(N-1) (Eqs. 19-21, pp. 94-95), and the bound-bound rate with I(omega) per unit bandwidth (Eq. 23);

  • photon statistics: W_N = sigma_N G_N, G_N = ^N coherent, N! ^N chaotic (Eqs. 44-49), so sigma_N is a coherent-light quantity (as OEP 8’s residues, TC-984 Q5); resonant two-photon ionisation above saturation is independent of statistics;

  • resonance shift-width R_MM = (s0 + s1 I) - i (g0 + g1 I) and the slope N -> N - 2 on resonance (p. 119); Eq. (58)’s Fano-like two-photon profile;

  • polarisation: circular usually larger for N = 2-4, linear for higher N; Klarsfeld and Maquet’s bound (2N - 1)!!/N!; Table III (alkali ratios) quoted.

• Checked: Tables I-III against their images (tbl_891f75dc43eb, tbl_1943bdb19b84, tbl_1d36c88a3c44; the extracted Table III runs theory cells together, e.g. ‘2.452.18’, which the image prints on separate lines); Eqs. (19)-(23), (44)-(49) and the quoted text against the page images.

• Not taken: Table I and the text’s alkali cross sections (no material; reproduced from Manakov et al. 1974a and others); Table II’s and the postscript’s noble-gas intensity exponents (Agostini et al. 1970b; Lompre et al. 1975; reproduced, no quantity); Figs. 3, 4 and 10 (raster, reproduced).

• Finding (two-photon, OEP 6): no noble-gas two-photon ionisation value; only Pindzola and Kelly’s argon calculation is mentioned (pindzola_1975). Krypton: no two-photon value in any form.

• Finding (the review’s own inconsistencies):

  • Lecompte et al.’s Xe multimode/single-mode ratio ‘about 10^(6.9 +- 0.3) (~ 11!)’ (p. 114): 11! = 10^7.60, 0.7 decade (2.3 times the error) higher;

  • Fig. 10’s caption says lambda = 0.53 um; the text and Table II’s K0 say 1.06 um;

  • ‘As seen in Table II’ (p. 136) means Table I; ‘(Fig. 10 and Table III)’ (p. 158) means Table II;

  • Cs circular/linear three-photon ratio 2.14 in the text, 2.15 in Table III; Fox, Kogan and Robinson’s paper is ‘Phys. Rev. Lett. 25, 1416 (1971)’ here and ‘Phys. Rev. Lett. 26, 1416 (1971)’ in pindzola_1975;

  • Flank and Rachman’s linear Cs three-photon 0.957e-77 cm6 s2 has Table I’s digits (9.57e-76) and is exactly 1/100 of it; their circular value is 1/58 of Table I’s: identical digits suggest an exponent or transcription error in one of them.

• Status: verified (2026-10-09).

TC-995 bebb_1966 (Bebb & Gold, Phys. Rev. 143, 1 (1966)): average-energy perturbation theory of N-photon ionisation of H and the rare gases at the ruby line; the Xe seven-photon cross section (2026-10-09)

• Where: src/optmat/data/sources/bebb_1966.toml, one inline dataset, sigma7_Xe (use check). The PDF is a scan; every figure is raster.

• Transcribed: the one rare-gas generalised cross section printed as a number, Xe seven-photon at 1.785 eV (the ruby line), theory, ‘4 x 10^-206’ (p. 22), in cm^14 s^6 (W = sigma F^7, F in photons cm^-2 s^-1, single-mode field, linear polarisation). The notes keep the definition (Eqs. 17-18, 39, 43), the photon-statistics factor <F^N> = N! ^N for Gaussian light (Eq. 45) against ^N for one mode (Eq. 44), the approximation (sums collapsed at an average energy, the first excitation energy; near-resonant orders summed explicitly, the rest at 1.2 hbar omega_I; scaled hydrogenic orbitals for the rare gases), and Table I (orders, ionisation energies, average energies, radii, Z, the levels summed and their Moore energies).

• Checked:

  • Table I against its image (tbl_59a6439e8eba), the p. 15 and p. 22 text against the page images;

  • the printed 4e-206 against Fig. 19(b), read from the page image at native resolution: ticks on one log scale (238.2 px per decade, residuals < 0.003 decade), curve at 1.785 eV 10^-205.32 = 4.8e-206 (+-0.015 decade): agreement to 0.08 decade;

  • the rate formula equals lambropoulos_1976’s Eq. (20) for sigma_N.

• Finding (two-photon, OEP 6): no two-photon ionisation value of any rare gas in any form. The rare gases are computed only at 1.785 eV: Xe 7, Kr 8, Ar 9, Ne 13, He 14 photons. pindzola_1975’s notes call the paper ‘H and the rare gases, 2-12 photons’: the 2-12 photons are hydrogen’s. Krypton: only an eight-photon raster figure (Fig. 18(b), 1.76-1.80 eV); no table, no vector figure.

• Finding (text against figure): p. 15 puts the Kr 6s[3/2]2/4d[3/2]1 peak at ‘hbar omega = 1.784’ and the 6s[3/2]1 peak at ‘~1.766’; Fig. 18(b) and Table I’s energies over seven put them at 1.764 and 1.769 eV. Fig. 18(a) labels the Kr limit 13.966 eV, Table I 13.996. The abstract’s initiation flux for Xe, Kr and Ar (~1e29 cm^-2 s^-1) differs from Sec. IV’s ~5e28. None touches the dataset.

• Not taken: Voronov and Delone’s measured ~5e-206 (reproduced; JETP Lett. 1, 66 (1965) not in the library); hydrogen (not a material); the rare gases’ raster dispersion and threshold-flux curves (not digitised: an order-of-magnitude method, lambropoulos_1976 p. 12, at 7-14 photons, with no printed number but Xe’s to check them); Table I’s average energies and Z (inputs chosen for the model, not fitted constants or properties of the gas) and Moore energies (reproduced).

• Status: verified (2026-10-09).

TC-996 zon_1972 (Zon, Manakov & Rapoport, Sov. Phys. JETP 34, 515 (1972)): quantum-defect Green’s function for multiphoton ionisation; three-photon ionisation of metastable He and its levels’ polarisabilities at the ruby line; notes only (2026-10-09)

• Where: src/optmat/data/sources/zon_1972.toml (no datasets). The PDF is a scan; Figs. 1-4 are raster.

• Transcribed: nothing. The notes keep the rate (Eq. 1, w = 2 pi (omega F/F0)^N |K|^2, F0 = c / 2 pi a0^3 = 3.22e34 cm^-2 s^-1), the linear and circular three-photon forms (from an s state, circular is the single path T_32 and vanishes between poles), the split w = B eta (Eq. 13), the optical theorem tying Im alpha to the one-photon cross section (Eq. 8), and the printed numbers: He 2 3S1 and 2 1S0 three-photon rates at the ruby frequency (linear), 3.09e-81 and 3.30e-78 F^3 s^-1; alpha(2 1S0) = 270 au; Re alpha(6 1S0) = 300 au, Im alpha(6 1S0) = 35 au; the B factors of H 1s, 2s and He 2 3S1, 2 1S0.

• Checked: every quoted number and equation against the page images (pp. 515-518). Through Eq. (8), Im alpha(6 1S0) = 35 au at 14402.2 cm^-1 is a 6 1S0 photoionisation cross section of 0.211 a0^2 = 5.9e-18 cm^2 (derived, not data).

• Not taken (awaiting vocabulary): the metastable-He three-photon cross sections (multiphoton_ionization_cross_section names no initial level; every curated value is a ground state’s) and the excited-level polarisabilities (polarizability is the ground state’s). Candidates: level_polarizability (shared with werbowy_2026 and manakov_1986; this source needs a real/imaginary part) and excited_state_multiphoton_ionization_cross_section. Not taken otherwise: hydrogen; Bakos et al.’s measured upper limit (reproduced; singlet and triplet mixed).

• Doubt: the 270 au of He 2 1S0 is read as the dynamic value at the ruby frequency from its paragraph; the paper does not state the frequency.

• Finding (two-photon, OEP 6): no noble-gas two-photon ionisation; krypton not treated.

• Finding: the flux unit and F0 are printed ‘cm^-2 sec’ on p. 516; s^-1 is meant (p. 517, and F0’s value).

• Status: verified (2026-10-09).

TC-997 lehmberg_1976 (Lehmberg, Reintjes & Eckardt, Phys. Rev. A 13, 1095 (1976)): the near-two-photon-resonant n2 of caesium; the theory behind lehmberg_1995’s Eq. (3) and OEP 8’s Eq. (9) (2026-10-09)

• Where: src/optmat/data/sources/lehmberg_1976.toml (no datasets; caesium is not an optmat material).

• Transcribed: nothing. The notes keep:

  • the convention: E = (1/2) e E exp(-iwt) + c.c., delta n = n2 <E^2>, <E^2> = (1/2)|E|^2 (Eqs. 2, 7b, 15), the per-<E^2> esu n2 of lehmberg_1995 (TC-854);

  • Eq. (8), the instantaneous n2 of a vapour, whose first term (2 pi N / hbar) |P-_beta|^2 / (w_beta0 - 2w) is the near-two-photon-resonant chi(3); the three-level forms (Eqs. 18b, 23, 24);

  • Table I: the Cs n2/N at 1.064 um, measured -1.4 +- 0.2 (linear) and -0.26 +- 0.03 (circular), calculated -2.62 and -0.525, in 10^-30 esu.

• Checked:

  • the equations, Table I and the numbers of p. 1099 against the page images;

  • n20, n10 and n21 recomputed from the printed |mu10| = 3.16 and |mu21| = 2.92 au, the 6p energy 11547 cm^-1 and w20 - 2w = -261 cm^-1: -2.364, 0.3364 and -0.2561 x 10^-30 N esu (printed -2.36, 0.335, -0.256), with 1 au of gamma = 5.0367 x 10^-40 esu;

  • Table I: column c is n20 - n10 and -n10; column b is column a over 1 + eta (eta = 0.08, 0.36); the ratios are 5.4 and 5.0.

• Finding (the equation): at degenerate frequencies OEP 8’s kernel is M = 2 P-, so the two-photon term is n2 = (pi/2) N |M|^2 / (E_f - 2 hbar w) = (pi/2) N gamma_res, with residue R_f = |M|^2 / hbar. That is OEP 8’s Eq. (9) at Gamma -> 0, with n2(esu, per <E^2>) = (pi/2) N gamma_T. The 1976 recomputation above confirms the factor and the au-to-esu conversion. Two points of the 1976 theory bear on the model:

  • it leaves the real two-photon population out of n2 as fourth order (‘unless w20 - 2w is comparable to the atomic linewidth’, p. 1097);

  • population terms from the one-photon resonance (the integrals of Eq. 20) add only when the pulse is not short against the dephasing time.

• Finding (the 6p[1/2]0 strength of lehmberg_1995’s own calculation; computed):

  • lehmberg_1995’s single-level Eq. (3) gives n2 = -1.539 x 10^-14 esu at 248.4 nm, 760 Torr and 300 K (N = 2.4463 x 10^19 cm^-3; E_f - 2 hbar w = -396.3 cm^-1 from NIST’s 80118.962 cm^-1). By the identity above, its ab initio matrix elements imply delta(6p[1/2]0) = 1436 au (1435 with its rounded -396 cm^-1).

  • This is 2.5 times kroll_1990’s 580 au (TC-890), 1.9 times henriksson_2005’s 752 au (TC-888), and near pindzola_1981b’s length-form 1541 au.

  • With 6p[1/2]0 alone, the measured n2 imply 1922 au (self-defocusing, -2.06) and 1698 au (compensation, -1.82). OEP 8 section 4.7 gives 1600-1820 with the other levels included.

  • With 6p[1/2]0 alone, the curated strengths give -0.62 (kroll_1990) and -0.81 (henriksson_2005) x 10^-14 esu.

  • So lehmberg_1995’s measurement and its calculation agree with each other (0.75 to 0.85) because both rest on a strength of about 1400-1900 au. The Q1 tension is between strengths: Lehmberg’s calculated matrix elements and the n2 measurement on one side, Kröll and Bischel’s measured cross section and Henriksson’s calculation on the other.

• Doubt: Table I prints ‘-1.5 +- 0.02’ for column a (linear), against +- 0.2 in column b after an 8 % adjustment. It is probably a misprint for +- 0.2. Nothing is taken, so there is no erratum.

• Not taken: every number. They are of caesium (n2, matrix elements, dimer absorption, the two- and four-photon estimates quoted from Miles and Harris and from Morton).

• Status: verified (2026-10-09).

TC-998 tunnermann_1992 (Tünnermann, Mossavi & Wellegehausen, Phys. Rev. A 46, 2707 (1992)): near-resonant two-photon excitation of Xe 6p by femtosecond KrF pulses; difference-frequency chi(3) magnitudes not taken (2026-10-09)

• Where: src/optmat/data/sources/tunnermann_1992.toml (no datasets).

• Transcribed: nothing. The notes keep the following.

  • The pump: 248.5 nm, 360 fs, about 100 cm^-1, up to 10^15 W/cm2, 0.05-760 Torr of Xe.

  • The detunings: 363 cm^-1 from 6p[1/2]0 and 1270 cm^-1 from 6p[3/2]2.

  • Two-photon excitation: the sideways 828 nm fluorescence grows as the square of the pump (Fig. 7), with ASE and hyper-Raman emission at 828 and 823 nm and four-wave parametric oscillation.

  • The level shift: the authors’ ponderomotive estimate, Eq. (1): 8 x 10^12 W/cm2 closes 363 cm^-1.

  • The susceptibilities: |chi(3)(280 nm)| = 5 x 10^-51 and |chi(3)(148.5 nm)| = 10^-48 m^5/V^2 for w_vuv = 2 w_p - w_vis, inferred from the parametric gain (Eq. 5) at an assumed 10^14 W/cm2 (p. 2715).

  • The calculation: Fig. 19’s four-level curve, drawn x0.25 (raster).

• Checked:

  • The text and figures against the page images (the PDF is scanned).

  • The detunings against NIST (TC-983): 2/248.5 nm minus the levels gives 363.9 and 1270.4 cm^-1, so 248.5 nm is the vacuum wavelength. The 828.01 and 823.16 nm of Fig. 6 are air wavelengths.

• Finding (light shifts): scaled linearly from the paper’s own calibration (363 cm^-1 at 8 x 10^12 W/cm2), lehmberg_1995’s 2 GW/cm2 shifts the 6p levels by 0.09 cm^-1. That is 2 x 10^-4 of its 396 cm^-1 detuning, so light shifts cannot affect OEP 8’s Q1.

• Finding (strength): nothing here implies a 6p[1/2]0 strength.

  • |chi(3)| is the magnitude of a nondegenerate susceptibility at an assumed intensity.

  • Its resonant part multiplies the two-photon amplitude by a (w_vis, w_vuv) amplitude whose oscillator strengths (Aymar and Coulombe) are not printed.

• Doubt:

  1. Fig. 19’s calculation is stated ‘for a fixed pump-laser detuning of 0.2 nm’. 363 cm^-1 is 1.12 nm of pump wavelength; 0.2 nm would be 65 cm^-1 in 2w. tunnermann_1993 states 363 cm^-1 for the same calculation.

  2. tunnermann_1993 puts the second FWPO value at 320 nm, this paper at 280 nm.

  3. ‘0.5 % of the atomic density’ and ‘about 10^15 cm^-3 at 30 Torr’ for the Xe2 dimer disagree: 0.5 % of 30 Torr is 4.8 x 10^15. lehmberg_1995 gives about 0.6 % at 1 atm.

• Not taken:

  • Awaiting vocabulary: the two |chi(3)| values and Fig. 19. nonlinear_susceptibility fits except for the convention: CONVENTIONS has no per-atom SI chi(3) of Hanna, Yuratich and Cotter (a candidate quantity).

  • Reproduced, no quantity: the ‘two-photon absorption cross sections around 10^-36 cm^4/W’ quoted from Kligler et al. (Ref. 32), a coefficient and not sigma_0^(2).

• Status: verified (2026-10-09).

TC-999 tunnermann_1993 (Tünnermann et al., IEEE J. Quantum Electron. 29, 1233 (1993)): femtosecond four-wave difference-frequency mixing in xenon near the 6p[1/2]0 two-photon resonance; chi(3) magnitudes not taken (2026-10-09)

• Where: src/optmat/data/sources/tunnermann_1993.toml (no datasets).

• Transcribed: nothing. The notes keep the following.

  • The scheme: w_s = 2 w_p - w_i with the 248.5 nm, 360 fs pump, 363 cm^-1 above 6p[1/2]0, and nanosecond seeds from 185 to 1905 nm; output from 133 to 355 nm at several uJ.

  • The examples: 141, 157 and 193 nm, with their pressures and energies.

  • The FWM equation, Eq. (1). Under plane-wave conventions it gives P(w_s) = (3/4) eps0 N chi E_p^2 E_i*, so gamma_T = 6 eps0 chi (derived). tunnermann_1992’s gain Eq. (5) gives the same factor.

  • Fig. 6 (raster): |chi(3)| from Eq. (1) at an assumed 10^14 W/cm2, against a four-level calculation drawn x0.25.

• Checked:

  • The text, Fig. 6 and Table I against the page images (the PDF is scanned).

  • The library’s extracted Table I misplaces rows. The image gives XeF 0.26 and 2.8, XeCl 0.50 and 3.0, ArF 0.26 and 1.9 mJ, which agrees with the text.

• Finding: the calculation lies about four times above the measured |chi(3)|.

  • The measured values scale as 1/I_p with the assumed I_p, so neither side constrains delta(6p[1/2]0).

  • The paper’s direction (calculation above measurement) is the opposite of lehmberg_1995’s n2 (measurement above the curated-strength prediction). This carries no weight, because the intensity is assumed.

• Doubt: the two papers disagree on two points:

  1. the FWPO point: 320 nm here, 280 nm in tunnermann_1992;

  2. the calculation’s detuning: 363 cm^-1 here, ‘0.2 nm’ there.

• Not taken:

  • Awaiting vocabulary: Fig. 6’s points and curve (raster), in the convention CONVENTIONS lacks (see tunnermann_1992).

  • Not a xenon property: Table I’s amplifier energies.

• Status: verified (2026-10-09).

TC-1000 blazewicz_1988 (Blazewicz & Miller, Phys. Rev. A 38, 2863 (1988)): two-colour multiphoton ionisation and third-harmonic generation at the Kr 5s and Xe 6s’ three-photon resonances; context only (2026-10-09)

• Where: src/optmat/data/sources/blazewicz_1988.toml (no datasets).

• Transcribed: nothing. The notes record what the paper shows:

  • third-harmonic cancellation at the three-photon J = 1 resonances (Kr 5s[3/2]1 at 370.6 nm, Xe 6s’[1/2]1 at 388.6 nm, 10 ns, about 5 x 10^8 and 10^9 W/cm2);

  • excitation of the upper levels by one third-harmonic photon plus one laser-two photon, which favours the J = 2 levels two-photon-allowed from the ground state (Xe 5f[5/2]2, 5f[3/2]2);

  • the phase-matching change induced by the second laser (the Delta k expression, p. 2870).

• Checked:

  • the text and captions against the page images (the PDF is scanned);

  • the wavelengths against NIST (TC-983). 3/E gives 370.75 and 388.68 nm in vacuum, so the printed 370.6 and 388.6 nm are air wavelengths. Fig. 4’s caption prints 370.7 nm.

• Not taken: everything.

  • The spectra are ion and third-harmonic yields in arbitrary units, in raster figures.

  • The paper prints no cross section, strength, Rabi frequency, n2 or chi(3).

  • For OEP 6 Q2, the paper has no krypton two-photon ionisation data of any kind.

• Status: verified (2026-10-09).

TC-1001 sabbagh_1977 (Sabbagh & Sadeghi, JQSRT 17, 297 (1977)): Xe I transition probabilities to 6s[3/2]2 and 6s[3/2]1, notes only; the source of Gornik et al.’s 6s-6p f values (2026-10-09)

• Where: src/optmat/data/sources/sabbagh_1977.toml (notes only).

• Transcribed: nothing as data. Table 2 prints Einstein A (10^6 s^-1) of 25 Xe lines (20 to 6s[3/2]2 from 6p, 6p’, 7p, 8p, 9p, 4f, 5f; 5 from 6p to 6s[3/2]1), relative absorption measurements in a 132Xe afterglow normalised to A(8819) = 30 ± 0.5 and A(8280) = 34 ± 2.5 x 10^6 s^-1 (literature means, Table 1); the vocabulary has no A (candidate transition_probability, with the 25 rows). Table images checked cell by cell; air wavelengths match NIST’s to 0.4 A.

• Finding (NIST, TC-983): NIST’s A equal this paper’s for 16 of the 20 lines to 6s[3/2]2 (tp_ref T3269); the four 7p lines differ (x 0.77-1.25, T8608); the five lines to 6s[3/2]1 are this paper’s times 36.9/34 = 1.085 (renormalised to A(8280) = 3.69e7 s^-1). A(7642)/A(8206) = 1.11 ± 0.13 against NIST’s 1.05.

• Finding (gornik_1981): Gornik et al.’s ‘experimental f values (Ref. 19)’ 0.12, 0.15, 0.30 for 6s[3/2]1 -> 6p[1/2]0, 6p[3/2]2, 6p[5/2]2 are this paper’s A of 8280, 8952.2 and 9923.2 A converted by its Eq. (3): 0.1165, 0.1502, 0.2953. NIST’s f are 0.127, 0.163, 0.321 (8-9 % higher), but NIST’s 0.265 for the resonance line against Gornik et al.’s 0.28 (matthias_1977) compensates: the products f1 f2 of the single path agree to 0.2, 2.8 and 1.3 %.

• Finding (bruce_1990): 6p[1/2]0 decays only by 8280 A (this paper), so Bruce et al.’s 26.8 ± 0.8 ns gives A = 3.73e7 s^-1, 10 % above the adopted 34 ± 2.5 x 10^6.

• Status: verified (2026-10-09).

TC-1002 matthias_1977 (Matthias et al., Chem. Phys. Lett. 52, 239 (1977)): resonance-line oscillator strengths of Kr and Xe from synchrotron lifetimes; Gornik et al.’s f = 0.28 traced (2026-10-09)

• Where: src/optmat/data/sources/matthias_1977.toml, tools/extract/ matthias_1977.py, data/values/absorption/{Kr,Xe}/matthias_1977__f_{Kr,Xe}.csv.

• Transcribed: Tables 1 (Kr) and 2 (Xe), row ‘this work’: the absorption oscillator strengths of the 3P1 -> 1S0 and 1P1 -> 1S0 resonance lines (Kr 0.208 ± 0.006, 0.197 ± 0.006; Xe 0.263 ± 0.007, 0.229 ± 0.007), oscillator_strength, label abscissa, use = "check". Scanned PDF; every cell checked against the table images. Levels mapped to NIST’s (2P3/2)ns 2[3/2] 1 and (2P1/2)ns 2[1/2] 1 by the headings’ wavelengths and Fig. 2.

• Erratum: Table 1’s heading ‘3f(1263 A)’ is 1236 A (NIST 123.5838 nm; Fig. 2 prints 1237 A; Table 1’s other rows satisfy Ladenburg at 1236, not 1263).

• Checked: every other pair of tau and f in both tables (39 pairs) against the Ladenburg relation at NIST’s wavelengths: within 1 % (one 2.3 %). The row ‘this work’ is not: its f are 0.963 (Kr 3P1), 0.937 (Xe 3P1) and 1.043 (Xe 1P1) times the f of its own lifetimes (Kr 1P1 agrees); script check.

• Finding (gornik_1981): Gornik et al.’s ‘f value of the 1S0 -> 6s[3/2]1 transition is 0.28 (Ref. 18)’ is not this paper’s printed 0.263 but the Ladenburg f of its lifetime 3.46 ns (0.281); 0.28 is also Table 2’s Chashchina-Shreider and Gruzdev values. NIST: 0.265 (A+).

• Finding (NIST): NIST’s 1/A is 3.356, 3.236, 3.663 and 3.953 ns against the measured 3.18, 3.11, 3.46 and 3.44 ns (5.2, 3.9, 5.5, 13.0 % shorter); NIST’s f 0.205, 0.189, 0.265, 0.191 against the printed 0.208, 0.197, 0.263, 0.229. Xe 5d[3/2]1: 1.40 ± 0.07 ns against NIST’s 1.68 ns.

• Not taken (awaiting vocabulary): the five lifetimes (the paper’s primary results; candidate radiative_lifetime). Not taken: the other rows (other papers’ values) and the figures.

• Status: verified (2026-10-09).

TC-1003 bruce_1990 (Bruce et al., J. Chem. Phys. 92, 2917 (1990)): radiative lifetimes and collisional quenching of two-photon excited Xe 6p, 6p’, 7p in Xe and Ar, notes only (2026-10-09)

• Where: src/optmat/data/sources/bruce_1990.toml (notes only).

• Transcribed: nothing as data; no quantity holds a lifetime or a quenching rate coefficient (candidates radiative_lifetime and collisional_quenching_rate_ coefficient, with every row). The notes list Table III’s nine lifetimes, Tables II and IV’s bimolecular (Xe, Ar) and termolecular (Xe) rates and the appendix’s state-to-state rates for 6p[1/2]0 <-> 5d[1/2]1 in Ar, all 2 sigma. Tables checked cell by cell against the images; levels mapped to NIST by Table I’s vacuum wavelengths (all within 0.05 nm) and the 132.3 and 77.7 cm^-1 gaps.

• Finding (NIST, TC-983): 1/sum A over NIST’s lines from each level against the measured lifetimes: 6p[5/2]2 39.4 / 36.0 ± 2.8 ns; 6p[3/2]2 27.3 / 31.3 ± 1.8; 6p[1/2]0 27.1 / 26.8 ± 0.8; the three 7p levels within 1 % (NIST T8608n); 6p’[3/2]2 22.8 / 32.1 ± 0.8 and 6p’[1/2]0 27.6 / 34.1 ± 0.8, where NIST’s main line alone (834.91 nm, 4.2e7 s^-1; 788.96 nm, 3.5e7 s^-1; both C+) exceeds the measured total decay rate and other branches lack A; 5d[1/2]1 65.6 / 111 ± 16 (trapped). OEP 8’s Gamma^rad from NIST is therefore 24 and 41 % too large for 6p’[1/2]0 and 6p’[3/2]2, 15 % for 6p[3/2]2 and 9 % too small for 6p[5/2]2, if these lifetimes are right.

• Doubt (as printed): 5d[1/2]1 + Xe 197 ± 26 (Table II), 196 ± 26 (text), 197 ± 27 (appendix); Moutard et al.’s 6p[3/2]2 termolecular rate 6.5 ± 5 x 10^-31 cm6/s (Table II) against 6.5 ± 0.5 x 10^-30 (note added in proof); 6p[1/2]0 + Ar 200 ± 4 (Table IV) against k1 = 183 ± 6 (appendix); chi = 0.1752 ‘at 300 K’ is the value at 296 K (0.1767 at 300 K).

• Finding (OEP 8): quenching is not the pure dephasing: 6p[1/2]0 + Xe, 5.9e-12 cm3/s, is a Lorentzian FWHM of 0.03 MHz/Torr, about 800 times below the 25 ± 15 MHz/Torr pressure broadening quoted in gornik_1981 (Hawkins et al. 1980); 6p[3/2]2 and 6p[5/2]2, 0.52 and 0.60 MHz/Torr.

• Status: verified (2026-10-09).

TC-1004 wiese_1989 (Wiese et al., Phys. Rev. A 39, 2461 (1989)): the Ar I 4s-4p and 4s-5p transition probabilities, held as notes awaiting a quantity (2026-10-09)

• Where: src/optmat/data/sources/wiese_1989.toml (no datasets); the candidate quantities transition_probability and radiative_lifetime with the exact rows drafted for the vocabulary (TC-1011).

• Transcribed: nothing. The paper prints A (1e6 s-1), branching ratios and lifetimes, no f, gf or weights. NOT TAKEN (awaiting vocabulary): Table IV, the recommended A of the 30 4s-4p lines (29 values, one bound, +-5 to +-30 %); Table VI, the 30 4s-5p lines (28 values, 2 sigma); Table I, the 16 measured branches of 5p[5/2]2 normalised to tau = 153 ns (the 12 5p-3d and 5p-5s ones are found nowhere else). Wavelengths are air. Tables II, III, V, VII and Fig. 2 are other papers’.

• Checked: every cell of Tables I, IV and VI against the table images (scanned PDF); every line identified by its printed air wavelength among NIST’s Ar I level pairs (residual <= 0.0006 nm, 750.384 nm 0.0028). Table I: sum of 100R = 100.01; every A = R / 153 ns within rounding but 3045.369 nm (0.148 against 0.1471). The sum of Table IV’s A per 4p level gives lifetimes within 3 % of Quadfasel and Helbig’s.

• Errata (labels and level energies; no A affected): Table IV 696.543 nm is 4p’[1/2]1 (printed 4p[1/2]1), 763.511 nm 4p[3/2]2 (printed primed); every [5/2]2 level printed primed in Tables II, IV and VI is unprimed; Table VI 394.898 nm is 5p’[1/2]1; Table I 5s[5/2]2 is 5s[3/2]2, 5s[1/2]1 is 5s’[1/2]1, E_i 99 143.80 is 93 143.80 and 114 716.61 is 113 716.61 (only the corrected energies give the printed wavelengths); Table IV 750.384 nm is 750.387 (Table III, NIST). The text’s adopted lifetime is printed “153 nm”.

• Finding: NIST ASD’s Ar I 4s-4p and 4s-5p A values (TC-983, key T5223) are this paper’s, rounded: Table IV / NIST mean 0.9996, mean |deviation| 0.17 %, largest 1.1 % (29 lines; 1148.811 nm via Shumaker and Popenoe renormalised, T1242n, the same value); Table VI / NIST mean 0.9987, largest 1.1 % (28 lines); all within NIST’s rounding, and NIST’s grades follow the paper’s uncertainties. The agreement is NIST quoting the paper, not an independent check. NIST’s 4p radiative widths therefore carry Wiese et al.’s scale (Quadfasel and Helbig’s lifetimes).

• Status: verified (2026-10-09).

TC-1005 dzierzega_2000 (Dzierżęga et al., Phys. Rev. A 62, 022505 (2000)): the Kr I 5p-5s transition rates, held as notes awaiting a quantity (2026-10-09)

• Where: src/optmat/data/sources/dzierzega_2000.toml (no datasets); the candidate quantities transition_probability and radiative_lifetime with the exact rows drafted for the vocabulary (TC-1011); wiese_1989 holds the argon counterpart.

• Transcribed: nothing. NOT TAKEN (awaiting vocabulary): Table IV, A_ki (1e6 s-1, one standard uncertainty, < 1 % to about 10 %) of all 30 5p-5s lines, 29 values and one bound, wavelengths in air; Table II, the semiempirical lifetimes of the ten 5p levels. Table I, Table V’s comparison columns and Table III’s LS transition moments (a model’s radial integrals, not state-to-state dipole moments) are not taken.

• Checked: every cell of Table IV against the PDF’s text layer and the table image; Table V’s A column identical to Table IV’s in all 30 rows; Table IV’s lifetimes are Table I’s beam-gas-laser values and Table II’s semiempirical ones, string for string; sum of F per level 0.999-1.001; sum of A per level = (1 - far-IR fraction) / tau within 0.15 % for all ten levels; every line identified by its air wavelength among NIST’s Kr I level pairs (residual <= 0.005 nm).

• Erratum (label): Tables IV and V print 2p9 (811.29 nm) as 5p[3/2]_3; it is 5p[5/2]_3, as Tables I and II print.

• Doubt: 2p7’s hollow-cathode branching fractions of 1286.19 nm (0.0031) and 1404.57 nm (0.0023) give F/tau 0.105 and 0.078, against the printed A 0.076 and 0.106: the F cells look interchanged; the A agree with Table V, with the order in every comparison column there, and with NIST.

• Finding: NIST ASD’s Kr I 5s-5p A values (TC-983, key T7199) are this paper’s, digit for digit (29 lines, ratio 1.0000); its missing A (557.468 nm vacuum, 2p1-1s4) is the paper’s bound < 0.04. The radiative widths of the ten 5p levels (sum of A) are 26.2 (2p10) to 43.3 (2p5) x 1e6 s-1.

• Status: verified (2026-10-09).

TC-1006 brandi_2002 (Brandi, Hogervorst & Ubachs, J. Phys. B 35, 1071 (2002)): absolute energies of three Kr levels including the two-photon 5p[1/2]0, and its measured light shift (2026-10-09)

• Where: src/optmat/data/sources/brandi_2002.toml, tools/extract/brandi_2002.py, data/values/ionisation/Kr/brandi_2002__level_{5d12_1,6s32_1,5p12_0}.csv.

• Transcribed: Table 4 (p. 1079): the energies of 86Kr 5d[1/2]1 (103 801.8002(12)), 6s[3/2]1 (99 894.0528(14)) and 5p[1/2]0 (94 092.8673(13) cm^-1) above the ground level, from 1VUV + 1UV and 2UV + 1UV photoionisation in a collision-free atomic beam calibrated on I2; three level_energy datasets (one-row files), isotope = "86Kr", uncertainties as printed (statistics, 30 MHz chirp, 20 MHz Doppler; level not stated). The text’s 86Kr ionisation energy, 112 914.516(14) cm^-1, inline, use = check: Yoon and Glab’s limit moved by this paper’s corrections. Labels mapped to NIST’s (2P*<3/2>) 5d 2[1/2]* 1, 6s 2[3/2]* 1, 5p 2[1/2] 0 by energy and J.

• Checked: the text’s mean difference from Kaufman and Humphreys, -0.0558 cm^-1 with standard deviation 0.0005, from the three printed differences (script); all cells against the table images; text values on the PDF text layer.

• Finding: NIST’s Kr I levels (no isotope stated, no reference key in the held file) are this paper’s energies moved to 84Kr by its own isotope shifts (Table 2, -206, -112, -138 MHz): within 0.0004, 0.0006 and 0.0001 cm^-1; the 86Kr values lie 0.004-0.007 cm^-1 above NIST’s (script check, 0.001 cm^-1).

• Finding: NIST’s limit, 112 914.433(16) cm^-1 (13.9996055 eV, nist_asd_2026 ie_Kr_I), is 0.083 cm^-1 below this paper’s 86Kr value and 0.067 below Klar et al.’s 112 914.50(2), beyond both uncertainties; the isotope shift (about 0.008 cm^-1 per two mass units) does not explain it.

• Finding (OEP 8): the ac Stark shift of the two-photon 4p6 - 5p[1/2]0 transition of 84Kr at 212.55 nm is +0.75(48) Hz (W cm^-2)^-1 (blue), linear to about 260 MW cm^-2, sub-linear with an asymmetric line at 2.6 GW cm^-2 (Sec. 3.3); the Stoicheff group’s 2.6(1.1) is quoted as not fully compatible. In OEP 8’s convention this is Re alpha_f - alpha_g = -16(10) au, the power density taken as the intensity. Not taken: no quantity (candidate light_shift_coefficient).

• Not taken (awaiting vocabulary): the isotope shifts of Table 2 (five transitions, five isotopes, MHz) and the 83Kr 5p[5/2]2 hyperfine constants A = -155.6(1.2), B = -428(25) MHz. Not a gas quantity: the King-plot factors (Table 3), the instrumental line widths.

