millot_1992#
G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger and J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2 and O2-N2”, J. Chem. Phys. 96, 961 (1992)
Source record · Catalogue · Review register
DOI: 10.1063/1.462116
Source kind: measurement
Recorded technique: Stimulated Raman gain spectroscopy (Dijon, p. 2): a frequency-stabilised single-mode Kr-ion probe (1 MHz jitter) and a narrow-band cw dye pump pulse-amplified to 750 kW, polarizations parallel; absolute frequencies by a Michelson wavemeter; a second (reference) cell recorded simultaneously for the differential line-shift measurement. Fundamental Q branch (v = 0 -> 1) of 16O2 at 295-1350 K and 150-1550 Torr (Table I); O2-N2 from dry air taken as 79 % N2, 21 % O2 (p. 5). Each spectrum fitted with Eq. (8): a sum of Galatry profiles with Rosenkranz first-order line mixing (Eq. (7)), the Dicke parameter fixed by Eq. (9), the apparatus function (a Gaussian of HWHM 1.1e-3 cm-1) neglected; the broadening coefficient of each Q(N) from a linear regression of the collisional widths over pressures >= 300 Torr.
Materials in structured entries: O2
Dataset quantities: raman_line_shift, raman_linewidth
Contents: 44 datasets; 6 formulas.
Curation notes#
Identity checked against the first page (the pdf has a publisher cover page: page numbers here are pdf pages, 2-12 = journal pp. 961-971). Material: 16O2, X 3Sigma_g-, rotational levels labelled by N (odd only); each triplet (J = N, N +- 1) is treated as one line (the 1Sigma approximation; the minimum pressure chosen so that the error is small, p. 3). No isotopologue is measured.
WIDTH CONVENTION. Every width is a HALF width at half maximum per atm: p. 4, ‘Gamma_N the collisional half-width at half-maximum (HWHM)’, p. 5, ‘gamma_N = Gamma_N/p represents the line broadening coefficient expressed in cm-1 atm-1’; Tables II, III, VI and VII: ‘HWHM in 10^-3 cm-1 atm-1’. Per atm at the stated temperature (not per amagat), except Table IV’s mean shifts, ‘in density units (mk amagat-1)’, 1 mk = 1e-3 cm-1. The Dicke effect is in the line shape (Galatry), not in the coefficients: the coefficients are the collisional (Lorentzian) part only. The polarized Q branch widths are taken as purely isotropic widths (depolarization ratios 1.8-4.9 %, p. 3).
UNCERTAINTIES. Tables II and III: ‘The uncertainties correspond to twice the standard deviation’ (captions, p. 7; also p. 6). Table IV: ‘one standard deviation’. The theoretical Tables VI-VIII have none. The printed errors of the reproduced columns of Table II (Ouazzany et al.) are as printed.
O2-N2 (Table III and the O2-N2 columns of Table IV) is derived from the air measurements by Eq. (10), gamma_N = C_O2 gamma_N(O2-O2) + C_N2 gamma_N(O2-N2), with the O2-O2 values (p. 6); the reference cell of the shift measurement held pure O2 at its partial pressure, so the O2-N2 shift is measured directly (p. 7).
TABLE I (p. 6), recording conditions (as the image shows; the extraction shifts the temperature cells): O2-O2 295 K 150-460 Torr N 1-9 and 150-1500 Torr N 11-23; 446 K 240-920 Torr N 1-21; 769 K 300-900 Torr N 3-19; 990 K 760-1520 Torr N 1-21; 1317 K 900-1530 Torr N 3-29; 1350 K 760 Torr N 39-55; O2-N2 295 K 740 Torr, 446 K 740 Torr, 990 K 740-1550 Torr, N 1-21.
TABLE IV. Its caption is extracted as a table note (‘Experimental line shifting coefficients (in 1e-3 cm-1 atm-1) for O2-O2 and O2-N2 measured at low pressure. The uncertainties correspond to one standard deviation.’) and the running head as the caption; identified by the image and the text (p. 7, ‘The results are reported in Table IV’). The shift is negative (to lower Raman frequency); ‘of the order of -3.5e-3 cm-1 atm-1 for O2 at 295 K’ (p. 3).
