nie_2025#
Z.-L. Nie, J. Wang, C.-L. Hu, Y. R. Sun, C.-F. Cheng, Y. Tan and S.-M. Hu, “Polarizability of molecular hydrogen and gas metrology”, Phys. Rev. A 111, 012801 (2025)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.111.012801
Source kind: measurement
Recorded technique: Fabry-Perot gas refractometers (USTC; the instrument of zhao_2026): 10 cm ULE cavities (R ~ 99.9 %, FSR 1.5 GHz, mode width ~0.4 MHz) in a vacuum cell in an aluminium cylinder at about 297.53 K (calibrated platinum resistance thermometer, < 5 mK), a 1566 nm fibre laser (< 10 kHz) PDH-locked to a cavity mode, the mode frequency beaten against a reference laser (drift ~0.1 Hz/s). n - 1 from the mode shift, Eq. (2), with the bulk modulus K = 3.3372e10 Pa and mirror-deformation d_1 = 1.6119e-13 Pa^-1 (Opt-1; d_2 = 0 for Opt-2) calibrated at 70 kPa with ARGON against a Fluke PG7601 piston gauge (11 ppm) taking A_eps(Ar) = 4.140686(10) cm^3/mol (Gaiser and Fellmuth 2018, gaiser_2018). Pressure from an Inficon CDGSci manometer calibrated against the optical gauge, u = sqrt((20e-6 p)^2 + (1.5 Pa)^2). Gases 99.9999 %; H2 through a liquid-nitrogen trap. Pressure points 2-100 kPa, several series; the static A_eps from each point through Eqs. (1) and (3), weighted mean (pp. 1-4).
Materials in structured entries: H2, N2, Ne
Dataset quantities: cauchy_moment, molar_refractivity
Contents: 15 datasets; 0 formulas.
Curation notes#
Identity VALIDATED; first page checked (pdf page 1: Phys. Rev. A 111, 012801 (2025), published 7 January 2025). Page numbers are the article pages 1-5 (= pdf pages).
WHAT IS MEASURED AND WHAT IS PRINTED (the same scheme as zhao_2026, whose record explains it at length). The refractometer measures n - 1 at 1566 nm (vacuum). Eq. (1) reduces it to the refractive molar polarization A_eps’(omega) + A_mu; the authors subtract A_mu (Table I; Refs. 32, 33) and convert to the static A_eps with Eq. (3), the electronic dipole sums S(-4), S(-6), S(-8) of Table I (‘S parameters are from Ref. [21]’, Olney et al. 1997, for all four gases). They are not Olney et al.’s own sums but comparison rows of Olney’s Table 3 (olney_1997, curated 2026-09-26): N2 and H2 are Zeiss et al.’s DOSD (zeiss_1977), Ne and Ar Kumar and Meath’s (kumar_1985); the parenthesised uncertainties are not in Olney et al. and are Nie et al.’s own. Only the static A_eps is printed (Table II, the text, the abstract). The datasets A_R_1566_* are RECONSTRUCTED by tools/extract/nie_2025.py, inverting Eq. (3) exactly (see its docstring: the reduced-mass factor applied to H2 with the proton mass, +5 ppm; omitted for N2 and Ne, < 0.1 ppm). Their A_mu convention is that of Rourke (A_mu = chi_M/3, SI): Ar -80.9(6)e-6 cm^3/mol equals rourke_2021’s -8.09(57)e-5, and Ne -29.2(6)e-6 is near lesiuk_2020’s chi_0 converted, -31.7e-6.
WHAT THE STATIC VALUES INCLUDE. As in zhao_2026: the electronic polarizability plus the (negative) infrared response at 1566 nm, which the conversion does not remove; no static vibrational polarizability. N2, Ne and H2 have no infrared-active vibration, so here the static values are the electronic (vibrationally and rotationally averaged, 297.53 K) static polarizabilities. For H2 the value is for normal hydrogen at 297.53 K; the natural D/H ratio ‘should be corrected by -2 x 10^-6’ (p. 4).
NOT INDEPENDENT OF ARGON: the pressure scale (K, d) is calibrated with argon’s A_eps from gaiser_2018 at one point (70 kPa); every result here is relative to it. zhao_2026 in turn calibrates with this paper’s N2 value.