• Status: verified (2026-10-09).

TC-1007 werbowy_2026 (Werbowy, J. Quant. Spectrosc. Radiat. Transfer 362, 110041 (2026)): static scalar and tensor polarisabilities of the Ar 4s and 4p levels from the dc Stark effect; notes only (2026-10-09)

• Where: src/optmat/data/sources/werbowy_2026.toml (no datasets).

• Transcribed: nothing as data. The notes record the paper’s quantities, all in kHz/(kV/cm)^2 (alpha/h, shift -(1/2) alpha F^2; divide by 0.2488319 for au): the measured scalar differences Delta alpha_0 of 21 Ar I 4s-4p lines (20 (5) to 230 (20), fields to 500 kV/cm; Table 1), the level alpha_0 fitted to them (4s 56-96, 4p 95-327 = 382-1314 au; Table 3), the calculated alpha_0 and alpha_2 (NIST, CI-MBPT, measured line strengths), and the bound |alpha_2| < 10 from the absence of splitting. The polarizability quantity is the ground-state per-particle value behind the refractivity, with no level parameter: an excited level’s value cannot go there. Candidates level_polarizability and polarizability_difference. Level labels mapped to NIST’s by energy (the paper’s energies are NIST’s to its three decimals; it omits the core).

• Checked: every fitted Delta alpha_0 of Table 1 (30 lines) is the difference of Table 3’s fitted level values, exactly; the calculated columns within 1 unit; every air wavelength is NIST’s level difference within 0.001 nm; all cells against the table images.

• Doubt: misprints outside any value: the text’s ‘772.367 nm’ (Table 1: 772.376); Table 2’s ‘1047.803’ (1047.005).

• Finding (OEP 8): these are static polarisabilities, dominated by 4p-3d and 4p-5s lines at 1.2-2.4 um; at the Ar 4p two-photon wavelengths (184-192 nm) the photon energy exceeds the 4p binding energy, so they do not give the light shifts Re alpha_f that OEP 8 needs.

• Status: verified (2026-10-09).

TC-1008 haber_2009 (Haber, Doughty & Leone, J. Phys. Chem. A 113, 13152 (2009)): two-colour two-photon ATI sidebands of argon (harmonic + 800 nm), cross-section ratios and anisotropy parameters; context only (2026-10-09)

• Where: src/optmat/data/sources/haber_2009.toml (no datasets).

• Transcribed: nothing. The notes keep Table 1 (p. 13157). It gives the ratio sigma(+)/sigma(-) of the argon sideband cross sections, absorption against emission of one 800 nm photon: 1.39 +- 0.04 with the 13th harmonic (20.1 eV) and 1.27 +- 0.05 with the 15th (23.2 eV). It also gives beta_2 and beta_4 of each sideband, from experiment, second-order perturbation theory (SOPT) and the soft-photon approximation (SPA), and the single-photon beta_2 and beta_4 at both harmonics (p. 13155). The uncertainty’s level is not stated.

• Checked: Table 1’s image against the extracted cells and the text (pp. 13155-13157); every value agrees except one (Doubt). The harmonic energies are inferred from the photoelectron peaks (4.30 and 7.42 eV) and match the 2P3/2 threshold, 15.7596 eV (NIST). The 2P3/2 and 2P1/2 cores are not resolved. The final waves are p and f.

• Doubt: the SOPT beta_2(-) for the 15th harmonic is printed 1.69 in Table 1 and 1.63 in the text (p. 13156). The text calls its agreement with the measured 1.63 +- 0.12 ‘fortuitous’. The paper does not show which is the misprint.

• Not taken: sideband cross-section ratios and photoelectron anisotropy parameters have no quantity. They await the vocabulary, with a candidate written. There is no absolute cross section, so multiphoton_ionization_cross_section cannot hold them, and the (-) sideband is not two-photon absorption. Also not taken: the background anisotropy parameters (instrumental, by the authors’ account); the SOPT sigma_pz/sigma_pxy ratios (model only); Figs. 1-6 (raster).

• Finding: for OEP 8 (TC-984, Q6), the (+) sideband is a nondegenerate amplitude with half-separation nu of about 9.3 and 10.8 eV. The harmonic alone ionises, far above Ar 4s[3/2]1 (11.62 eV), so the harmonic-first intermediate is on shell in the continuum. Like mccann_1988 it tests nothing at small splits. It is also summed over channels, and only as a ratio.

• Status: verified (2026-10-09).

TC-1009 vinbladh_2022 (Vinbladh, Dahlström & Lindroth, Atoms 10, 80 (2022)): relativistic two-colour two-photon matrix elements (RRPA, length gauge) for RABBIT delays of Ar, Kr, Xe; context only (2026-10-09)

• Where: src/optmat/data/sources/vinbladh_2022.toml (no datasets).

• Transcribed: nothing. The paper publishes only delays, all in vector figures (Figs. 2-7):

  • the atomic and Wigner delays per fine-structure channel (Ar 3p_j, Kr 4p_j, Xe 5p_j and Xe 4d_j), against the total absorbed photon energy;

  • two text values at the 90 eV sideband (pp. 17-18).

  It prints no cross section, no amplitude modulus and no IR photon energy for its calculations. The notes keep its matrix-element definition (eq. 46), which has the XUV-first time order only and is in length gauge.

• Checked: the captions’ thresholds against NIST (ionization_energies.csv and <X>_II_levels.tsv): Ar 15.76/15.94, Kr 14.00/14.67 and Xe 12.13/13.44 eV agree to their last digit.

• Doubt: a misprint, not an erratum (no dataset holds it). The argon fine-structure splitting is printed ‘0.18 meV’ (p. 15). The paper’s own thresholds differ by 0.18 eV, and NIST’s Ar II 2P1/2 level is 0.1775 eV.

• Not taken: the delays (Figs. 2-7) have no quantity. They await the vocabulary, with a candidate written. The thresholds are NIST’s, rounded.

• Finding: for OEP 8 (TC-984, Q6), the amplitudes are nondegenerate and resolved by channel (core j, final kappa), but only their phases are published. They are for pairs whose XUV photon alone ionises, above every first intermediate resonance (Ar 11.62, Kr 10.03, Xe 8.44 eV). Nothing is at small splits.

• Status: verified (2026-10-09).

TC-1010 OEP 8’s literature (TC-986 to TC-1009): what it settles, what it moves and what awaits vocabulary (2026-10-09)

• Where: the 24 records of TC-986 to TC-1009; OEP 8 (docs/oeps/oep-0008-bound-two-photon-response.md, Draft), revised with these findings; pindzola_1975’s notes (its description of bebb_1966 corrected: the rare gases at the ruby line only).

• Datasets taken:

  • brandi_2002: three Kr level energies (86Kr) and its ionisation limit.

  • matthias_1977: the Kr and Xe resonance-line oscillator strengths.

  • manakov_1986: He and Xe alpha and gamma at 1060 and 695 nm, reproduced.

  • bebb_1966: the Xe seven-photon cross section, a check.

  The other 20 records hold notes only. No krypton two-photon ionisation cross section was found in any form beyond those of TC-942, so OEP 6’s Q2 stands.

• Settled for OEP 8:

  • The equations. Its coupling and light-shift conventions agree with Kaufman et al., Tóth et al., Knight et al. and Manakov et al. (TC-989 to TC-991, TC-993). Ackerhalt and Shore’s rate reduces to its \(W=\sigma_0g\Phi^2\) (TC-992).

  • The residue. Lehmberg et al.’s 1976 n2 theory is OEP 8’s Eq. (9) at \(\Gamma\to0\), with \(M=2P^-\); recomputed to the printed digits (TC-997).

  • The pair form. It is confirmed by the Cs dark-pulse experiments, and fails measurably when an intermediate pole lies inside the spectrum (Rb, TC-986 to TC-988).

• Moved for OEP 8:

  • A field-strength condition for adiabatic elimination, \(|d E_0|/(2\hbar D)\ll1\), alongside the spectral one. Kaufman et al.’s error is the intermediate-state admixture, \(2(\mu E_0/2\hbar D)^2\), 3.1 % in their case against the spectral bound’s 0.2 % (TC-990).

  • The xenon real-part tension (Q1) is between strengths, not between theory and measurement.

    • Lehmberg et al.’s own calculated n2 implies \(\delta(6p[1/2]_0)=1436\) au. The measured n2 with that level alone implies 1698–1922 au. Pindzola et al.’s length form gives 1541 au.

    • Kröll and Bischel’s measurement (580 au) and Henriksson et al.’s TDDHF (752 au) are the other side.

    • Light shifts are ruled out: about 0.09 cm⁻¹ at Lehmberg’s intensity (TC-997, TC-998).

  • The radiative widths. Bruce et al.’s measured Xe lifetimes differ from NIST’s \(1/\sum A\):

    • 6p′[3/2]₂ and 6p′[1/2]₀: 32.1 and 34.1 ns against 22.8 and 27.6 ns;

    • 6p[3/2]₂: 31.3 against 27.3 ns;

    • 6p[5/2]₂: 36.0 against 39.4 ns;

    • 6p[1/2]₀ agrees.

    For these levels NIST’s A values are incomplete or graded C+ (TC-1003).

  • The independence of the NIST A values. NIST’s Ar 4s-4p and 4s-5p values are Wiese et al.’s, its Kr 5s-5p values are Dzierżęga et al.’s, and its Xe lines to 6s[3/2]₂ are Sabbagh and Sadeghi’s. Agreement with NIST is therefore not an independent check (TC-1001, TC-1004, TC-1005).

  • The He 1s2s light shift. Kumar et al.’s continuum term follows Knight et al.’s co-rotating Eq. 2.10 only; the counter-rotating term (Knight’s Eq. 3.29) may be missing, of unknown size (TC-989).

  • The first measured Kr two-photon light shift: 5p[1/2]₀ at 212.55 nm, +0.75(48) Hz/(W cm⁻²) (TC-1006).

• Single-path inputs traced: Gornik et al.’s 6s–6p f values (0.12, 0.15, 0.30) are Sabbagh and Sadeghi’s A values converted, and their resonance f = 0.28 is converted from Matthias et al.’s lifetime. NIST’s values are 8–9 % higher and 0.265. The two offsets cancel in the single-path product to within 0.2–2.8 % (TC-1001, TC-1002).

• Awaiting vocabulary (rule 7; candidates with their exact rows, put to the maintainer). Nothing below is a dataset until a quantity is approved:

  • transition probabilities (wiese_1989, dzierzega_2000, sabbagh_1977);

  • radiative lifetimes (bruce_1990, matthias_1977, dzierzega_2000, wiese_1989);

  • collisional quenching rate coefficients (bruce_1990);

  • excited-level polarisabilities (werbowy_2026, manakov_1986, zon_1972);

  • light-shift coefficients (brandi_2002);

  • isotope shifts and hyperfine constants (brandi_2002);

  • two-colour sideband ratios and anisotropy parameters (haber_2009);

  • photoionisation delays (vinbladh_2022);

  • the excited-state three-photon cross sections of He (zon_1972);

  • a per-atom SI chi(3) convention (tunnermann_1992).

• Finding, not a change: NIST’s Kr ionisation limit (nist_asd_2026/ie_Kr_I, 112914.433(16) cm⁻¹) is 0.067–0.083 cm⁻¹ below brandi_2002’s and Klar et al.’s values, more than either uncertainty. No recommended value is changed here.

• Papers to request:

  • Kligler et al., J. Appl. Phys. 49, 2219 (1978): a third measurement of the Xe 6p[1/2]₀ strength;

  • Toma and Muller, J. Phys. B 35, 3435 (2002): Ar two-colour matrix elements;

  • Hutchinson and Ness (Xe LICS light shifts);

  • Bowering, Bruce and Keto (1986; Xe 6p lifetimes);

  • Nandi et al., Nature 608, 488 (2022) (He resonant two-photon ionisation).

  Full citations are in the records.

• Status: verified (2026-10-09).

TC-1011 Vocabulary: five quantities for the bound levels’ radiative and collisional data (2026-10-09)

• Where: src/optmat/vocabulary.py, docs/data.md (the quantities table).

• Added (all in the absorption family; approved by the maintainer on 2026-10-09, from the candidates of TC-1010):

  • transition_probability. The Einstein A_ki of a transition, in 1/s, against its wavelength or a label. It requires notation, the level notation of the labels.

  • radiative_lifetime. The collision-free lifetime of a labelled level, in fs, ps, ns or s. It requires method.

  • level_polarizability. The dipole polarizability of a stated level, static (inf) or at a wavelength, in au, SI, angstrom3, cm3 or kHz/(kV/cm)2. It requires configuration, term, j, component (scalar, vector or tensor; vector and tensor parts with the source’s shift formula in definition), complex_part (real or imaginary; not part, which the loader reserves for the third-order parts) and method. It is kept apart from polarizability, the gas’s value that the refractivity and n2 models read.

  • light_shift_coefficient. The shift of a multiphoton transition’s frequency per unit intensity, in Hz/(W/cm2), against the exciting photon’s wavelength. It requires final_level, photons and intensity_definition.

  • collisional_quenching_rate_coefficient. The collisional removal of a labelled level by a perturber, in cm3/s or m3/s (bimolecular) and cm6/s or m6/s (termolecular). It requires perturber, order and channel. It is a population loss, not pure dephasing.

• Not added (the maintainer’s decision, as recommended): isotope shifts and hyperfine constants, two-colour sideband ratios and anisotropy parameters, photoionisation delays, excited-state multiphoton cross sections and a per-atom SI chi(3) convention. They stay in their records’ notes.

• Use: OEP 8’s radiative widths (measured lifetimes preferred to NIST’s sum of A), light shifts and collisional dephasing.

• Status: decided (2026-10-09).

TC-1012 wiese_1989: the datasets under the quantities of TC-1011 (2026-10-09)

• Where: src/optmat/data/sources/wiese_1989.toml (TC-1004’s notes-only record, now with four datasets and eleven errata), tools/extract/wiese_1989.py, data/values/absorption/Ar/wiese_1989__{A_4s_4p,A_4s_5p,A_5p52_branches}.csv.

• Transcribed:

  • transition_probability (1/s, scale 1e6, notation = "racah"; label abscissa: x the transition lower-upper as printed, the row the printed air wavelength):

    • A_4s_4p: Table IV, all 30 lines (29 values, the <0.001 bound excluded), per-row relative uncertainties ±5-30 %, level not stated; primary.

    • A_4s_5p: Table VI, 28 values, ±5-20 %, 2 sigma; primary.

    • A_5p52_branches: Table I, the 15 measured branches of 5p[5/2]2 (419-4939 nm), Delta R as each row’s relative uncertainty (2 sigma); the lifetime’s common ±4.6 % is not included. check: Table VI supersedes its three 4s-5p lines.

  • radiative_lifetime: lifetime_5p52, the adopted 153 ± 7 ns of 5p[5/2]2 (text p. 2464, printed “153 nm”; mean of the authors’ 152 and Stryla et al.’s 154 ns), inline; primary.

  • Errata on x (the label), each with its evidence: the primed [5/2]2 levels (978.450, 842.465, 801.479, 462.844, 430.010, 419.071 nm), 696.543 nm (4p’[1/2]1), 763.511 nm (4p[3/2]2), 394.898 nm (5p’[1/2]1), and Table I’s 5s[5/2]2 (5s[3/2]2) and 5s[1/2]1 (5s’[1/2]1). Table IV’s 750.384 nm (750.387) is a row id and stays in the notes.

• Checked: by the script, which fails otherwise: every row’s label after the errata is the NIST Ar I level pair whose air wavelength is the printed one (unique within 0.006 nm, 0.08 nm for Table I’s infrared lines from older levels), so the errata are exactly the misprints; the record’s per-row uncertainties are the printed ones; Table I’s A are 100R / 153 ns within the rounding except 3045.369 nm, and its 100R sum to 100.01. The cells were checked against the table images (scanned PDF). The library test reproduces the files.

• Status: verified (2026-10-09).

TC-1013 dzierzega_2000: the datasets under the quantities of TC-1011 (2026-10-09)

• Where: src/optmat/data/sources/dzierzega_2000.toml (TC-1005’s notes-only record, now with two datasets and one erratum), tools/extract/dzierzega_2000.py, data/values/absorption/Kr/dzierzega_2000__{A_5p_5s,lifetime_5p}.csv.

• Transcribed:

  • A_5p_5s (transition_probability, 1/s, scale 1e6, notation = "racah"): Table IV, all 30 5p-5s lines; the row the printed air wavelength, x upper-lower in J_cK notation (Paschen labels kept in printed); per-row absolute uncertainty, 1 sigma; the <0.04 bound (557.31 nm) excluded; primary.

  • lifetime_5p (radiative_lifetime, ns, method semiempirical): Table II “This work”, the ten 5p levels, rows Paschen, x J_cK, 1 sigma; primary.

  • Erratum on x: 811.29 nm’s upper level printed 5p[3/2]3 is 5p[5/2]3 (2p9).

• Checked: by the script, which fails otherwise: every taken cell is in the PDF’s text layer (Table IV p. 5, Table II p. 3); Table V’s A column equals Table IV’s in all 30 rows; Table IV’s italic lifetimes are Table II’s; the sum of A per level is (1 - far-IR fraction) / tau within 0.2 % for all ten levels; every label after the erratum is the NIST Kr I level pair whose air wavelength is the printed one (unique within 0.006 nm). The interchanged-looking F of 2p7 (1286.19 and 1404.57 nm, TC-1005) do not touch the taken A. The library test reproduces the files.

• Status: verified (2026-10-09).

TC-1014 sabbagh_1977: the datasets under the quantities of TC-1011 (2026-10-09)

• Where: src/optmat/data/sources/sabbagh_1977.toml (TC-1001), tools/extract/ sabbagh_1977.py, data/values/absorption/Xe/sabbagh_1977__A_{6s2,6s1,reference}_Xe.csv.

• Transcribed: Table 2’s ‘Present work’, all 25 Xe I lines, as transition_probability (10^6 s^-1, scale 1e6), x the printed air wavelength in Angstrom (wavelength_medium = "standard_air"), rows in the paper’s Racah notation (notation = "racah"): the 19 lines to 6s[3/2]2 normalised to A(8819) = 30e6 and the 4 to 6s[3/2]1 normalised to A(8280) = 34e6 (primary, parameters.normalisation), and the two reference lines (check: means of Table 1’s literature values, not measured). Uncertainties per row as printed, level not stated. The library cell ‘6p[1/2]_6’ is labelled 6p[1/2]0 as the image prints it (kept in printed). The NIST configuration/term/J of every row is in the notes.

• Checked: the abstract’s counts (19 and 4 lines besides the references); the references equal Table 1’s mean values; gornik_1981’s f values 0.12, 0.15, 0.30 are Eq. (3) applied to the 8280, 8952.2 and 9923.2 Angstrom rows (script checks). The comparisons with NIST are TC-1001’s.

• Status: verified (2026-10-09).

TC-1015 matthias_1977: the datasets under the quantities of TC-1011 (2026-10-09)

• Where: src/optmat/data/sources/matthias_1977.toml (TC-1002), tools/extract/ matthias_1977.py, data/values/absorption/{Kr,Xe}/matthias_1977__tau_{Kr,Xe}.csv.

• Transcribed: the five measured lifetimes as radiative_lifetime (ns, label, use = "primary", method: resonance fluorescence after synchrotron excitation, extrapolated to zero pressure): Table 1 ‘this work’ Kr 3P1 3.18 ± 0.12 and 1P1 3.11 ± 0.12; Table 2 Xe 3P1 3.46 ± 0.09 and 1P1 3.44 ± 0.07 (script, rows 3P1/1P1, x the column heading as printed); Xe 5p5(2P3/2)5d J = 1 1.40 ± 0.07 ns (text p. 242 and abstract, inline tau_5d_Xe). ‘Cumulative errors’, level not stated. The f datasets of TC-1002 stay check.

• Checked: every table cell against the images (TC-1002); the Ladenburg checks of TC-1002 still run in the script. NIST mapping of each level in the notes.

• Status: verified (2026-10-09).

TC-1016 bruce_1990: the datasets under the quantities of TC-1011 (2026-10-09)

• Where: src/optmat/data/sources/bruce_1990.toml (TC-1003), tools/extract/ bruce_1990.py, data/values/absorption/Xe/bruce_1990__{tau,tau_5d,kq_self,kq3_self, kq3_bound,kq_Ar,kq_Ar_coupled}_Xe.csv; six inline appendix datasets.

• Transcribed (‘This work’, all 2 sigma as the paper states):

  • radiative_lifetime: Table III, eight 6p, 7p, 6p’ levels (primary); 5d[1/2]1, 111 ± 16 ns (check: radiation trapped, an intercept of intercepts).

  • collisional_quenching_rate_coefficient, perturber self: Table II bimolecular, nine levels (primary); termolecular 6p[1/2]0, 7.0 ± 0.5 x 10^-31 cm^6/s (primary); 6p[3/2]2 ‘<4’ held as the interval 0-4 (value 2, bound half-width 2; check).

  • perturber Ar: Table IV, the seven single-decay levels (primary); the coupled pair’s three rates, 6p[1/2]0 200 ± 4.0 and 5d[1/2]1 5.9 ± 0.4 and 5.5 ± 0.4 (check); the appendix’s state-to-state k12 = 170 ± 3 (channel 5d[1/2]1), k10 = 13 ± 6 (other Xe* states), k21 = 30 ± 1 (channel 6p[1/2]0), k20 = 4.6 ± 1.6, and totals k1 = 183 ± 6, k2 = 34 ± 2 (inline, primary). Not taken: k_Xe5d = 197 ± 27 (Table II’s 197 ± 26 is taken).

• Finding: Table IV’s 6p[1/2]0 and 5d[1/2]1 argon rates are the argon slopes of the coupled pair’s two decay eigenvalues, k12 (1 + chi) = 199.8 and (k10 chi + k20) / (1

  • chi) = 5.85 with the appendix’s rates (Eqs. A11-A12), not the levels’ removal coefficients k1 = 183 and k2 = 34; this explains the 200 against 183 that TC-1003 listed as a doubt. Also checked: k21 = chi k12 (29.8), k1 = k12 + k10, k2 = k21 + k20 (34.6), chi = 0.1752 at 296 K (script).

• Doubts (notes, no erratum): 197 ± 26 / 196 ± 26 / 197 ± 27 for 5d[1/2]1 + Xe; Moutard et al.’s termolecular rate 10^-31 (table) against 10^-30 (text); chi printed ‘at 300 K’ is the 296 K value.

• Status: verified (2026-10-09).

TC-1017 brandi_2002: the datasets under the quantities of TC-1011 (2026-10-09)

• Where: src/optmat/data/sources/brandi_2002.toml (two inline datasets); the record of TC-1006.

• Transcribed: light_shift_coefficient, Hz/(W/cm2), at 212.55 nm (vacuum, the photon of the two-photon 4p6 - 5p[1/2]0 transition, NIST (2P*<3/2>) 5p 2[1/2] J = 0), photons = 2: ls_5p12_0, the paper’s 84Kr measurement 0.75(48) (p. 1081; linear to about 260 MW cm^-2; positive, to the blue), use = primary, intensity_definition the paper’s power density (pulse energy over 6 ns and a 90 um Gaussian focus, 50 %); and ls_5p12_0_stoicheff, the Stoicheff group’s 2.6(1.1) quoted on p. 1082, use = reproduced from Balakrishnan, Smith and Stoicheff (1992, 1994; not in the library). Polarisation not stated. Isotope shifts and hyperfine constants stay in the notes as declined (TC-1011).

• Checked: both values and their wording on the PDF text layer (pp. 1071, 1081, 1082, 1083); the power density’s definition on p. 1080. In OEP 8’s convention 0.75(48) is Re alpha_f - alpha_g = -16(10) au (derived, in the notes only).

• Status: verified (2026-10-09).

TC-1018 werbowy_2026: the datasets under the quantities of TC-1011 (2026-10-09)

• Where: src/optmat/data/sources/werbowy_2026.toml, tools/extract/werbowy_2026.py, data/values/absorption/Ar/werbowy_2026__alpha{0,2}_<level>.csv (25 files); the record of TC-1007.

• Transcribed: level_polarizability, kHz/(kV/cm)2 as printed, static (x = inf), one dataset per level, the NIST configuration/term/J of each: alpha0_<level>, the 14 alpha_0 ‘Fitted to the experiment’ of Table 3 (4s 56-96, 4p 95-327; component scalar, complex_part real), use = check because only the differences between levels are measured and the paper does not say how the common zero of the fitted set was fixed; alpha2_<level>, the measured bound |alpha_2| < 10 (Table 3 note a; no Delta M splitting up to 500 kV/cm) for the 11 levels with J >= 1, as 0 with 10 at level bound, component tensor with Eq. 1 as the definition, use = check. Table 1’s measured differences and Table 3’s calculated columns stay in the notes (differences declined, TC-1011).

• Checked: by the script, every fitted Delta alpha_0 of Table 1 (30 lines) is the difference of the fitted level values, exactly; the abstract’s alpha_0 ranges are Table 3’s; every level energy is NIST’s (Ar_I_levels.tsv) to the printed three decimals. All cells taken against the table image.

• Status: verified (2026-10-09).

TC-1019 manakov_1986: the datasets under the quantities of TC-1011 (2026-10-09)

• Where: src/optmat/data/sources/manakov_1986.toml (three inline level_polarizability datasets; the record’s earlier entry is TC-993).

• Transcribed: the text of p. 376, He 1s.2s 3S J = 1, all quoted by the review, so use = reproduced:

  • he_2s3s1_tensor_static: the tensor part measured in a dc field, ‘alpha^T_{2 3S1}(0) = (3.53 +- 0.14) x 10^-2 atomic units’ (scale 0.01, sigma 0.14 in the printed scale, level not stated). It is reproduced_from Player and Sandars, Phys. Lett. 30A, 475 (1969). The x is inf nm (static).

  • he_2s3s1_vector_omega_n (-12.1 au) and he_2s3s1_tensor_omega_n (4.04 au): the vector (axial) and tensor parts at omega_N = 0.043 hartree (1.17 eV), calculated, no uncertainty. Both are reproduced_from Manakov and Ovsiannikov, Zh. Eksp. Teor. Fiz. 75, 803 (1978).

  • Every dataset has complex_part real. definition is the review’s shift formula, Eqs. 5.6-5.8 (p. 373): the linear bracket for the tensor parts, and the circular one, alpha^a M/(2J), for the vector part. That Player and Sandars’s value uses the same normalisation is the review’s statement; their paper is not in the library. The scalar part of 2 3S1 is not printed.

• Checked: the three values against the rendered p. 376. The datasets load and give 0.0353 +- 0.0014, -12.1 and 4.04 au at inf and 1059.6 nm.

• Status: verified (2026-10-09).

TC-1020 zon_1972: the datasets under the quantities of TC-1011 (2026-10-09)

• Where: src/optmat/data/sources/zon_1972.toml (TC-996), three inline datasets of level_polarizability, all He, scalar, use check (the authors’ quantum-defect Green’s function calculations; no uncertainty stated):

  • alpha_1s2s_1S0: 1s.2s 1S J = 0, real, ‘270 atomic units’ (p. 518); wavelength cell ‘not stated’: the paper does not write the frequency. Its paragraph (the shift of 2 1S0 in the ruby field) implies the ruby frequency, 14402.2 cm^-1 (p. 517); the doubt is in the dataset’s notes and parameters.

  • alpha_1s6s_1S0_real and alpha_1s6s_1S0_imaginary: 1s.6s 1S J = 0, 300 and 35 au ‘for the frequency corresponding to a ruby laser’, at 14402.2 cm^-1 as printed (vacuum wavenumber, 694.34 nm).

• Transcribed: the three printed values, as printed, with the paper’s shift convention (-(1/4) E^2 alpha, the quantity’s). The excited-level three-photon cross sections stay in the notes, declined (TC-1011).

• Checked: the values against the page image of p. 518 and the ruby frequency against p. 517. Im alpha = 35 au corresponds through the paper’s Eq. (8) to a 1s6s photoionisation cross section of 5.9e-18 cm^2 at 1.786 eV (derived, not data).

• Status: verified (2026-10-09).

TC-1021 kligler_1978 (Kligler, Pritchard, Bischel & Rhodes, J. Appl. Phys. 49, 2219 (1978)): two-photon excited Xe at 248.4 nm; a lower bound and an estimate, not a third 6p[1/2]0 strength (2026-10-09)

• Where: src/optmat/data/sources/kligler_1978.toml, tools/extract/kligler_1978.py, data/values/ionisation/Xe/kligler_1978__sigma_over_I_Xe.csv.

• Transcribed: Table I’s Xe+ row (1930 Angstrom), the estimated two-photon ionisation coefficient sigma/I = 1 x 10^-34 cm^4/W (one intermediate state, mu^2 = 1 D^2, 16 x 10^3 cm^-1, linewidth ~10^9 MHz), multiphoton_ionization_cross_section, unit cm4 W-1, use = check. Everything else is in the notes: the measured lower bound sigma_Xe >= 5 x 10^-27 cm^2 at 3 x 10^9 W/cm^2 (unit branching assumed), Table I’s line-centre estimates for bound transitions (Xe 6p 3 x 10^-31 cm^4/W at 2484 Angstrom, Kr 6p, H2, CO, N2, I2, N2O), and the XeO* quenching rates. None of these fits a quantity.

• Checked: Table I’s cells against the image. The script checks three things:

  • Table I’s 3 x 10^-31 times 3 x 10^9 W/cm^2 is the text’s sigma ~ 10^-21 cm^2.

  • The Xe+ value equals bischel_1979’s copy (TC-917).

  • The lower bound recomputes from the printed counts, efficiency, volume, duration, intensity and density: 5 x 10^20 cm^-3 s^-1, then 5.3 x 10^-27 cm^2.

• Finding (OEP 8, Q1): this paper is not a third measurement of the Xe 6p[1/2]0 strength.

  • Its measurement is a lower bound on unresolved Xe* production. The laser is at 248.4 nm, 396 cm^-1 from 6p[1/2]0 on the two-photon scale, and the paper does not give its bandwidth. In TC-952’s terms the bound is sigma_2 >= 1.4 x 10^-54 cm^4 s. With an assumed 100 cm^-1 Gaussian laser (bischel_1979’s estimate) at resonance, that gives sigma_0 >= 4 x 10^-41 cm^4, 10^-6 of kroll_1990’s value: uninformative.

  • The 6p estimate uses placeholder moments. From Table I’s inputs alone (printed), TC-952’s convention gives delta^TP = |M|^2 = 5.9 au, sigma_0 = 5.1 x 10^-37 cm^4.

  • The printed 3 x 10^-31 cm^4/W can be converted with a 10^6 MHz Lorentzian (the line shape is assumed). That gives sigma_0 = 2.4 x 10^-36 cm^4, 27 au (Gaussian: 19 au).

  • Both are 20 to 100 times below kroll_1990 (580 au, TC-890) and henriksson_2005 (752 au, TC-888).

  • Eq. (2) reproduces the printed estimates (Xe 2.6, Kr 2.9, N2 1.05, I2 1.64 against 3, 3, 1.1, 1.7) only if g is normalised in ordinary frequency. Xe+ gives 1.0 x 10^-33 against the printed 10^-34.

• Finding (bischel_1979, TC-917): that record’s DOUBT (Table I’s Kr level ‘103,762’ against the text’s ‘103 363’) is answered. 103,762 cm^-1 is NIST’s Kr 4p5 6p[1/2]0 (103761.634) and 103 363 is 6p[3/2]2 (103362.612): two real levels, no misprint. bischel_1979’s Xe and Kr bound estimates are this paper’s, scaled by its 3x wider laser line.

• Doubt: footnote (g) on the Xe+ and N2O linewidths (‘Cordes bands’, which belong to I2) appears misplaced. No value depends on it.

• Status: verified (2026-10-09).

TC-1022 hawkins_1980 (Hawkins, Egger, Bokor & Rhodes, Appl. Phys. Lett. 36, 391 (1980)): the Xe 6p[1/2]0 two-photon line with a 150 MHz KrF laser; its pressure broadening awaits vocabulary (2026-10-09)

• Where: src/optmat/data/sources/hawkins_1980.toml (quantity of TC-1040).

• Transcribed: the measured line position 80118.73 ± 0.10 cm^-1 (p. 392), level_energy of 5p5(2P*3/2)6p 2[1/2] J = 0, inline, use = primary.

• Checked: on the rendered p. 392 and Fig. 2.

• Finding: NIST gives 80118.962 cm^-1, 0.23 cm^-1 above this paper, which is 2.3 times the paper’s stated ± 0.10. The printed 249.63 nm is the two-photon vacuum wavelength (249.6296 nm). It agrees with gornik_1981 (TC-922), kroll_1990 (TC-890), lehmberg_1995 (TC-854) and kligler_1978.

• Finding: the paper quotes its widths on the KrF (one-photon) scale.

  • Fig. 2’s Doppler bar (about 1.3 GHz) is xenon’s co-propagating two-photon Doppler width (2.58 GHz, kroll_1990), halved.

  • The pressure broadening ‘25 ± 15 MHz/Torr’ does not state FWHM or HWHM, its frequency scale, perturber, temperature or the level of the ±.

  • gornik_1981 reads it as an ordinary-frequency FWHM. bruce_1990 (TC-1003) compares it with quenching as ‘about 800 times’: that holds on the two-photon scale. On the KrF scale the ratio is about 1600.

• First held as notes, then taken (below, after TC-1040): the broadening coefficient. The candidate pressure_line_coefficient (broadening and shift, with effect, transition, photons, frequency_scale, width, frequency_variable and perturber) would also hold gornik_1981’s Table II shifts (-2.5 x 10^-9 s^-1 cm^3 = -13.0 MHz/Torr).

• Status: verified (2026-10-09).

Taken after TC-1040 (2026-10-09)

• Transcribed: the pressure broadening ‘25 ± 15 MHz/Torr’ (p. 392) as pressure_line_coefficient, inline broadening_Xe, unit MHz/torr, use = primary. Parameters: effect broadening, transition 1S0 -> 6p[1/2]0, photons 2, frequency_variable ordinary. frequency_scale and width are held as ‘not stated’. The perturber is self, inferred, because pure xenon is the only gas named.

• Changed: the record’s NOT TAKEN (awaiting vocabulary) sentence now says what is taken.

• Checked: gornik_1981’s Fig. 6 slope (~25 MHz/Torr, on the two-photon scale, not deconvolved) agrees, as gornik_1981 says. So the two-photon-scale reading is the consistent one, but Hawkins et al. do not state it.

• Status: verified (2026-10-09).

TC-1023 gornik_1980 (Gornik et al., Phys. Rev. Lett. 45, 1941 (1980)): dipole-forbidden two-photon excitation of Xe 5d J = 3; the model’s oscillator strengths (2026-10-09)

• Where: src/optmat/data/sources/gornik_1980.toml.

• Transcribed: two oscillator_strength model inputs (p. 1943), inline, use = check, assumed = true:

  • f = 0.28 for the 5p6 -> 6s[3/2]1 resonance line (‘taken from the measured lifetime’, reproduced_from matthias_1977);

  • f = 0.232 for 6p[3/2]2 -> 5d[5/2]3 (Aymar and Coulombe 1978, not in the library).