TABLE V (p. 9, not in the extracted tables: a ‘code’ block; page image checked): the inputs of the semiclassical calculation, reproduced from Refs. 33-38 (not extracted): atom-atom e_OO = 0.26e-10 erg A^6/molecule, d_OO = 0.25e-7 erg A^12/molecule, e_NN = 0.25e-10, d_NN = 0.29e-7; Lennard-Jones eps(O2) = 120 K, sigma(O2) = 3.55 A, eps(N2) = 97 K, sigma(N2) = 3.73 A; quadrupole moments Q(O2) = -0.39 D A, Q(N2) = -1.4 D A; vibrational parameters of O2 (1/alpha) d alpha/d xi = 1.32, (1/Q) dQ/d xi = -2, <1|xi|1> - <0|xi|0> = 0.826e-2, a_01 = 1.09e-2, b_01 = -3.3e-2. The semiclassical shifts use an adjustable y = 2 (p. 10).
OTHER TEXT VALUES. The collisional reorientation contribution gamma_elas^ori is about 4e-3 cm-1 atm-1 at room temperature (average over N, p. 7). The Q(N) depolarization ratios (1.8 % for N = 1 to 4.9 % for N = 11) and R = 0.717 are Hill et al.’s (p. 3). For O2, D_m0 = 0.189 cm2 s-1 at 1 atm and 273.15 K (Jost), D = (2/3) D_m and alpha = 1.5 are assumed (p. 5).
FORMULAS (Table IX, p. 10). The fits were checked by recomputing Table II and Table III from Eq. (12), gamma(N) = -sum_{N’ != N} W_{N’N}, with the O2 levels E_N = B N(N+1), B = 1.438 cm-1 (shelton_1987 Table 2; D neglected), odd N to 119, downward rates by detailed balance (scratch, 2026-09-26): see each formula’s check. Eq. (16) as printed, with exp[(E_N’ - E_N>)/kT], violates detailed balance (rho_N W_N’N is not symmetric) and gives widths two to three times Table II’s at 295 K (N = 7: 138 against 45.3 mk/atm, ECS-P); with exp[(E_N - E_N>)/kT] (E_N the initial level) it is symmetric and reproduces the tables (see the ECS formulas): the printed E_N’ is probably a misprint for E_N. The adiabatic factor Omega is not defined in the paper (‘the adiabatic factor proportional to l_c’); the checks assume De Pristo’s form Omega_N = [1 + (omega_{N,N-1} l_c/v)^2/6]^-1 with omega_{N,N-1} = 2 pi c (E_N - E_{N-1}) and v the mean relative speed (8kT/pi mu)^(1/2); with omega from the N -> N-2 spacing, or without the 2 pi, the reproduction is 2-8 times worse.
solprop: its O2 vibrational width, 2933389355.65 Hz/amagat FWHM, is Table II’s Q(7) at 295 K, 45.3 +- 0.8 (2 sigma) x 1e-3 cm-1/atm HWHM, doubled and converted with 1 atm = 0.92593 amagat at 295 K (ideal gas): 2 x 45.3e-3 x 29.9792458e9 / 0.92593 = 2.9334e9. The HWHM-to-FWHM doubling is right.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
millot_1992/table2_295K#
{
"id": "table2_295K",
"material": "O2",
"file": "O2/millot_1992__table2_295K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 295
}
}
Table II (p. 7), 295 K: O2 self-broadening coefficient of the Q(N) lines of the fundamental (v = 0 -> 1), HWHM in 1e-3 cm-1 per atm, 2 sigma. solprop’s O2 vibrational width is the N = 7 value.
millot_1992/table2_446K#
{
"id": "table2_446K",
"material": "O2",
"file": "O2/millot_1992__table2_446K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 446
}
}
Table II (p. 7), 446 K: O2 self-broadening coefficient of the Q(N) lines of the fundamental (v = 0 -> 1), HWHM in 1e-3 cm-1 per atm, 2 sigma.
millot_1992/table2_769K#
{
"id": "table2_769K",
"material": "O2",
"file": "O2/millot_1992__table2_769K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 769
}
}
Table II (p. 7), 769 K: O2 self-broadening coefficient of the Q(N) lines of the fundamental (v = 0 -> 1), HWHM in 1e-3 cm-1 per atm, 2 sigma.
millot_1992/table2_990K#
{
"id": "table2_990K",
"material": "O2",
"file": "O2/millot_1992__table2_990K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 990
}
}
Table II (p. 7), 990 K: O2 self-broadening coefficient of the Q(N) lines of the fundamental (v = 0 -> 1), HWHM in 1e-3 cm-1 per atm, 2 sigma.
millot_1992/table2_1317K#
{
"id": "table2_1317K",
"material": "O2",
"file": "O2/millot_1992__table2_1317K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 1317
}
}
Table II (p. 7), 1317 K: O2 self-broadening coefficient of the Q(N) lines of the fundamental (v = 0 -> 1), HWHM in 1e-3 cm-1 per atm, 2 sigma.