UNCERTAINTY (Table II, ppm; the level is not stated in the table, taken as one standard uncertainty like the paper’s k = 1 gauge uncertainties): T 16, p 25, K 11, purity 1, outgas 0.2/0.9/0.5, frequency and L_cav < 0.1, statistics 9/26/5, A_mu 0.1/0.6/0.2, B_eps 3/<0.1/2, B_T 12/20/4, S(i) 7/1/12 (N2/Ne/H2); totals 36, 46, 35 (each the root sum of squares, checked). The reconstructed A_R keeps all but S(i) and A_mu: 35.2 (N2), 45.6 (Ne), 32.4 (H2) ppm.
COMPARISONS (computed 2026-09-25): H2 static 2.031027(71) is 26 ppm above raj_2018’s normal-H2 static average at 296.15 K (5.4332744 au = 2.030975 cm^3/mol) and 0.00023 above Sun et al.’s 2.03080(12), which omits relativistic and QED terms (the authors estimate 60 ppm, p. 4). Ne static 0.994742(46) is 31 ppm above gaiser_2018’s 0.9947114(24). N2 4.38705(16) is 59 ppm above the Egan et al. value 4.38679(7). The reconstructed Ne A_R(1566) 0.995627(45) is 44 ppm above rourke_2021’s A_R at 1550 nm (0.9956018(34)) moved to 1566 nm with Olney’s sums (0.995583). Lesiuk et al.’s Ne value as quoted, 0.99470(13) cm^3/mol, is 2.66103 au, not lesiuk_2020’s alpha_0 2.66080 au (0.994615 cm^3/mol; 86 ppm lower): the quoted value may include something else (the magnetic term would lower it); not resolved.
Text values not extracted as datasets: Egan et al.’s Ne 0.994598(16) cm^3/mol (p. 4; Nie et al.’s conversion of egan_2019, like the N2 value of Table II); Klopper et al.’s 0.99503(75) (already gaiser_2018/klopper_2004_Ne); the calibration value A_eps(Ar) = 4.140686(10) (gaiser_2018’s). Not extracted: Table I’s B_T and B_eps (Ar -16.1(5), 1.72(11); Ne 11.0(5), -0.0930(5); N2 -5.5(3), 1.12(30); H2 14.1(1), 0.06(10); cm^3/mol and cm^6/mol^2 at about 297.5 K, sources Refs. 34-37 not assigned per gas), the argon column (a calibration input, not a result), the per-pressure points (figures only).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
nie_2025/A_R_1566_N2#
{
"id": "A_R_1566_N2",
"material": "N2",
"file": "N2/nie_2025__A_R_1566_N2.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 297.53
}
}
RECONSTRUCTED (not printed): A_eps’(omega) + A_mu at 1566 nm (vacuum) and 297.53 K, = Table II’s static 4.38705 + (4 pi/3) N_A a0^3 [S(-4) w^2 + S(-6) w^4 + S(-8) w^6] (Table I, Olney’s sums) + A_mu (-52.1e-6), by tools/extract/nie_2025.py. Uncertainty: Table II without S(i) and A_mu, 35.2 ppm, one sigma. Tied to gaiser_2018’s argon A_eps through the pressure calibration.
nie_2025/A_R_1566_Ne#
{
"id": "A_R_1566_Ne",
"material": "Ne",
"file": "Ne/nie_2025__A_R_1566_Ne.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 297.53
}
}
RECONSTRUCTED (not printed), as A_R_1566_N2: 0.994742 + Olney’s dispersion + A_mu (-29.2e-6) at 1566 nm, 297.53 K; 45.6 ppm. 44 ppm above rourke_2021’s 1550 nm A_R moved to 1566 nm (source notes).
nie_2025/A_R_1566_H2#
{
"id": "A_R_1566_H2",
"material": "H2",
"file": "H2/nie_2025__A_R_1566_H2.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 297.53
}
}
RECONSTRUCTED (not printed), as A_R_1566_N2: 2.031027 + (1 + m_e/m_p)^3 x Olney’s dispersion + A_mu (-17.0e-6) at 1566 nm, 297.53 K, normal hydrogen (natural D/H; -2 ppm for pure H2 isotopologue, p. 4); 32.4 ppm.