• Not taken: the measured rates (0.03 and 0.02 s^-1 to 5d[5/2]3 and 5d[7/2]3, at ~5 MW/cm^2 and 15 GHz, factor 3) and the quadrupole matrix elements: no quantity.

• Checked: on the rendered pp. 1942-1943. The two-photon lines’ 242.6 and 247.0 nm are NIST’s 5d[5/2]3 and 5d[7/2]3 (242.63 and 247.01 nm).

• Finding: 0.28 is the Ladenburg conversion of matthias_1977’s 3.46 ns (0.281), not its printed 0.263 (as TC-1002 found for gornik_1981). NIST gives 0.265. NIST’s 3107.77 nm line has f = 0.15 (C), so Aymar and Coulombe’s 0.232 is 1.55 times NIST’s.

• Finding: the E1-E1 rate quoted from Ref. 13 (3.5 x 10^3 s^-1, 1.8 MW/cm^2, 2.8 GHz) equals gornik_1981’s (TC-922). Eq. (2)’s line factor is the Gaussian gornik_1981 states, without the Doppler term. No 6p[1/2]0 number is given.

• Status: verified (2026-10-09).

TC-1024 gornik_1982 (Gornik, Matthias & Schmidt, J. Phys. B 15, 3413 (1982)): Xe2 g states; the forbidden 6s[3/2]2 two-photon line and a quoted three-body rate (2026-10-09)

• Where: src/optmat/data/sources/gornik_1982.toml.

• Transcribed: two inline datasets.

  • The atomic line at 67 073 cm^-1, as level_energy of 6s[3/2]2. Use = check; the tuning accuracy ‘better than 10 cm^-1’ is held as a bound.

  • The quoted k3 = 5 x 10^-32 cm^6 s^-1 for the 3P1 and 3P2 levels (Bonifield et al. 1980, ‘approximate’), as collisional_quenching_rate_coefficient. Order 3, perturber self, use = check, assumed = true.

• Not taken: everything about Xe2 (not a material). Also alpha = 2 x 10^-35 cm^4 W^-1 and W = 10^-2 s^-1 for the forbidden 1S0 -> 6s[3/2]2 line: a line-centre coefficient for a 25 GHz laser, not the frequency-integrated quantity.

• Checked: on the rendered pp. 3414, 3416, 3420.

  • alpha I^2 / hbar omega at 20 MW/cm^2 is 1.2 x 10^-2 s^-1, the printed W.

  • NIST’s 67067.547 cm^-1 lies within the bound.

• Finding: in this paper’s alpha, gornik_1981’s measured 6p rates (TC-922) give 7.9 x 10^-27 (6p[1/2]0) and 8.5 x 10^-28 (6p[3/2]2) cm^4 W^-1. Those are 4 x 10^8 and 4 x 10^7 times 2 x 10^-35: the paper’s ‘about seven orders’ holds for 6p[3/2]2. No 6p[1/2]0 strength is given.

• Status: verified (2026-10-09).

TC-1025 bowering_1986 (Böwering, Bruce & Keto, J. Chem. Phys. 84, 709 (1986)): state-to-state rate constants of two-photon excited Xe 6p in xenon (2026-10-09)

• Where: src/optmat/data/sources/bowering_1986.toml, tools/extract/ bowering_1986.py, data/values/absorption/Xe/bowering_1986__k_{2p6,2p7,2p8,2p9,2p10, 1s2,sum}_Xe.csv.

• Transcribed: Table II (p. 711), collisional_quenching_rate_coefficient (TC-1011), perturber self, order 2: the rate constants from 6p[1/2]0, 6p[3/2]2 and 6p[5/2]2 into each product (one dataset per channel: 6p[3/2]2, 6p[3/2]1, 6p[5/2]3, 6p[5/2]2, 6p[1/2]1, 6s’[1/2]1), 0.069 to 46 x 10^-12 cm3/s, primary; the row Sigma_j nu_ij, the sum of the observed channels, check. Uncertainty level not stated. Scanned PDF; the tables checked cell by cell against the images.

• Erratum: Table II’s caption prints ‘10^-2 cm3 s-1’; the unit is 10^-12 (scale errata on all seven datasets; evidence: the sums against paper II’s totals, and the gas-kinetic limit).

• Checked: the sums (6.57, 87.3, 77.0 against 6.6, 87, 77); Table III’s measured fractions for 6p[1/2]0 and 6p[3/2]2 within 0.006; Table I’s ten air wavelengths against NIST’s vacuum wavelengths (TC-985) converted to air, within 0.05 nm (the level mapping); the 2p10 - 1s2 gap 84 cm-1 (NIST 84.104).

• Finding: Table I’s branching ratios (Horiguchi et al.) against NIST: 2p6 0.700 / 0.300 (NIST 0.779 / 0.221), 2p9 0.363 / 0.637 (0.488 / 0.512), 2p7 and 2p10 within 0.03. Against ku_1986’s Table III the 6p -> 6p transfers agree within the errors except 2p6 -> 2p7 (0.64 against 1.3 x 10^-11); the 6s’[1/2]1 channel disagrees (2p9 -> 1s2 2.2 +- 0.8 here, < 0.2 there).

• Doubt: Table III’s 6p[5/2]2 column sums to 1.03 and does not reproduce from Table II (0.18 against 0.16 for 6p[5/2]3); Table I’s 2p10 branching ratios sum to 1.010.

• Status: verified (2026-10-09).

TC-1026 bowering_1986b (Böwering, Bruce & Keto, J. Chem. Phys. 84, 715 (1986)): lifetimes and total quench rates of two-photon excited Xe 6p in xenon (2026-10-09)

• Where: src/optmat/data/sources/bowering_1986b.toml, tools/extract/ bowering_1986b.py, data/values/absorption/Xe/bowering_1986b__{tau,tau_low,kq_self, kq3_self,kc_1s2,kc_1s3,k12,k13,k10,k21,k31}_Xe.csv; three inline text datasets.

• Transcribed: radiative_lifetime: Table I, 2p5 28 +- 1, 2p6 35 +- 3, 2p9 30 +- 4 ns (primary); 2p9 36 +- 4 from 1-10 Torr (check; the library cell ‘30 ± 436 ± 4^a’ split as the image shows); 2p10 49.6 +- 17.5 and 43.8 +- 8.0 ns (text, check). collisional_quenching_rate_coefficient, perturber self: Table II binary, the six 6p levels, 5.9 (2p5) to 295 (2p10) x 10^-12 cm3/s, and tertiary 2p5 6.5 +- 0.6 x 10^-31 cm6/s (primary); 2p8 (4.5 +- 1.0) x 10^-11 from the time-integrated ratios (text, check); Table III’s coupled 6s’[1/2]1 and 6s’[1/2]0 rates (check: eigenvalue slopes of the pairs with 2p10, the caution of TC-1016); Table IV’s model rates k12, k13, k10, k21, k31 (check: derived, no uncertainties; k21 set to Ref. 4’s total). Uncertainty level not stated (Fig. 3’s errors 2 sigma). Scanned PDF; tables checked cell by cell.

• Checked: Table IV against detailed balance at 294 K with NIST energies (kappa 1.509 and 63.4 against 1.51 and 63.5), k10 = k1tot - k12 - k13, Eq. (10) (2.74e-10 against ‘on the order of’ 2.8e-10), Eq. (8) (43.8 ns).

• Finding: Table V’s cross sections are Table II’s rates over one mean relative speed, 2.97e4 cm/s, the speed at 273 K, not at the measurement’s 296 K: about 4 % high. Lifetimes against NIST’s 1/sum A (TC-985): 2p6 35 against 27.2, 2p10 43.8 against 30.4; 2p5, 2p9 consistent within the errors. No 6p’ or 7p level is measured: the paper does not bear on bruce_1990’s 6p’ disagreement with NIST (TC-1003, TC-1010).

• Doubt: Table IV prints k12 and k21 as ‘kappa12’, ‘kappa21’, the equilibrium coefficient’s letter; the stated temperature is 296 K (p. 716) and 294 K (p. 721).

• Status: verified (2026-10-09).

TC-1027 ku_1986 (Ku & Setser, J. Chem. Phys. 84, 4304 (1986)): lifetimes, total and state-to-state quenching of Xe 6p in xenon and argon (2026-10-09)

• Where: src/optmat/data/sources/ku_1986.toml, tools/extract/ku_1986.py, data/values/absorption/Xe/ku_1986__{tau,tau_Ar,kq_self,kq_slow,kq_Ar,kq_Ar_coupled, k_2p6,k_2p7,k_2p8,k_2p9,k_2p10,k_1s2,k_1s3_6s,k_2p10_bound,k_1s2_bound}_Xe.csv; five inline text datasets.

• Transcribed (300 K): radiative_lifetime: Table I, the six 6p levels in xenon, 32.3-39.3 ns (primary); Table II, 2p5, 2p6, 2p9 from the argon intercepts (check). collisional_quenching_rate_coefficient: Table I’s k_Q by xenon, six levels, 0.58 to 13.3 x 10^-11 cm3/s (primary), the 2p10 slow component’s slope (check, coupled pair); Table II, Ar: 2p6, 2p9 (primary), 2p5’s fast and slow components (check, coupled with 3d5); Eqs. (1a)-(2c), the 2p5/3d5 rate scheme in Ar (1a, 1b primary, +-20 %; 2a, 2b and the 3d5 + Xe rate check); Table III, the state-to-state k_ij by xenon, one dataset per channel (primary), the two ‘<0.2’ as intervals 0-0.2 (check). Level of uncertainty not stated. Table III’s stacked lines, which the library joins, held as the image shows and checked to join to the cells.

• Checked: each reactant’s k_ij sum against Table I’s k_Q and every Gamma = k_ij / k_Q (within 0.012); detailed balance at 300 K with NIST energies (1s2 -> 2p10 6.68 against 6.7; 3d5 -> 2p5 1.77 against 1.8; the ‘(1/57)’ equilibrium constant); Fig. 1’s twelve level energies exceed NIST’s by a uniform 0.50-0.54 cm-1 (the level mapping).

• Finding: lifetimes against NIST’s 1/sum A (TC-985): 2p6 36.0 against 27.2 and 2p10 38.2 against 30.4 (NIST about 25 % short), 2p7, 2p8, 2p9 within 3 %; 2p5 32.6 against 27.1, and against bruce_1990’s 26.8 and bowering_1986b’s 28. No 6p’ or 7p level: the paper does not bear on TC-1003’s 6p’ question. In argon, 2p5’s fast slope 14.0 and state-to-state 2p5 -> 3d5 10.0 x 10^-11 against bruce_1990’s 20.0 and 17.0 (TC-1016), from 3-10.6 Torr Ar and an assumed 2 us 3d5 lifetime.

• Not taken (no quantity; declined, TC-1040): the depolarisation rate constants of 2p6/2p9 by xenon, 5.7 +- 0.6 and 9.2 +- 2.5 x 10^-10 cm3/s.

• Doubt: Table III’s footnote d has no mark; the slow component’s slope is 3.4 +- 0.5 x 10^-11 (Table I) and ‘3.5 +- 0.5 x 10^-10’ (text); Ref. 8 printed ‘15, 1207’.

• Status: verified (2026-10-09).

TC-1028 duzy_1980 (Duzy & Hyman, Phys. Rev. A 22, 1878 (1980)): photoionisation cross sections of the J-averaged first excited s, p, d configurations of Ne-Xe; Table II and the Xe 6p curve (2026-10-09)

• Where: src/optmat/data/sources/duzy_1980.toml, tools/extract/duzy_1980.py (Table II; Fig. 3, raster).

• Transcribed: Table II (p. 1882), excited_state_photoionization_cross_section in 10^-18 cm^2 (length form, Eqs. 1-2): Ar 3p5 4p 5.4, 3p5 3d 2.4, Kr 4p5 5p 5.2, 4p5 4d 2.8 at 248 nm; Ne 2p5 3p 2.3, 2p5 3d 0.6, Xe 5p5 6p 7.6, 5p5 5d 9.3 at 308 nm. Each is an average over all J levels of the configuration (a semiempirical central-field model, one potential fitted to the J-averaged binding energies, no spin-orbit). No uncertainty is stated. Fig. 3’s Xe 6p (dash-dot) curve, read from the image (73 points, 514-392, 333-246, 219-205 and 146-109 nm, where it can be told from the others; between 333 and 246 nm it is drawn on the Kr 5p line and the value is that line’s), 5 % (the reading). All use = check.

• Checked: Table II cell by cell against the table image; the figure’s ticks (every one within 2.5 pixels of its decade’s fit, 3.5 in wavelength); the overlay inspected. Fig. 3 against Table II: Ne 3p 0.98, Kr 5p 1.07.

• Finding: Fig. 3 and Table II disagree for Ar and Xe beyond the reading: Ar 4p at 248 nm reads 4.55 x 10^-18 cm^2 (0.84 of 5.4), Xe 6p at 308 nm 8.48 (1.12 of 7.6). The text sides with the table for Ar (‘~25% higher’ than hyman_1977’s 4.3, TC-933: 5.4/4.3 = 1.26; the figure gives 1.06). For Xe which is right is not known.

• Finding: for Xe 6p at 248-250 nm the curve gives 5.56-5.63 x 10^-18 cm^2: 1.29 and 1.50 times kroll_1990’s measured 6p[1/2]0 and 6p[3/2]2 values (TC-890), 1.6 times chang_1982’s velocity curve (TC-931), 1.85 and 2.4 times pindzola_1981’s Dirac-Fock and Hartree-Fock length totals for 6p[1/2]0 (TC-932), 1.9 times payne_1981’s 3 x 10^-18 (TC-937). At 308 nm Table II’s 7.6 is 1.10 times chang_1982’s 6.9 and 1.65 times pindzola_1981’s Dirac-Fock length (4.62). The J average is the largest of the calculations held and lies above the measurement. Kr 5p at 215 nm reads 4.07 x 10^-18 cm^2, 1.07 times dakka_2018’s 2p6 value as printed (3.8, TC-892) and 2.1 times it on the photon flux; payne_1981’s 10^-18 for Kr 5p[1/2]0 at 326.2 nm is a ninth of the Kr line there (9.3). No level is common with hummer_1998 (He).

• Finding: chang_1982’s ‘Duzy and Hyman’ column (TC-931) is this Table II exactly; chang_1982 prints the reference as ‘Phys. Rev. A 22, 1978’ (page 1878) and its record says the original is not in the library, which it now is.

• Not taken: Table I (the model potential’s r0 and alpha, an effective parameter ‘much larger than’ the core’s true polarisability); Figs. 1, 2, 4, 5 and Fig. 3’s other curves (configurations OEP 8 does not use; Fig. 4 prints no oscillator strength); Dunning and Stebbings’s threshold upper bounds (quoted, no wavelength).

• Status: verified (2026-10-09).

TC-1029 hutchinson_1988, tang_1989, hutchinson_1989 (Phys. Rev. Lett. 60, 105 (1988); 62, 111 and 112 (1989)): laser-induced continuum structure in xenon and the dispute over it; notes only (2026-10-09)

• Where: src/optmat/data/sources/hutchinson_1988.toml, tang_1989.toml, hutchinson_1989.toml (notes only).

• Transcribed: nothing; no value of a quantity is printed. hutchinson_1988: (2+1) ionisation of Xe through 5p5 6p (J = 0) at 249.63 nm with a second laser at 401.73 nm coupling 5p5 10p (J = 0) to the continuum at 3 hbar omega_1; 12 ns pulses, 0.1-1 GHz bandwidth, 5-10 Torr, probe-only working range 10-100 MW/cm^2 (ground-state depletion above); Fig. 4, ion signal (arbitrary units) against omega_d with a GHz scale bar only, at I_d = 80 and 100 MW/cm^2 and I_uv = 30-40 MW/cm^2; no fitted q, width, shift or cross section. tang_1989: a time-dependent calculation with the 6p-10p Raman coupling through far-detuned bound states and the 6p ionisation by omega_d added, which does not reproduce the data at 30 and 80 MW/cm^2; ‘ac Stark shifts were found negligible’; 65-70 % ionisation at 5-10 Torr. hutchinson_1989: the profile was never fitted; collisions, ionisation and stimulated emission at high density, absent from the calculation, are blamed. None quantified.

• Checked: against nist_asd_2026: 249.63 nm is the vacuum wavelength of two photons to 6p[1/2]0 (80 118.962 cm^-1; 249.6288 nm); with it, 401.73 nm (vacuum) puts 3 omega_1 - omega_d at 95 286.10 cm^-1, 0.04 cm^-1 from 10p[1/2]0 (95 286.06), so the dressed level is 10p[1/2]0 and both wavelengths are vacuum ones; 2 omega_1 + omega_d (105 011 cm^-1) lies between the 2P3/2 and 2P1/2 limits, as tang_1989 says.

• Finding: knight_1990 (TC-989, p. 52) cites hutchinson_1988 for Stark shifts ‘measured to be an order of magnitude less than the peak-to-window spacing’; the Letter contains no such measurement. The request of TC-1010 for these papers’ ‘Xe LICS light shifts’ finds none: only tang_1989’s calculated ‘negligible’ at 30 and 80 MW/cm^2.

• Finding (OEP 8, sections 4.3-4.4): the experiment is a two-colour LICS, the interference of 6p’s (2+1) ionisation with the path through 10p; it neither measures nor bounds the interference of OEP 8’s (2+1) and direct three-photon channels. tang_1989 shows that far-detuned bound-bound Raman couplings contribute to such continuum-mediated couplings as much as the continuum does.

• Status: verified (2026-10-09).

TC-1030 toma_2002 (Toma & Muller, J. Phys. B 35, 3435 (2002)): two-colour (harmonic + 800 nm) two-photon ATI matrix elements of argon 3p, lowest-order SAE theory; context only (2026-10-09)

• Where: src/optmat/data/sources/toma_2002.toml (no datasets).

• Transcribed: nothing. The notes hold what the paper prints:

  • Table 1 (p. 3440): the m-independent radial parts (psp, pdp, pdf) of the complex two-photon elements, in atomic units. There are eight rows: harmonics 11-17 plus one 800 nm photon, and 13-19 minus one. Real part is the principal value; imaginary part is the on-shell term.

  • Fig. 1’s angular factors (p. 3441).

  • Table 2’s continuum phase shifts for sidebands 12-18 (p. 3442).

  • The definition: length gauge, both time orders summed, fields factored out.

• Checked:

  • Every Table 1 and Table 2 string, on the table images and the rendered pages.

  • Against haber_2009 (TC-1008), whose SOPT values come from these tables. sum|M(+)|^2/sum|M(-)|^2 gives 1.418 and 1.279 (Haber et al. 1.42 and 1.28). The m = 0 to m = 1 ratios give 2.19, 2.62, 2.57 and 2.99 (theirs, exactly).

• Doubt: Haber et al.’s SOPT beta_2 and beta_4 are not reproduced from the formula on p. 3441 with Table 2’s phases (13 + IR: 2.72 and 1.18 against 1.68 and 0.54). Neither paper states the phase convention. No dataset depends on it.

• Not taken:

  • No absolute cross section is printed, so nothing fits multiphoton_ionization_cross_section.

  • Table 1 is not taken: two_photon_transition_amplitude was approved for bound levels only (TC-1040). Its values are relative only, since the continuum normalisation is not stated.

  • Table 2’s phase shifts have no quantity and are not proposed.

• Finding: for OEP 8 (TC-984, Q6) and OEP 6 Q9:

  • Each sideband has two rows at the same total energy (11 + IR with 13 - IR, and so on). They sit at nu = 5-10 IR photons (7.75-15.5 eV). The ‘-’ row is an absorption-emission term, outside OEP 8’s eq. 1.

  • Every XUV photon (about 17-29 eV) ionises alone, above Ar 4s (11.62 eV).

  • Nothing is at small splits, and OEP 8’s eq. 4 cannot be tested.

  • Computed here: the ‘+’ to ‘-’ ratio of sum|M|^2 at a common sideband is 2.45, 2.18, 2.06 and 2.03 (sidebands 12-18).

• Status: verified (2026-10-09).

TC-1031 vinbladh_2019 (Vinbladh, Dahlström & Lindroth, Phys. Rev. A 100, 043424 (2019)): two-colour two-photon RPAE matrix elements, both gauges and all time orders, for RABBIT delays of Ne 2p and Ar 3p/3s; context only (2026-10-09)

• Where: src/optmat/data/sources/vinbladh_2019.toml (no datasets).

• Transcribed: nothing. The paper publishes delays only, in vector figures (Figs. 3-9), at hbar omega = 1.55 eV:

  • Ne 2p in both gauges, diagram by diagram;

  • Ar 3p and 3s, and the 3s-3p difference.

  The notes keep:

  • the definitions: eq. 10, the amplitude; eqs. 39-43, both time orders (TO:1 and TO:2) and the correlated remainder; eq. 25, the symmetrised second-order correction;

  • the off-shell gauge factor, eqs. 48-50;

  • the text values.

• Checked: identity on the first page. The figure ranges and the text values were read on the rendered pages 8-12. The figures are vector paths; the PDF’s only images are the diagrams.

• Not taken:

  • The delays (no quantity; declined, TC-1011).

  • The Ar 3s one-photon partial cross section, ‘~0.003 Mb’ near 40 eV (p. 12). It is approximate, and a subshell value, not the total photoionization_cross_section.

• Finding: for OEP 8 (TC-984, Q6) and OEP 6 Q9:

  • The method is the one OEP 8’s kernel (its eq. 2) asks for: nondegenerate, both time orders, gauge invariant.

  • It is applied only to pairs whose XUV photon ionises alone (totals of 28 eV and above), far above Ar 4s (11.62 eV), at half-separations of about 12-33 eV. Only phases are published.

  • The IR-first order is negligible in length gauge but not in velocity gauge.

  • Eq. 50 bounds the gauge disparity of a single off-shell term by ((Omega_1 + Omega_2)/2)^2/(Omega_1 Omega_2). That bound is 1 for equal photons, so the disparity is a large-split effect.

  • Nothing is at small splits.

• Status: verified (2026-10-09).

TC-1032 nandi_2022 (Nandi et al., Nature 608, 488 (2022)): Rabi dynamics on He 1s2-1s4p with a seeded FEL; two transition dipoles (2026-10-09)

• Where: src/optmat/data/sources/nandi_2022.toml (inline datasets, no script).

• Transcribed: two transition_dipole_moment datasets for He 1s2 1S0 - 1s4p 1P1 (au, label, the M = 0 component): z_ba_chan 0.1318 (p. 489, use = "reproduced", reproduced_from = ["chan_1991"]) and z_ba_cis 0.124 (Methods, the paper’s CIS value, use = "check"). No uncertainty stated. The experiment’s numbers (AT splitting 80 +- 2 meV, 56 +- 13 fs, 11 meV blue shift, effective intensity 2 x 10^13 W/cm2, E0 = 0.02388 au, Omega/omega_ba = 0.34 %, tau_a+b about 100 ps) and the TDCIS parameters are in the notes.

• Checked:

  • 0.1318 is chan_1991’s f = 0.0303(7) (chan_1991, TC-86, f_present row 4) converted with f = 2 dE z^2 at 23.742 eV: 0.13177; Fernley’s 0.03028 and Wiese’s 0.0302 give 0.1317 and 0.1316. The CIS value gives f = 0.0273 at the CIS 24.1432 eV, 10 % low.

  • The intensity chain: 80 meV with z = 0.124 gives E0 = 0.02371 au and 1.97 x 10^13 W/cm2; the printed E0 = 0.02388 is sqrt(2 x 10^13 / 3.51 x 10^16) = 0.02387, from the rounded intensity. With 0.1318 the same splitting means 1.75 x 10^13 W/cm2.

  • Rabi period h/80 meV = 51.7 fs (‘about 52’); Omega/omega_ba = 0.337 %; the Gaussian field area 1.505 tau (the paper’s ‘about 1.5’) makes 56 fs 1.63 Rabi periods; the pulse range 44.7-68.2 fs, 59.1 meV bandwidth and 6.26 mm Rayleigh length recomputed; Fig. 3’s 23.3076 eV is the CIS 2 x 24.1432 - 24.9788.

  • Extended Data Table 1 against its image (not taken).

• Doubt: the peak intensity ‘about 1.4 x 10^14 W/cm2’ is not reproducible from the printed 87 uJ, 56 fs and w0 = 10.2 um (about 8.9 x 10^14 at full transmission); the beamline transmission is not stated.

• Finding: the resonance is one-photon (1s2 -> 1s4p), not a bound two-photon one (TC-1010 listed the paper as ‘He resonant two-photon ionisation’). It tests the one-photon analogue of OEP 8’s Eq. (7) (resonant Rabi cycling, excited-level photoionisation, a direct two-photon continuum from the ground level), not its two-photon coupling M_f. Its central effect, coherent interference of one- and two-photon ionisation amplitudes, lies outside OEP 8’s rate treatment of ionisation but touches only the photoelectron spectrum (about 6 x 10^-4 of the atoms ionised). Its Omega is OEP 8’s Omega_R convention (the AT splitting, twice the off-diagonal element).

• Not taken: the AT splitting and Rabi period (no quantity; the intensity is derived from it), the blue shifts (interference, not a light shift), Extended Data Table 1 (bound-free elements of unstated normalisation; not proposed), the NIST and CIS energies, Zitnik et al.’s ‘about 4 ns’ (a rounded quotation).

• Status: verified (2026-10-09).

TC-1033 meyer_2008 (Meyer et al., Phys. Rev. Lett. 101, 193002 (2008)): He two-colour ATI sidebands against polarisation, notes only (2026-10-09)

• Where: src/optmat/data/sources/meyer_2008.toml (no datasets).

• Transcribed (notes): FLASH 13.7 nm (90.5 eV) and 25.5 nm (48.6 eV) with 800 nm or 523 nm dressing; low field (about 8 x 10^10 W/cm2) contrast 3.4 +- 0.5 and S0:S2 = 1.25 +- 0.3 (theory 0.98 and 1.0); 48.6 eV S0:S2 about 0.9 +- 0.3 (simulation 0.85); high field (about 6 x 10^11 W/cm2) SB1 contrast 1.5 +- 0.3 (1.47), SB2 about 3.3 (about 3.5).

• Checked: Eq. (1)’s contrast (5 S0 + 4 S2)/(3 S2) = 3.4 gives S0:S2 = 1.24 (printed 1.25); 0.98 gives 2.97 (printed ‘theoretical value of 3’); 5 x 1.25/4 = 1.56 (printed 1.5); photon energies 48.62 and 90.50 eV; Fig. 2’s main line near 66 eV.

• Not taken: the ratios and contrasts (sideband ratios, declined, TC-1011). No absolute two-photon amplitude, phase or cross section is printed; the figures are normalised (arbitrary units).

• Finding: no bound two-photon or resonant physics; nothing for OEP 8 beyond the quoted Johansson et al. (2003) d/s > 10 for resonant ionisation through He 1snp 1P (n = 2, 3).

• Status: verified (2026-10-09).

TC-1034 quattropani_1982, drachman_1990, hansch_1975 (Quattropani, Bassani & Carillo, Phys. Rev. A 25, 3079 (1982); Drachman, Bhatia & Shabazz, Phys. Rev. A 42, 6333 (1990); Hänsch et al., Phys. Rev. Lett. 34, 307 (1975)): hydrogen 1s-ns two-photon amplitudes against the exact result, held as notes awaiting a quantity (2026-10-09)

• Where: src/optmat/data/sources/quattropani_1982.toml, drachman_1990.toml and hansch_1975.toml (no datasets); tools/extract/quattropani_1982.py and drachman_1990.py, which carry the exact hydrogen amplitude as a check. The quantity is two_photon_transition_amplitude (TC-1040).

• Transcribed (below, after TC-1040; first held as notes):

  • quattropani_1982 Table I: the totals D_1^n[J0] and D_1^n[J] against nu_1, for n = 3, 6 and 20 (53 rows, two gauges).

  • drachman_1990 Table IV: the N0 = 15 values of D1 and D2 (and D3) at nine omega for 1s-2s, and the reproduced Bassani et al. (1977) column.

  The amplitude is signed and dimensionless, with denominators in rydberg. It is (3/4) of OEP 8’s M_zz in au, so delta^TP = (16/9) D^2. It is not delta^TP (TC-872, TC-952).

• Checked: against the exact amplitude, a Dalgarno-Lewis solve in a Sturmian basis at 80-120 digits, converged to 1e-9.

  • drachman_1990: all nine D1 and D2 agree to the printed digits. So do the ‘Ref. 1’ column and Tables II-III’s N = 20 sums (-11.78048).

  • drachman_1990, Table I’s pseudostate energies are recomputed to every digit with a = 1 and a = 0.55.

  • quattropani_1982 Table I: every total agrees within 0.0055, at most 1e-5 relative away from the zeros.

  • quattropani_1982 Table II, the 1s-3s and 1s-20s transparency zeros: within 0.0006.

  • quattropani_1982 Table III: the radial integrals squared.

  • quattropani_1982 Table IV: the n = 45 column within 0.3 %, except near the zero.

  • Exact per-level values (TC-952’s convention):

    transition	delta^TP	sigma_0
    1s-2s	246.72 au	2.246e-35 cm4
    1s-3s	18.329 au	2.344e-36 cm4
    1s-6s	1.0063 au	1.539e-37 cm4

• Errata (for when the amplitude is taken): quattropani_1982 Table I, confirmed on the image:

  • (a) nu_1 = 0.6875, both gauges: printed ‘0.6963’, correct -0.6963.

  • (b) nu_1 = 0.9400, J: printed ‘-115.1149’, correct -151.1149.

• Doubt:

  • quattropani_1982:

    • Table II’s 1s-6s zeros are off by up to 0.0030, although Table I’s 1s-6s values are right (0.6882 against the exact 0.69013).

    • Three J-gauge part pairs do not sum to their totals.

    • Eq. (1)’s rate prefactor is 1/(128 pi^3) of the golden-rule rate of Eqs. (2a) and (3a).

  • drachman_1990:

    • Table I is headed ‘a = 0.5’ for 0.55.

    • The text’s ‘seven’ negative energies is what a = 0.5 gives.

    • Eq. (4) counts j from 1.

  • hansch_1975:

    • The printed rate ‘Gamma ~ 7 x 10^-4 I^2/Delta omega’ is 33-205 times the exact strength’s, depending on the bandwidth convention.

    • That rate gives 1.5e8 excited atoms per pulse under the stated conditions, against the text’s 3e5. The text’s 3e5 agrees with the exact strength to a factor 2.5.

• Finding (OEP 8, Eq. 4): from the exact amplitude:

  transition	kappa (hartree^-2)	D_eff
  1s-2s	36.83	0.879 D_1
  1s-3s	7.47	2.39 D_1
  1s-6s	-16.3 (negative)	—

  • 1s-2s lies inside the rule D_eff >= 0.75 D_1.

  • For 1s-3s, the opposite-signed mu = n path cancels part of the curvature.

  • For 1s-6s, bandwidth lowers the probability.

  • drachman_1990’s Table IV is the 1S-2S two-colour kernel. Its ratio to the degenerate value runs from 1.2505 at omega = 0.525 to 113.27 at 0.7475 rydberg.

• hansch_1975: measured the 1S Lamb shift, 8.6 +- 0.8 GHz (H) and 8.3 +- 0.3 GHz (D), from the 1S-2S to Balmer-beta separation. It prints no level energy and no strength. Its light shift (about 5.5 Hz/(W/cm2)) is not taken: its sign and intensity definition are not stated.

• Status: verified (2026-10-09).

After TC-1040: quattropani_1982 and drachman_1990, the datasets under two_photon_transition_amplitude (2026-10-09)

• Where:

  • src/optmat/data/sources/quattropani_1982.toml and drachman_1990.toml;

  • tools/extract/quattropani_1982.py and drachman_1990.py;

  • src/optmat/data/values/absorption/H/quattropani_1982__D_{3,6,20}s_{length,velocity}.csv;

  • src/optmat/data/values/absorption/H/drachman_1990__{D1_N15,D2_N15,D3_N15,ref1_bassani_1977}.csv.

  The quantity is approved for bound final levels. The notes-only entry is above.

• Transcribed:

  • quattropani_1982 Table I: the totals, 3s, 6s and 20s in the length and velocity gauges, 106 values. Unit 1. The abscissa is nu_1 in rydberg. use = primary.

  • drachman_1990 Table IV, 2s:

    • D1 (length) and D2 (velocity) at N0 = 15, use = primary;

    • D3 (the commutator form), use = check;

    • the ‘Ref. 1’ column (Bassani, Forney and Quattropani 1977, not in the library), use = reproduced.

    Nine values each.

  • All datasets have m_zz_per_unit = 4/3, from Eq. (3a)/(5): rydberg denominators, radial integrals, angular factor 1/3, both orderings.

  • The digit-group spaces of Table IV are removed in value and kept in printed.

• Errata: quattropani_1982 Table I, evidence the table image:

  • (a) nu_1 = 0.6875: ‘0.6963’ corrected to -0.6963, in both gauges.

  • (b) nu_1 = 0.9400, velocity: ‘-115.1149’ corrected to -151.1149.

• Checked: by the scripts, which fail on a miss.

  • The exact amplitude: a Dalgarno-Lewis solve, Decimal arithmetic, standard library only.

    • Every Quattropani total is within 0.006 of it. The worst is 0.0052, near the poles of n = 6 and 20.

    • Each erratum’s correction agrees with it, and the printed value does not.

    • Drachman’s D1, D2 and ‘Ref. 1’ agree within 1.5 units of their last printed digit; D3 within 5e-6 relative.

    • Tables II-III’s N = 20 sums are within 1.5e-5 of it.

    • Their first term equals the closed-form 2p term, -17.878453.

  • Quattropani’s internal relations:

    • The parts sum to the total within 1.5e-4: every length-gauge row, and every velocity-gauge row except three whose parts are inconsistent. The script asserts that those three stay inconsistent.

    • The two gauges agree within 0.011.

• Status: verified (2026-10-09).

TC-1035 balakrishnan_1992 (Balakrishnan, Smith & Stoicheff, Phys. Rev. Lett. 68, 2149 (1992)): the Letter on D0(H2), all check (2026-10-09)

• Where: src/optmat/data/sources/balakrishnan_1992.toml, tools/extract/ balakrishnan_1992.py (Table I from the library’s JSON cells), data/values/ionisation/H2/balakrishnan_1992__d0_H2.csv.

• Transcribed: dissociation_energy, cm-1, all use = "check" because balakrishnan_1994 reports the same spectra in full (primary there): Table I’s ‘Present’ D0(H2) = 36 118.11(8); inline D_L(H2) = 118 377.06(4) and D0(H2+) = 21 379.36(8) (IP(H2) the mean of Jungen 1990’s 124 417.501 and McCormack 1989’s 124 417.524, liu_2009’s held values).

• Checked: by the script, 118 258.57 + 118.49 = 118 377.06; minus 82 258.95 = 36 118.11 (Table I); D0(H2+) = 21 379.3615. The uncertainty budget (0.064 with a 0.024 hyperfine term, 0.04 and 0.03 in quadrature, 0.081) by hand.

• Finding: the Letter prints no Kr light-shift coefficient; its 2 nu1 = 94 093.00(4) cm-1 is the light-shifted resonance (balakrishnan_1994), not taken.

• Status: verified (2026-10-09).