millot_1992/table2_1350K#
{
"id": "table2_1350K",
"material": "O2",
"file": "O2/millot_1992__table2_1350K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 1350
}
}
Table II (p. 7), 1350 K: O2 self-broadening coefficient of the Q(N) lines of the fundamental (v = 0 -> 1), HWHM in 1e-3 cm-1 per atm, 2 sigma. (the fundamental Q branch at 1350 K is measured only for N = 39-55; Table I)
millot_1992/table2_ouazzany_295K#
{
"id": "table2_ouazzany_295K",
"material": "O2",
"file": "O2/millot_1992__table2_ouazzany_295K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"Y. Ouazzany, J. P. Boquillon and B. Lavorel, Can. J. Phys. 65, 1588 (1987)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 295
}
}
Table II (p. 7), column ‘295 K^a’, note a ‘Data from Ref. 5’: high-resolution CARS Q(N) HWHM (N = 1-17) of Ouazzany, Boquillon and Lavorel, as Millot et al. print them; ‘the agreement ... is quite correct ... our data are more accurate’ (p. 6).
millot_1992/table2_anisotropic_295K#
{
"id": "table2_anisotropic_295K",
"material": "O2",
"file": "O2/millot_1992__table2_anisotropic_295K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N) anisotropic (depolarized) component, v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 295
}
}
Table II (p. 7), column ‘295 K^b’, note b ‘Pure anisotropic linewidths’: this paper’s Q(N) widths with crossed pump and probe polarizations (the anisotropic Q-branch component), HWHM in 1e-3 cm-1/atm; ‘the precision of our measurements is not very high’ (p. 3); none for N = 1, 3.
millot_1992/table2_berard_293K#
{
"id": "table2_berard_293K",
"material": "O2",
"file": "O2/millot_1992__table2_berard_293K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"M. Berard, P. Lallemand, J. P. Cebe and M. Giraud, J. Chem. Phys. 78, 672 (1983)"
],
"parameters": {
"transition": "S(N) pure rotational, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 293
}
}
Table II (p. 7), column ‘293 K^c’, note c ‘Experimental data from Ref. 29’: the pure rotational Raman S(N) HWHM of Berard et al. (rows by the N of the lower level), as printed, no errors; compared with this paper’s anisotropic Q widths (p. 7).
millot_1992/table2_hot1_1350K#
{
"id": "table2_hot1_1350K",
"material": "O2",
"file": "O2/millot_1992__table2_hot1_1350K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 1 -> 2, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 1350
}
}
Table II (p. 7), column ‘1350 K^d’, note d ‘First hot band’: the Q(N) self-broadening HWHM of the v = 1 -> 2 band at 1350 K, 2 sigma; ‘no significant systematic differences’ from the fundamental at 1317 K (p. 7).
millot_1992/table2_hot2_1350K#
{
"id": "table2_hot2_1350K",
"material": "O2",
"file": "O2/millot_1992__table2_hot2_1350K.csv",
"table": "tbl_23bcbc0cdebf",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 2 -> 3, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 1350
}
}
Table II (p. 7), column ‘1350 K^e’, note e ‘Second hot band’: Q(N) HWHM of the v = 2 -> 3 band at 1350 K, 2 sigma.
millot_1992/table3_N2_295K#
{
"id": "table3_N2_295K",
"material": "O2",
"file": "O2/millot_1992__table3_N2_295K.csv",
"table": "tbl_7b0c5f5de7ea",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "N2",
"temperature_k": 295
}
}
Table III (p. 7), 295 K: broadening coefficient of the O2 Q(N) lines by N2, HWHM in 1e-3 cm-1/atm (of N2), 2 sigma; derived from the air measurement by Eq. (10) with the O2-O2 values.
millot_1992/table3_N2_446K#
{
"id": "table3_N2_446K",
"material": "O2",
"file": "O2/millot_1992__table3_N2_446K.csv",
"table": "tbl_7b0c5f5de7ea",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "N2",
"temperature_k": 446
}
}
Table III (p. 7), 446 K: broadening coefficient of the O2 Q(N) lines by N2, HWHM in 1e-3 cm-1/atm (of N2), 2 sigma; derived from the air measurement by Eq. (10) with the O2-O2 values.