nie_2025/static_N2#
{
"id": "static_N2",
"material": "N2",
"file": "N2/nie_2025__static_N2.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 297.53
}
}
Table II ‘This work’: A_eps = 4.38705(16) cm^3/mol (36 ppm, k = 1), the static electronic value derived from the 1566 nm measurement with Olney’s sums. Not independent of A_R_1566_N2: a check. zhao_2026 calibrates its cavity with this value. At 297.53 K.
nie_2025/static_Ne#
{
"id": "static_Ne",
"material": "Ne",
"file": "Ne/nie_2025__static_Ne.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 297.53
}
}
Table II ‘This work’: A_eps = 0.994742(46) cm^3/mol (46 ppm), static, from A_R_1566_Ne: a check. 31 ppm above gaiser_2018 (0.7 sigma).
nie_2025/static_H2#
{
"id": "static_H2",
"material": "H2",
"file": "H2/nie_2025__static_H2.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 297.53
}
}
Table II ‘This work’ and Eq. (4): A_eps = 2.031027(71) cm^3/mol at 297.53 K (35 ppm), normal hydrogen, static electronic, from A_R_1566_H2: a check. 26 ppm above raj_2018’s normal-H2 static average at 296.15 K.
nie_2025/egan_2019_N2#
{
"id": "egan_2019_N2",
"material": "N2",
"file": "N2/nie_2025__egan_2019_N2.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "check",
"reproduced_from": [
"egan_2019"
],
"uncertainty": {
"column": true,
"level": "1 sigma"
}
}
Table II ‘Expt.’ (note a, Ref. 40, Egan et al. 2019): ‘The static polarizability according to the value obtained by Egan et al.’ (p. 4), 4.38679(7) cm^3/mol: Nie et al.’s static conversion of egan_2019’s optical A_R, not a printed Egan value. Derived: a check.
nie_2025/gaiser_2018_Ne#
{
"id": "gaiser_2018_Ne",
"material": "Ne",
"file": "Ne/nie_2025__gaiser_2018_Ne.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"gaiser_2018"
],
"uncertainty": {
"column": true,
"level": "1 sigma"
}
}
Table II ‘Expt.’ (note a, Ref. 39): 0.9947114(24) cm^3/mol, identical to gaiser_2018’s molar_polarizability_Ne (DCGT).
nie_2025/hohm_kerl_1990_H2#
{
"id": "hohm_kerl_1990_H2",
"material": "H2",
"file": "H2/nie_2025__hohm_kerl_1990_H2.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"hohm_1990"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table II ‘Expt.’ (note a, Ref. 25, Hohm and Kerl, Mol. Phys. 69, 803 (1990) = hohm_1990): 2.033(4) cm^3/mol. The number itself is not printed in hohm_1990 (its H2 values are temperature fits at 632.99 nm and a 0 K extrapolation); how Nie et al. derived a static molar value from it is not said. Level not stated.
nie_2025/olney_1997_N2#
{
"id": "olney_1997_N2",
"material": "N2",
"file": "N2/nie_2025__olney_1997_N2.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"olney_1997"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table II ‘Theor.’ (note b, Ref. 21): 4.3887(18) cm^3/mol, ‘with an uncertainty of 410 ppm’ (p. 4); a dipole-sum (DOSD) static value. Olney et al. (curated since 2026-09-26 as olney_1997) print no such number: 4.3887 cm^3/mol is 11.7407 au, and their N2 values are 11.75 (Table 3, refined, the Hohm and Kerl 1990 polarizability it was renormalised to: 4.3922 cm^3/mol), 11.74 (Zeiss et al.’s DOSD row: 4.3885), 11.743 (Langhoff and Karplus: 4.3896) and 11.54 (Table 1, unrefined); nor do they print an uncertainty. How Nie et al. obtained 4.3887(18) is not established (checked 2026-09-26).