TC-1036 balakrishnan_1994 (Balakrishnan, Smith & Stoicheff, Phys. Rev. A 49, 2460 (1994)): dissociation energies of H2, D2, H2+, D2+, and the Kr 5p[1/2]0 light shift of the Stoicheff group (2026-10-09)

• Where: src/optmat/data/sources/balakrishnan_1994.toml, tools/extract/ balakrishnan_1994.py, data/values/ionisation/{H2,D2,H2+,D2+}/balakrishnan_1994__*.csv.

• Transcribed: dissociation_energy, cm-1. Table III (p. 2468): D0(H2) = 36 118.11(8) and D0(D2) = 36 748.38(7), primary; D0(H2+) = 21 379.37(8) and D0(D2+) = 21 711.64(7), check (derived with others’ ionisation energies); the other rows reproduced (Herzberg 1970, Stwalley 1970, LeRoy & Barwell 1975, McCormack & Eyler 1991, Eyler & Melikechi 1993, Wolniewicz 1993, Kolos, Szalewicz & Monkhorst 1986, Wolniewicz & Orlikowski 1991). Text, inline: the second limits D_L(H2) = 118 377.06(4) and D_L(D2) = 119 029.72(4) (products H(1s) + H(2s), primary); D_L(D2) from J’’ = 2, De(H2), De(D2) (check). Kr (pp. 2466-2467): light_shift_coefficient of the two-photon 4p6 - 5p[1/2]0 resonance, printed (8.6 +- 3.8) x 10^-11 cm-1 per W/cm2, scale 1e-11 c = 2.58(1.14) Hz/(W/cm2) at 212.6 nm, primary (intensity definition not stated beyond ‘about 8e8 W/cm2’ at the focus); level_energy of 5p[1/2]0 extrapolated to zero intensity, 94 092.93(5) cm-1, natural Kr, check.

• Checked: by the script, D_L = 118 258.57 + F’’(1) 118.49; D0 = D_L - E(2s-1s); De = D0 + zero-point energy; D0(ion) = D0 + I(atom) - I(molecule); D_L(D2) from J’’ = 2; Table II’s budget (0.079, 0.066 against 0.08, 0.07); the Kr shift (0.07 cm-1 over 8e8 W/cm2 = 8.8e-11, inside 8.6 +- 3.8). Table III and the text values against the rendered pages.

• Finding: brandi_2002’s reproduced Stoicheff value 2.6(1.1) Hz/(W cm-2) (TC-1017) is exactly this paper’s 8.6(3.8) x 10^-11 cm-1/(W/cm2) converted; it is in this paper only, not in the 1992 Letter, and brandi_2002 cites it as ‘Phys. Rev. A 48, 2460 (1994)’ (the volume is 49). Against brandi_2002’s 0.75(48), 1.5 combined sigma apart; OEP 8 convention about -55 au against -16(10) au (derived). The extrapolated level, 94 092.93(5), is 0.067 above brandi_2002’s 84Kr value and NIST. H2 and D2: D0 lies 0.04 (H2) and 0.017 (D2) cm-1 above liu_2009/komasa_2011 and liu_2010, inside the uncertainties; no H2/D2 dissociation_energy dataset was held before. The ionisation energies used: Jungen et al.’s I(H2) 124 417.484 is 0.017 below liu_2009’s jungen_1990_H2 (the revision the paper mentions); the I(D2) attributed to Jungen et al. is liu_2010’s gilligan_1992_D2.

• Doubt: the printed ‘average’ I(H2) = 124 417.500 of 124 417.507 and 124 417.484 is 124 417.4955; D0(H2+) follows the printed value (21 379.374 against 21 379.379). Not an erratum.

• Status: verified (2026-10-09).

TC-1037 kligler_1980 (Kligler, Bokor & Rhodes, Phys. Rev. A 21, 607 (1980)): H2 E,F (v = 2) lifetime, collisional removal and photoionisation at 193 nm (2026-10-09)

• Where: src/optmat/data/sources/kligler_1980.toml (ten inline datasets, H2).

• Transcribed: radiative_lifetime: E,F (v = 2) 100(20) ns (reproduced from Kligler & Rhodes, PRL 40, 309 (1978), not in the library), the calculated 90 ns (reproduced, Wolniewicz; Spindler), C 1Pi_u (v = 2) 0.88 ns (the authors’ sum of Allison & Dalgarno’s rates, check). collisional_quenching_rate_coefficient: by H2 2.1(4)e-9 and by He 0.8(4)e-9 cm3/s (total, reproduced from the 1978 Letter); the paper’s first-Born rate to C 1Pi_u (v = 2), 2.3e-9 cm3/s at 300 K (primary); rotational relaxation J = 2 -> 0 <= 3e-12 and J = 3 -> 1 <= 6e-12 cm3/s (check, limit = "upper"). excited_state_photoionization_cross_section at 193 nm: the printed 8e-19 <= sigma <= 4e-18 cm2 held as 2.4(1.6)e-18, bound (check: the collisionally mixed E,F + C population), and Cohn’s 2.6e-18 (reproduced).

• Checked: against the rendered pages 607, 610, 612-614; Fig. 3’s level energies against Table II’s lines (with F’’(1) = 118.49) by hand.

• Finding: Tables I and II disagree by 1 cm-1 at three branch ends (rounding). The vocabulary’s wording of the three quantities says ‘the atom’; taken for the molecule’s rovibronic level with the same meaning (flagged for the vocabulary). No two-photon cross section or three-photon ionisation cross section is printed.

• Doubt: the E,F level energies (Fig. 3, Dieke’s tables) are not taken (no quantity; molecular_level_energy declined, TC-1040); marinero_1982 shows the same tables put the E,F - X (0,0) lines about 8 cm-1 low.

• Status: verified (2026-10-09).

TC-1038 marinero_1982 (Marinero, Rettner & Zare, Phys. Rev. Lett. 48, 1323 (1982)): (2+1) REMPI detection of H2 through E,F, notes only (2026-10-09)

• Where: src/optmat/data/sources/marinero_1982.toml (no datasets).

• Transcribed: nothing: the E,F lifetime 100(20) ns is quoted (held by kligler_1980); the two-photon coefficient 1.6e-30 cm4/W at 0.92 cm-1 bandwidth is a bandwidth-dependent peak coefficient reproduced from bischel_1979 (TC-917), not two_photon_excitation_cross_section; Table I’s relative Q-branch line strengths have no quantity; no three-photon ionisation cross section is printed (the third step is assumed saturated).

• Checked: identity and every number quoted against the rendered pages 1323-1325; the library’s paper.md appends the next Letter (Hannaford & Series), noted.

• Finding: Fig. 2’s Q1(0,0) = 99 101.12 cm-1 (deduced from Dieke’s tables) is 8.61 cm-1 below Hannemann et al.’s EF(0,1) - X(0,1) = 99 109.73139(18) held in liu_2009’s notes (TC-575), and Q0(0,0) = 99 156.76 is 7.8 cm-1 below the T0 = 99 164.58 from nist_webbook_2026’s band origins (TC-863). Q0 is therefore not taken as the E,F T0.

• Status: verified (2026-10-09).

TC-1039 gornik_1981: the pressure shifts under pressure_line_coefficient (2026-10-09)

• Where: src/optmat/data/sources/gornik_1981.toml (TC-922), tools/extract/ gornik_1981.py (new), data/values/absorption/Xe/gornik_1981__beta_shift_Xe.csv.

• Transcribed:

  • Table II (p. 72), the self-shift parameters beta/N: -2.5 (0.2), -2.7 (0.2) and -2.8 (0.2) x 10^-9 s^-1 cm^3 for 1S0 -> 6p[1/2]0, 6p[3/2]2, 6p[5/2]2. Held as pressure_line_coefficient, unit cm3/s, scale 1e-9, sign as printed (negative = red). Parameters: effect shift, width none, frequency_variable angular (‘beta is the line shift in angular frequencies’), photons 2, perturber self, frequency_scale transition. Use = primary; the uncertainty level is not stated.

  • Fig. 6’s ‘~25 MHz/Torr’ (p. 72): the observed 6p[1/2]0 linewidth slope, not deconvolved from the 18 GHz laser. Held inline (broadening_Xe, MHz/torr, effect broadening, width not stated, ordinary, transition scale) as a check.

  • The record’s ‘NOTHING IS TAKEN’ and ‘no quantity’ sentences are replaced. The rest of the record is unchanged (it had no datasets).

• Checked:

  • Table II’s cells against the table image.

  • The script checks each value and uncertainty against the abstract, and the 6p[1/2]0 Delta C6 (2.0) against the text.

  • -2.5e-9 s^-1 cm^3 is -9.77 GHz/bar in ordinary frequency at 295 K, Fig. 5’s 6p[1/2]0 slope (about -15 GHz over 1.5 bar, read by eye). In ordinary frequency the three shifts are -13.0, -14.1 and -14.6 MHz/torr.

• Decided (frequency scale): the paper does not state the scale in words; it is taken as the transition’s (two-photon), for two reasons:

  • Fig. 6’s zero-pressure width, ‘around 30 GHz’, is sqrt(2) x 18 GHz (laser) with the Doppler term, about 25 GHz, on the two-photon scale; the laser scale would give about 18 GHz.

  • Delta C6 is derived from beta as the ground-to-6p difference potential.

• Not taken: Hawkins et al.’s ‘(25 ± 15) MHz/Torr’, quoted as gamma/(pi p); hawkins_1980 holds it.

• Status: verified (2026-10-09).

TC-1040 Vocabulary: pressure-line coefficients and two-photon amplitudes; three definitions widened to molecules (2026-10-09)

• Where: src/optmat/vocabulary.py, docs/data.md.

• Added (the maintainer’s approval, 2026-10-09, from the candidates of TC-1021 to TC-1039):

  • pressure_line_coefficient (absorption). The collisional broadening or shift of a bound atomic line, one- or two-photon, per unit perturber pressure or density, in the impact regime.

    • Units: MHz/torr, MHz/mbar, GHz/amagat, cm-1/amagat or cm3/s.

    • Abscissa: label or temperature.

    • Requires effect, transition, photons, frequency_scale (transition, laser or not stated), width (fwhm, hwhm, not stated or none), frequency_variable and perturber.

    • A two-photon line’s broadening is the decay of its ground-to-final coherence. OEP 8’s pure dephasing is what remains after the radiative and quenching parts.

  • two_photon_transition_amplitude (absorption). The signed second-order amplitude of a bound two-photon transition, both photons along z, against the first photon’s energy.

    • Units: 1 or au.

    • Abscissa: wavelength or label.

    • Requires final_level, gauge, polarization, definition, m_zz_per_unit (OEP 8’s M_zz in au per printed unit) and method.

    • Bound final levels only. A continuum amplitude (toma_2002’s) was not approved until a small-split source exists.

• Widened: radiative_lifetime, collisional_quenching_rate_coefficient and excited_state_photoionization_cross_section now read “the atom or molecule”, so kligler_1980’s H2 E,F values belong. The meanings are otherwise unchanged.

• Declined:

  • collisional_depolarization_rate_coefficient (ku_1986);

  • molecular_level_energy (kligler_1980; Dieke’s levels, about 8 cm⁻¹ off modern values; a primary source is wanted).

  Their values stay in the records’ notes.

• Status: decided (2026-10-09).

TC-1041 OEP 8’s literature (TC-1021 to TC-1039): what it settles and what it leaves open; corrections to TC-1010 (2026-10-09)

• Where: the records of TC-1021 to TC-1039; OEP 8 (docs/oeps/oep-0008-bound-two-photon-response.md, Draft), revised.

• Settled:

  • OEP 8’s kernel against hydrogen. The exact signed amplitudes are now held (TC-1034).

    • 1s–2s gives \(D_\mathrm{eff}=0.88\,D_1\), inside the 0.75 rule.

    • 1s–3s gives 2.4 \(D_1\), because of a cancelling path.

    • 1s–6s has \(\kappa<0\): bandwidth lowers the transfer.

    So the rule bounds \(|\kappa|\), and OEP 8 now says so. Hydrogen’s per-level strengths, in TC-952’s convention, are 246.72 au (1s–2s), 18.329 (1s–3s) and 1.0063 (1s–6s).

  • The xenon 6p lifetimes against NIST. Three independent groups (bruce_1990, bowering_1986b, ku_1986) agree with each other.

    • NIST’s \(1/\sum A\) is about 25 % short for 6p[3/2]₂ and 6p[1/2]₁.

    • It agrees within 3 % for 6p[3/2]₁, 6p[5/2]₃ and 6p[5/2]₂.

    • The 6p′ levels rest on bruce_1990 alone. Inoue, Ku and Setser, J. Chem. Phys. 81, 5760 (1984), would settle them; it is to be requested.

  • The krypton light shift. The Stoicheff group’s value is in balakrishnan_1994, (8.6 ± 3.8)×10⁻¹¹ cm⁻¹/(W cm⁻²), which is 2.58 ± 1.14 Hz/(W cm⁻²). It is 1.5 combined sigma from brandi_2002’s 0.75(48) (TC-1036).

  • Pressure effects on the Xe 6p lines.

    • gornik_1981’s shifts: −2.5 to −2.8×10⁻⁹ cm³/s, angular frequency, about −13 to −15 MHz/Torr.

    • hawkins_1980’s broadening: 25 ± 15 MHz/Torr, with neither the width convention nor the frequency scale stated.

    • Depolarisation puts the elastic rates 6–100 times above quenching (TC-1022, TC-1027, TC-1039).

• Left open:

  • The Xe 6p[1/2]₀ strength (OEP 8 Q1). kligler_1978, requested as a third measurement, gives only a lower bound and an estimate built on placeholder dipole moments (TC-1021).

  • Small-split continuum amplitudes (Q6). toma_2002 and vinbladh_2019 are at splits of 7.75 eV and more, above every intermediate resonance (TC-1030, TC-1031).

• Corrections to TC-1010:

  • nandi_2022 is a one-photon resonance (1s² → 1s4p), not resonant two-photon ionisation. It checks only the one-photon analogue of OEP 8’s Bloch equations (TC-1032).

  • hutchinson_1988 prints no light shift, nor do its comment and reply. knight_1990’s citation of measured Stark shifts there is not borne out (TC-1029).

  • The Stoicheff group’s krypton value is in Phys. Rev. A 49, 2460 (1994), not volume 48 as brandi_2002 prints; nor is it in their 1992 Letter.

  • Pindzola, Payne and Garrett (1981) is held as pindzola_1981b. gornik_1982’s notes are corrected to say so.

• Papers still wanted:

  • Inoue, Ku and Setser (1984);

  • Kligler and Rhodes, Phys. Rev. Lett. 40, 309 (1978) (H2 E,F);

  • Bassani, Forney and Quattropani, Phys. Rev. Lett. 39, 1070 (1977);

  • Johansson et al., Eur. Phys. J. D 22, 3 (2003);

  • Fushitani et al., Nat. Photon. 10, 102 (2016) (two-photon Rabi oscillations in He);

  • a modern primary source of the H2 E,F levels.

• Status: verified (2026-10-09).

TC-1042 inoue_1984 (Inoue, Ku & Setser, J. Chem. Phys. 81, 5760 (1984)): radiative lifetimes and total quenching by Ne and Ar of 22 Xe 6p, 6p’, 7p and 6d levels (2026-10-09)

• Where: src/optmat/data/sources/inoue_1984.toml, tools/extract/inoue_1984.py, data/values/absorption/Xe/inoue_1984__{tau_Ne,tau_Ar,tau_Ne_check,tau_Ar_check, kq_Ne,kq_Ar,kq_self}_Xe.csv.

• Transcribed (‘This work’ only; uncertainty level not stated; no temperature stated): radiative_lifetime: Table I, the zero-pressure intercepts in neon (11 levels, primary) and argon (19 levels, primary), 30-166 ns; the three values the authors call the less reliable of a pair (2p4 and 3p9 in neon, 3p10 in argon) as check. collisional_quenching_rate_coefficient (order 2, channel total): Table II, by neon (22 levels) and by argon (20 levels), 0.2 to 71 x 10^-11 cm3/s (primary); by xenon, 2p10’s fast component 13 +- 2 (primary). Rows in Paschen notation; the NIST configuration/term/J of each in the record. Not taken: the theoretical and other experiments’ columns, the parenthesised values, Table II’s 2p5/2p6 xenon values (= ku_1986, note added in proof) and 2p10’s ‘(41 +- 5)’ (Ref. 10 by detailed balance); Tables III and IV (branching fractions; no quantity).

• Checked: every taken cell against the table images (a scanned PDF); Table I’s Racah labels against the NIST mapping; Fig. 2’s eighteen energies exceed NIST’s by 0.43-0.57 cm-1; nine gaps and five air wavelengths the text prints against NIST (levels and vacuum lines); K(4d1’/2p1) = 33, K(4d1’/2p2) = 1.5 and K(2p10/1s3) = 57 at 300 K; every value the text repeats (3p10, 2p10, 4d1’, 2p2, 3p8, 4d6, the ratios); the 6p/6p’ average discrepancy from tau_v, 1.69 against ‘1.7 ns’; the record’s NIST 1/sum A for all 24 levels.

• Finding (6p’): the paper sides with bruce_1990 (TC-1003), not NIST. 6p’[1/2]0 40 +- 2 (Ne), 38 +- 2 (Ar) against bruce_1990’s 34.1 +- 0.8 and NIST’s 27.5; 6p’[3/2]2 37 +- 2 against 32.1 +- 0.8 and 22.8; 6p’[1/2]1 38 +- 2 and 6p’[3/2]1 48 +- 2 against NIST’s 25.9 and 22.8. NIST’s 6p’ -> 6s’ lines alone (C/C+) exceed the measured total decay rates by 1.3-2.0. Inoue is 4-5 ns above Bruce (1.8 and 2.3 combined errors).

• Finding (7p): neither side. Where bruce_1990 measures, NIST agrees with it within 1 %; Inoue differs by -10 to +29 % (3p9 = 7p[5/2]2: 166 +- 9 against 128.6 +- 5.6 and 129.2), tracking Aymar and Coulombe’s tau_v; bruce_1990 is the better 7p measurement.

• Finding (6p): a fourth group agrees with TC-1041: 6p[3/2]2 31 and 6p[1/2]1 38 ns against NIST’s 27.2 and 30.4; 6p[3/2]1, 6p[5/2]3, 6p[5/2]2 within 7 % of NIST.

• Finding (quenching): by argon, 6p’[1/2]0, 6p’[3/2]2 and 7p[5/2]2 agree with bruce_1990; 7p[3/2]2 23 +- 2 against 34.8 +- 3.2, and 6p[3/2]2 2.2 +- 0.2 against bruce_1990’s 4.0 +- 0.2 and ku_1986’s 4.7 +- 0.5. ku_1986 quotes this paper’s 2p6 argon rate as ‘2.2 +- 0.5’; its other quotes match. By xenon, 2p10 13 +- 2 against ku_1986’s 13.3 +- 0.5 and bowering_1986b’s 29.5 +- 4.8.

• Doubt: Table I’s footnote a cites ‘Reference 15’ for Aymar and Coulombe (Ref. 17). The text puts 3p8 -> 1s5 ‘at 452.7 nm’ (NIST 467.25 nm, vacuum). It writes ‘2p4’ for 2p2 in the paragraph on 2p2, 4d1’’ and 2p3 (p. 5766). K(4d1’/2p2) is printed as the inverse of K(4d1’/2p1)’s convention. The 7p ‘3 ns’ average discrepancy is not reproduced.

• Status: verified (2026-10-09).

TC-1043 kligler_1978b (Kligler & Rhodes, Phys. Rev. Lett. 40, 309 (1978)): H2 E,F (v = 2) lifetime and quenching by H2 and He, the original (2026-10-09)

• Where: src/optmat/data/sources/kligler_1978b.toml (four inline datasets, H2; p. 311 and the abstract, p. 309).

• Transcribed: radiative_lifetime: E,F 1Sigma_g+ (v = 2, inner well; J = 0-2 excited together by the 0.5 nm ArF* band) 100(20) ns, the zero-pressure intercept of the fluorescence decay rate against H2 pressure (primary); the ‘theoretical value of 90 ns derived from’ Wolniewicz’s transition moments and Spindler’s Franck-Condon factors (check). collisional_quenching_rate_coefficient (order 2, total): by H2 2.1(4)e-9 cm3/s (primary, the slope) and by He 0.8(4)e-9 cm3/s (primary, He/H2 mixtures). Uncertainty level and temperature not stated.

• Checked: against the rendered pages 309-312. kligler_1980 (TC-1037) holds the same four numbers as reproduced from this Letter: all agree (value, uncertainty, method); marinero_1982’s 100 +- 20 ns and bischel_1979’s (TC-917) measured alpha ~ 1e-32 cm4/W agree. The Letter’s E,F (v = 2) J = 0, 1, 2 energies (103 552, 103 598, 103 682 cm-1) equal kligler_1980’s Fig. 3. The excited density n* = Phi tau / V = 2.5e11 cm-3 follows from the printed Phi, tau and V.

• Finding: the two-photon coefficient alpha = sigma / I (rate alpha I^2 / hbar omega, Eq. 3), measured ~1e-32 cm4/W and estimated 9e-33 cm4/W (Eqs. 4-5), is a band-averaged peak coefficient over three rotational lines for a free-running ArF* laser (0.5 nm full bandwidth; photon statistics and polarisation not stated): not taken as two_photon_excitation_cross_section (frequency-integrated, cm4), as for bischel_1979 and marinero_1982. Eq. (4) with the stated inputs reproduces 1.0e-32 cm4/W only with g = 1/(2e13 s-1), i.e. the ‘2 x 10^7 MHz’ linewidth is an angular width (106 cm-1), Bischel et al.’s 100 cm-1 line. Eq. (3) gives 1.3e-32 at I = 2e8 W/cm2 (3e8 scaled to 10 mJ) and 0.57e-32 at 3e8; the I used is not stated. The excited density is printed in ‘cm3’ for cm-3.

• Doubt: ‘4 x 10^12 photoelectrons per second’ at ‘0.15 % detection efficiency’ is 2.7e15 photons/s, not the printed Phi = 4.5e15 (factor 1.7, unexplained; it enters alpha, which is not taken).

• Status: verified (2026-10-09). kligler_1980’s tau_EF_v2, kq_self_EF and kq_He_EF stay reproduced; their reproduced_from citation and the notes of kligler_1980, bischel_1979 and marinero_1982 still say the Letter is not in the library (they may be pointed at this record).

TC-1044 bassani_1977 (Bassani, Forney & Quattropani, Phys. Rev. Lett. 39, 1070 (1977)): hydrogen 1s-2s two-photon amplitude in the length and velocity gauges (2026-10-09)

• Where: src/optmat/data/sources/bassani_1977.toml, tools/extract/bassani_1977.py, src/optmat/data/values/absorption/H/bassani_1977__*.csv.

• Transcribed: under two_photon_transition_amplitude (TC-1040), the totals of Table I (D[J0], gauge length, tbl_76d993024c8f) and Table II (D[J], gauge velocity, tbl_bb20405731ed) at nine nu1 = 0.3750-0.7475 rydberg (the other photon 3/4 - nu1), final level 2s, linear_parallel, use = primary, no uncertainty stated. m_zz_per_unit = 4/3, derived from Eq. (3a): the same numerators as OEP 8’s M_zz, denominators in rydberg (twice hartree), and both orderings summed, so M_zz = 2 x (2/3) D. The partial sums and continuum parts are not taken (gauge-dependent).

• Checked: by the script, all 270 printed cells of both tables: every one equals the computed value rounded (248) or truncated (22) to its printed digits, none off; the partial sums N = 2-13 and N -> infinity from Eqs. (4a, 4b) with the closed-form radial integrals, the totals against the exact amplitude of quattropani_1982’s script (e.g. -11.780483 at 0.3750, -1334.326138 at 0.7475), the continuum parts against the exact amplitude less the exact discrete sum. drachman_1990’s (TC-1034) column ‘Ref. 1’ equals D[J0] as printed strings at all nine nu1.

• Finding: (a) the column ‘Ref. 1’ of drachman_1990 is the length-gauge row: at 0.6875 it prints -49.6878 with D[J0], where D[J] prints the truncated -49.6877 (the exact value is -49.687778); drachman_1990’s dataset says the gauge is unknown. (b) Eq. (2)’s prefactor is the golden-rule rate exactly for the Letter’s own definitions (fields E cos omega t, omega = 2 pi R nu, R = 3.29e15 s-1): checked numerically. quattropani_1982 prints the same prefactor in its Eq. (1) with fields E0 (e^{i omega t} + c.c.) and omega = R nu; under those, 16 x 8 pi^3 = 128 pi^3 is the factor that record’s notes find. The 1982 prefactor was carried over without the change of definitions. (c) Eq. (4b) prints [nu1 (1/4 - nu1)]^-1 for [nu1 (3/4 - nu1)]^-1 (with 1/4 no N = 3 sum reproduces; Eq. 5b has 3/4); Eq. (7) prints ‘1/g’ and ‘epsilon^2’ for 1/9 and epsilon2. No taken value depends on them. (d) Gauge comparison: equal totals, but the 2p term is 152 % of the total at 0.3750 in J0 and zero in J, and the continuum is -14 % (J0) against +60.2 % (J). The text’s ‘more than half’ for the A.p continuum holds only up to nu1 = 0.7250 (49.8 % at 0.7375, 48.8 % at 0.7475).

• Status: verified (2026-10-09).

TC-1045 johansson_2003 (Johansson et al., Eur. Phys. J. D 22, 3 (2003)): He 1s2p and 1s3p 1P lifetimes and photoionisation cross sections, pump and probe parallel (2026-10-09)

• Where: src/optmat/data/sources/johansson_2003.toml, tools/extract/johansson_2003.py, data/values/absorption/He/johansson_2003__*.csv.

• Transcribed:

  • tau (radiative_lifetime, inline, p. 7): 1s2p 1P1 0.57 +- 0.03 ns and 1s3p 1P1 1.76 +- 0.1 ns, primary; level not stated (the abstract says about 15 %).

  • sigma_1s2p, sigma_1s3p (excited_state_photoionization_cross_section, Table 1, tbl_c7aba2f99989): sigma_par in Mb against the probe wavelength. 1s2p: 16.6 (355 nm) and 6.6 (266). 1s3p: 24.4 (752), 10.5 (532) and 4.2 (355). Pump and probe polarisations parallel, the level aligned (M = 0). 25 % uncertainty, level not stated. Primary.

• Checked:

  • Table 1 against its image. Each E_exc recomputed from NIST’s levels and ionisation energy, within 0.003 eV.

  • Eq. (7) derived from Eqs. (5)-(6), 6j symbols 1/3 and 1/30. d/s = 13 gives sigma_par/sigma_perp = 1.590 (printed 1.6).

  • The widths 3.5, 5.7 and 0.3 pm give 1.27, 2.07 and 0.109 meV (printed 1.3, 2.0 and 0.11). 13 ns^-1 x 70 ps = 0.91 (printed 0.9).

  • NIST’s 1/A to the ground state: 0.5559 ns (1s2p) and 1.7657 ns (1s3p). These are upper bounds, and both measurements agree with them within their +-.

• Doubt:

  • 16.6 Mb at 5 x 10^8 W/cm2 and 355 nm gives sigma I/h nu = 14.8 ns^-1, against the printed Gamma = 13 ns^-1.

  • The dye wavelengths 759 and 753 nm put the 13th and 14th harmonics 18 meV above 1s2p and 35 meV below 1s3p, against a 1.3 meV harmonic width. They are nominal.

  • Fig. 11’s solid curve is the theory’s in the caption but ‘the fit’ in the text. Its contrast, about 1.57 read by eye, is that of d/s = 13, not 20.

  • Table 1 may repeat Gisselbrecht et al., Phys. Rev. Lett. 82, 4607 (1999), which is not in the library. The two must not be fitted side by side.

• Not taken:

  • d/s = 20/1 measured and 13/1 theoretical, and sigma_par/sigma_perp = 1.6: partial-wave ratios, declined (TC-1011).

  • The 1s2p line’s broadening (2.0 meV) and blue shift (0.11 meV) under the 5 x 10^8 W/cm2 probe: the shifting field is a second colour, not the exciting light, so light_shift_coefficient does not apply.

  • The zero-delay ‘direct two-photon’ spike, in arbitrary units.

• Finding:

  • meyer_2008’s quotation, d-wave ‘more than 10 times’ the s-wave (TC-1033), agrees with both 20/1 and 13/1.

  • No bound two-photon resonance is driven. For OEP 8 the paper gives Gamma^PI_f of He 1s2p and 1s3p near threshold for an aligned level (sigma_par, not sigma_iso; with d/s = 13, sigma_iso = 0.753 sigma_par) and the 1snp lifetimes.

• Status: verified (2026-10-09).

TC-1046 fushitani_2015 (Fushitani et al., Nat. Photon. 10, 102 (2016)): two-photon Rabi oscillations He 1s2p-1s6f at 795 nm; three transition dipoles and a lifetime (2026-10-09)

• Where: src/optmat/data/sources/fushitani_2015.toml (inline datasets, no script).

• Transcribed:

  • Three transition_dipole_moment datasets (au, label, the |z| element between the M = +-1 sublevels), from the four-level model’s Methods (PDF p. 5): mu_2p_3d 2.1645, mu_3d_6f 0.7425, mu_3d_5f 1.338. These are use = "reproduced", from Wiese and Fuhr’s line strengths (J. Phys. Chem. Ref. Data 38, 565 (2009), not in the library).

  • tau_2p: 560 ps (Fig. 1 caption), with no source given, use = "check".

  • The rest is in the notes: levels, detunings, intensities, pulse, the 44 and 83 THz Rabi frequencies, the 22 % loss, the Up formula and Fig. 4’s M dependence.

• Identity: the library copy is the advance online publication (30 November 2015, pp. 1-5). The issue is Nat. Photon. 10, 102-105 (2016). The id keeps 2015.

• Checked:

  • Fig. 1b’s 1.86, 2.83, 2.99 and 3.37 eV and the text’s 0.54 and 0.38 eV bindings against NIST: 1.8561, 2.8251, 2.9914, 3.3694, 0.5442 and 0.3779 eV.

  • delta = 0.1277 eV (printed 0.13) and Delta = 0.2965 eV (printed 0.30).

  • Up = 0.295 eV at 5 TW/cm2 (printed 0.3). The printed coefficient 9.334e-14 is 0.04 % below 9.3373e-14.

  • 2/(45 fs) = 44.4 THz and 22.7 fs (printed 44 THz and 23 fs). The three-level formula with the printed dipoles reaches 83.0 THz at 6.00 TW/cm2 (NIST’s Delta) or 82.0 THz (Delta = 0.30 eV), with I = eps0 c E0^2/2. So the printed 83 THz is at the peak, at 6 TW/cm2.

  • The 2 1P lifetime against NIST’s 1/A, 555.9 ps (an upper bound), and johansson_2003’s 0.57 +- 0.03 ns.

• Finding:

  • The paper’s Omega^(2) = Omega_1 Omega_2/(2 Delta), with Omega_i = mu_i E0/hbar, is OEP 8’s full Omega_R = |M||E+|^2/hbar, not the off-diagonal half (TC-990’s naming trap does not apply here).

  • Implied |M| = 2 mu_1 mu_2/Delta = 291.6 au (295.0 au with NIST’s Delta). The effective 44 THz at 6 TW/cm2 gives 156 au, half of that.

  • ‘45 fs’ is not defined. If it is the intensity FWHM of the squared-sine field envelope, two cycles is a 4 pi area at a peak of about 43 THz. If it is the full width, the peak is 118 THz.

• Finding: this is not a direct test of OEP 8’s -(1/2) M_f (E+)^2.

  • The lower level is an excited 1P1 level in M = +-1, not the ground state, so two_photon_transition_amplitude and TC-952’s convention do not apply.

  • The field-strength condition of OEP 8 §4.3 fails: |d E0|/(2 hbar D) = 1.30 for 2p-3d at 6 TW/cm2.

  • It tests Eq. (6)-(7)’s structure in strong field. The Freeman-resonance shift is -alpha_f |E+|^2 with the free-electron alpha_f = -e^2/(m omega^2), which equals Up exactly. Rabi flopping outruns ionisation (22 % loss), and the coupling depends on M. It is a TDSE validation case for an excited-level extension.

• Doubt: hydrogenic m = 1 elements (computed, a model) are 2.123, 0.860 and 1.587 au. The printed 2p-3d is within 2 % of its value, which confirms the M = +-1 reading (m = 0 would be 2.452). The 3d-6f and 3d-5f values lie 14 % and 16 % low. This cannot be checked here: Wiese and Fuhr are not held, and NIST’s held He lines cover 40-60 nm only.

• Not taken: the Rabi frequencies, period and implied |M| (no quantity for an excited-to-excited two-photon coupling); NIST’s energies; photoelectron energies; the figures (arbitrary units).

• Status: verified (2026-10-09).

TC-1047 OEP 8’s literature (TC-1042 to TC-1046): the xenon 6p′ lifetimes settled; notes corrected (2026-10-09)

• Where: the records of TC-1042 to TC-1046; OEP 8’s Draft. The notes of kligler_1980, marinero_1982, bischel_1979 and drachman_1990 are corrected.

• Settled:

  • The xenon 6p′ lifetimes. inoue_1984 measures 37–48 ns in argon, against NIST’s 1/ΣA of 23–28 ns (TC-1042).

    • It sides with bruce_1990, 4–5 ns above it, at 1.8 and 2.3 combined errors.

    • NIST’s 6p′ lines that carry an A already exceed the measured decay rates by 1.3–2.0. Its missing lines can only shorten its figure.

    • For 6p, a fourth group confirms TC-1041: NIST is 12–20 % short for 6p[3/2]₂ and 6p[1/2]₁.

    • For 7p, NIST agrees with bruce_1990 within 1 %. inoue_1984 differs from both by −10 to +29 % and is held as a check.

    • inoue_1984’s 6d lifetimes are the only ones held.

  • The H2 E,F (v = 2) lifetime and quenching are now held from their original, kligler_1978b (TC-1043). kligler_1980’s reproduced values match it exactly.

  • The hydrogen 1s–2s amplitude. bassani_1977’s 270 printed cells all equal the exact amplitude, to rounding or truncation (TC-1044).

    • drachman_1990’s “Ref. 1” column is bassani_1977’s length-gauge table. Its gauge parameter now says so.

    • The prefactor discrepancy that quattropani_1982’s notes report is explained: that paper kept Bassani et al.’s Eq. 2 prefactor while changing the field and frequency definitions, a factor of 128π³.

• Not a test of OEP 8’s coupling:

  • fushitani_2015 couples two excited helium levels, outside the adiabatic elimination regime (|dE₀|/2ħD = 1.3). Its Rabi frequency is OEP 8’s full Ω_R; the implied |M| is 292 au (TC-1046).

  • johansson_2003 has no bound two-photon resonance. It gives the He 1s2p and 1s3p lifetimes and aligned-level photoionisation cross sections (TC-1045).

• Notes corrected (no values changed):

  • kligler_1980, marinero_1982 and bischel_1979 no longer list Kligler and Rhodes (1978) as not in the library. bischel_1979 likewise for kligler_1978.

  • kligler_1980’s three reproduced_from now name kligler_1978b.