millot_1992/table3_N2_990K#
{
"id": "table3_N2_990K",
"material": "O2",
"file": "O2/millot_1992__table3_N2_990K.csv",
"table": "tbl_7b0c5f5de7ea",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "N2",
"temperature_k": 990
}
}
Table III (p. 7), 990 K: broadening coefficient of the O2 Q(N) lines by N2, HWHM in 1e-3 cm-1/atm (of N2), 2 sigma; derived from the air measurement by Eq. (10) with the O2-O2 values.
millot_1992/table4_self_295K#
{
"id": "table4_self_295K",
"material": "O2",
"file": "O2/millot_1992__table4_self_295K.csv",
"table": "tbl_84280b026de1",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 295
}
}
Table IV (p. 8), 295 K, O2-O2: collisional shift coefficient of the O2 Q(N) lines, 1e-3 cm-1 per atm, 1 sigma; differential two-cell measurement.
millot_1992/table4_self_446K#
{
"id": "table4_self_446K",
"material": "O2",
"file": "O2/millot_1992__table4_self_446K.csv",
"table": "tbl_84280b026de1",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 446
}
}
Table IV (p. 8), 446 K, O2-O2: collisional shift coefficient of the O2 Q(N) lines, 1e-3 cm-1 per atm, 1 sigma; differential two-cell measurement.
millot_1992/table4_self_990K#
{
"id": "table4_self_990K",
"material": "O2",
"file": "O2/millot_1992__table4_self_990K.csv",
"table": "tbl_84280b026de1",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 990
}
}
Table IV (p. 8), 990 K, O2-O2: collisional shift coefficient of the O2 Q(N) lines, 1e-3 cm-1 per atm, 1 sigma; differential two-cell measurement.
millot_1992/table4_self_1317K#
{
"id": "table4_self_1317K",
"material": "O2",
"file": "O2/millot_1992__table4_self_1317K.csv",
"table": "tbl_84280b026de1",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 1317
}
}
Table IV (p. 8), 1317 K, O2-O2: collisional shift coefficient of the O2 Q(N) lines, 1e-3 cm-1 per atm, 1 sigma; differential two-cell measurement.
millot_1992/table4_N2_295K#
{
"id": "table4_N2_295K",
"material": "O2",
"file": "O2/millot_1992__table4_N2_295K.csv",
"table": "tbl_84280b026de1",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "N2",
"temperature_k": 295
}
}
Table IV (p. 8), 295 K, O2-N2: shift coefficient of the O2 Q(N) lines by N2, 1e-3 cm-1 per atm (of N2), 1 sigma; the reference cell held pure O2 at its partial pressure in air, so the difference is the N2 shift (p. 7).
millot_1992/table4_N2_446K#
{
"id": "table4_N2_446K",
"material": "O2",
"file": "O2/millot_1992__table4_N2_446K.csv",
"table": "tbl_84280b026de1",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "N2",
"temperature_k": 446
}
}
Table IV (p. 8), 446 K, O2-N2: shift coefficient of the O2 Q(N) lines by N2, 1e-3 cm-1 per atm (of N2), 1 sigma; the reference cell held pure O2 at its partial pressure in air, so the difference is the N2 shift (p. 7).
millot_1992/table4_mean_self#
{
"id": "table4_mean_self",
"material": "O2",
"file": "O2/millot_1992__table4_mean_self.csv",
"table": "tbl_84280b026de1",
"quantity": "raman_line_shift",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q branch, v = 0 -> 1, mean over N",
"perturber": "self"
}
}
Table IV (p. 8), last row: ‘Mean value in density units (mk amagat^-1)’ over N, O2-O2, against temperature, 1 sigma. ‘the mean values over N expressed in density units weakly depend on the temperature’ (p. 7).
millot_1992/table4_mean_N2#
{
"id": "table4_mean_N2",
"material": "O2",
"file": "O2/millot_1992__table4_mean_N2.csv",
"table": "tbl_84280b026de1",
"quantity": "raman_line_shift",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q branch, v = 0 -> 1, mean over N",
"perturber": "N2"
}
}
Table IV (p. 8), last row: mean shift over N per amagat, O2-N2, at 295 and 446 K, 1 sigma.
millot_1992/table6_Q_295K#
{
"id": "table6_Q_295K",
"material": "O2",
"file": "O2/millot_1992__table6_Q_295K.csv",
"table": "tbl_6eda03db14cb",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 295
}
}
Table VI (p. 9), 295 K: O2 self-broadening HWHM of Q(N) calculated with the semiclassical theory of Robert and Bonamy (Ref. 12; Eq. (14), parameters of Table V): theory, compared, not fitted.
