sneep_2005#
M. Sneep and W. Ubachs, J. Quant. Spectrosc. Radiat. Transfer 92, 293 (2005)
Source record · Catalogue · Review register
DOI: 10.1016/j.jqsrt.2004.07.025
Source kind: measurement
Recorded technique: Pulsed cavity ring-down extinction (mirror reflectivity above 99.98 %, 82 cm cavity), the decay rate recorded during a 15 min pressure ramp from vacuum to about 1 bar; the cross section is the slope of the loss rate against the density (Eq. 8), the density from a capacitance manometer (2 hPa) and the cell temperature (about 20 C) by the ideal gas law (‘a negligible error of < 0.5%’, p. 7). Nd:YAG-pumped dye laser (0.05 cm^-1) at 470-490 nm (Ar, N2) and 470-570 nm (CO2), and the unseeded Nd:YAG second harmonic at 18 788.4 +- 0.4 cm^-1 (532.2 nm, 1 cm^-1 bandwidth) for Ar, N2, CO, CO2, CH4, N2O, SF6 and O2 (pp. 5-7, 12).
Materials in structured entries: Ar, CH4, CO, CO2, N2, N2O, O2, SF6
Dataset quantities: rayleigh_cross_section
Contents: 15 datasets; 19 formulas.
Curation notes#
The measured quantity is the total extinction, taken to be the Rayleigh scattering cross section (all Cabannes, Brillouin, Raman and wing contributions; no absorption assumed), per molecule. Comparison ‘n-based’ cross sections use Eq. (2), sigma = 24 pi^3 nu^4 / N^2 ((n^2 - 1)/(n^2 + 2))^2 F_k(nu), with the refractive index at 15 C and 1013 hPa and N = 25.47e18 cm^-3 (the ideal-gas density there, p. 8). Forward and backward scattering kept in the cavity bias the result low by ‘less than 0.01%’ (p. 7).
Datasets: the 532.2 nm cross sections of Table 2 (measured, primary; n-based, check) and oxygen’s Rayleigh part from a three-component fit (text, p. 15). The wavelength-resolved Ar, N2, CO2 data (13, 23 and 47 new frequencies, with earlier Naus and Ubachs 2000 data) are shown in Figs. 4 and 5 only and are not extracted; Table 1 gives power-law fits to them (formulas *_power_*).
Carbon monoxide (section 5.1, pp. 12-13; Table 2): purity 99.997 %, three pressure ramps; measured 6.19 (0.4) against n-based 6.82 x 10^-27 cm^2, 9 % low, one of the ‘somewhat larger discrepancies’ of the abstract. Table 2’s (n - 1) = 325e-6 is from the authors’ Eq. (17), a fit to Smith et al.’s 38 values (smith_1976 Table VII, both the measured and the interpolated cells), and F_k = 1.016 from Bridge and Buckingham’s rho_p = 0.0048 at 632.8 nm (Eq. 7 gives 1.0161), taken as wavelength-independent after Oddershede and Svendsen (1982). Eq. (2) with 325e-6 and 1.016 gives 6.817e-27 (printed 6.82; checked 2026-09-25).
Table 2’s (n - 1) x 10^6 at 15 C, 101 325 Pa, from the formulas below, are Ar 268, N2 284, CO2 427, CH4 481, N2O 483, SF6 733; its F_k are Ar 1, N2 1.035, CO2 1.145, CH4 1.000, N2O 1.225, SF6 1.000. With these, Eq. (2) reproduces the n-based column (Ar 4.561, N2 5.298, CO2 13.31, CH4 14.684, N2O 18.182, SF6 34.108 x 10^-27 cm^2 against 4.56, 5.30, 13.29, 14.69, 18.19, 34.1; checked 2026-09-25).
The measured values lie below the n-based ones by 2.5-4 % for Ar, N2 and CO2 at 532.2 nm and by up to 15 % for CH4 (‘We do not have an explanation for the obtained differences’, p. 14); over 470-645 nm Ar and N2 agree with the n-based values to 1 % on average and CO2 is 3.9 % low (Table 1). Purities (Table 2): Ar 99.999, N2 99.9, CO2 99.7, CH4 99.5, N2O 99.7, SF6 99.8 %. Pressure ramps: 3, 3, 4, 3, 2, 2.