  • drachman_1990’s Ref. 1 dataset now has reproduced_from bassani_1977 and gauge length.

• Status: verified (2026-10-09).

TC-1048 travers_2026_trecx_two_photon (tRecX, the two-photon campaign): two-photon ionisation cross sections of He and Ar and the one-electron Ar 3p -> 4p amplitudes, with the campaign archived (2026-10-11)

• Where: src/optmat/data/sources/travers_2026_trecx_two_photon.toml, tools/extract/travers_2026_trecx_two_photon.py, src/optmat/data/external/trecx/two_photon/ (PROVENANCE.md, the run tables run1/results_sae.csv, run1/results_hacc.csv, run2/ … run6/results.csv, manifest_runs2to6.csv, REPORT.md, STATUS.md, NOTES.md, the two summaries, the input and extraction scripts as .py.txt, the job lists, and the 203 input decks under inputs/), data files values/ionisation/{He,Ar}/travers_2026_trecx_two_photon__*.csv.

• Held: J. C. Travers’s two-photon tRecX campaign (OEP 6 Q9 and OEP 8), run on a Slurm cluster on 9-11 October 2026 with tRecX a987d7c (run 5 with an uncommitted patch that writes the Occupation states’ energies, occE_patch_20261010.diff, sha256 prefix bd3c33ee, not archived). Tier 3, use = check throughout. Datasets: sigma2_hacc_He (haCC He19, one channel, 13-20 eV, the spectrum peak), sigma2_sae_He (one-electron Tong-Lin He, 13-20 eV, the projection less the no-field drift), sigma2_sae_Ar (one-electron Tong-Lin Ar, 8-11 eV in seven points, the atom as 2 P(m = 0) + 4 P(m = 1) from the spectrum peaks): multiphoton_ionization_cross_section, photons = 2, linear, velocity gauge, 1e12 W/cm2, 20 fs Gaussian (intensity FWHM), sigma2 = P / int Phi^2 dt, cm4 s against the photon energy, each model’s own threshold (24.5410, 24.5937, 15.774 eV). M_4p_m0 = +8.914061 au and M_4p_m1 = +2.418379 au (two_photon_transition_amplitude, length gauge, lowest order, one time ordering, m_zz_per_unit = 2, phase u = rR positive near the origin with Condon-Shortley; inline, from extract_runs.py’s M_PT). Runs 2 (He two-colour kernel), 3’s two-colour points, 5 (He 1s2s in haCC) and 6 (He broadband) have no quantity: held in the archive and described in the record’s notes. Not archived: the pulse files (1.2 GB on the cluster; run 1’s five on a workstation, sha256 in PROVENANCE.md), the run directories’ outputs, run 5’s P(1s2s)(t).

• Checked: the script reproduces all 15 sigma2 the runs’ summaries print, to the printed digits (haCC 11.890-10.175 and one electron 7.456-9.346 e-52 cm4 s at 13-20 eV; argon 1.921-3.052 e-50 at 8-11 eV), and haCC’s tabulated sigma2 from its P_peak2 to 1e-12. The curator’s rerun of the archived pt_two_photon.py prints M_0 and M_1 to every digit held. Every archived file’s sha256 is in PROVENANCE.md.

• Convergence (the record’s uncertainties, level bound, the larger of the family’s largest convergence change and the row’s spread between two readings of the same run): haCC (16 eV) lMax 15 +0.003 %, rMax 60 -0.25 %, spectrum against norm-loss <= 0.1 %: 0.25 %. One-electron He (16 eV, each variant less its own drift) angular 15 0.000 %, ECS angle x 2/3 -0.25 %, step x 2/3 and cutEnergy 150 +1.6 %, BOX 80 and 120 on the projection <= 0.29 % over the five energies, the BOX 80 and 120 spectra within 1.9 % of the projection: 1.6 to 1.9 %. One-electron Ar (9 eV, m = 0, peak) angular 15, step, ECS angle 0.000 %, cutEnergy 150 +0.02 %, BOX 120 +0.18 %; the spectrum against the drift-corrected projection +10.9 % at 8 eV, -1.8 to -3.6 % at 8.5-9.5 eV (the atom; per m -1.2 to -3.7 %), +0.5 to +1.1 % at 10-10.5 eV, 0.1 % at 11 eV, which dominates: 0.18 to 10.9 %. P proportional to I^2 from 1e11 to 1e13 W/cm2 to 1.4 % (He, both models); Ar 1e11 within 0.3 % of 1e12 (1.1 % at 11 eV), 1e13 -3.4 to +1.6 % (8-10 eV) and -7.0 % at 11 eV, 0.27 eV below the model’s 4s. Run 4: TDSE/PT of the 4p population 0.9982 to 0.9996 at 1e10 W/cm2 (|M_m| to 0.1

  signs are perturbation theory’s, not the TDSE’s.

• Doubt: the runs’ summary says the argon spectrum and projection agree “elsewhere <= 2 %” beyond 8 eV; 9 and 9.5 eV differ by 2.4 to 3.7 % (both m). Which reading is right is not established; the record carries the spread as the uncertainty. The 203 input decks are the local copies as generated, not compared with tRecX’s own inpc on the cluster; run1/hacc/eig_l10_r40.inp was generated but not run.

• Status: verified (2026-10-11) against the archived tables and summaries; the physics findings are entered separately. docs/two_photon.md’s coverage tables and the counts need regenerating (the new He and Ar datasets).

TC-1049 The tRecX two-photon runs against OEP 6 and OEP 8: what they confirm, and one open discrepancy (2026-10-11)

• Where: travers_2026_trecx_two_photon (TC-1048); OEP 8’s Draft, revised. The comparisons below were computed for this entry from the archived results, optmat’s models and the curated records. They are findings, not data.

• Helium cross section (run 1). haCC’s σ⁽²⁾ is 0.90, 1.01, 1.03, 1.06 and 1.16 of optmat’s reference model (mihelic_2021, TC-943) at 13, 14, 16, 18 and 20 eV. That validates the model independently, within its spread envelope.

  • The one-electron model is 0.56–1.07, lowest near threshold.

  • Both are tier 3.

• The continuum two-colour kernel (run 2; OEP 6 Q9, OEP 8 Q6).

  • Direct reading. With equal per-colour intensities and a one-colour reference at Ω/2, P_cross/P_ref = 4|M(ω₁,ω₂)/M(Ω/2,Ω/2)|² in lowest order. The photon-flux factors cancel.

  • haCC, |M/M₀|² at full splits ν = 0.5, 1, 2, 4 and 6 eV:

    • Ω/2 = 14 eV: 1.0012, 1.0063, 1.026, 1.113, 1.286;

    • Ω/2 = 17 eV: 1.0015, 1.0077, 1.034, 1.163, 1.561;

    • Ω/2 = 20 eV: 1.027 at ν = 0.5 and 1.136 at ν = 1.

  • The sign and size. κ > 0 in every case, and the effective pole distance is 1.1–2.2 times D₁ = E(1s2p) − Ω/2. The one-electron model gives 1.03–1.8 times.

  • So OEP 8’s rule, D_eff ≥ 0.75 D₁, holds for the helium continuum in both models (tier 3).

  • Argon (one electron, Ω/2 = 8.5 eV, the only point with a degenerate reference): |M/M₀|² = 0.999, 1.013, 1.036 and 1.070 at ν = 0.5–2 eV. That gives D_eff ≈ 5.3 eV, 1.9 times the model’s D₁.

• Broadband yield (run 6, one electron, He 14 eV).

  • The 1 fs transform-limited yield exceeds the narrowband scaling ∫Φ²dt by 0.75 % against 5 fs, and by 1.2 % against the ±5 fs² chirped pulses.

  • OEP 8’s Eq. 5 with run 2’s κ predicts +1.7 % for the transform-limited pulse and about 0 for the chirped ones.

  • The ± chirps agree to 0.01 %, as lowest order requires.

• Argon 3p⁵4p strengths (run 4; TC-952’s open argon question). Frozen-core LS recoupling of the one-electron amplitudes, with OEP 8’s M = 2M_m, gives per level δ(¹S) = (2/3)(M₀ + 2M₁)² = 504 au and δ(¹D) = (4/3)(M₀ − M₁)² = 225 au. Their sum is 2ΣM_m².

  • Absolute values: ¹S is 2.6 times hattig_1998b’s CCSD (197.7 au, the same in either convention for J = 0) and 3.1 times henriksson_2005’s TDHF (161.5). ¹D is 2.0 times TDHF (113.4). Like run 3’s cross sections (1.5–2.7 times mckenna_2004), the one-electron model overestimates argon by 2–3.

  • The ratio ¹D/¹S is 0.45. TDHF per level gives 0.70; a one-component reading would give 0.14. It favours the per-level convention, weakly.

  • henriksson_2005’s J-resolved TDDHF sums (J = 2: 115.0; J = 0: 162.4) reproduce its LS values (113.4, 161.5), a check of the per-level reading.

  • Argon’s assessment stays unresolved. The convention was decided by xenon (TC-952), and mccann_1988’s ambiguity is not touched.

• Helium 1s2s (run 5, haCC) against OEP 8’s weak-field form. The comparison uses P = |M|²|S₂(Ω_f)|²/4 with hattig_1998b’s δ = 12.306 au, the pulse as defined in the report and haCC’s own 1s2s energy (20.636 eV); NIST’s gives the same within 2 %.

  • 3 fs: 1.00 (10¹² W/cm²) and 0.95 (10¹³).

  • 1 fs: 1.21 (10¹²) and 1.04 (10¹³).

  • 3 fs chirped ±10 fs²: 1.07 and 0.92 at 10¹², 0.96 and 0.94 at 10¹³. Lowest order predicts the two signs equal.

  • 10 fs: 0.52 at 10¹² and 0.46 at 10¹³.

  • Open discrepancy, put back to the TDSE runs. The 10 fs shortfall in the perturbative regime equals a two-photon resonance about 0.12 eV from where haCC’s reported 1s2s energy places it. The broadband 3 fs case is insensitive to that. Together with the chirp asymmetry at 10¹², which the one-electron run 6 does not show, it suggests a haCC-specific issue. Until it is checked, run 5 qualifies OEP 8’s weak-field form only at 3 fs and 1 fs (10¹³), to 5 %.

• Status: open (run 5’s 10 fs discrepancy); the other findings verified (2026-10-11).

TC-1050 travers_2026_trecx: helium with two active electrons at 390 nm (part K); Parker et al. confirmed, haCC’s helium low (2026-10-11)

• Where: src/optmat/data/external/trecx/he_two_electron/results_*.csv, PROVENANCE.md there, travers_2026_trecx.toml (twoelectron_normloss_gauss6_390nm_He, _box60, _m5; hacc_normloss_gauss6_390nm_He; normloss_ and ionised_ipmatched_390nm_{base,m5,tl}_He), tools/extract/travers_2026_trecx.py, optmat.gas.ionisation_validation (parker_pulse_yield, HELIUM_TWO_ELECTRON, helium_two_electron_ratios), tools/ionisation_rate_tables.py (ionisation-rate-helium-two-electron; the helium table’s columns), src/optmat/data/gas/ionisation_rates.toml (helium’s uncertainty reason), docs/ionisation_rates.md, tests, tests/data/golden_models.json (helium’s identity only), the counts.

• Transcribed: J. C. Travers’s tRecX runs of 4 to 11 October 2026 (part K, step 2): helium with both electrons active in A2’s 6 fs Gaussian at 390 nm, the norm-loss 1000 au after the pulse: 7.330e-3 (5.69e14 W/cm2) and 8.623e-4 (3.68e14), BOX 40; 6.901e-3 with BOX 60; 7.207e-3 with |m| <= 2 (its ionisation energy 0.14 % higher). haCC’s helium (He19, one channel, lMax 40): 5.595e-3 and 6.777e-4. One electron at the two-electron bases’ ionisation energies and at Tong and Lin’s. Tier 3. Uncertainty: two electrons 5.85 % (the box; BOX 80 not run, the maintainer’s decision), haCC 2.1 % (the He+ n = 2 channels), one electron 1.7 % (ionised fraction) and 5.0 % (norm-loss, the box).

• Checked: the runs’ table against the report to the last digit; drift, norms, warnings (PROVENANCE.md). The five-channel haCC run’s job was cancelled in the iSurff pass after propagating; its row was refreshed from the expectation file (11 October 18:10) and gives +2.082 %, the report’s +2.08 %. The extraction refuses a variation whose row is not done.

• Finding (helium_two_electron_ratios, parker_pulse_yield):

  • the atom over one electron at the same ionisation energy: 1.71 (5.69e14), 1.79 (3.68e14), 1.72 with |m| <= 2, 1.69 with both boxes enlarged; as Sato et al.’s converged helium at 800 nm (1.53 to 1.71, TC-860);

  • Parker et al.’s rate integrated over the pulse: 7.00e-3 and 8.49e-4, 1.05 and 1.02 of the two-electron yield at BOX 40, 0.99 at BOX 60: their rate is confirmed, and the default’s N_eff of 1.47 (from their static rates) stands;

  • haCC’s helium is 0.76 and 0.79 of the two-electron yield (0.81 at the larger boxes), converged in lMax, rMax and channels: the factor 1.25 between haCC and Parker et al. (TC-848’s reason) was haCC’s. Whether haCC’s argon (Ar_qz; 0.76 to 0.87 of one electron, TC-847, TC-861) is low by as much is not known; the published all-electron argon (0.87 to 1.10, TC-860) sits above it. The manual says so at haCC’s argon.

• Correction: since TC-848 the manual’s helium table labelled the static Coulomb factor’s column default; it now has the default’s (frequency-dependent) column and the static factor’s beside it.

• Status: verified (2026-10-11). Closes part K of the runs. Corrected (2026-10-17) by TC-1092: the norm-losses compared here are not one measure.

TC-1051 travers_2026_trecx_two_photon, run 5b: haCC’s 1s2s resolved; OEP 8’s weak-field form and helium’s strength confirmed (2026-10-11)

• Where: src/optmat/data/external/trecx/two_photon/ (run5b/results.csv, run5b/scan_fit.csv, extract_run5b.py.txt; REPORT.md, NOTES.md and STATUS.md updated, PROVENANCE.md hashes); travers_2026_trecx_two_photon’s notes; OEP 8’s Draft. Closes TC-1049’s open item.

• The runs: the campaign’s four follow-up checks: 11 haCC runs on 11 Oct 2026, populations every 1 au.

• What resolved the discrepancy:

  • The resonance. haCC’s propagated 1s2s lies at 2ω = 20.7386 eV, from a 10 fs carrier scan fitted to P = K|S₂(Ω)|², to a few meV. That is 0.103 eV above its Occupation set’s 20.636 eV, which TC-1049 used. The 1s2s–ground beat after the pulse (20.738 eV) measures the same spacing independently.

  • The beat. P(1s2s)(t) does not decay after the pulse, but beats with the ground state through the projector’s floor, |ε|² = 2.862e-9 (a no-field run). Run 5’s end values were single samples of that beat. That explains the 16 % chirp difference and most of the 1 fs excess.

• Result:

  • With the propagated resonance and the post-pulse means, lowest order holds to ≤ 1 % at 10¹² W/cm² for 3 and 10 fs and both chirps, and to 3 % at 1 fs.

  • The ±10 fs² pair agrees to 0.07 %.

  • The fitted coupling, |M|² = 4K = 12.31 au², equals hattig_1998b’s CCSD δ = 12.306 au to 0.04 %. That confirms OEP 8’s weak-field form P = |M|²|S₂|²/4 and TC-952’s per-level convention δ = |M_zz|² for helium 1s2s, independently, at tier 3.

• Beyond lowest order: ratios to lowest order at 10¹³ and 10¹⁴ W/cm² are 1.013 and 0.952 (1 fs), 0.983 and 0.748 (3 fs), and 0.858 and 0.079 (10 fs). The chirp pair differs by 6.6 % at 10¹⁴. These are the validation targets for OEP 8’s Bloch equations (Phase 1) with haCC’s own resonance.

• Caveat for TC-1049’s run 2 pole distances: haCC’s 1s2p (21.209 eV) is also an Occupation energy, and the propagated value is not measured. A shift of order 0.1 eV changes D₁ by under 10 % at Ω/2 = 14 and 17 eV, and by about 8 % at 20 eV, so the conclusion D_eff ≥ 0.75 D₁ stands.

• Status: verified (2026-10-11).

TC-1052 travers_2026_trecx_two_photon, run 5c: haCC’s propagated 1s2p equals its Occupation value; its 1s2p dipole (2026-10-12)

• Where: src/optmat/data/external/trecx/two_photon/ (run5c/results.csv, run5c/scan_fit.csv, extract_run5c.py.txt; REPORT.md, NOTES.md and STATUS.md updated, PROVENANCE.md hashes); travers_2026_trecx_two_photon (dataset dz_1s2p_hacc, notes). Closes TC-1051’s caveat.

• The runs: a further follow-up check, 5 haCC runs on 11-12 Oct 2026. One photon at 21.21 eV, plus carriers at ±50 and ±100 meV; 10 fs; 1e9 W/cm².

• Method. The check as planned asked for a beat in P(1s2p). That cannot exist: the ¹P projector cannot see the ¹S ground state (floor 1.27e-19), and the plan was wrong to suggest it. The runs instead fitted the beat of ⟨z⟩(t) after the pulse, and a carrier scan with P = K|S₁(Ω)|².

• Results:

  • The propagated 1s2p is 21.208918 eV from the beat (both dipole forms, 10 fits, 0.9 µeV spread) and 21.20892 eV from the scan. That equals the Occupation set’s 1s2p to 1e-8 au.

  • Run 2’s pole distances (TC-1049), which used haCC’s Occupation 1s2p, stand unchanged. Only the ¹S excited level was misplaced, by +0.10 eV (TC-1051); the cause is not found.

  • The dipole. K = |z|² = 0.169939 au² gives |z| = 0.41224 au, 2.0 % below NIST’s 0.4208 (from f = 0.2762). It is held as a check (dz_1s2p_hacc).

  • First order holds to 5e-5 at all five carriers.

  • Gauge. The velocity-to-length ratio of the beat amplitudes departs by 5.9 % from exact-eigenstate equality. The two dipole forms are not equivalent in this one-channel basis, though the frequency is the same.

• Status: verified (2026-10-12).

TC-1053 The author’s decisions of 2026-10-12: OEP 6 is Final; argon qualified in OEP 8 on calculated strengths (2026-10-12)

• Where:

  • docs/oeps/archive/oep-0006-two-photon-ionisation.md (moved from docs/oeps/; its links fixed, and the index, toctrees, roadmap and two-photon manual updated);

  • docs/oeps/oep-0008-bound-two-photon-response.md (Draft), sections 1, 5, 6, 11, 12 and 13 (Q7).

• Decision 1 (John Travers, 2026-10-12, as recommended). OEP 6 is Final.

  • Its Phases 1 and 2a are implemented.

  • Its Phase 2b (the complex evaluator) and optional Phase 3 pass to OEP 8, as Q9’s fallback provided.

  • Its open items go on the roadmap: Q2, krypton; Q3, xenon between its thresholds; Q7, Dakka et al.’s factor; the continuum’s time-resolved loss, for a new OEP.

• Decision 2 (the same, as recommended). OEP 8 qualifies argon’s 3p⁵4p J = 0 and J = 2 levels, for absorption and populations, on calculated strengths labelled “calculated only”:

  • The reference is henriksson_2005’s J-resolved TDDHF strengths, held per level in two_photon_bound since TC-953.

  • The uncertainty is −5 % and +30 %.

• Basis:

  • The convention is per level, decided by xenon (TC-952).

  • Correlation. hattig_1998b’s CCSD is 1.22 times henriksson_2005’s TDHF for ¹S (197.71 against 161.45 au). For ¹D it is 1.23 times (139.45 against 113.40 au), its printed single-component S⁰ᶠ of 104.59 au times 4/3, read from the paper’s Table V and not yet held as data. CC2 and the reprinted MCSCF lie within 4 % of CCSD.

  • TDDHF’s J sums (115.0 for J = 2, 162.4 for J = 0) reproduce its LS values.

  • mccann_1988 agrees in its 0.85 reading.

  • The one-electron TDSE (2–3 times high; TC-1049) does not enter.

• Consequences:

  • OEP 8 Phase 1 takes hattig_1998b’s ¹De rows as data (one_component) and changes argon’s assessment in data/gas/two_photon_bound.toml from “unresolved” to “calculated”. That is a change of a record’s status, made in Phase 1 with this authority.

  • The 4p levels’ photoionisation at the drive, their light shifts and their pressure broadening stay unqualified. They are on the papers-wanted list.

  • No value changes now.

• Status: decided (2026-10-12).

TC-1054 OEP 8 AI review: coherence sign, energy balance and qualification limits (2026-10-12)

• Where: docs/oeps/oep-0008-bound-two-photon-response.md, sections 4, 6–8 and 12–13; its roadmap summary.

• Checked: deriving the density equations from the stated Hermitian Hamiltonian gives a minus sign for the excited-state coherence sum in Eq. (7). A direct three-state matrix-commutator check with complex amplitudes gave a residual of 7.9e-17 with the corrected sign, against 0.229 with the original sign (dimensionless test). The equation for the excited-state coherences is now explicit.

• Finding: the derivative of a Hermitian Hamiltonian supplies the conservative polarisation; photoionisation’s absorptive polarisation and population sink must be accounted for separately. The local energy identity is the change of Tr(rho H) minus the integral of Tr(H D[rho]), plus photoionisation field work. The draft’s scalar sink formula omitted pure-dephasing work and was not a general multilevel or broadband theorem. Radiative decay into a lower excited level retains energy in that level; the whole outgoing energy is not fluorescence. He 1s2s radiatively returns to the ground state, unlike the np-to-ns sinks. The total polarisation must not duplicate a propagation solver’s existing ground-state linear response. OEP 6 supplies no qualified time-local continuum depletion rate.

• Checked against primary sources: Kumar et al. (2026), Eq. (7), Gaussian pulse Eq. (2) and Table I (table image); Lehmberg et al. (1995), Table 1 (table image); Drake et al. (1969), Table II (table image and the source record’s normalisation). Lehmberg’s compensation is with CO2 gas, not a CO2 laser.

• Reproduced: Kumar’s one-colour result with Table I’s printed coefficients, peak E0 squared = 2.84882e-4 au, detuning hbar(2 omega - Omega_f) = +14.3 meV, intensity spectral FWHM 9 meV (intensity duration 202.77234 fs), initial ground state and integration from -5 to +5 durations. DOP853 at relative tolerances 1e-9 and 1e-11, absolute tolerances one hundredth as large, maximum step duration/30, gives Pg = 0.39726990, Pe = 0.27612491 and ionisation = 0.32660519; Pe agrees with the paper’s about 28 %. This reproduces its effective model, not an independent validation of its coefficients or of its continuum light shift.

• Finding: the Gaussian split correction must use the magnitude of kappa when stated as an error estimate; negative kappa is already demonstrated by TC-1034. The adopted 0.75 D1 rule (TC-984) is empirical and leading order, not a guaranteed bound for cancelling amplitudes, arbitrary phase shaping or higher-order terms. D1 and the bandwidth are angular frequencies; tabulated eV values represent hbar D1.

• Finding: the same residue controls absorption and dispersion. The unexplained xenon n2 discrepancy cannot be declared irrelevant to population predictions if its cause is a strength error. TC-984’s chosen strengths and TC-1053’s argon decision remain unchanged; missing light shifts, photoionisation and pressure coefficients limit dynamical qualification separately. A model spread is not a confidence level.

• Doubt: Q8–Q10 in the reviewed draft remain open: a consistent broadband response; omitted effective couplings, shared loss and correlated dephasing among excited levels; and the data quantity and extraction for the helium decay spectrum, which currently remains in notes. A squared decay amplitude alone does not supply an arbitrary complex, off-shell two-colour kernel. Review completion is not acceptance.

• Not checked: no TDSE runs were repeated, and the other drafting numerical residuals and literature comparisons were not all independently reproduced. They remain Phase 1 fixture targets. No curated values or implemented models changed.

• Status: corrected (2026-10-12); Q8–Q10’s initial scope and data choices were subsequently resolved in TC-1055; the broader scientific qualification is deferred.

TC-1055 OEP 8 Q8–Q10: approved local scope, qualification boundary and helium decay data (2026-10-12)

• Where: docs/oeps/oep-0008-bound-two-photon-response.md, sections 1–2, 6–7, 9 and 12–13; docs/roadmap.md. Resolves the initial choices left by TC-1054.

• Decision: John Travers approved the AI review’s recommendations for Q8–Q10.

  • Q8: qualify the local effective dynamical model within its demonstrated spectral and field-strength limits; helium’s two-colour kernel supplies perturbative on-shell yields only. General frequency-dependent dynamics and their consistent polarisation/work balance are deferred.

  • Q9: He 1s2s is the first qualified nonlinear dynamical example. Its required light-shift curation moves from Phase 2 into Phase 1. The approved Xe and Ar coefficients remain, with weak-field applications; strong-field multilevel qualification requires evidence for omitted couplings, shared loss and correlated dephasing. TC-1053’s argon strength choice is unchanged.

  • Q10: add two_photon_decay_rate and two_photon_decay_spectrum to the absorption vocabulary, and an energy_fraction abscissa in unit 1. Required state, isotope, method and counting metadata distinguish the physical quantities. Store rates as printed; derive lifetimes and kernel ratios. Drake Table II supplies the spectrum; Bondy Table VI supplies the preferred helium decay rate.

• Checked: the existing vocabulary holds signed two-photon amplitudes and lifetimes, not the printed differential two-photon decay spectrum. It must not be relabelled as a signed amplitude or as an ordinary wavelength abscissa.

• Checked against primary sources: Drake Table II and Bondy Table VI, table images and source records (drake_1969, bondy_2020). Bondy’s helium total is 5.093(7) times 10^1 s^-1 = 50.93 ± 0.07 s^-1; its uncertainty includes the estimated relativistic correction and is not assigned a statistical confidence level. The inverse is 0.01963479 s, a derived lifetime. The library’s extracted Table VI CSV is scrambled and must be repaired and checked against the image before data ingestion. The text’s 50.093 s^-1 is not the table’s value (already noted by the source record).

• Checked: Drake’s A(y) counts photons. Its symmetric distribution obeys Gamma = (1/2) integral_0^1 A(y) dy = integral_0^(1/2) A(y) dy. Simpson quadrature of the extracted He column gives 51.1457 s^-1 against the printed 51.3 s^-1; preserve this check and the raw values without silently renormalising the data. The normalised spectral shape does not acquire Bondy’s total-rate accuracy.

• Consequence: Phase 1 includes the quantity definitions, extraction, helium shifts, local dynamics and separately labelled paper-reproduction and curated-input fixtures. The continuum-first RDW diagnostic of TC-1056 can start with OEP 6 independently.

• Doubt: the broader response derivation and multilevel/pump-dressing qualification remain scientific work on the roadmap. Approval settles scope, not their accuracy. No source dataset, numerical model or recommended default changes in this update.

• Status: decided (2026-10-12). OEP 8 remains Draft, with review status Reviewed; the maintainer has not accepted the whole proposal or authorised implementation here.

TC-1056 The initial Ar/He RDW question: continuum-first diagnostic and its limits (2026-10-12)

• Where: OEP 8 section 2.1 and its Phase 1 handoff; docs/roadmap.md.

• Context supplied by the maintainer: a 6 fs, 800 nm pulse self-compresses in argon and emits a weaker VUV RDW. Pressure/phase-matching tuning towards the two-photon ionisation threshold suppresses the RDW. Pump-driven ionisation disrupting phase matching can explain the observation; whether two-photon effects can also explain it is open. Helium is a second target. This context is not a curated measurement.

• Checked: docs/two_photon.md’s NIST-derived thresholds (TC-943), the NIST argon atomic-data table (15.759610 eV) and helium elemental data (24.587389011 eV). Two equal photons reach the continuum at 157.344 nm (Ar) and 100.852 nm (He). OEP 8’s first bound levels are Ar 4p, about 185–192 nm, and He 1s2s, 120.28 nm. Higher bound series near threshold are not covered by these low-level strengths.

• Derived: an 800 nm photon has 1.54980 eV. With an Ar-threshold VUV photon its total is 9.42961 eV, below Ip; the field-free ground-state mixed two-photon channel would require a VUV photon at 87.253 nm or shorter. This does not exclude dressing, higher-order mixed processes, excited atoms or different parts of the actual spectrum.

• Checked: the current public Ar continuum model returns unavailable at 7.87981 and 7.90 eV per photon, unsupported_detail at 7.95 eV, and supported at 8.0 and 8.1 eV. The manual identifies unresolved fine-structure detail between the two thresholds (157.34–155.59 nm). Thus simply drawing a sharp loss onset at the nominal threshold is not a prediction qualified by the existing model.

• Recommendation: first evaluate OEP 6’s perturbative pair-spectral yield and energy loss on matched solprop fields with pump ionisation disabled and enabled. Use local VUV fields, density and spatial overlap along propagation; an input pump duration does not specify them. Retain the model’s masks and uncertainty types. The quasi-monochromatic beta I squared law is a scale check only where its spectral assumptions hold. If feedback can matter, compare neither/pump-only/VUV-only/both channels with explicit field-energy and electron accounting and no double counting.

• Doubt: the continuum’s integrated yield does not determine an ionisation-time history or spectral loss current (OEP 6; OEP 8 Q6). A phenomenological solprop closure is an exploratory assumption and needs sensitivity tests. A small direct loss does not by itself exclude an effect on phase matching from added electrons. No propagation or new atomic calculation was run, and no mechanism is selected.

• Status: open; the experimental mechanism, near-threshold response and continuum timing remain to be tested. The diagnostic is a recommendation, not a new approved fit, response model or extension of OEP 8’s first dynamical scope.

TC-1057 OEP 8: material-data boundary and the continuum follow-up (2026-10-12)

• Where: OEP 8, sections 1–2, 4, 7, 9 and 12–13; docs/roadmap.md. Clarifies the follow-up to TC-1055 and TC-1056 without changing their material choices.

• Decision: John Travers specified that optmat supplies material properties and basic data. The resulting polarisation, electron accounting, plasma coupling and propagation energy balance belong in solprop. Ionisation rates without a plasma polarisation, and Raman responses without the resulting field polarisation, are the existing pattern. OEP 8’s internal single-atom derivations and fixtures check material coefficients and conventions; they do not define an optmat propagator.

• Consequence: the broadband continuum response belongs in a solprop SEP. A coupled optmat OEP is needed only for additional material quantities, models or interfaces that the SEP identifies. OEP 8’s phases and its Q8–Q10 material choices remain unchanged. No new OEP or SEP is created by this clarification.

• Recommendation: an effective continuum driven by the squared positive-frequency VUV field, with coupling strengths matched to OEP 6’s cross sections, is a candidate for the SEP to derive and validate. Missing published nondegenerate amplitudes do not forbid an explicit approximation. Cross sections and agreement with integrated yields do not uniquely determine or validate the transient polarisation, electron production or plasma response. No such model is approved or qualified here.

• Doubt: evidence for pump-driven departure from a phase-matching curve does not by itself establish what sets the shortest observable RDW. Frequency-selective loss can also shift a spectral centroid. Comparisons must distinguish the centroid, blue edge and detection limit, and use the actual input duration of the selected dataset; the maintainer’s initial 6 fs context is not a universal simulation specification.

• Checked: the clarified division of responsibility against OEP 8’s coefficient interface and internal validation plan. No new primary-source values were extracted, and no propagation or atomic calculation was performed for this clarification.

• Status: decided (2026-10-12) for package ownership; the experimental mechanism and continuum-response qualification remain open as in TC-1056. OEP 8 remains Draft, with review status Reviewed.

TC-1058 Vocabulary: ground-state survival (2026-10-12)

• Where: src/optmat/vocabulary.py, docs/data.md.

• Added (the maintainer’s approval, 2026-10-12): ground_state_survival (ionisation). The probability that a pulse leaves the atom in its initial (ground) state, against the peak intensity, read at a stated time.

  • Unit: 1. Abscissa: intensity.

  • Requires wavelength_nm, pulse_fs, polarization and read_at (when the population is read); pulse_envelope and cep where stated.

  • Its complement counts excitation as well as ionisation, so it is not an ionization_yield. A one-electron calculation can be read the same way, which makes a many-electron calculation’s survival a test of the effective number of electrons.

• Why: hartmann_2022’s RMT xenon (TC-1059) gives only this. Ground-state probabilities had been left out for want of a quantity (bauer_2018, TC-834).

• Status: decided and implemented (2026-10-12).

TC-1059 hartmann_2022 (Hartmann et al., J. Phys. B 55, 245601 (2022)): RMT xenon ground-state survival at 759 nm; hutcheson_2025 recorded without values; seven R-matrix harmonic papers read (2026-10-12)

• Where: src/optmat/data/sources/hartmann_2022.toml, hutcheson_2025.toml; tools/extract/hartmann_2022.py, hutcheson_2025.py; data file values/ionisation/Xe/hartmann_2022__rmt_ground_survival_Xe.csv; docs/ionisation_rates.md (the krypton and xenon bullet); the counts.

• Found by the literature search for R-matrix ionisation data (12 October 2026), for an all-electron route beside haCC’s Ar_qz. No R-matrix argon yield at 800 nm is published in absolute terms (Pauly et al. 2020 normalise theirs; not in the library).

• Transcribed: hartmann_2022’s RMT population of xenon’s ground state at the end of the run (t = 2999.81 au), 1.1 to 2.5e14 W/cm², 0.812 to 0.208, from the authors’ Zenodo archive attached in the library (ATAS_xenon-v1.1.zip, sha256 checked by the script). Theory, use = check, no stated uncertainty.

• Checked (the script fails otherwise):

  • The pulse, from the fields RMT wrote (every delay, every intensity): E0 exp(-((t - t0)/w)²) cos(omega (t - t0)), omega = 0.06 au (759.4 nm), w = 186 au, CEP 0, E0 = 0.05336 sqrt(I/1e14), all to 1e-6; at most 2e-10 au left away from the XUV.

    • The paper’s “FWHM 4.5 fs” is w, the field’s 1/e half-width (4.499 fs). The intensity FWHM is 5.297 fs.

    • The archived gaussian.f90 is a stale example (0.06798 au, w = 155 au), not the generator.

    • The archive’s field convention puts the intensities 0.076 % above E0 = sqrt(I / 3.50945e16).

  • The input: the ground state’s energy set to -0.444 au below the ion (Adjust_GS_Energy), the field from a file, Final_T 3000 au, ml_max 0.

  • The populations: they fall monotonically with intensity, and get_pop_GS.sh reads the last line of the run.

• hutcheson_2025: nothing taken. Its archive’s populations of Fig. 4 (ground, bound, beyond 20 au, eight intensities) were not made with the paper’s 760 nm.

  • The populations oscillate at 2 omega with omega = 0.0675 to 0.0683 au at every intensity (hutcheson_2025.py), and the authors’ own plot_rmt_populations.py draws them with IR_freq=0.06798 (670 nm).

  • At the same label they deplete the ground state less than hartmann_2022’s runs (0.883 against 0.812 at 1.1e14).

  • To be used only once the authors confirm the field.

• Read, not curated (harmonic generation or relative yields only; no absolute single-ionisation probability of a neutral atom):

  • Hassouneh, Brown & van der Hart, PRA 90, 043418 (2014): Kr and Xe at 1300 to 1800 nm.