millot_1992/table6_Q_446K#
{
"id": "table6_Q_446K",
"material": "O2",
"file": "O2/millot_1992__table6_Q_446K.csv",
"table": "tbl_6eda03db14cb",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 446
}
}
Table VI (p. 9), 446 K: O2 self-broadening HWHM of Q(N) calculated with the semiclassical theory of Robert and Bonamy (Ref. 12; Eq. (14), parameters of Table V): theory, compared, not fitted.
millot_1992/table6_Q_769K#
{
"id": "table6_Q_769K",
"material": "O2",
"file": "O2/millot_1992__table6_Q_769K.csv",
"table": "tbl_6eda03db14cb",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 769
}
}
Table VI (p. 9), 769 K: O2 self-broadening HWHM of Q(N) calculated with the semiclassical theory of Robert and Bonamy (Ref. 12; Eq. (14), parameters of Table V): theory, compared, not fitted.
millot_1992/table6_Q_990K#
{
"id": "table6_Q_990K",
"material": "O2",
"file": "O2/millot_1992__table6_Q_990K.csv",
"table": "tbl_6eda03db14cb",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 990
}
}
Table VI (p. 9), 990 K: O2 self-broadening HWHM of Q(N) calculated with the semiclassical theory of Robert and Bonamy (Ref. 12; Eq. (14), parameters of Table V): theory, compared, not fitted.
millot_1992/table6_Q_1317K#
{
"id": "table6_Q_1317K",
"material": "O2",
"file": "O2/millot_1992__table6_Q_1317K.csv",
"table": "tbl_6eda03db14cb",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 1317
}
}
Table VI (p. 9), 1317 K: O2 self-broadening HWHM of Q(N) calculated with the semiclassical theory of Robert and Bonamy (Ref. 12; Eq. (14), parameters of Table V): theory, compared, not fitted.
millot_1992/table6_Q_1350K#
{
"id": "table6_Q_1350K",
"material": "O2",
"file": "O2/millot_1992__table6_Q_1350K.csv",
"table": "tbl_6eda03db14cb",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 1350
}
}
Table VI (p. 9), 1350 K: O2 self-broadening HWHM of Q(N) calculated with the semiclassical theory of Robert and Bonamy (Ref. 12; Eq. (14), parameters of Table V): theory, compared, not fitted.
millot_1992/table6_S_295K#
{
"id": "table6_S_295K",
"material": "O2",
"file": "O2/millot_1992__table6_S_295K.csv",
"table": "tbl_6eda03db14cb",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "S(N) pure rotational, per row",
"width": "hwhm",
"perturber": "self",
"temperature_k": 295
}
}
Table VI (p. 9), column ‘295 K^b’, note b ‘S(N) linewidths’: the semiclassical O2 self-broadening HWHM of the pure rotational S(N) lines at 295 K (rows by the lower N). Theory.
millot_1992/table7_N2_295K#
{
"id": "table7_N2_295K",
"material": "O2",
"file": "O2/millot_1992__table7_N2_295K.csv",
"table": "tbl_6dcaeaf58dd1",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "N2",
"temperature_k": 295
}
}
Table VII (p. 9), 295 K: O2-N2 broadening HWHM of Q(N) calculated with the semiclassical theory (Ref. 12). Theory.
millot_1992/table7_N2_446K#
{
"id": "table7_N2_446K",
"material": "O2",
"file": "O2/millot_1992__table7_N2_446K.csv",
"table": "tbl_6dcaeaf58dd1",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "N2",
"temperature_k": 446
}
}
Table VII (p. 9), 446 K: O2-N2 broadening HWHM of Q(N) calculated with the semiclassical theory (Ref. 12). Theory.
millot_1992/table7_N2_990K#
{
"id": "table7_N2_990K",
"material": "O2",
"file": "O2/millot_1992__table7_N2_990K.csv",
"table": "tbl_6dcaeaf58dd1",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "N2",
"temperature_k": 990
}
}
Table VII (p. 9), 990 K: O2-N2 broadening HWHM of Q(N) calculated with the semiclassical theory (Ref. 12). Theory.
millot_1992/table7_N2_1315K#
{
"id": "table7_N2_1315K",
"material": "O2",
"file": "O2/millot_1992__table7_N2_1315K.csv",
"table": "tbl_6dcaeaf58dd1",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "N2",
"temperature_k": 1315
}
}
Table VII (p. 9), 1315 K: O2-N2 broadening HWHM of Q(N) calculated with the semiclassical theory (Ref. 12). Theory.