nie_2025/lesiuk_2020_Ne#
{
"id": "lesiuk_2020_Ne",
"material": "Ne",
"file": "Ne/nie_2025__lesiuk_2020_Ne.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"lesiuk_2020"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table II ‘Theor.’ (note b, Ref. 23): 0.99470(13) cm^3/mol. Does not equal lesiuk_2020’s alpha_0 = 2.66080 au, which is 0.994615 cm^3/mol (86 ppm lower); 0.99470 is 2.66103 au. Not resolved; use lesiuk_2020 itself.
nie_2025/sun_2021_H2#
{
"id": "sun_2021_H2",
"material": "H2",
"file": "H2/nie_2025__sun_2021_H2.csv",
"table": "tbl_2c3bf20e3331",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"D. Sun, Y. P. Zhang, X. J. Wei, L. M. Wang and Z.-C. Yan, Phys. Rev. A 103, 062813 (2021)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"temperature_k": 297.53
}
}
Table II ‘Theor.’ (note b, Ref. 26): 2.03080(12) cm^3/mol at 297.53 K, non-Born-Oppenheimer static polarizabilities of the rotational levels in Hylleraas coordinates, thermally averaged; ‘the contributions from the relativistic and QED effects have not been included’, estimated at 60 ppm (p. 4). The original is not in the library.
nie_2025/olney_moments_N2#
{
"id": "olney_moments_N2",
"material": "N2",
"file": "N2/nie_2025__olney_moments_N2.csv",
"table": "tbl_c8f73c6e439f",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "reproduced",
"reproduced_from": [
"zeiss_1977"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table I: S(-4) 30.11(9), S(-6) 101.8(9), S(-8) 385(6) au (‘S parameters are from Ref. [21]’, Olney et al. 1997). CORRECTED ATTRIBUTION (2026-09-26): these are not Olney et al.’s sums (their own N2 row is 30.02, 100.8, 378.7: olney_1997/moments_N2) but the Zeiss et al. (1977) DOSD row [49] of Olney’s Table 3 (30.11, 101.8, 384.6; olney_1997/zeiss_1977_N2), identical to zeiss_1977/moments_N2 (385 is 384.6 rounded): reproduced_from set to zeiss_1977. The parenthesised uncertainties (0.3, 0.9, 1.6 %) are printed by neither Olney nor Zeiss: Nie et al.’s own.
nie_2025/olney_moments_Ne#
{
"id": "olney_moments_Ne",
"material": "Ne",
"file": "Ne/nie_2025__olney_moments_Ne.csv",
"table": "tbl_c8f73c6e439f",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "reproduced",
"reproduced_from": [
"kumar_1985"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table I: S(-4) 2.886(2), S(-6) 5.063(18), S(-8) 10.86(4) au. Neon has curated ab initio moments (lesiuk_2020, pawlowski_2005): this copy is a check on them. CORRECTED ATTRIBUTION (2026-09-26): Nie et al. cite Olney et al. (Ref. [21]), but these are the Kumar and Meath (1985) DOSD row [54] of Olney’s Table 3 (olney_1997/kumar_1985_Ne), identical to kumar_1985/moments_Ne; Olney et al.’s own neon sums are 2.938, 5.137, 10.95 (olney_1997/moments_Ne). reproduced_from set to kumar_1985. The parenthesised uncertainties are Nie et al.’s own.
nie_2025/olney_moments_H2#
{
"id": "olney_moments_H2",
"material": "H2",
"file": "H2/nie_2025__olney_moments_H2.csv",
"table": "tbl_c8f73c6e439f",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "reproduced",
"reproduced_from": [
"zeiss_1977"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table I: S(-4) 19.96(8), S(-6) 82.94(51), S(-8) 367(4) au. Hydrogen has curated ab initio dispersion (raj_2018, rychlewski_1983): this copy is a check on them. CORRECTED ATTRIBUTION (2026-09-26): Nie et al. cite Olney et al. (Ref. [21]), but these are the Zeiss et al. (1977) DOSD row [49] of Olney’s Table 3 (19.96, 82.94, 367.0; olney_1997/zeiss_1977_H2), identical to zeiss_1977/moments_H2; Olney et al.’s own H2 sums are 20.04, 83.18, 367.0 (olney_1997/moments_H2). reproduced_from set to zeiss_1977. The parenthesised uncertainties are Nie et al.’s own.
Formulas#
No formulas are recorded.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.