  • Hassouneh et al., PRA 98, 043419 (2018): Ar and Ar+ at 800 nm, the Cooper minimum.

  • Hamilton, van der Hart & Brown, PRA 95, 013408 (2017): Ne, 800 + 400 nm.

  • Finger et al., PRA 106, 063113 (2022): Ne at 2000 to 3000 nm, conversion efficiencies.

  • Bondy & Bartschat, PRA 113, 063108 (2026): Ar at 850 nm; “about 90 %” ground-state survival in the text only.

  • Brown & van der Hart, PRA 88, 033419 (2013): Ar+, relative yields.

  • Hutcheson, van der Hart & Brown, J. Phys. B 56, 135402 (2023): Ar and Xe, intensity-averaged harmonics.

• Next: part N of the tRecX runs, one electron of xenon in hartmann_2022’s field, read as its ground-state survival, for the all-electron check of xenon’s N_eff (1.5, on Wallace et al. alone).

• Status: verified (2026-10-12).

TC-1060 asghar_2020 (Asghar et al., Appl. Opt. 59, 4240 (2020)): measured Ar I 4p-4s transition probabilities and the lifetimes they are scaled to (2026-10-12)

• Where: src/optmat/data/sources/asghar_2020.toml, tools/extract/asghar_2020.py, data/values/absorption/Ar/asghar_2020__{A_4p_4s,lifetime_chang_1978,lifetime_erman_1978}.csv.

• Transcribed:

  • transition_probability A_4p_4s (1/s, scale 1e6, notation = "racah"; row the printed air wavelength, x upper-lower as printed): Table 1’s 27 lines with a value, with the printed absolute uncertainty (lifetime and 5-7 % intensity added, level not stated); primary. 747.2, 857.8 and 1148.81 nm print no value.

  • radiative_lifetime (ns), reproduced: lifetime_chang_1978, the eight lifetimes of Table 1 footnote b (Chang and Setser, J. Chem. Phys. 69, 3885 (1978)), and lifetime_erman_1978, footnote a (Erman and Huldt, Phys. Scr. 17, 473 (1978)), 2p1 and 2p5.

  • Not taken: Table 2’s S and f (conversions of Table 1’s A), Table 3 (J-file sums), the NIST and Garstang-Van Blerkom comparison columns.

• Checked: by the script, which fails otherwise: each printed wavelength is NIST’s air wavelength of the labelled 4p-4s pair (within 0.006 nm; 747.2 nm is 747.117), the two misprinted lower levels (747.2 nm 4s’[3/2]1, 857.8 nm 4s[1/2]1) are in rows without a value; the Paschen column matches; each lifetime’s printed percentage is its ratio; the “NIST [24]” column is NIST ASD’s A in all 29 rows that print one; Table 2’s S and f follow from Table 1’s A by Eqs. (3), (4) within 3 % but f of 714.71, 751.47 and 747.2 nm, which follow NIST’s A. Table 1’s cells were checked against the image.

• Finding: against wiese_1989 (TC-1012) the 27 A have mean ratio 1.058 (median 1.010, mean |deviation| 12.8 %, 0.817 at 922.45 nm to 1.92 at 714.71 nm); 22 of 27 within twice the paper’s uncertainty; NIST the same (its A are Wiese’s). Eq. (2) (sum A tau = 1) holds within 2 % for 2p5-2p10 but gives 0.870, 1.152, 0.939, 1.077 for 2p1-2p4 with the printed lifetimes; the per-level 1/sum A are 23.00, 23.00, 29.40, 30.82, 21.00, 27.01, 29.31, 32.80, 30.10, 42.18 ns (2p1-2p10) against Wiese’s 22.35-39.22 ns. The branching fractions are independent of Wiese; the scale is Chang and Setser’s (the values wiese_1989’s Table II lists and did not adopt) and Erman and Huldt’s, so the per-level radiative widths carry no new information.

• Status: verified (2026-10-12).

TC-1061 savukov_2018 (Savukov, J. Phys. B 51, 065006 (2018)): CI+MBPT Ar I ground-state oscillator strengths and a 4d lifetime, as checks (2026-10-12)

• Where: src/optmat/data/sources/savukov_2018.toml, tools/extract/savukov_2018.py, data/values/absorption/Ar/savukov_2018__f_ground.csv.

• Transcribed:

  • oscillator_strength f_ground: Table 5’s f_CI-MBPT from 3p6 1S0 to the 12 J = 1 odd levels (row the printed NIST energy, x the NIST level’s Racah label); rows 119847.77 and 119760.1725 cm-1 excluded (their configurations, 6s and 4d, are swapped against NIST, Table 1 and chan_1992, so the level of each CI f is ambiguous); check.

  • radiative_lifetime lifetime_4d12_1: 80.9 ns, calculated (text p. 6), inline; check.

  • Not taken: the line strengths S of Tables 6-8 (no quantity: S is not transition_dipole_moment); g factors (no quantity); the CI-MBPT energies of Tables 1-4, aligned to an experimental level (Table 2 puts the ground state at 3109 cm-1), so not level_energy.

• Checked: by the script, which fails otherwise: Table 5’s NIST energies are NIST’s J = 1 odd levels and its configurations theirs but rows 9-10; its f_expt column is chan_1992’s “present” Ar values row by row; Tables 2-4’s experimental 4p/5p energies and Tables 6-8’s energies identify NIST levels. Table 5’s cells were checked against the image.

• Finding: the 4p-4s S converted to A (derived, record notes only) agree with wiese_1989 within 4 % for the strong lines but 4p[3/2]2-4s[3/2]1 (0.74), and to 35 % for weak ones; only transitions to the J = 1 4s levels are given, so no 4p width follows. Table 5’s f_Th column (“Lee and Lu [31]”) matches neither chan_1992’s Lee and Lu column nor the values the text quotes from [31].

• Status: verified (2026-10-12).

TC-1062 aymar_1978 (Aymar and Coulombe, At. Data Nucl. Data Tables 21, 537 (1978)): calculated Kr and Xe lifetimes and A values (2026-10-12)

• Where: src/optmat/data/sources/aymar_1978.toml, tools/extract/aymar_1978.py, ten files values/absorption/{Kr,Xe}/aymar_1978__*.csv.

• Transcribed: Table VI (p. 564) tau_r and tau_nabla of Kr 5p, 5p’, 6p, 6p’ (20 levels); Table VIII (p. 566) of Xe 6p, 6p’, 7p, 6d (24); Table III (p. 544) AKI of the 30 Kr 5s - 5p, 5p’ transitions; Table IV AKI of the 30 Xe 6s - 6p, 6p’ transitions (p. 556) and of the 19 decays of 6p’ and 6p[1/2]0 to 5d (p. 558). Length and velocity forms as separate datasets; radiative_lifetime and transition_probability (TC-1011), all use = "check" (calculated, no stated uncertainty). Rows in the paper’s Jl notation, mapped to NIST configuration/term/J in the notes.

• Checked: every taken cell against the rendered scanned pages; seven OCR misreads of the library’s cells corrected in the script (none a misprint); per row 1e8/LAMBDA = EK - EI within 1 cm^-1, g = 2J + 1, A and f from the printed S through Eqs. (1), (2) within 1 %; each level’s NIST energy within 1 cm^-1; 1 / sum A of the library’s rows reproduces tau_r and tau_nabla within 1 % for Kr 5p, 5p’ and Xe 6p, 6p’.

• Finding: (1) Xe 6p’ lifetimes (TC-1042): Aymar’s tau_nabla 36.0-48.5 ns agrees with bruce_1990 and inoue_1984 (32-50 ns) within 1-4 ns; NIST’s 22.8-27.6 ns come from its 6s’ - 6p’ A values (accuracy C, C+), 1.25-2.1 times Aymar’s length and 1.7-3.5 times its velocity A, which alone exceed the measured total decay rates of 2p3 and 2p1. Aymar’s 6p’ decays include 5d (15-25 %) and 7s branches NIST lacks; adding them makes NIST shorter still. NIST’s 6s’ - 6p’ A values are the outliers. (2) Xe 6p: the velocity form lies within the measurements’ spread (bruce_1990, ku_1986, inoue_1984, bowering_1986b); the length form is 3-10 ns short except 2p6. (3) Kr 5s - 5p strong lines: A_nabla / NIST 0.78-1.20 (median 0.98), A_r / NIST median 1.24. (4) Quoting records: bruce_1990 (18 values), bowering_1986b (6) and gornik_1980 (f = 0.232) agree with the original; inoue_1984 47 of 48, its 6d[1/2]0 tau_v 63.7 against 63.8; ku_1986’s ‘86-218 ns’ for 5d[1/2]1 against the printed 88.9 and 218; bowering_1986 does not cite the paper.

• Doubt: the library lost the last 20 rows of PDF p. 21 (Xe 6p[5/2]2 - 5d[7/2]3 to 6p[3/2]1 - 5d[3/2]1, 5d upper) and truncated others; those arrays and the lifetime sums of Kr 6p, 6p’ and Xe 7p, 6d are not taken or not checked until re-extraction.

• Status: verified (2026-10-12).

TC-1063 windholz_1980 (Windholz, Phys. Scr. 21, 67 (1980)): dc Stark coefficients of 49 upper Ar I levels (5p to 9s), none for 4s or 4p; notes only (2026-10-12)

• Where: src/optmat/data/sources/windholz_1980.toml (no datasets).

• Transcribed (notes): what Tables I-VI print: 91 lines (4100-6800 A) to fields of about 700 kV/cm; per upper level and Stark component the fit coefficients a1, a2 of Delta nu = a1 F^2/(a2 - Delta nu) and the Lindholm constant C4 = c e^2 Delta nu/F^2 (CGS) at F = 0 and F_max (Table III); polynomial coefficients for three levels whose shifts turn over (Table IV); single-field shifts (Table V); Minnhagen’s 1950 line shifts, reproduced (Table VI).

• Not taken: everything. The levels are the upper levels of 4s-5p and 4p-nd/ns lines (5p, 5p’, 4d to 8d, 6s to 9s); the 4s and 4p lower levels are assumed unshifted, so nothing is given for them. level_polarizability (TC-1011) does not fit: the printed constants are C4 in Hz cm^4 and non-quadratic fit coefficients, not a polarisability in any of its units; the components are not assigned to m (not scalar or tensor, except the four J = 0 levels); each is a line shift attributed to the upper level. Line and level shifts at a field: declined (TC-1011).

• Checked: all 65 C4(F = 0) equal c e^2 (a1/a2) with 1 kV/cm = 3.33564 statV/cm and all 65 C4(F_max) follow from Eq. 4, within the last digit (so C4 is in cm^4 s^-1, ordinary frequency; a1 is in cm^-2 (kV/cm)^-2, printed ‘kV^-2’); all 49 level energies are NIST’s within 0.1 cm^-1, and each label nl (K) J maps to NIST’s (2P*<3/2> or <1/2>).nl 2[K] J. Misprints outside any value: Table II’s 6212.93 for 6215.93 (Table I, Fig. 2); ‘2.10e–01’ on the text layer is 2.10e-01 on the image.

• Finding: derived (not printed) scalar alpha_0/h of the J = 0 levels: 5p[1/2]0 3590, 5p’[1/2]0 2768, 5d[1/2]0 6719 kHz/(kV/cm)^2. Against werbowy_2026 (TC-1007, TC-1018): no common level; Werbowy’s 4s alpha_0 (56-96) and 4p alpha_0 (95-327) give lower-level shifts of 0.46-0.78 and 0.78-2.7 cm^-1 at 700 kV/cm, against the paper’s +-1 cm^-1 fit accuracy: the unshifted-lower-level assumption holds for 4s-5p lines and is marginal for 4p-nd lines at the highest fields.

• Status: verified (2026-10-12).

TC-1064 schinkoth_2000 (Schinköth, Kock & Schulz-Gulde, J. Quant. Spectrosc. Radiat. Transfer 64, 635 (2000)): plasma Stark constants and widths of 15 Ar I 4s-4p and 12 Kr I 5s-5p lines; notes only (2026-10-12)

• Where: src/optmat/data/sources/schinkoth_2000.toml (no datasets).

• Transcribed (notes): Tables 1 (Ar) and 2 (Kr): C4 (10^-22 m^4 s^-1; Ar 1.03-1.63, 10 % or 15 %; Kr 1.18-2.04, 12 % or 19 %), HWHM (Ar 3.30-5.08 pm, Kr 3.99-5.66 pm) and A (0.042-0.049) at n_e = 10^22 m^-3, T = 10^4 K; other authors’ C4 and Griem’s widths, reproduced.

• Not taken: all. pressure_line_coefficient (TC-1040) is broadening by a perturber gas per unit pressure or density in the impact regime; these are plasma widths by electrons and quasistatic ions, quoted in pm at a reference electron density. C4 is a line’s Stark constant (a polarisability difference; declined, TC-1011). No new quantity proposed: OEP 8’s argon broadening is by neutral argon.

• Checked: both tables against the page images; every argon and krypton label against NIST’s near-infrared lines (TC-983).

• Finding: the 738.4 nm row’s label ‘4s[3/2]1-4p’[3/2]1’ has the wrong upper J: NIST’s 738.6014 nm (vac) line ends on 4p’[3/2] J = 2 (107 289.700 cm^-1); J = 1 would be near 747.1 nm. milosavljevic_2006 (its ref. 9) quotes these widths doubled (FWHM) and these A exactly. werbowy_2026’s ‘Ref. [2]’ column (TC-1007) is this paper’s C4 range (‘This work’ and Refs. 2-5) times about 127 (125-130 reproduces 14 of 15; 772.376 nm does not); 2 C4 would give 154 (angular) or 965 (ordinary) per 10^-22 m^4 s^-1, so Werbowy’s conversion is not reproduced.

• Status: verified (2026-10-12).

TC-1065 milosavljevic_2006 (Milosavljević, Ellingboe & Djeniže, Spectrochim. Acta B 61, 81 (2006)): electron and ion Stark widths and shifts of seven Ar I 4s-4p lines at 16 000 K; notes only (2026-10-12)

• Where: src/optmat/data/sources/milosavljevic_2006.toml (no datasets).

• Transcribed (notes): Tables 1-3: three pulsed-arc discharges (N 6.7-7.1 x 10^22 m^-3, T 15.6-16.2 x 10^3 K); per line the total, electron and ion FWHM and shifts (W_e 41.0-70.6 pm, d_e 6.4-34.4 pm, 12 %), A 0.057-0.084, D, E; other authors’ values, reproduced. Labels mapped to NIST’s lines (all seven).

• Not taken: all; plasma Stark widths and shifts at stated N and T are not pressure_line_coefficient (TC-1040; neutral perturber gas, per unit density, impact). No new quantity proposed.

• Checked: Tables 2 and 3 against the images; W_t,st = W_e + W_i,st and d_t,st = d_e + d_i,st within 0.1 pm on all 21 rows but two (0.2 pm). The printed Table 3 shifts the second 696.543 nm row one column right; read in order it satisfies the sums. Its ref. 9 rows are schinkoth_2000’s HWHM doubled and A, exactly.

• Finding: W_e/N per 10^22 m^-3 at 16 000 K is 0.96-1.45 times schinkoth_2000’s FWHM at 10 000 K (no temperature scaling). werbowy_2026 (TC-1007) quotes Delta alpha_0 from this paper’s A for five of the seven lines (160, 160, 160, 160, 130 kHz/(kV/cm)^2), not 696.543 or 727.294 nm.

• Status: verified (2026-10-12).

TC-1066 sadeghi_2001 (Sadeghi et al., J. Chem. Phys. 115, 3144 (2001)): quenching and lifetimes of two-photon excited Ar 4p J = 0, 2 (2026-10-12)

• Where: src/optmat/data/sources/sadeghi_2001.toml, tools/extract/sadeghi_2001.py, 23 files values/absorption/Ar/sadeghi_2001__kq_*.csv.

• Transcribed: Tables II (p. 3148) and III (p. 3150), the k_Q columns (10^-10 cm3/s): total quenching of Ar 2p1, 2p5, 2p6, 2p8 (4p’[1/2]0, 4p[1/2]0, 4p[3/2]2, 4p[5/2]2) by 22 gases, one collisional_quenching_rate_coefficient dataset per gas (TC-1011; perturber as printed, argon as self; order 2, channel total), primary; Kr’s two 2p6 values split (0.75, the low-pressure fit, in kq_Kr; 0.47, a lower limit, kq_Kr_full, check). Uncertainties from the footnotes (10 %, d 30 %, Table III f 20 %). Text p. 3147: radiative lifetimes 24 +- 2, 24 +- 2, 28 +- 3, 29 +- 3 ns (radiative_lifetime, inline). Excitation one-colour two-photon at 184.0-189.4 nm (vacuum), 1e7-1e8 W/cm2.

• Checked: every taken cell against the table images; Table I’s energies against 2 / lambda_VUV (within the 0.1 nm rounding) and NIST’s levels (within 1 cm^-1); the lifetimes against the printed decay rates 4.2, 4.2, 3.6, 3.4 x 10^7 s^-1; the text’s k_Ar values and k_Kr(2p8) against the tables.

• Finding: lifetimes agree with NIST’s 1/sum A (22.1, 25.0, 29.07, 30.99 ns, TC-985) and wiese_1989’s (22.35, 24.88, 29.04, 31.01 ns, TC-1012) within the stated errors; the measurement is independent of both (NIST’s A for these lines are wiese_1989’s). Self-quenching 0.12-0.24 x 10^-10 cm3/s: at 1 bar 2.9-5.9 x 10^8 s^-1, 7-17 times the radiative rate (46-94 MHz FWHM per bar), a population loss, not the pure dephasing.

• Doubt: printed inconsistencies, no value changed: Table I labels 2p6 and 2p8 ‘4p[1/2]0’; Table II’s footnote b prints ‘cm^-3 s^-1’ and ‘+10%’; its footnote f calls 0.75 the full-data fit, the text and footnote c make 0.47 that fit; ‘below 25 mbar’ (text) against ‘below 15 mbar’ (Fig. 5); Cl2 +-30 % (text) against 20 %/10 % (Table III).

• Status: verified (2026-10-12).

TC-1067 petrov_2011 (Petrov et al., Eur. Phys. J. D 62, 347 (2011)): photoionisation of the excited np levels of Ar, Kr, Xe near threshold (2026-10-12)

• Where: src/optmat/data/sources/petrov_2011.toml, tools/extract/petrov_2011.py, 120 files values/absorption/{Ar,Kr,Xe}/petrov_2011__{tot,s32,s12,fig}_*.csv.

• Transcribed: excited_state_photoionization_cross_section (TC-872, TC-1040), Mb, for the 30 levels mp5 (m+1)p J = 0-3 (CIPFCP, length gauge; initial_level gives the jK label, NIST’s configuration/term/J and each gas’s Paschen label). Table 2 (p. 352): sigma_tot^0, sigma_3/2^0 (at the 2P1/2 threshold) and sigma_1/2 at omega_1/2 = Delta_FS, one point each, primary. Figs. 3-5 (p. 351): the total against the photon energy, 0-6 eV above the 2P1/2 threshold, every vertex of the vector drawing (42-61 per level), check, 0.1 Mb. The printed axis omega_1/2 is converted to photon energy by adding the level’s 2P1/2 threshold from NIST’s levels (a decision recorded in the notes).

• Checked: Table 2 cell by cell against its image; the ratio column r against sigma_1/2 / sigma_3/2 for all 30 rows; the paper’s Delta_FS (0.178, 0.666, 1.306 eV) against NIST’s; every axis’s ticks (within 0.05 pt) and every panel’s labels; each curve at threshold against Table 2’s sigma_tot^0 by jK label (worst 0.057 Mb), which also settles footnote e (Kr 2p2/2p3, Xe 2p8/2p9 Paschen labels reversed with respect to Ar: Table 2’s rows follow the jK label); overlays inspected.

• Finding: the range covers OEP 8’s drives: Ar 2p1/2p5/2p6/2p8 at their own 184.0/186.8/188.3/189.4 nm, 2.39/2.03/2.31/2.55 Mb (omega_1/2 3.7-4.3 eV); Xe 6p[1/2]0 at 248 nm 3.35 Mb; Kr 5p[1/2]0 at 212.6 nm 3.03 Mb. Against held values: Ar 4p at 248 nm level mean 4.72 Mb against duzy_1980 5.4, chang_1982 4.8, hyman_1977 4.3; Xe 6p[1/2]0 3.35/1.47 Mb at 248/193 nm against kroll_1990’s measured 4.3 +- 0.7/1.9 +- 0.7 and pindzola_1981 DFL 3.05 (4.97 eV); Xe 6p[3/2]2 2.70/1.21 against kroll_1990 3.7 +- 0.7/1.8 +- 0.5; payne_1981’s Kr 5p[1/2]0 ‘10^-18 cm2’ at 326.2 nm is 7 times below Petrov’s 7.0 Mb.

• Status: verified (2026-10-12).

TC-1068 Argon’s literature (TC-1060 to TC-1067): what it settles for OEP 8’s argon, and what remains (2026-10-12)

• Where: the records of TC-1060 to TC-1067; OEP 8’s Draft (sections 1 and 5), revised.

• Settled for argon (OEP 8, Q7; TC-1053):

  • Radiative widths of the two-photon 4p levels.

    • sadeghi_2001 two-photon-excites 4p’[1/2]0, 4p[1/2]0, 4p[3/2]2 and 4p[5/2]2 at 184.0-189.4 nm and measures their lifetimes, 24, 24, 28 and 29 ns (±2-3).

    • That is independent of wiese_1989 and NIST (22.4, 24.9, 29.0 and 31.0 ns), and agrees within its errors (TC-1066).

    • asghar_2020’s branching fractions are independent too: median ratio 1.01 to Wiese’s A, 22 of 27 lines within twice the error. Its absolute scale is Chang and Setser’s quoted lifetimes (TC-1060).

    • savukov_2018’s ab initio strong lines agree with Wiese’s to 4 %, except 4p[3/2]2-4s[3/2]1 at 0.74 (TC-1061).

  • Quenching of the 4p levels by argon and 21 other gases (sadeghi_2001). Self quenching is 0.12-0.24e-10 cm3/s: 7-17 times the radiative rate at 1 bar. It is population loss, not pure dephasing.

  • Photoionisation of each 4p level at the drive (petrov_2011, calculated, length gauge): 2.0-2.6 Mb at 184-189 nm (TC-1067).

    • At 248 nm its level mean, 4.7 Mb, lies between the J-averaged duzy_1980 (5.4), chang_1982 (4.8) and hyman_1977 (4.3).

    • For Xe 6p, Petrov is 0.75-0.78 of kroll_1990’s measurements at 248 and 193 nm (1.2-1.4 sigma).

    • The same calculation gives Kr 5p[1/2]0 at 326 nm seven times payne_1981’s “about 1 Mb”.

• Not settled for argon:

  • The light shifts of the 4p levels: windholz_1980 assumes the 4s and 4p levels unshifted and fits only upper levels (TC-1063).

  • Pressure broadening (pure dephasing) by neutral argon: schinkoth_2000 and milosavljevic_2006 are plasma Stark widths, not taken (TC-1064, TC-1065).

  • A measured two-photon strength of the 4p levels: none in these records.

• Xenon, for the record (deferred): aymar_1978 shows that NIST’s 6p’ lifetimes are short because of its own 6s’-6p’ A values (1.25-2.1 times Aymar’s length form). Aymar’s velocity-form lifetimes agree with bruce_1990 and inoue_1984 within 1-4 ns (TC-1062). Quotations checked:

  • bruce_1990, bowering_1986b and gornik_1980 agree with the original;

  • inoue_1984 prints 63.7 for 63.8;

  • ku_1986 prints ‘86-218 ns’ for 88.9-218.

• A doubt about werbowy_2026 (TC-1007, TC-1018): its “Ref. [2]” column is schinkoth_2000’s C4 range times about 127 kHz/(kV/cm)^2 per 1e-22 m4/s. That conversion could not be reproduced from its stated Delta alpha0 = 2 C4 (TC-1064). No value is changed.

• Papers to request:

  • R. S. F. Chang and D. W. Setser, J. Chem. Phys. 69, 3885 (1978) (the Ar 4p lifetimes asghar_2020 scales to, and quenching);

  • Francis et al., Eur. Phys. J. Appl. Phys. 4, 239 (1998) and their earlier Letter (sadeghi_2001’s two-photon Ar 4p lifetimes and quenching);

  • Stellpflug et al., Eur. Phys. J. D 23, 35 (2003) (two-photon excited Xe);

  • P. Erman and S. Huldt, Phys. Scr. 17, 473 (1978).

• Status: verified (2026-10-12).

TC-1069 chang_1978 (Chang and Setser, J. Chem. Phys. 69, 3885 (1978)): lifetimes, argon quenching and A values of Ar 4p, 4p’ (2026-10-12)

• Where: src/optmat/data/sources/chang_1978.toml, tools/extract/chang_1978.py, 12 files values/absorption/Ar/chang_1978__*.csv.

• Transcribed: Table II (p. 3889), ‘Present work’: radiative lifetimes of 2p2, 2p3, 2p4, 2p6-2p10 (26.5-42.2 ns, printed +-), radiative_lifetime, primary (2p1 and 2p5 not measured). Table III (p. 3889), deactivation by ground-state argon (10^-11 cm3/s, TC-1011, perturber self, order 2): total k_Q of seven levels with +- (primary); 2p6 ‘<=1.8’ as the interval 0-1.8 (check); the state-to-state k34, k36, k67, k68, k69, k78, k89 one dataset per product (primary); k43 and k98 by detailed balance (check); the intermultiplet sums to 4s, 4s’ that are numbers (difference, check). Table IV (p. 3892), CS column: A of the 26 4p-4s lines of the eight levels (transition_probability, Paschen labels, 10 %, primary).

• Checked: every taken cell against the table images and the rendered pages; each Paschen label against its Racah label and NIST’s levels; Table IV’s 30 wavelengths against NIST’s levels in standard air (within 1 Angstrom) and g_k, g_i against J; sum A x tau = 1 per level (within 0.4 %); k_Q = sum k_nn’ + sum k_nm’ for every row; sigma = k_Q / with the Ar-Ar mean relative speed at 300 K; k43 and k98 by detailed balance from NIST’s energies (1.72, 0.58).

• Finding: asghar_2020’s lifetime_chang_1978 (TC-1060) and wiese_1989’s Table II column (TC-1012) equal Table II, values and +-. Against wiese_1989’s 1/sum A (28.39, 28.93, 30.17, 29.04, 29.70, 31.01, 30.21, 39.22 ns) the ratios are 0.93, 0.95, 1.10, 0.93, 1.00, 1.06, 1.00, 1.08: 5-10 % differences in both directions except 2p7 and 2p9, not a common scale. sadeghi_2001 (TC-1066) overlaps only at 2p6 (28 +- 3 against 27.0 +- 1.0) and 2p8 (29 +- 3 against 32.8 +- 0.7). CS / NIST A (TC-985): 0.89-1.14 for the 13 lines with A >= 7e6 s^-1; wiese_1989 used this paper’s branching ratios for 2p8 and 2p10. State-to-state against nguyen_1978: within 26 % for k34, k36, k43, k78, k89, k98; a factor 1.3-2 for the small k67, k68, k69 (0.1-0.8 x 10^-11, near this paper’s ~1e-11 limit); k_{9,10} ‘> 1.8’ against 0.51; the note added in proof quotes Nguyen and Sadeghi’s k58 as 0.9 where their Table II gives 9.5 x 10^-12.

• Doubt: printed inconsistencies in columns not taken: Table IV’s f of 2p10-1s2 is 0.028 for the formula’s 0.0028, 2p10-1s5’s 0.134 for 0.1318; Lilly’s lifetimes of 2p2 and 2p9 differ by 0.1 ns from wiese_1989’s copy.

• Status: verified (2026-10-12).

TC-1070 nguyen_1978 (Nguyen and Sadeghi, Phys. Rev. A 18, 1388 (1978)): state-to-state transfer between Ar 4p levels by argon at 300 K (2026-10-12)

• Where: src/optmat/data/sources/nguyen_1978.toml, tools/extract/nguyen_1978.py, 8 files values/absorption/Ar/nguyen_1978__k_to_2p*.csv.

• Transcribed: Table II (p. 1392), the 28 k_ij (10^-12 cm3/s) of collisional transfer from 2p_i to 2p_j in ground-state argon at 300 K, collisional_quenching_rate_coefficient (TC-1011), perturber self, order 2, temperature_k 300, channel = the product level, one dataset per product (2p3-2p10), rows the initial levels 2p2-2p9; 20 % (‘better than 20%’), primary. No 2p1 or 2p10 initial level, no totals (the intercepts were not determinable).

• Checked: every cell against the table image and the rendered page; Table III’s experimental ratios against Table II within its rounding; its theoretical ratios against detailed balance (Eq. 6) with NIST’s energies at 300 K (within 3 %); the text’s k3 = 0.76 x 10^-10 as the sum of Table II’s 2p3 row; the 2p10 gap ‘>= 1361 cm-1’ (NIST 1360.7).

• Finding: on sadeghi_2001’s caveats (TC-1066): 2p1 is not resolved (no 2p1 data here or in chang_1978). 2p5: the transfers out of 2p5 sum to 0.225 x 10^-10 cm3/s, 1.9 times sadeghi_2001’s total 0.12, so that value is a lower limit by about two; the missing part matches the 2p5 -> 2p6 transfer (0.113), whose emission the filter may pass. 2p8: k89 = 0.182; sadeghi_2001’s 0.24 (the 2p8 + 2p9 pair to other states) + 0.182 = 0.42, inside chang_1978’s total 0.47 +- 0.07. 2p6: transfers sum to 0.111 against sadeghi_2001’s 0.13 and chang_1978’s <= 0.18, consistent. sadeghi_2001’s quotations of this paper (0.22, 0.11, 0.18) are right. Against chang_1978: within 26 % for k34, k36, k43, k78, k89, k98, a factor 1.3-2 for k67, k68, k69, and k_{9,10} 0.51 against ‘> 1.8’.

• Doubt: Table I (not taken) labels the 2p9 row’s sensitized line 8424.65 Angstrom ‘3P1-2p9’ (it is 3P1-2p8) and prints 2p5’s fluorescence line 7514.18 against the laser’s 7514.65.

• Status: verified (2026-10-12).

TC-1071 baig_2008 (Baig et al., Phys. Rev. A 78, 032524 (2008)): measured photoionisation of Ar 4p’[3/2]1, [3/2]2, [1/2]1 at the 2P1/2 threshold (2026-10-12)

• Where: src/optmat/data/sources/baig_2008.toml (inline datasets, no script).

• Transcribed: excited_state_photoionization_cross_section (TC-872, TC-1040), Mb, one point per level, primary: 4p’[3/2]1 34 +- 5 at 467.1 nm, 4p’[3/2]2 31 +- 5 at 470.5 nm, 4p’[1/2]1 28 +- 4 at 475.17 nm (p. 5 and the abstract; saturation of the two-step ion signal in a dc discharge; +- level not stated, budget “about +-18%”). The wavelengths are the vacuum wavelengths of the 3p5 2P1/2 threshold (wavelength_medium = vacuum). The Table II oscillator strengths of the autoionising 4p’ -> nd’ transitions are not taken: oscillator_strength has no lower-level parameter and holds ground-state f values only.

• Checked: the identity on p. 1; the three values on pp. 1, 5 and 8; the threshold wavelengths against the paper’s limit and NIST’s levels (467.079, 470.551 and 475.173 nm vacuum).

• Finding: compared with petrov_2011’s calculated sigma_tot^0 at the same thresholds (TC-1067; 10.82, 10.71 and 9.95 Mb), Baig / Petrov is 3.14 +- 0.46, 2.89 +- 0.47 and 2.81 +- 0.40. That is 4.1-4.6 times Baig’s +-. The two agree on the order of the levels. This is the only measured absolute photoionisation of Ar 4p levels in the library. It applies at the threshold and to J = 1, 2 primed levels, none of them OEP 8’s levels, so nothing is derived for the 184-190 nm drive.

• Doubt:

  • The conclusion (p. 8) assigns 34/31/28 Mb to [1/2]1/[3/2]1/[3/2]2. Sec. III B and the abstract assign them differently; those two agree and are followed.

  • The beam area is printed as 0.002(1) cm2, a 50 % uncertainty, against the 10 % beam-diameter term in the error budget.

  • Discharge ionisation of the unresolved nd’ Rydberg members near the threshold is not discussed.

  • Table II’s first two wavelength columns are swapped with respect to their headings (shown by Table I and NIST energies).

  • p. 4 calls the 4s[3/2]2 metastable “4p’[3/2]2” and prints 715.01 nm for a line that NIST gives as 714.704 nm in air.

• Status: verified (2026-10-12).

TC-1072 sadeghi_2022 (Sadeghi, Magnan and Massines, JQSRT 288, 108264 (2022)): self broadening and shift of the Ar 772.376 and 772.4207 nm lines (2026-10-12)

• Where: src/optmat/data/sources/sadeghi_2022.toml (inline datasets, no script).

• Transcribed: pressure_line_coefficient (TC-1040), MHz/mbar, photons 1, frequency_scale transition, ordinary frequency, perturber self (Ar + 200 ppm NH3), 300 K, 312-1000 mbar. Two rows per dataset, 772.376 nm (1s5-2p7, 4s[3/2]2 - 4p[3/2]1) and 772.4207 nm (1s3-2p2, 4s’[1/2]0 - 4p’[1/2]1), air wavelengths:

  • broadening_self (FWHM): 14.2 +- 1.0 and 18.2 +- 0.3;

  • shift_self (negative = red): -5.8 +- 0.4 and -6.4 +- 0.4.

  • Source: the abstract’s GHz at 1 bar (equal to MHz/mbar). The +- is 2 sigma plus 1.3 %.

  • The values are the authors’ T^-0.7 scaling of slopes measured at about 310 K (27.7, 11.3, 35.5 and 12.5 pm/bar, not taken: no unit).

• Checked: the identity on the HAL cover and manuscript p. 1. The library copy is the HAL manuscript (hal-03782652v1), not the typeset version. The pm-to-GHz conversions reproduce the printed values within rounding. Table 1 prints the same pm values. The 310 K to 300 K scaling reproduces three values; s1 would round to 11.6, not the printed 11.5 (0.06 pm, inside +-0.8).

• Finding:

  • These are one-photon 4s-4p lines broadened by ground-state argon. They are not the ground-to-4p two-photon coherence that OEP 8 needs, and nothing is derived for it.

  • Neither upper level is one of OEP 8’s two-photon levels.

  • The A values used (5.18e6 and 1.17e7 s-1) are NIST’s.

• Status: verified (2026-10-12).

TC-1073 eshel_2016 (Eshel, Rice and Perram, JQSRT 179, 40 (2016)): broadening and shift of Ar 801.7, 800.8 and 795.0 nm lines in Ar-He (2026-10-12)

• Where: src/optmat/data/sources/eshel_2016.toml, tools/extract/eshel_2016.py, 8 files values/absorption/Ar/eshel_2016__{broadening,shift}_mix{2p5,5,10,25}.csv.

• Transcribed: pressure_line_coefficient (TC-1040), MHz/torr, photons 1, frequency_scale transition, ordinary frequency, 440 K, 10-160 Torr total pressure, vacuum wavelengths.