millot_1992/table7_N2_2000K#
{
"id": "table7_N2_2000K",
"material": "O2",
"file": "O2/millot_1992__table7_N2_2000K.csv",
"table": "tbl_6dcaeaf58dd1",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"width": "hwhm",
"perturber": "N2",
"temperature_k": 2000
}
}
Table VII (p. 9), 2000 K: O2-N2 broadening HWHM of Q(N) calculated with the semiclassical theory (Ref. 12). Theory.
millot_1992/table8_self_295K#
{
"id": "table8_self_295K",
"material": "O2",
"file": "O2/millot_1992__table8_self_295K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 295
}
}
Table VIII (p. 10), 295 K, (A) pure O2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
millot_1992/table8_N2_295K#
{
"id": "table8_N2_295K",
"material": "O2",
"file": "O2/millot_1992__table8_N2_295K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "N2",
"temperature_k": 295
}
}
Table VIII (p. 10), 295 K, (B) O2-N2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
millot_1992/table8_self_446K#
{
"id": "table8_self_446K",
"material": "O2",
"file": "O2/millot_1992__table8_self_446K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 446
}
}
Table VIII (p. 10), 446 K, (A) pure O2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
millot_1992/table8_N2_446K#
{
"id": "table8_N2_446K",
"material": "O2",
"file": "O2/millot_1992__table8_N2_446K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "N2",
"temperature_k": 446
}
}
Table VIII (p. 10), 446 K, (B) O2-N2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
millot_1992/table8_self_769K#
{
"id": "table8_self_769K",
"material": "O2",
"file": "O2/millot_1992__table8_self_769K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 769
}
}
Table VIII (p. 10), 769 K, (A) pure O2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
millot_1992/table8_N2_769K#
{
"id": "table8_N2_769K",
"material": "O2",
"file": "O2/millot_1992__table8_N2_769K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "N2",
"temperature_k": 769
}
}
Table VIII (p. 10), 769 K, (B) O2-N2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
millot_1992/table8_self_990K#
{
"id": "table8_self_990K",
"material": "O2",
"file": "O2/millot_1992__table8_self_990K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 990
}
}
Table VIII (p. 10), 990 K, (A) pure O2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
millot_1992/table8_N2_990K#
{
"id": "table8_N2_990K",
"material": "O2",
"file": "O2/millot_1992__table8_N2_990K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "N2",
"temperature_k": 990
}
}
Table VIII (p. 10), 990 K, (B) O2-N2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
millot_1992/table8_self_1317K#
{
"id": "table8_self_1317K",
"material": "O2",
"file": "O2/millot_1992__table8_self_1317K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 1317
}
}
Table VIII (p. 10), 1317 K, (A) pure O2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
millot_1992/table8_N2_1317K#
{
"id": "table8_N2_1317K",
"material": "O2",
"file": "O2/millot_1992__table8_N2_1317K.csv",
"table": "tbl_9dc671631d22",
"quantity": "raman_line_shift",
"unit": "cm-1/atm",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q(N), v = 0 -> 1, per row",
"perturber": "N2",
"temperature_k": 1317
}
}
Table VIII (p. 10), 1317 K, (B) O2-N2: Q(N) line-shift coefficient calculated with the semiclassical theory (y = 2), 1e-3 cm-1/atm. Theory.
Formulas#
millot_1992/meg_O2_O2#
{
"id": "meg_O2_O2",
"material": "O2",
"equation": "Eq. (15), p. 10; Table IX (tbl_e1df02577bc9), p. 10",
"printed": "-Re W_N'N = alpha (T/T0)^-N [(1 + a E_N/kT delta)/(1 + a E_N/kT)]^2 exp(-beta E_N'N/kT), N' > N; gamma(N) = -sum_{N' != N} W_N'N (Eq. (12))",
"variable": "T in K, T0 = 295 K; E_N the rotational energy of the (lower) level N, E_N'N = |E_N' - E_N|; a = 1.5 (the paper's choice, p. 10); alpha in mk/atm (1 mk = 1e-3 cm-1): the rates and the HWHM gamma(N) in 1e-3 cm-1 per atm; downward rates by detailed balance",
"state": "pure O2",
"density": "unknown",
"range": "295-1350 K, N 1-55 (the data fitted)",
"coefficients": {
"alpha": "16.70",
"alpha_error": "0.20",
"N": "1.32",
"N_error": "0.01",
"delta": "1.32",
"delta_error": "0.03",
"beta": "1.45",
"beta_error": "0.03",
"a": "1.5",
"sigma": "0.99",
"T0": "295"
},
"check": "Recomputed Table II (56 values, 295-1350 K) from Eqs. (12) and (15) with the O2 levels of B = 1.438 cm-1 (scratch, 2026-09-26): rms 0.78 mk/atm, worst 2.7 (N = 21 at 295 K and N = 55 at 1350 K), against the printed sigma = 0.99. Reproduces the fit."
}
MEG law of Koszykowski et al. (Ref. 14). The +- are the fit errors; sigma is ‘the standard deviation obtained for the whole set of data (all temperatures)’, in mk/atm. ‘The MEG law seems to be the best model’ (p. 11).
millot_1992/meg_O2_N2#
{
"id": "meg_O2_N2",
"material": "O2",
"equation": "Eq. (15), p. 10; Table IX (tbl_e1df02577bc9), p. 10",
"printed": "-Re W_N'N = alpha (T/T0)^-N [(1 + a E_N/kT delta)/(1 + a E_N/kT)]^2 exp(-beta E_N'N/kT), N' > N; gamma(N) = -sum_{N' != N} W_N'N (Eq. (12))",
"variable": "T in K, T0 = 295 K; E_N the rotational energy of the (lower) level N, E_N'N = |E_N' - E_N|; a = 1.5 (the paper's choice, p. 10); alpha in mk/atm (1 mk = 1e-3 cm-1): the rates and the HWHM gamma(N) in 1e-3 cm-1 per atm; downward rates by detailed balance",
"state": "O2 perturbed by N2",
"density": "unknown",
"range": "295-990 K, N 1-21",
"coefficients": {
"alpha": "17.00",
"alpha_error": "0.40",
"N": "1.31",
"N_error": "0.01",
"delta": "1.30",
"delta_error": "0.05",
"beta": "1.41",
"beta_error": "0.05",
"a": "1.5",
"sigma": "0.74",
"T0": "295"
},
"check": "Recomputed Table III (27 values) as for meg_O2_O2 (scratch, 2026-09-26): rms 1.03 mk/atm, worst 2.2, against the printed sigma = 0.74."
}
Fitted to the O2-N2 coefficients of Table III (derived from air by Eq. (10)).
millot_1992/ecs_p_O2_O2#
{
"id": "ecs_p_O2_O2",
"material": "O2",
"equation": "Eqs. (16)-(17), p. 10; Table IX (tbl_e1df02577bc9), p. 10",
"printed": "Re W_N'N = (2N'+1) exp[(E_N' - E_N>)/kT] Omega_N>^2 sum_L (N N' L; 0 0 0)^2 (2L+1) Omega_L^-2 Re W_0L (Eq. (16)), with -Re W_0L = A0 (T/T0)^-N / [L(L+1)]^gamma (ECS-P)",
"variable": "T in K, T0 = 295 K; N> the greater of N and N'; Omega the adiabatic factor 'proportional to the characteristic interaction length l_c' (not defined further); A0 in mk/atm; gamma(N) = -sum W_N'N (Eq. (12)) the HWHM in 1e-3 cm-1/atm",
"state": "pure O2",
"density": "unknown",
"range": "295-1350 K, N 1-55",
"coefficients": {
"A0": "24.50",
"A0_error": "0.80",
"N": "1.01",
"N_error": "0.01",
"l_c": "1.23",
"l_c_error": "0.09",
"gamma": "0.90",
"gamma_error": "0.01",
"sigma": "1.34",
"T0": "295"
},
"check": "Recomputed Table II (56 values) from Eqs. (12), (16), (17) (scratch, 2026-09-26) only after two assumptions: exp[(E_N - E_N>)/kT] for the printed exp[(E_N' - E_N>)/kT] (the printed form breaks detailed balance and gives two to three times the widths at 295 K), and De Pristo's Omega_N = [1 + (omega_{N,N-1} l_c/v)^2/6]^-1, omega_{N,N-1} = 2 pi c (E_N - E_{N-1}), v = (8kT/pi mu)^(1/2), l_c in A: rms 1.27 mk/atm, worst 4.8, against the printed sigma = 1.34."