  • Tables 1 and 2: this work’s rows for the 2.5, 5, 10 and 25 % Ar in He mixtures (perturber “Ar-He mixture”; rates per Torr of total pressure). The rows are 801.699 nm (s5 -> p8, 4s[3/2]2 - 4p[5/2]2), 800.836 nm (s4 -> p6, 4s[3/2]1 - 4p[3/2]2) and 795.036 nm (s3 -> p4, 4s’[1/2]0 - 4p’[3/2]1); the 800.836 nm line has no value at 25 %.

  • The broadening rates are the Lorentzian FWHM (Eq. 2 and Eq. 9; the table calls it “2 gamma”); shifts are positive to the blue. 22 values, primary, 95 % confidence.

  • Inline, use check: the authors’ Ar-Ar and Ar-He separation, “8, 38 and 12” and “16, 16 and 19” MHz/Torr (perturber self and He). It is a fit extrapolated in the Ar fraction, without uncertainty.

• Checked: the identity on p. 1. Both tables were checked cell by cell against their images. The 10 % rows match the abstract and the Figs. 6-7 captions (script check), and the line wavelengths match NIST’s vacuum wavelengths.

• Finding:

  • These are one-photon 4s-4p lines in an Ar-He mixture. They are not the ground-to-4p two-photon coherence that OEP 8 needs, and nothing is derived for it. The upper levels of the 801.7 and 800.8 nm lines (4p[5/2]2 and 4p[3/2]2) are OEP 8 levels.

  • The Ar-Ar fit (8 and 12 MHz/Torr for 801.7 and 795.0 nm) is below the paper’s literature rows scaled to 440 K (9.6-14.9).

  • The text gives 10-200 Torr; the tables give 10-160.

  • The paper also misprints the line labels “794.036”, “800.036” and “801.669”.

• Status: verified (2026-10-12).

TC-1074 Argon’s literature, continued (TC-1069 to TC-1073): the 4p quenching reconciled, a photoionisation conflict, one-photon broadening (2026-10-12)

• Where: the records of TC-1069 to TC-1073; sadeghi_2001’s notes (TC-1066) and OEP 8’s Draft (section 5), revised.

• The 4p lifetimes. chang_1978’s measured lifetimes are 0.93-1.10 times wiese_1989’s 1/ΣA, scattering both ways beyond its errors.

  • asghar_2020’s quoted values and wiese_1989’s “Chang and Setser” column equal the original exactly.

  • Wiese’s widths stay the reference. Their spread against the measurements is about 10 %.

• Argon self-quenching of the two-photon levels, sadeghi_2001’s caveats resolved:

  • 2p5 (4p[1/2]0): nguyen_1978’s transfers out of it sum to 0.225e-10 cm3/s, 1.9 times Sadeghi’s 0.12. Sadeghi’s is a lower limit by about 2. The shortfall matches the 2p5->2p6 transfer (0.113), whose 763.5 nm line the filter may pass.

  • 2p8 (4p[5/2]2): k(2p8->2p9) = 0.18 (Nguyen 0.182, Chang 0.17). Sadeghi’s 0.24 plus 0.18 gives 0.42, inside chang_1978’s 0.47 ± 0.07, so the total is about twice Sadeghi’s value.

  • 2p6 (4p[3/2]2): consistent: Nguyen 0.111, Sadeghi 0.13, Chang ≤ 0.18. Sadeghi drops Chang’s “≤”.

  • 2p1 (4p’[1/2]0): unresolved. Neither 1978 paper excites it.

• Chang against Nguyen, state to state:

  • the main transfer rates agree within 26 %;

  • the small k67, k68 and k69 differ by 1.3-2;

  • k(2p9->2p10) conflicts: Chang’s “> 1.8” against Nguyen’s 0.51;

  • Chang’s note added in proof misquotes Nguyen’s k58 (0.9 for 9.5e-12).

• A photoionisation conflict. baig_2008’s measured threshold cross sections of 4p’[3/2]1, 4p’[3/2]2 and 4p’[1/2]1 (34, 31 and 28 ± 4-5 Mb) are 2.8-3.1 times petrov_2011’s calculation for the same levels and photon energies. That is 4-5 times Baig’s stated errors.

  • Doubts about Baig (TC-1071): a saturation measurement in a discharge; the beam area uncertain by 50 % against a 10 % budget; unresolved Rydberg levels below threshold.

  • For xenon, Petrov is 0.75 of kroll_1990’s measurements.

  • So the calculation’s absolute scale for argon’s 4p photoionisation is uncertain by up to a factor of 3. OEP 8 states that.

• Pressure broadening, one-photon only. sadeghi_2022 (Ar self, 300 K) and eshel_2016 (Ar-He, 440 K) give FWHM broadening and shifts of 4s-4p lines:

  • self-broadening 14.2 and 18.2 MHz/mbar at 772 nm;

  • Ar-He mixtures at 795-802 nm.

  These are not the ground-4p two-photon coherence that OEP 8’s dephasing needs, and nothing is derived for it.

• Status: verified (2026-10-12).

TC-1075 franta_2017: the newAD2 UDM of c-Si and the refractiveindex.info tables (2026-10-14)

• Where: franta_2017 (extended). The newAD2 site’s files c-Si.par and c-Si.Enk, attached to the paper in the library (retrieved 2026-09-26 from newad.physics.muni.cz); refractiveindex.info main/Si/nk/Franta-20C.yml, Franta-25C.yml and Franta-300K.yml (commit c5c2f18, in data/external/refractiveindex_info/; SHA-256 2f692bcd…a376a, c3e042b7…cb16a, 45e271e0…5f969).

• Transcribed:

  • Formula udm_c_si (form udm, range 145.9 nm-125 um, the file’s “80 1/cm - 8.5 eV”): the 161 values of c-Si.par as the file prints them, first line he:ex=4:ut:loc=11:ph=36 as attributes, generated from the file and compared with it value by value.

  • Check datasets newad2_n, newad2_k: c-Si.Enk, photon energy (eV), 2930 rows, 0.01-8.49 eV (the file’s range; the 1071 rows above 8.5 eV are extrapolation). Temperature not stated.

  • rii_20C_n, rii_20C_k (primary, temperature_k = 293.15), rii_25C_* (check, 298.15 K), rii_300K_* (check, 300 K): n and k against vacuum wavelength (um), 3664 rows each, 0.0309963-142.663 um (40 eV to 70 cm-1, the measured range of franta_2018 Table III); the 337 rows beyond 70 cm-1 are model extrapolation. The printed strings are kept; the script checks each page’s REFERENCES and COMMENTS. grade = "float zone", form = "bulk".

  • Uncertainty: none stated by the pages or the newAD2 files, and none recorded. The fit configuration sets sigma. franta_2018 gives the model’s statistical uncertainty of n as about 2e-5 at room temperature in the infrared (Fig. 9), and ties the absolute n to Frey et al. (1e-4).

• What the pages say:

  • REFERENCES: franta_2017 (the DOI link is printed without the “10.1016/” prefix) and “(Numerical data kindly provided by Daniel Franta)”.

  • COMMENTS: “Float zone c-Si; [heterogeneous, misspelt] data processing combining ellipsometric and spectrophotometric measurements with refractive index determined in” Frey, Leviton and Madison, Proc. SPIE 6273, 62732J (2006). Then “Numerical procedures updated in” franta_2018 (J. Appl. Phys. 123, 185707), and “Temperature …”.

  • The 13 pages (10-500 K, 20 and 25 °C) have identical headers apart from the temperature.

  • CONDITIONS: Franta-20C says 293 and Franta-25C says 25 (Celsius, where the other pages give kelvin).

• Checked (2026-10-14):

  • The record’s UDM against the authors’ table. It equals the file exactly (maximum |delta eps| = 0). On the authors’ grid it reproduces c-Si.Enk to 0.57 unit of the seventh significant digit in n (5.7e-7 absolute) and 0.74 unit in k, over 0.01-100 eV. Above 1 eV the agreement is 0.50 unit, which is exact rounding. published_models() contains franta_2017/udm_c_si. The total transition strength is 550.6 eV^2.

  • What the pages are: franta_2017’s ADM as revised in franta_2018. The pages’ n at 2 um follows franta_2018’s two-term ABESF Sellmeier formula within 1e-5 at every temperature from 10 K to 500 K. Franta-20C agrees at 293.15 K (+2.7e-6), not at 293 K (+2.8e-5), so its temperature is 20 °C. Franta-25C agrees at 298.15 K (+4.4e-6). franta_2017’s own Eq. (3) is 9e-4 lower at 500 K.

  • One model at three temperatures: the 20 °C page is the same model as the 300 K page at another temperature. Linear interpolation of the 250 K and 300 K pages to 293.15 K matches it within 6.8e-5 in n over 1.2-6 um, up to 0.022 near E_1 in the UV.

  • The three pages at 2 um: n = 3.453229 (20 °C), 3.454084 (25 °C), 3.454400 (300 K). n(300 K) - n(20 °C) = 1.17e-3 at 2 um, between -0.029 and +0.017 over the whole grid. At 632.8 nm, k = 0.01522, 0.01547, 0.01556.

  • The newAD2 UDM against the pages: it disagrees with them. Its n is 3.468960 at 2 um, against 3.454400 on the 300 K page and 3.45351 at 295 K from franta_2017’s Eq. (3), fitted to Frey et al. Its k at 632.8 nm is 0.03988, against 0.01556 (2.6 times). Its n is high by 0.013-0.026 at 0.02-1.5 eV (TC-388).

• Doubt:

  • Double counting. In the transparent range, the pages’ n is tied to Frey et al. (2006) through franta_2018’s Sellmeier pseudo-data at 2 um (5-700 K). A fit that also uses Frey et al.’s silicon must not treat the two as independent there.

  • Two minor errors in the database metadata, recorded here and in the notes but not corrected: the DOI link, and Franta-25C’s CONDITIONS value of 25.

  • The model above 6 eV rests on reflectance at 300 K only (Elettra, 6-40 eV). The 20 °C page there is the model’s temperature dependence, not data at 20 °C.

• Decision:

  • Franta-20C is primary. It is the model at optmat’s reference temperature. Franta-25C and Franta-300K are checks.

  • The newAD2 UDM is recorded as a check only. It is an unpublished model, and it disagrees with the measurements.

  • The other ten temperatures are not extracted.

• Status: verified (2026-10-14).

TC-1076 franta_2014c (2026-10-14)

• Where: D. Franta, D. Nečas, L. Zajíčková and I. Ohlídal, Thin Solid Films 571, 490 (2014), doi:10.1016/j.tsf.2014.03.059, the source franta_2014c. Table 1 (p. 493) and the text (pp. 492-494).

• Transcribed: no datasets: nothing printed has an optmat quantity. Formula effective_electrons holds Table 1’s effective numbers of electrons at 300-600 K:

  • n_K, n_L, n_ve, n_vx and n_vc (constant);

  • n_idt and n_dt (linear);

  • n_fc, n_mph, n_2ph, n_3ph and n_4ph.

  It also holds the text’s N_a(300 K) = 108.2 eV^2, U = 1.0002735, alpha_A2u = 0.1914, alpha_A2u+A1g(300 K) = 0.0025, alpha_1ph = 0.0172 and the O_i modes at 1107 and 1721 cm-1.

• Checked (2026-10-14, table and page images): the cells agree with the image, and the caption’s sums hold:

  • n_vx + n_vc = 4.12;

  • n_idt + n_dt = 3.88 at every temperature;

  • n_2ph + n_3ph + n_4ph = 1.162e-7 (printed 1.16e-7).

• Doubt:

  • Two misprints in the equations (page images): Eq. (17) gives N_O with Z_Si^2 m_e/m_O, where Eq. (8) requires Z_O^2. Eq. (23) reads n_ve + n_L + n_L where n_K is meant. Neither affects a recorded value.

  • n_K, n_L and n_ve are not c-Si values. They are Shiles et al.’s values for aluminium, taken for a-Si:H and “suitable also for crystalline silicon”.

  • No n or k is printed, and the model’s dispersion formulas are not given.

• Decision: recorded for the model’s construction only. No dataset.

• Status: verified (2026-10-14).

TC-1077 franta_2018 (2026-10-14)

• Where: D. Franta, P. Franta, J. Vohánka, M. Čermák and I. Ohlídal, J. Appl. Phys. 123, 185707 (2018), doi:10.1063/1.5026195, the source franta_2018. Tables I-III (pp. 185707-2, -5, -7) and the text.

• Transcribed: no datasets; the formulas are:

  • sellmeier_abesf (Eqs. (9)-(10), Table II): one-term and two-term Sellmeier formulas whose pole energies are ABESF functions of T, fitted to Frey et al.’s formula values.

  • thermal_expansion (Eqs. (2)-(3), Table I): Watanabe et al.’s polynomial and four ABESF fits, with their chi values. The cells were read from the image, because the CSV loses the minus signs and the powers of ten.

  Table III (the 22 data sets, 85 078 points) is summarised in the record’s technique. The text values are kept in the notes: the wafer thicknesses, the LSM uncertainty 2e-5 of n, Frey’s 1e-4 and Lu et al.’s lattice spacings.

• Checked (2026-10-14):

  • The Sellmeier formula. Table II agrees with the image. The two-term formula gives n(2 um) = 3.453541 at 295 K, against 3.45351 from franta_2017’s Eq. (3). The refractiveindex.info Franta pages equal it within 1e-5 at 10-500 K.

  • Table III’s points sum to the printed 85 078.

  • The Theta_j convert to the THz the text quotes: 16.5, 11.8, 32.4, 4.1, 13.6, 6.69, 12.35 and 4.35.

• Corrected: Table I prints the ABESF coefficients e_j of the 1st-4th fits without their factor 1e-4.

  • As printed, e(300 K) = 2.2-3.5. The reference temperature is 300 K, so e(300 K) must be 0.

  • With the factor, e(300 K) = -1.0e-7 to 6.5e-7, zero to the rounding of the printed e_0.

  • franta_2019 Table 1 reprints the 4th fit as -0.00017(2), 0.00332(3) and 0.00186(12).

  • The correction: eight [[formulas.corrections]] entries, fit1_e1 to fit4_e3.

• Doubt:

  • Reference temperature of the polynomial. Table I’s polynomial column is Watanabe et al.’s formula with their 293 K reference: e(293 K) = -8e-7 and e(300 K) = 1.8e-5. The text says the results use 300 K.

  • Frey et al.’s ranges are quoted inconsistently: 1.1-5.6 um and 20-300 K against 1.1-5.5 um and 30-295 K.

  • The effective numbers of electrons: “approximately 2.6 and 2.8”, where N_a = 108.2 eV^2 gives 2.61 and 2.74.

  • The ADM’s parameters (“more than one thousand”) are not printed.

• Decision: no datasets. The Sellmeier formula is a fit to Frey et al.’s formula and is not to be fitted beside Frey et al.’s silicon data.

• Status: corrected (2026-10-14).

TC-1078 franta_2019 (2026-10-14)

• Where: D. Franta, J. Vohánka, M. Čermák, P. Franta and I. Ohlídal, J. Electr. Eng. 70 (7s), 1 (2019), doi:10.2478/jee-2019-0036, the source franta_2019. Tables 1-3 (pp. 4, 12, 13). The library identity is VALIDATED_WITH_WARNINGS: the issue is printed “NO7S”.

• Transcribed:

  • Datasets band_gap_0K and band_gap_300K (band_gap, kind optical, use check): 1.134 and 1.086 eV, written by tools/extract/franta_2019.py from the Table 2 CSV.

  • Formula critical_points (Table 2, Eqs. (42)-(45)): all the energies and Thetas.

  • Formula thermal_expansion (Table 1, Eqs. (20)-(21)): the values, their parenthesised uncertainties and chi, for franta_2018’s 4th fit and three new fits with Middelmann et al.’s PTB data.

  • Table 3 is franta_2018’s two-term Sellmeier formula cell for cell. It is not recorded again.

• Checked (2026-10-14, images):

  • Table 2’s CSV and Table 1’s JSON agree with the images.

  • Table 1’s “4-th fit in [12]” is franta_2018’s 4th fit, rounded. This confirms the 1e-4 correction above.

  • Table 2 against franta_2017’s Table 2:

    • E_g 1.134/1.086 eV, Theta 382.9 K, against 1.14/1.087 eV and 248.6 K.

    • E_0(Gamma) at 300 K is now 4.023 eV, so franta_2017’s E_0 rising with T (TC-388) is gone.

    • E_3(Delta), as printed, rises by 7 meV from 0 K to 300 K.

• Doubt:

  • Which thermal-expansion fit the current model uses is not stated.

  • The band gaps are not independent of franta_2017’s: they are a refit of the same samples and data by the same group.

• The 2017 ADM’s parameters: neither franta_2018 nor franta_2019 prints them. That covers:

  • the path amplitudes A_0-A_11 and their spline nodes;

  • the indirect-transition strengths and phonon energies;

  • the free-carrier, vx, core and Urbach parameters;

  • the broadenings and Rydberg parameters;

  • the phonon-band amplitudes, f_nu and the phonon Theta.

  The model cannot be evaluated from the papers. The only numerical form of it is the refractiveindex.info tables.

• Decision: franta_2017’s band gaps stay primary and franta_2019’s are checks; a fit takes one of the two.

• Status: verified (2026-10-14).

TC-1079 frey_2006 (2026-10-14)

• Where: B. J. Frey, D. B. Leviton and T. J. Madison, Proc. SPIE 6273, 62732J (2006), doi:10.1117/12.672850 (the NASA NTRS scan, OCR text layer). Silicon Tables 1-5 (pp. 3-5), germanium Tables 6-10 (pp. 5-8). The library attaches each caption to the wrong table: tbl_032f91d73970 (labelled Figure 1) is Table 2, tbl_7450bffe6825 (unlabelled) is Table 4, and Table 4’s caption sits on tbl_e700ce199afe (Table 5).

• Transcribed:

  • Table 2: absolute n of Si, 13 wavelengths 1.1-5.5 um, 12 temperatures 30-295 K (n_Si_<T>K, 12 datasets, primary). Uncertainty ±1e-4 (“typical measurement uncertainty”, p. 3; level not stated); Table 1’s values (4.5e-5 to 1.35e-4) are in the notes.

  • Table 4: Si dn/dT (1/K) on the same grid (dndt_Si_<T>K, 12 datasets, primary). No uncertainty stated.

  • Table 7: absolute n of Ge, 9 wavelengths 1.8-5.5 um, same temperatures (n_Ge_<T>K, ±1e-4); Table 9: Ge dn/dT (dndt_Ge_<T>K). The text gives Ge’s measured range as 1.9-5.5 um; the 1.8 um row is printed without comment.

  • Tables 5 and 10: the temperature-dependent Sellmeier models (quartic S_i(T) and lambda_i(T)) as formulas sellmeier_Si and sellmeier_Ge, form n2_sellmeier_temperature, reference 295 K, 20-300 K.

  • Index medium vacuum (“in the absolute sense (in vacuum)”, p. 1). The wavelength medium is not stated; taken as vacuum. At 1.2 um an air wavelength would move n by 6e-5, at 2 um by 2e-5.

  • Tables 1, 6 (uncertainty) and 3, 8 (dn/dlambda) are in the record’s notes only.

• Checked:

  • Every cell against the table images and the PDF’s text layer (OCR confusions allowed for): no misread cell.

  • The Sellmeier coefficients against the images and the library cells (the script checks them).

  • The coefficients evaluated through optmat: n(2 um, 295 K) = 3.45352 (Table 2: 3.45354; franta_2017’s frey_index_2um: 3.45351).

• Doubt:

  • The tables are not the printed Sellmeier. The paper says every tabulated index was calculated from the Sellmeier models (p. 2), but Tables 5 and 10 as printed reproduce Tables 2 and 7 only to about 1e-4:

    • Si, 1.2-5.5 um: rms 1.35e-4, largest 3.9e-4; at 295 K, rms 1.4e-4, formula 7.8e-5 below the table on average; at 1.1 um and 295 K, 1.04e-3 below.

    • Ge, 2.0-5.5 um: rms 1.9e-4, largest 4.8e-4; at 295 K, 2.9e-4 below on average; at 1.8 um, 2.1e-3 below.

    • The differences step by whole temperature columns (Si 90 to 100 K: +0.7 to +1.2e-4 at every wavelength from 1.3 to 5.5 um), so they are not noise.

    • Rounding of the coefficients accounts for at most 7.5e-6.

    The tables are the closer statement of the measurement; the formulas are kept as printed.

  • dn/dT. How Tables 4 and 9 were derived is not stated, and they have no stated uncertainty. At 295 K, Si Table 4 is 3-8 % above the T-derivative of the Table 5 formula (12 % at 1.1 um): 1.78e-4 against 1.71e-4 at 2 um.

• Decision:

  • The n tables are primary at the paper’s ±1e-4.

  • The 295 K dn/dT (frey_2006/dndt_Si_295K) is the measured coefficient from which to take n_Si_295K to 293.15 K (thermo_optic): it shifts n by -3.3e-4 at 2 um (1.85 K x 1.78e-4), and a 4 % error in it is 1.3e-5, well below the index uncertainty. Taken there, n = 3.52250 (1.2 um), 3.48268 (1.5 um), 3.45321 (2.0 um), 3.43272 (3.0 um).

  • The Sellmeier formulas are published models for comparison, not fit inputs.

• Status: verified (2026-10-14).

TC-1080 li_1980 (2026-10-14)

• Where: H. H. Li, J. Phys. Chem. Ref. Data 9, 561 (1980), doi:10.1063/1.555624 (AIP’s scan; PDF page = journal page - 558). Si Table 1 (n) on PDF p. 17, Table 2 (dn/dT) on p. 19; Eq. (22) on pp. 8-9.

• Transcribed:

  • The kind is compilation: a critical evaluation by CINDAS. The recommended values come from Eq. (22), n^2 = epsilon(T) + L(T)(A_0 + A_1 T + A_2 T^2)/lambda^2, fitted to Salzberg and Villa (1957), Primak (1971) and Icenogle et al. (1976).

  • Table 1’s 293 K column: n at 35 wavelengths, 1.20-14.00 um (n_293K, check, ±2e-3, level not stated).

  • Table 2’s 293 K column: dn/dT in 10^-4 K^-1 (dndt_293K, scale 1e-4, check, ±0.15e-4 K^-1).

  • Eq. (22) as a formula with no form (eq22_Si). It is not implemented: it needs the piecewise Delta L/L.

  • The appendix’s 55 Si data sets of others (Tables A-1 to A-4) are listed in the notes and not transcribed: their originals are the primary sources.

  • The other 13 temperature columns are not transcribed: a scratch across rows 1.30-1.60 of the scan leaves cells that cannot be read with certainty.

• Checked:

  • Each 293 K cell against the scan’s pixels and against Eq. (22). The library misreads two cells, corrected in the script as misreadings, not errata:

    • Table 1, 1.50 um: the library reads 3.4796; the page prints 3.4799, as Eq. (22) gives (3.47986).

    • Table 2, 1.20 um: the library reads 1.963; the page and the text layer print 1.983, as Eq. (22)’s derivative gives (1.984).

  • Corrected as below, Eq. (22) reproduces Table 1 within 0.7e-4 at 100-350 K (its rounding) and within about 1.8e-4 at 500-750 K. Its one-sided T-derivative reproduces Table 2’s 293 K column within 0.001 x 10^-4 K^-1.

  • All 35 values of Table 1’s 293 K column equal refractiveindex.info’s main/Si/nk/Li-293K.yml (which also has 3.4799 at 1.50 um).

  • The uncertainty: Table 1’s footnote reads ±2x10^-3 on the image (the library’s text has 10^-4), as the text says (p. 9).

• Doubt:

  • A formula misprint. The constant terms of Delta L/L_293 are printed in percent (-0.021, -0.071); the other terms are fractions. As printed, L(100 K) = 1.065 and n(2 um, 100 K) = 3.42617, against the table’s 3.4240. Corrected to -0.00021 and -0.00071 ([[formulas.corrections]]), Delta L/L is +1.6e-6 and -2.5e-6 at 293 K and the table is reproduced. The two branches do not meet at 293 K (a 4e-6 step in Delta L/L), so dn/dT there must be taken one-sided.

  • Medium. Li never says whether the index is absolute or relative to air. For Ge it corrected Rank et al. “from vacuum values to air values” (p. 24), which suggests an air-relative evaluation. Recorded as index_medium = "not stated". The two readings differ by about 9e-4.

  • Disagreement with frey_2006. At 293 K, Li minus Frey (taken to 293.15 K):

    • -2.2 to -4.2e-3 at 1.3-5.0 um, and -5.8e-3 at 1.2 um;

    • -1.3 to -3.3e-3 (-4.9e-3) if Li is relative to air.

    These are beyond Li’s ±2e-3. Li’s form drops the band-gap term (B = 0), so it cannot follow n’s rise towards 1.1 um.

    Li’s dn/dT is 0.9-6.0 % below Frey’s 295 K values, within Li’s ±0.15e-4.

• Decision:

  • Both datasets are check: an evaluation, 20 times Frey’s uncertainty, medium not stated, and outside its own error bar against CHARMS. It is not a candidate thermo_optic source while frey_2006’s measured dn/dT exists.

• Status: verified (2026-10-14).

TC-1081 green_2008 (2026-10-14)

• Where: M. A. Green, Solar Energy Materials and Solar Cells 92, 1305 (2008), Table 1, pp. 1306-1307 (three library tables: tbl_85bbdac968fa, tbl_282abc185c1f, tbl_76272313742f); accuracy statement Section 5, p. 1308; temperature coefficients Section 6, Eqs. 6-10.

• Transcribed: three datasets of crystalline Si at 300 K against the free-space wavelength (um), 0.25-1.45 um at 0.01 um steps: alpha_300K (absorption coefficient, cm^-1, base e, 121 rows, 1.84E6 to 1.2E-8), n_300K (121 rows, 1.665-6.891) and k_300K (76 rows, 0.25-1.00 um; the table prints a dash from 1.01 um). The normalised coefficients C_n = (1/n) dn/dT and C_k,alpha = (1/k) dk/dT (10^-4/K) stay in each row’s printed cells. Uncertainty: the paper’s “error limits”, level bound, as relative_rows: alpha and k 0.3 % at 0.25 um, 4 % at 0.47-1.20 um, 10 % at 1.21-1.40 um; n 1 % at 0.25-0.29 um, 0.5 % at 0.30-1.00 um, 0.1 % at 1.01-1.45 um. No number is stated for alpha and k at 0.26-0.46 um (where the limit rises from 0.3 to 4 %) or beyond 1.40 um (“even larger”); those rows carry none.

• Checked: every cell of the three parts against the table images and against the PDF’s text layer (pdftotext -layout): all 121 rows agree. k = alpha lambda / (4 pi) in every row to the rounding of the two printed columns. epsilon_2 = 2nk at 0.29 um is 46.05, the paper’s 46.1 +- 0.9 at 290 nm. refractiveindex.info’s main/Si/nk/Green-2008.yml (121 rows) has the table’s n exactly, its k exactly at 0.25-0.44 um, and from 0.45 um k recomputed from alpha (agreeing with alpha lambda / (4 pi) to 4e-5 relative, its five figures).

• What it is built from: not a measurement. Green assembled a reflectance curve from 0.005 eV to 30 keV (1-6 eV: Herzinger et al. 1998 as the baseline, adjusted by 0.2 % for Jellison 1992, Philipp 1972, Aspnes and Studna 1983; below 1 eV: his Eq. 4, n = 3.4164 + 0.085818 E^2 + 0.010149 E^4, fitted to the prism indices of Salzberg and Villa, Lukes, Primak and Icenogle et al. corrected to 300 K; 6-30 eV Philipp, Hunter; above, Henke et al.), took its Kramers-Kronig phase, and computed n and k. Above 0.5 um k is from measured alpha (Weakliem and Redfield, MacFarlane et al., Keevers and Green, Trupke et al., Reece et al., “highest weighting from 0.47 to 1.45 um”) and n from that k and R. No column reproduces one source’s numbers, but n rests mainly on Herzinger et al. and Eq. 4’s prism data, and alpha above 0.47 um on the five alpha sets.

• Temperature coefficients: C_p = (1/p) dp/dT = d ln p / dT (Eq. 6), to be used as p(T) = p(T0) (T/T0)^b with b = C_p T0 (Eqs. 9-10). Normalised, so not a thermo_optic_coefficient (dn/dT, 1/K); not recorded as one. dn/dT = n C_n would be 2.1e-4 /K at 1.04-1.45 um (C_n = 0.6e-4, one significant figure), 2.9e-4 n at 0.25 um, down to -9e-4 n at 0.29 um. As a thermo-optic source they are coarse (one or two figures) and themselves derived from Jellison and Modine and the cited data.

• Against schinke_2015 (alpha at 295 K; sigma = Schinke’s standard uncertainty): Green/Schinke 0.985-1.023 at 250-360 nm, where Schinke’s k = 2 uncertainty is 0.18-0.66 % (up to 16 sigma; Green’s own limit is 0.3 % at 0.25 um); 0.88-1.00 at 380-520 nm, mostly 0.90-0.96 (up to 10 sigma); 0.97-1.08 at 540-880 nm (within 2.5 sigma); 1.03-1.05 at 900-1050 nm (3-10 sigma, where Schinke’s RT uncertainty is 1-2 %); 1.00-1.16 at 1060-1180 nm; 1.46-2.06 at 1190-1400 nm (up to 10 sigma). Green is at 300 K: shifted to 295 K with his own C_k,alpha and Eq. 9 (alpha lower by 2.7 % at 0.9 um, 4.4 % at 1.0 um, 16 % at 1.2 um, 30 % at 1.4 um) the ratio is 0.99-1.02 at 880-1000 nm (within 3.5 sigma), but 0.93-0.98 at 1020-1120 nm (2-6.5 sigma low) and still 1.24-1.48 at 1190-1350 nm; the shift changes 250-520 nm by 1.5 % or less. So the temperature accounts for Green’s 3-5 % excess at 0.9-1.0 um, and the shift (one-figure C at 300 K) overshoots beyond it. Schinke et al. state the same overall result (their Fig. 16): agreement except beyond 1200 nm.

• Doubt: the error limits are Green’s estimates, not an uncertainty analysis; k’s printed resolution (0.001) exceeds the 4 % limit from 0.68 um (k <= 0.012), and at 0.94-1.00 um k = 0.001 rounds alpha lambda / (4 pi) by up to a factor of two: use alpha, not k, there. 300 K (27 C), 6.85 K above the fit’s 293.15 K.

• Decision: all three datasets use = "check": a self-consistent evaluation of others’ measurements (some of which are curated on this branch: Herzinger 1998, Jellison 1992, Aspnes 1983), never fitted beside them; k duplicates alpha. Kind compilation.

• Status: verified (2026-10-14).

TC-1082 schinke_2015 (2026-10-14)

• Where: C. Schinke et al., AIP Adv. 5, 067168 (2015), Table I (Appendix A, PDF pp. 20-21; tbl_80266e561237, tbl_8c2f326870f4); uncertainty convention p. 6; methods Sections III-IV.

• Transcribed: one dataset, alpha_295K: the band-to-band absorption coefficient alpha_bb (cm^-1, base e) of crystalline Si at 295 K, 250-1450 nm at 10 nm steps, 121 rows (1.804e6 to 9.447e-9), each cell’s own power of ten written in e-notation (the library CSV drops the superscript: 1.804×106; the script reads the exponent as the rest of the cell after ×10). Uncertainty: the table’s relative expanded uncertainty U/alpha (%, coverage factor k = 2, “rounded to two significant digits”), as relative_rows (U/100) with level 2 sigma; the extraction script checks that the record’s 121 values are the table’s, row by row. Vacuum wavelength assumed (not stated; the air-vacuum difference, 0.3 nm, is far below the grid and the uncertainties). Table II (c_T = (1/alpha) d alpha/dT, 295 K) is not extracted: no quantity.

• Checked: every cell of both parts against the table images and the PDF’s text layer: all 121 rows agree. refractiveindex.info’s main/Si/nk/Schinke.yml (121 rows, same grid) has k = alpha lambda / (4 pi) from this table to 4e-5 relative (its five figures) in every row; its n is from M. R. Vogt’s PhD thesis (2015), not printed in the paper, and is not used (it differs from green_2008’s n by up to 0.17 at 0.29 um, by -0.009 at 0.6 um and +0.003 at 1.0 and 1.4 um).

• Uncertainty level (k = 2): 0.18-0.66 % at 250-360 nm; 1.1-13 % at 370-670 nm (13 % at 630-670 nm, the ellipsometry’s signal-to-noise); 0.98-2 % at 900-1060 nm (reflectance/transmittance); 10-13 % at 1170-1220 nm; 17-36 % at 1230-1350 nm; 42-180 % at 1370-1450 nm. The abstract quotes 0.4 % at 250 nm and 12 % at 1200 nm where the table prints 0.26 and 11; the table is recorded, the difference is unexplained.

• Doubt: from 650 nm into the reflectance/transmittance range the values are a Tauc parametrisation, alpha = [beta (hc/lambda - E_G)]^2, fitted at 650-1050 nm to the ellipsometry and RT data, with its uncertainty interpolated linearly between 650 and 930 nm: smooth, correlated values, not independent points. The 250-640 nm values are per-wavelength ellipsometric fits on a front-polished wafer with a native oxide modelled with WVASE’s “Herzinger 2008” thermal-oxide constants; their uncertainty (0.2-0.7 % below 360 nm) does not cover green_2008 (1.5-2.3 % off) there. The luminescence and SR data (1100-1450 nm) are relative and scaled to RT and EL alpha at 1100-1140 and 1200-1250 nm (scale uncertainty 2.8 %, included). Free-carrier absorption is subtracted (below 2-6 %). 295 +- 1 K, 1.85 K above 293.15 K.

• Decision: use = "primary": the only source with a per-wavelength uncertainty analysis over the whole edge (250-1450 nm), measured, original data. Kind measurement.

• Status: verified (2026-10-14).

TC-1083 aspnes_1983 (2026-10-14)

• Where: D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983), Tables II (Si), III (Ge), V (GaAs), VI (GaSb), VII (InP); Table I (samples); pp. 2-9 (method, Si), p. 23 (conclusion).

• Transcribed: for each of the five registered materials, 46 rows at 1.500-6.000 eV (0.1 eV steps) of n and k (primary) and <epsilon_1>, <epsilon_2> (check), three decimals as printed; R and 10^-3 alpha kept in printed. Pseudodielectric functions from rotating-analyzer ellipsometry at 67.08 deg on chemically stripped surfaces in dry N2, uncorrected for overlayers (Si and Ge <111>, GaAs and InP <100>, GaSb <111>). Temperature not stated (room temperature); no temperature_k. No uncertainty recorded: the paper states precision (+-0.1 % of the E1 structure for Si) and Kramers-Kronig self-consistency (+-0.5 % for Si), and expects the values to change by ‘certainly no more than 5% and probably no more than 1 or 2%’ (p. 23). Si k and epsilon_2 at 1.5-2.8 eV are excluded rows: below 1.93 eV epsilon_2 is computed from Dash and Newman’s absorption (Phys. Rev. 99, 1151 (1955), not in the library), and at 1.93-2.84 eV it is a linear blend of theirs and the measurement (p. 6). GaP, InAs and InSb (Tables IV, VIII, IX) are not registered and not extracted.