}
ECS-P of Bonamy et al. (Ref. 16). The l_c unit A is printed.
millot_1992/ecs_p_O2_N2#
{
"id": "ecs_p_O2_N2",
"material": "O2",
"equation": "Eqs. (16)-(17), p. 10; Table IX (tbl_e1df02577bc9), p. 10",
"printed": "Re W_N'N = (2N'+1) exp[(E_N' - E_N>)/kT] Omega_N>^2 sum_L (N N' L; 0 0 0)^2 (2L+1) Omega_L^-2 Re W_0L (Eq. (16)), with -Re W_0L = A0 (T/T0)^-N / [L(L+1)]^gamma (ECS-P)",
"variable": "T in K, T0 = 295 K; N> the greater of N and N'; Omega the adiabatic factor 'proportional to the characteristic interaction length l_c' (not defined further); A0 in mk/atm; gamma(N) = -sum W_N'N (Eq. (12)) the HWHM in 1e-3 cm-1/atm",
"state": "O2 perturbed by N2",
"density": "unknown",
"range": "295-990 K, N 1-21",
"coefficients": {
"A0": "23.00",
"A0_error": "0.70",
"N": "1.03",
"N_error": "0.02",
"l_c": "1.60",
"l_c_error": "0.20",
"gamma": "0.87",
"gamma_error": "0.01",
"sigma": "0.99",
"T0": "295"
},
"check": "Recomputed Table III (27 values) with the assumptions of ecs_p_O2_O2 and mu = 14.93 amu (scratch, 2026-09-26): rms 1.72 mk/atm, worst 4.3, against the printed sigma = 0.99."
}
Fitted to Table III.
millot_1992/ecs_ep_O2_O2#
{
"id": "ecs_ep_O2_O2",
"material": "O2",
"equation": "Eqs. (16), (18), p. 10; Table IX (tbl_e1df02577bc9), p. 10",
"printed": "Re W_N'N = (2N'+1) exp[(E_N' - E_N>)/kT] Omega_N>^2 sum_L (N N' L; 0 0 0)^2 (2L+1) Omega_L^-2 Re W_0L (Eq. (16)), with -Re W_0L = A0 (T/T0)^-N / [L(L+1)]^gamma exp(-beta E_L/kT) (ECS-EP)",
"variable": "T in K, T0 = 295 K; N> the greater of N and N'; Omega the adiabatic factor 'proportional to the characteristic interaction length l_c' (not defined further); A0 in mk/atm; gamma(N) = -sum W_N'N (Eq. (12)) the HWHM in 1e-3 cm-1/atm",
"state": "pure O2",
"density": "unknown",
"range": "295-1350 K, N 1-55",
"coefficients": {
"A0": "19.08",
"A0_error": "0.52",
"N": "1.02",
"N_error": "0.01",
"l_c": "4.26",
"l_c_error": "0.49",
"gamma": "0.81",
"gamma_error": "0.01",
"beta": "0.056",
"beta_error": "0.003",
"sigma": "1.11",
"T0": "295"
},
"check": "Recomputed Table II (56 values) with the assumptions of ecs_p_O2_O2 (scratch, 2026-09-26): rms 1.01 mk/atm, worst 3.8, against the printed sigma = 1.11."
}
ECS-EP (Refs. 13, 17, 39): E_L the rotational energy of level L. The l_c unit A is printed.
millot_1992/ecs_ep_O2_N2#
{
"id": "ecs_ep_O2_N2",
"material": "O2",
"equation": "Eqs. (16), (18), p. 10; Table IX (tbl_e1df02577bc9), p. 10",
"printed": "Re W_N'N = (2N'+1) exp[(E_N' - E_N>)/kT] Omega_N>^2 sum_L (N N' L; 0 0 0)^2 (2L+1) Omega_L^-2 Re W_0L (Eq. (16)), with -Re W_0L = A0 (T/T0)^-N / [L(L+1)]^gamma exp(-beta E_L/kT) (ECS-EP)",
"variable": "T in K, T0 = 295 K; N> the greater of N and N'; Omega the adiabatic factor 'proportional to the characteristic interaction length l_c' (not defined further); A0 in mk/atm; gamma(N) = -sum W_N'N (Eq. (12)) the HWHM in 1e-3 cm-1/atm",
"state": "O2 perturbed by N2",
"density": "unknown",
"range": "295-990 K, N 1-21",
"coefficients": {
"A0": "20.13",
"A0_error": "0.62",
"N": "1.04",
"N_error": "0.02",
"l_c": "3.86",
"l_c_error": "0.73",
"gamma": "0.81",
"gamma_error": "0.01",
"beta": "0.050",
"beta_error": "0.002",
"sigma": "0.79",
"T0": "295"
},
"check": "Recomputed Table III (27 values) with the assumptions of ecs_p_O2_O2 and mu = 14.93 amu (scratch, 2026-09-26): rms 1.14 mk/atm, worst 2.9, against the printed sigma = 0.79."
}
The O2-N2 l_c is printed ‘3.86 +- 0.73’ without the unit A the other l_c carry (image checked); taken as A.
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.