• Checked: Table II against its image cell by cell; every row of the five tables with its redundant columns: epsilon = (n + ik)^2, R from N and alpha = 4 pi k E/(hc) all hold within the printed rounding, except Si 3.100 eV <epsilon_2>, printed 4.321 (image checked), where n = 5.570 and k = 0.387 give 2nk = 4.311 and alpha = 121.62 requires epsilon_2 = 4.3120: corrected to 4.312 by an erratum (a transposition). The refractiveindex.info page Si/Aspnes equals Table II’s n and k in all 46 rows.

• Doubt: the surfaces retain a residual layer: herzinger_1998 finds oxide thicknesses fitted with this Si table 0.18 nm lower than with Si-Jellison or its own Si-final, as if the table retained 0.18 nm of SiO2. Against jellison_1992’s (100) table, n is 0.10-0.135 lower at 4.3-5.3 eV (1.570 against 1.683 +- 0.013 at 5.0 eV) and 0.03-0.08 lower at 3.5-4.2 eV, and k is 27-63 % higher at 2.0-3.0 eV (0.269 against 0.196 at 3.0 eV); within 1-4 % in k above 3.3 eV and within 0.015 in n below 3.0 eV. Jellison and Herzinger both cite Aspnes and Studna’s Si as Phys. Rev. B 27, 7466 (1983), not 985; that paper is not in the library, and whether it holds a different Si table is open.

• Decision: n and k primary, epsilon checks (the fit models n and k); uncertainty left to the fit configuration; Si’s low-energy k excluded (not this measurement). For the Si fit, a validator over E1/E2 rather than a fitted set, until the overlayer offset is weighed against jellison_1992.

• Status: corrected (2026-10-14) (the 3.100 eV epsilon_2), open (the use in the Si fit; PRB 27, 7466).

TC-1084 jellison_1992 (2026-10-14)

• Where: G. E. Jellison Jr., Optical Materials 1, 41 (1992), Table 1 (pp. 3-4, two pages, unlabelled in the library), Table 2 (p. 6), pp. 1-2 (method).

• Transcribed: Table 1: (100) silicon (n-type, 0.2-0.3 Ohm cm, HF etched, native oxide of 0.77 nm removed in the analysis), 234-840 nm (2 nm steps to 450 nm, 5 nm above), 187 rows of n and k (primary) with the paper’s error limits as per-point sigma (propagated errors from wavelength, N, S, C, beta correction, angle and oxide thickness; level not stated; 0.4-1.2 % of n, 0.001-0.003 in k above 450 nm). Wavelength in nm is the abscissa, the printed energy is kept in printed. Table 2: (111) and (110) faces at 248, 292, 362, 400, 450, 515, 635 nm (check, 7 rows each); the comparison rows from Palik (b) and Jellison & Modine 1982 (c) are not extracted. ‘Room temperature’, no number. The k rows at 765-805 nm (9) are excluded: the oxide thickness was set to match Dash and Newman’s absorption there.

• Checked: both pages of Table 1 and Table 2 against their images; the script checks that Table 2’s (100) rows equal Table 1’s. Three misprints corrected by errata (the image prints them): 595.0 nm n 2.948 for 3.948 and 705.0 nm n 2.766 for 3.766 (smooth neighbours, error limits of n ~ 3.9; refractiveindex.info Si/Jellison has 3.948 and 3.766), 495.0 nm error of n 0.002 for 0.020 (neighbours 0.021, 0.020). The printed energy at 386.0 nm, 3.221, is 3.211 (not extracted). The energy column is 1239.5/lambda in every other row, which is also the vacuum photon energy of a standard-air wavelength: the wavelength medium is not stated, vacuum recorded; the difference moves n by up to 0.012 (288 nm) and k by up to 0.015 (372 nm), under the error limits. refractiveindex.info Si/Jellison: 186 rows, equal to Table 1 with the two n errata, but it leaves out the 640.0 nm row.

• Doubt: Table 2’s Palik value at 248 nm (1.589, 3.354) is Aspnes and Studna’s 5.2 eV row (238.4 nm), so the paper’s ‘~6 % discrepancy in n at 248 nm’ compares different wavelengths (against the 5.0 eV row it is 0.113, 7 %). k below ~3 eV depends on the Dash-Newman normalisation of the oxide thickness. The wavelength medium.

• Decision: (100) n and k primary with the printed error limits; other faces as checks on the face dependence (1-2 % in epsilon at 292 and 362 nm).

• Status: corrected (2026-10-14) (three errata), open (wavelength medium).

TC-1085 herzinger_1998 (2026-10-14)

• Where: C. M. Herzinger et al., J. Appl. Phys. 83, 3323 (1998), pp. 2-5 (method, Sellmeier forms), pp. 11-14 (correlation, comparisons), Figs. 4, 10, 11, Tables V-VI.

• Transcribed: nothing. The silicon result (Si-final, 0.75-6.5 eV, multi-sample VASE of six thermal oxides and one native oxide, Kramers-Kronig consistent parametric model of 58 parameters) is printed only as figures; its table was deposited with AIP’s Physics Auxiliary Publication Service (no document number printed), not in the library; the model’s parameters are not printed. The figures are not digitised (the numbers exist in the deposit; TC-699). The record holds the method, the oxide and interface Sellmeier parameters (in notes: no thermal-oxide material exists) and the findings.

• Checked: the Sellmeier parameters on the page image (Eq. 4, n^2 = offset + a lambda^2/(lambda^2 - b^2) - c lambda^2): SiO2-final (1.3000, 0.81996, 0.10396 um, 0.01082) gives 1.46546 at 546.1 nm (printed 1.4655); Glass-Sellmeier (1.4923, 0.61497, 0.115 um, 0.01059 um^-2) gives 1.46036 (Palik 1.4602). Interface-final is printed a = 0.69417, but the text says it uses the glass a, b, c with only the offset fitted, and its printed n = 2.04 at 546.1 nm is reproduced with a = 0.61497 (2.035), not 0.69417 (2.055): presumably a transposition of 0.61497.

• Doubt: Si-final’s E2 peak height depends on the interface offset (3.5), chosen by judgement (Fig. 9, p. 12). Its finding that Si-Aspnes behaves as if it retained 0.18 nm of oxide bears on aspnes_1983.

• Decision: a notes-only record; Si-final to be curated when the deposit is in hand.

• Status: open (the Si-final deposit).

TC-1086 edwards_1985: Table XII, silicon’s compiled n and k (2026-10-14)

• Where: D. F. Edwards, “Silicon (Si)”, Palik’s Handbook (1985), pp. 547-569; Table XII pp. 555-568 (pdf 9-22), fourteen library parts (tbl_fe55a657b8ec, _646c7991193c, _c55280ac2760, _3ad03cca75e0, _5f02459e2946, _465e3c66d70e, _0f7731d732b9, _6a64c6e4156f, _9f49ec26fcd8, _66f11f14a901, _afc5f60ea2d9, _1eb73f7d4ec6, _f5e644f1b126, _f4f72cdf8301), read from their JSON cells (one part has no CSV).

• Transcribed: 653 printed lines, 2000 eV (6.199 A) to 0.00372 eV (333.3 um); the wavelength as abscissa (angstrom to 650 A, micrometre from 0.06526 um). One dataset per column kind and reference tag, the tag carried down the column to the next: 20 datasets, 1166 points, all material Si:

  • henke_n, henke_k (127 each; [30], 6.199-124.0 A, 2000-100 eV): reproduced (Henke et al. 1981, calculated by Edwards).

  • gahwiller_brown_k (25; [31], 59.04-112.7 A and 130.5 A): reproduced.

  • brown_k (31; [32], 118.1-125.2 A, 105-99.0 eV): reproduced (Brown, Bachrach and Skibowski 1977).

  • hunter_n, hunter_k (58 each; [29], 125-650 A): primary (unpublished, first published here); form film; four rows above 95 eV (rows 171, 173-175) excluded as Edwards’ interpolation between 95 and 99 eV (p. 552).

  • philipp_n_angstrom, philipp_k_angstrom (2 each; 620, 635.8 A) and philipp_n_um, philipp_k_um (61 each; 0.06526-0.2480 um, 19.0-5.0 eV): [26], reproduced (Philipp 1972 and a 1982 private communication); split by unit.

  • aspnes_theeten_n, aspnes_theeten_k (226 each; [20], 0.2066-0.8266 um, 6.0-1.5 eV, 0.02-eV steps): reproduced (Aspnes and Theeten 1980; k below 2.5 eV combined with Hulthen’s eps_2, so k also lists Hulthen).

  • hulthen_k (9; [21], 0.6199-1.033 um): reproduced; read by Edwards from Hulthen’s graphs.

  • mcfarlane_roberts_k (12; [23], 0.9686-1.170 um): reproduced; 290 K.

  • ir_n (29; [1, 2, 3, 8], 1.12-25.00 um): reproduced (Primak; Salzberg and Villa; Edwards and Ochoa; li_1980).

  • far_ir_n (13; [5, 6], 30.30-333.3 um): reproduced (Loewenstein et al.; Randall and Rawcliffe).

  • hordvik_skolnik_k (2; [12], 2.7144, 3.80 um), bendow_k (20; [15], 5.00-9.091 um), johnson_k (67; [14], 7.143-29.41 um), afsar_hasted_k (10; [19], 62.50-250.0 um, 303 K): reproduced.

• Structural fixes (script): (1) exponent inheritance: a bare mantissa under “m x 10^-e” takes 10^-e until a cell with its own power or a plain decimal, across empty cells, page breaks and tags (Hunter’s “1.0 [29]” is 1.0e-3 under Henke’s 1.54e-3; Brown’s “1.08 [32]” 1.08e-2; Afsar’s “1.7 [19]” 1.7e-4; Gahwiller’s 95 eV “4.9 [31]” 4.9e-3); reset at the angstrom-to-micrometre header, because the second k column’s next value, Aspnes’ “2.909 [20]” at 6.0 eV, is a plain k (continuing smoothly to 0.945 at 3.26 eV); (2) the untagged k “9.3 x 10^-2” at 630 A, under Philipp’s “0.122 [26]”, is Hunter’s (its row’s n is tagged [29], on Hunter’s 10-A grid; override in the script); (3) six lines with no energy or wavelength (Philipp at 20.00 eV; Johnson at 7.143, 7.692, 8.333, 9.091 um) take the wavelength of the line above.

• Checked: every part against its table image, cell by cell (one pass; all cells agree with the images, including every “x 10^-e”); eV x wavelength against hc on every line; wavenumber against wavelength; each dataset’s wavelengths strictly increasing; n columns for jumps (none beyond the physical structure). The infrared n from 2.4373 to 25 um equals Edwards and Ochoa’s 1980 Herzberger-type formula (refractiveindex.info’s main/Si/nk/Edwards.yml coefficients, comparison only) within +-0.5e-4 on all 19 rows; below 2.4 um it does not (that formula’s range starts at 2.4373 um). The ir_n values are not li_1980’s Table 1 at 293 K (3.5193 against 3.5167 at 1.20 um; 3.4710 against 3.4719 at 1.60 um).

• Checked against Franta’s 300 K data (refractiveindex.info main/Si/nk/Franta-300K.yml, linear interpolation, comparison only): 0.15 um: Philipp n 0.442, k 1.895 against 0.576, 1.833 (-23 %, +3 %); 0.21 um: Philipp 1.171, 3.111 (+4.0 %, +5.6 %), Aspnes and Theeten 1.081, 2.979 (-4.1 %, +1.1 %) against 1.127, 2.946; 0.25 um: Aspnes 1.580, 3.632 against 1.645, 3.603 (-4.0 %, +0.8 %); 0.30 um: 5.004, 4.162 against 4.999, 4.136 (+0.1 %, +0.6 %); 0.37 um: 6.811, 2.033 against 6.855, 2.125 (-0.6 %, -4.3 %). Edwards.yml there is Edwards and Ochoa’s infrared formula, not this table; it has no UV values.

• Doubt:

  • Printed misprints outside the values (the abscissa is right on each row, so no erratum): 640 A printed with 10.37 eV for 19.37; 1,492 cm-1 for 1,429 at 7.00 um; 608 for 606 cm-1 at 16.50 um; 21,660 for about 21,620 cm-1 at 0.4626 um.

  • Henke rows 166 and 162 eV print identical n and k (0.99235, 1.45e-2) against both columns’ trend: probably a repeated line; kept as printed (no evidence of the intended values; Henke’s 1981 tables are not in the library).

  • Hunter’s k at 330 A prints “1.0” (1.0e-2) between 1.04e-2 and 1.13e-2; Bendow’s k at 6.897 um, 2.45e-5 with its power printed, is ten times its neighbour at 6.667 um. Kept as printed.

  • Hunter’s samples were evaporated films, ‘probably amorphous’ (p. 552); filed under crystalline Si, form film, primary. Whether a crystalline-silicon model should fit them (20-95 eV, where they are the only measurement in the table) is a fit decision.

  • Philipp’s [26] values could be first published here (part private communication, 1982); recorded as reproduced from J. Appl. Phys. 43, 2836 (1972), which is not in the library.

  • Table XII does not reproduce philipp_1963 (it cites Philipp and Taft 1960, Philipp 1972, Philipp and Ehrenreich 1967), nor aspnes_1983 (its ellipsometry is Aspnes and Theeten 1980), nor jellison_1992 or green_2008 (later).

• Decision: Hunter’s range primary; every other range reproduced, with the original named (li_1980 the only one curated, for ir_n); none of the other originals is in the library. Not transcribed: the Herzberger and Sellmeier fits of p. 548 (text coefficients), Table XIII (Icenogle’s dn/dT polynomials; B1 at 2.732 um, -1.0255e-5, is ten times smaller than its neighbours’).

• Status: verified (2026-10-14) for the transcription; open for the Henke 166/162 eV rows and for the use of Hunter’s film data in the silicon fit.

TC-1087 philipp_1963 (2026-10-14)

• Where: pp. 1550-1560; Fig. 3 (pp. 1552-1553: R, eps_1, eps_2, -Im eps^-1 of Si, Ge, InAs, GaAs, GaP to 25 eV), Fig. 4 (p. 1556), Figs. 5-6 (p. 1557), Fig. 7(b) (p. 1559), Table I (p. 1558, tbl_9092a0513e62).

• Transcribed: nothing as a dataset. Table I’s plasma energies (eV) are recorded in the notes, checked against the table image: Si free-electron omega_Pv 16.6, effective Omega_Pv 16.6, eps_1 = 0 at 15.0, maximum of -Im eps^-1 16.4 (optical) and 16.9 (energy loss, Dimigen); Si’s tau_v = 1.6e-16 s (Fig. 4 caption); n_eff saturates near four electrons per atom (p. 1557).

• Checked: that silicon’s optical constants are in figures only, and that no tabulation reproduces them: edwards_1985’s Philipp rows ([26], 5-20 eV) are from Philipp 1972 and a 1982 private communication; Edwards does not cite this paper.

• Doubt: the vocabulary has no quantity for a plasma energy or an energy-loss maximum; samples ‘conceivably subject to atmospheric contamination’ (p. 1551).

• Decision: not digitised (TC-699): the curves are superseded for silicon by Philipp’s later data, which edwards_1985 prints as numbers over the same range.

• Status: decided (2026-10-14).

TC-1088 fit/Si: the recommended index of crystalline silicon at 20 C (2026-10-14)

• Where: data/solid/fits/Si.toml, data/solid/models/fitted/Si.json, data/solid/defaults.toml, docs/silicon.md; optmat.solid.fitting now fits an absorption_coefficient as k = alpha lambda / (4 pi) (base e or 10, cm-1 or m-1), with its relative uncertainty carried to log k unchanged.

• Start: franta_2017/udm_c_si, newAD2’s unpublished UDM of float-zone c-Si (TC-1075). It is 0.0158 above Frey et al. at 2 um (3.4690 against 3.4532 at 20 C) and 2.6 times Schinke’s k at 633 nm.

• Fitted:

  • frey_2006/n_Si_295K, 1.2-5.5 um (the 1.1 um row, on the absorption edge, left out), sigma 1e-4 as stated, taken to 293.15 K with dndt_Si_295K (-3.3e-4 at 2 um; TC-1079).

  • schinke_2015/alpha_295K, 250-1200 nm, its k = 2 uncertainties as one-sigma halves plus 1 % in quadrature (295 K against 293.15 K, and the model’s shape; TC-1082). Beyond 1200 nm alpha falls below 0.1 cm-1 (k < 1e-7) and drops 5 decades in 0.15 eV: the model’s Urbach tail cannot follow it, and in wafers that absorption is the free carriers’ and the sample’s anyway.

  • franta_2017/rii_20C_n outside Frey’s range: 31-1150 nm (sigma 5e-3) and 5.6-143 um (sigma 1e-3, a dense curve tied to Frey’s index through franta_2018’s Sellmeier, so a soft one); rii_20C_k at 31-250 nm (sigma 5 %) and in the lattice bands, 6-64 um (sigma 20 %; beyond, the sample’s free carriers). Franta’s window n is not fitted beside Frey’s (it is derived from it; TC-1075).

  • Free: the interband, higher-energy and Urbach parameters (Nvc, Eg, Eh, Nvx, Ex, Nut, Eu), the eleven localised-state strengths (and the first one’s position and width), the four excitons’ strengths, positions and widths, and one factor on the 36 phonon terms.

• Result: chi2 9349 for 4985 dof (reduced 1.87). Frey: chi2 7.8 for 12, within 1.4e-4 everywhere (-1.4e-4 at 1.2 um, at the edge; +0.6 to +1.2e-4 at 2.5-5.5 um, the model’s shape in the window). Schinke: k within 4 % below 370 nm, -8 to +13 % at 370-550 and 810-1100 nm, 5-19 % high at 550-810 nm (where Schinke’s own k = 2 band reaches 13 % and the values come from a Tauc fit), up to 27 % low at 1100-1150 nm and 2.5 times high at 1200 nm. Franta’s ultraviolet n: mean -3e-3 at 120-250 nm and -7e-3 at 31-120 nm, up to 0.04 at sharp structure; infrared n within 1.5e-4; lattice k at 6-64 um 10 % rms (up to 45 % on the sharpest bands); the phonon factor 1.006.

• Validators (mean deviation, model minus data):

  • Jellison n -0.013 (0.05-0.06 low at 234-322 nm, outside his +-0.02-0.04 there), k +4.6 %; Aspnes n +0.026, k -2.8 %: the two ellipsometric sets bracket the model in the ultraviolet (Aspnes 0.10-0.13 below Jellison at 4.3-5.3 eV; TC-1083, TC-1084).

  • Green 2008 (300 K): n 1.7-3.3e-3 above it at 0.93-1.45 um, where Frey’s dn/dT puts 300 K 1.2e-3 above 20 C (Green lies 3-4.5e-3 below Frey’s level); alpha +4 % on average at 250-1200 nm.

  • Li 1980 n +3.3e-3 (Li lies 2-4e-3 below Frey; TC-1080).

  • Franta’s 20 C window n: mean -5e-6 at 1.15-5.6 um.

  • newAD2’s own table: n 0.012 above on average; superseded.

• What it gives: n = 3.47835 at 1550 nm, 3.45323 at 2 um; GVD 1112 fs^2/mm at 1550 nm and 815 at 2 um, within 1-4 % of Frey’s temperature-dependent Sellmeier at 20 C from 1.55 to 5 um (6 % at 1.2 um, at the edge).

• Limitations:

  • 20 C only; Frey’s temperature-dependent Sellmeier (frey_2006/sellmeier_Si, 20-300 K, 1.1-5.6 um) is the model for other temperatures in the window.

  • k beyond 1.2 um (1.4e-10 at 2 um) is an upper bound set by the model’s tail, not a measurement; free-carrier absorption of a doped wafer exceeds it.

  • Franta et al.’s 2017 temperature-dependent model, which follows the indirect edge’s phonon structure, cannot be implemented: its parameters are not printed in franta_2017, franta_2018 or franta_2019 (TC-1075, TC-1077, TC-1078).

• Status: decided (2026-10-14).

TC-1089 The solid fits’ refit tests: a flat minimum, not a regression (2026-10-14)

• Where: tests/solid/test_solid_fitting.py, docs/developers/testing.md; the stored fits data/solid/models/fitted/SiO2.json (TC-399) and Si.json (TC-1088), unchanged.

• Finding: test_the_stored_silica_fit_reproduces failed on main: a refit gives Nvc = 358.651053 against the stored 358.650415 (1.8e-6 relative, over the test’s 1e-6). The same refit, to every digit, is obtained at b6299619 (the commit that stored the fit), at 6477f3e6 and on main, with the same numpy 2.5.3, scipy 1.18.1, Python 3.14.5 and machine, and with Accelerate limited to one or two threads. So the stored record has never matched a refit of the committed code at that precision; its “test-fits passed” in 6477f3e6 cannot have been this test.

• Checked: the objective of the committed code at the stored parameters is the stored chi2 exactly (2309.780908303484), so the data and model are those of the record. The refit stops on scipy’s xtol at chi2 higher by 4.6e-6 (2e-9 relative); three scalings of the unknowns stop at Nvc 358.65003, 358.65105 and 358.65118, the stored point lying among them. The minimum is flat along a few combinations: the parameters move by up to 3.3e-3 of their standard uncertainties, n by 1.9e-6 relative (at 57 nm; 2e-9 in the window), k by 2.9e-5 relative. The stored point was most likely written by an intermediate state of solid/fitting.py, which b6299619 changed by 60 lines in the same commit. fit/Si refits to every digit today.

• Decision: test the refit as the hyperpolarizability fits are (8d029f9c): exact digest, dof, offsets and point counts; parameters, scales and offsets within 1e-2 of their stored sigma; n within 1e-5 and k within 1e-4 relative on a grid over the range (k > 1e-12); chi2 within 1e-8 relative. Mutation tests reject a 0.05-sigma parameter shift, a changed objective, dof or dataset selection, and a 7-sigma group scale. The stored records are not refitted or rewritten.

• Status: decided (2026-10-14).

TC-1090 The gas fits’ and compact models’ refit tests (2026-10-15)

• Where: tests/test_stored_fits.py, tests/test_compact.py, docs/developers/testing.md; the stored records in data/gas/models/fitted/ and data/gas/models/compact/, unchanged.

• Finding: poe test-fits failed for most gas fits and four compact models. The gas test compared alpha at 15 energies from 0 to 0.7 hartree (to 65 nm, through poles beyond most fits’ ranges) to 1e-7 relative; the compact test compared pole strengths and energies to 1e-9.

• Checked (2026-10-14/15):

  • For all fifteen gases the data chi-squared of the committed code at the stored parameters equals the stored chi-squared to round-off (at most 2e-16 relative): the data, model and code are those of the records.

  • A refit stops elsewhere: single parameters move by up to 52 (CH4) and 3e7 (SF6) of their stored sigma, whose covariance is singular along the degenerate oscillators, while alpha within the fit’s range moves by at most 1.1 % of its own band (He; 0.2 % Ar, the others at most 0.03 %) and 1.5e-5 relative (Ne), and the full objective, priors included, by at most 1.1e-3 (Ne; 4.1e-4 Ar), either sign.

  • fit/He refitted at da647d1a, the commit that stored it, with its own lock, moves its parameters by 13 % relative, as on main; with Accelerate limited to one or four threads, the same. As for silica (TC-1089), the stored records never matched a refit of their committed code at the tests’ precision in this environment; how they were written is not established.

  • The compact re-derivations move CO2’s pole strengths by 4.4 % and N2O’s by 0.5 % (CH4, CO 5e-7; SF6 keeps its parent’s poles), while the worst residuals on the check grid move by at most 2.2e-3 sigma (N2O D3; stored 0.069, fresh 0.071).

• Decision: the gas refit test checks dof and per-dataset point counts exactly, alpha within each qualified interval to 0.05 of the stored band and 1e-4 relative, and the full objective to 0.01 in chi-squared (a 0.1-sigma move); mutation tests reject a 1e-4 change in one strength, a changed dof and a dropped dataset. The compact test checks the pole count, regions, kept poles, starting point, moments (1e-12) and the worst residuals to 0.01 sigma. The stored records are not refitted.

• Status: decided (2026-10-15).

TC-1091 Unphysical wavelengths are refused, not evaluated (2026-10-16)

• Where: src/optmat/_validity.py (checked_wavelength), the evaluation methods of optmat.solid.models.base.Model, optmat.gas.models.base.Model and optmat.gas.air.AirModel; tests/test_validity.py.

• Finding: a model evaluated at a zero, negative or (for a solid) infinite vacuum wavelength returned a value, not an error. fit/SiO2 gave n = 0.99978 + 1.1e-5 i at -1 um, because the omega = 2 pi c / lambda it evaluates at is negative and its terms are defined there; a Sellmeier formula, even in lambda, gave its value at +|lambda|. At 0 and inf the solids returned NaN under a flood of NumPy division warnings. A propagation code that converts a frequency grid reaching omega <= 0 and silences NumPy’s warnings would take these values as data.

• Decision: every evaluation refuses a wavelength at or below zero with ArgumentError, and a solid refuses inf (omega = 0, which no solid model states). A gas and air keep inf as the static limit, as documented. NaN still passes through as a missing value and gives NaN (test_a_gap_between_intervals_warns, tests/test_solid_tables.py). No value at a positive wavelength changes.

• Status: decided (2026-10-16).

TC-1092 travers_2026_pyroraptor: helium on matched measures; TC-1050’s haCC and atom ratios corrected (2026-10-17)

• Where: src/optmat/data/sources/travers_2026_pyroraptor.toml (nine datasets), src/optmat/data/external/pyroraptor/ (the four result tables, PROVENANCE.md, the converter and the records’ sha256), tools/extract/travers_2026_pyroraptor.py, optmat.gas.ionisation_validation (HELIUM_MATCHED, YieldRatio, helium_matched_ratios), tools/ionisation_rate_tables.py (ionisation-rate-helium-matched), the manual’s laser and static pages, travers_2026_trecx.toml (part K’s notes), src/optmat/data/gas/ionisation_rates.toml (helium’s uncertainty text), tests.

• Transcribed: J. C. Travers’s pyroraptor runs of 8 to 14 October 2026, tier 3: helium with both electrons active, haCC with one and with five He+ channels, and one electron of Tong and Lin’s potential, in part K’s 390 nm pulse (A2’s 6 fs Gaussian; 3.684031e14 and 5.68981e14 W/cm2), read 1000 au after the pulse as N0 - P(ground) - P(bound, n <= 4) (“above4”: ionisation plus excitation to n >= 5) and the same above n <= 5; and haCC in Sato et al.’s 800 nm sin^2 pulse with their measure (1 - P(both inside 20 bohr)). Two electrons (inner = 2, R0 = 97 bohr) 8.464e-4 and 7.244e-3; haCC(1) 8.092e-4 and 6.985e-3; haCC(5) 8.277e-4 and 7.150e-3; one electron 5.119e-4 and 4.504e-3. The tables were written from the runs’ JSON records by a converter kept beside them, every row checked against its record (112 rows).

• Checked:

  • The measures are converged in the box: the two-electron above4 changes by 0.03 % and 0.01 % from R0 = 78 to 97 bohr, while 1 - P(bound) falls by 3.6 % as each box binds another shell; haCC’s above4 and above5 agree to 0.01 % at R0 = 40, 60 and 80.

  • The three analyses cut at n by the same rule, n = round(1/sqrt(-2E)) (the runs’ scripts). pyroraptor’s reports compared haCC’s above5 (7.113e-4; their “ionisation plus n >= 5”) with the two-electron and one-electron above4: one shell apart. Their haCC deficit at 390 nm (8 to 13 %), and its contrast with 800 nm, came from that. pyroraptor confirmed and corrected it on 17 October 2026 (merged at 295a255b): the deficit, its frozen-core interpretation and the “not seen at 800 nm” statement are withdrawn; its corrected haCC(1) and haCC(5) above4 values are those here.

  • The 390 nm pulse is the same in all three: the haCC records’ max |A| matches the intensity to 1e-4, and the one-electron driver uses the same max |A|.

  • haCC at 800 nm reproduces the report’s values (2.961e-4, 1.5445e-2, 0.1536 and 3.023e-4, 1.5825e-2, 0.1578).

• Doubt: the two-electron basis (inner = 2) lies above its angular limit by 3.1 %, from an inner-arm ladder of the absorbed norm-loss at BOX 40 and 3.684e14 W/cm2 (inner 2 -> 3 -> 4: -0.97 %, -0.67 %, extrapolated geometrically); it was not run at 5.69e14 nor on above4, and is the datasets’ stated uncertainty, an excess. True ionisation without the Rydberg shells is not converged in any of the boxes.

• Finding (helium_matched_ratios, ionisation-rate-helium-matched):

  • The atom over one electron at the same ionisation energy: 1.65 and 1.61 (1.60 and 1.56 at the angular limit), not TC-1050’s 1.71 and 1.79, which set the two-electron norm-loss (ionisation plus the Rydberg shells beyond BOX 40) against one electron’s. Sato et al.’s helium at 800 nm gives 1.71 to 1.53 (TC-860).

  • haCC(5) is 0.978 and 0.987 of the two electrons (0.979 and 0.990 above n <= 5), and 0.998, 0.996 and 0.981 of MCTDHF at 800 nm; haCC(1) 0.956 and 0.964, and 0.978, 0.972 and 0.955. TC-1050’s 0.76 to 0.81 set haCC’s norm-loss, which is ionisation alone (its bound states are converged at 40 bohr), against the two-electron one: haCC’s helium is not low, and the factor 1.25 between haCC and Parker et al. (TC-848) was the measure’s.

  • Parker et al.’s rate integrated over the pulse is 1.003 and 0.966 of the two electrons (about 1.03 and 1.00 at the angular limit): confirmed, as TC-1050 found; the default’s N_eff of 1.47 stands.

• Correction: TC-1050’s finding that haCC’s helium is 0.76 to 0.81 of the exact yield, and the atom 1.71 to 1.79 of one electron, is withdrawn; the manual (laser page, the argon bullet of the static page), part K’s notes in travers_2026_trecx and helium’s uncertainty text now give the matched values. The part K datasets and their table are unchanged: they are what was run.

• Status: corrected (2026-10-17).

TC-1093 travers_2026_trecx part N: one electron of xenon in RMT’s field; RMT’s atom against it and the default (2026-10-17)

• Where: travers_2026_trecx.toml (ground_survival_rmtpulse_m{0,1}_Xe, _unscaled), src/optmat/data/external/trecx/xe_rmt/ (results.csv, manifest.csv, tables.md, the inputs; PROVENANCE.md), tools/extract/travers_2026_trecx.py (xe_rmt_uncertainty), optmat.gas.ionisation_validation (XENON_RMT, SurvivalRatio, xenon_rmt_ratios, XENON_SURVIVAL, xenon_survival; the depletion quantity of RateComparison), tools/ionisation_rate_tables.py (ionisation-rate-xenon-rmt), the manual’s static page, xenon’s reasons in ionisation_rates.toml, tests.

• Transcribed: J. C. Travers’s tRecX runs of 12 to 15 October 2026 (part N), tier 3: xenon 5p, m = 0 and m = 1, in part G’s potential scaled by beta = 0.9997362280 to RMT’s -0.444 au, and unscaled (-0.4448129 au) at 1.1, 1.5 and 2.5e14 W/cm2, in the field RMT wrote (hartmann_2022, TC-1059: E(t) = E0 exp(-((t - 900)/186)^2) cos(0.06 (t - 900)) au, E0 = 0.05336 sqrt(I/1e14)), read as RMT’s measure, the 5p population at 3000 au: m = 0 0.7170 to 0.0584, m = 1 0.9797 to 0.7302.

• Checked: every run done; the 5p energy -0.44400000012 au (unscaled -0.4448128882); the pulse file reproduces the formula to 6e-8 E0, A(3000) = -1.2e-10 E0; the population at 1500 au equals that at 3000 au to 1.005e-5; convergence at 1.5 and 2.5e14 (m = 0): the depletion moves by at most 0.43 % (cutEnergy 150), the stated uncertainty carried to P; no field, P = 1 to every digit. The table agrees with the runs’ report to the last printed digit.

• Finding (xenon_rmt_ratios, xenon_survival, ionisation-rate-xenon-rmt):

  • RMT’s atom depletes like 0.53 to 0.63 of one m = 0 electron (ln P / ln P_0), 0.23 to 0.28 of the shell’s six electrons taken as independent; at the potential’s own ionisation energy 0.56 to 0.64. 0.18 % in the ionisation energy moves the depletion by 0.2 to 2.7 %.

  • The default (1.5 electrons, from Wallace et al.’s yields: about 1.1 of one m = 0 electron, TC-849) depletes 1.54 to 2.09 times as much as RMT (-ln P, at the field’s intensity, 0.076 % below RMT’s label), more at higher intensity.

  • RMT depletes less than both measurements of xenon in few-cycle pulses: Wallace et al.’s (through the default) and Hartmann et al.’s own (TC-1094, up to 1.9e14 W/cm2). Its ion states are the frozen Hartree-Fock 4d^-1, 5s^-1 and 5p^-1, and it has no double ionisation.

• Decision: xenon’s N_eff (1.5) and uncertainty factor (3) are unchanged: the gap to RMT lies within the factor, and the measurements do not support moving towards it. The comparison is recorded in xenon’s uncertainty text and on the static page.

• Status: decided (2026-10-17).

TC-1094 hartmann_2022: the measured neutral abundance of xenon (2026-10-17)

• Where: hartmann_2022.toml (measured_neutral_abundance_Xe; the notes), tools/extract/hartmann_2022.py (measured), optmat.gas.ionisation_validation (XENON_SURVIVAL), tools/ionisation_rate_tables.py (ionisation-rate-xenon-measured), the manual’s static page, tests.

• Transcribed: the authors’ archive (data/experimental/gs_pop.csv, the paper’s Fig. 5(a)): the relative abundance of neutral xenon, pop_xe0, at ten peak intensities from 0.945 to 2.502e14 W/cm2, as printed (0.8465 to 0.1279); the column of ground_state_survival (the population left in the ground state, here measured through the neutral’s 4d - 6p line).

• Checked: Xe, Xe+ and Xe2+ sum to 1 in every row (rounding); the paper’s statements quoted in the record (p. 2: the 4.5 fs d-scan FWHM; p. 4: the intensities from average power, up to 11 %, and the simulations’ systematic overestimation of Xe+; Fig. 5(a), p. 6).

• Doubt: not stated: the delay at which the abundances were read, the polarisation, the NIR’s intensity over the XUV-probed volume, and the abundances’ uncertainty. The record states each as not stated.

• Finding (xenon_survival, ionisation-rate-xenon-measured): the default’s depletion at the peak intensity, in a 4.5 fs pulse at 760 nm, is 0.96 to 1.13 of the measured up to 1.6e14 W/cm2 and 1.4 to 1.8 above, where the average over the focus (not modelled) lowers the measured depletion most. The measured survival is below RMT’s up to 1.9e14 W/cm2 (0.767 at 1.10e14 against RMT’s 0.812 at 1.1e14; 0.518 against 0.623 at 1.5e14) and about equal from 2.3e14. With up to 11 % in the intensity (a factor of about 1.7 in the rate) it supports the default’s xenon, not RMT’s.

• Status: verified (2026-10-17).