Oxygen at 532.2 nm shows a quadratic density dependence from the O2-O2 collision-induced absorption peaking at 532.2 nm (Eq. 22); the three-component fit gives sigma_R = (4.50 +- 0.15) x 10^-27 cm^2 (p. 15). With the Rayleigh part fixed at the n-based value, sigma_CIA = (1.01 +- 0.03) x 10^-46 cm^5 molecule^-2 (not extracted; no quantity). The n-based oxygen value is printed ‘4066 x 10^-27 cm^2’ (p. 16, page image checked), evidently 4.066 x 10^-27; it is not reproduced by Eqs. (23) and (24) (see o2_eq23).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
sneep_2005/rayleigh_O2#
{
"id": "rayleigh_O2",
"material": "O2",
"table": "text",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
}
}
1 inline points in the source record.
p. 15: ‘A three-component fit results in a value (4.50 +- 0.15) x 10^-27 cm^2’, the Rayleigh (linear-in-density) part at 532.2 nm with the collision-induced absorption fitted as a quadratic term; level not stated. No King factor is attached to the measured value; Bates’s F_k of Eq. (24) is about 1.10 here.
sneep_2005/rayleigh_Ar#
{
"id": "rayleigh_Ar",
"material": "Ar",
"file": "Ar/sneep_2005__rayleigh_Ar.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"king_factor": 1.0
}
}
Table 2, measured extinction cross section at 18 788.4 +- 0.4 cm^-1 (532.2 nm), the total over all scattering channels (absorption assumed absent), averaged over the pressure ramps; +- in parentheses is one sigma. king_factor is Table 2’s F_k (1), the factor of the n-based comparison: unity for the spherical atom (p. 8). Table 1’s Ar power-law fit to the 470-490 nm and earlier 555-645 nm data (Figs. 4-5; figures only) agrees with the n-based values to 0.4 % on average.
sneep_2005/rayleigh_N2#
{
"id": "rayleigh_N2",
"material": "N2",
"file": "N2/sneep_2005__rayleigh_N2.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"king_factor": 1.035
}
}
Table 2, measured extinction cross section at 18 788.4 +- 0.4 cm^-1 (532.2 nm), the total over all scattering channels (absorption assumed absent), averaged over the pressure ramps; +- in parentheses is one sigma. king_factor is Table 2’s F_k (1.035), the factor of the n-based comparison: Bates’s Eq. (12).
sneep_2005/rayleigh_CO#
{
"id": "rayleigh_CO",
"material": "CO",
"file": "CO/sneep_2005__rayleigh_CO.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"king_factor": 1.016
}
}
Table 2, measured extinction cross section at 18 788.4 +- 0.4 cm^-1 (532.2 nm), the total over all scattering channels (absorption assumed absent), averaged over three pressure ramps; +- in parentheses is one sigma. king_factor is Table 2’s F_k (1.016), the factor of the n-based comparison: from Bridge and Buckingham’s depolarization ratio 0.0048 at 632.8 nm (p. 13). 9 % below the n-based value, whose n - 1 is an extrapolation of a fit to 168-288 nm data (co_eq17).
sneep_2005/rayleigh_CO2#
{
"id": "rayleigh_CO2",
"material": "CO2",
"file": "CO2/sneep_2005__rayleigh_CO2.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"king_factor": 1.145
}
}
Table 2, measured extinction cross section at 18 788.4 +- 0.4 cm^-1 (532.2 nm), the total over all scattering channels (absorption assumed absent), averaged over the pressure ramps; +- in parentheses is one sigma. king_factor is Table 2’s F_k (1.145), the factor of the n-based comparison: the authors’ Eq. (14), fitted to Alms et al.’s depolarization ratios. CO2’s measured values over 470-570 nm (figures only) lie 3.9 % below the n-based ones on average (Table 1).
sneep_2005/rayleigh_CH4#
{
"id": "rayleigh_CH4",
"material": "CH4",
"file": "CH4/sneep_2005__rayleigh_CH4.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"king_factor": 1.0
}
}
Table 2, measured extinction cross section at 18 788.4 +- 0.4 cm^-1 (532.2 nm), the total over all scattering channels (absorption assumed absent), averaged over the pressure ramps; +- in parentheses is one sigma. king_factor is Table 2’s F_k (1.000), the factor of the n-based comparison: assumed unity: CCl4’s depolarization, rho_p < 0.2e-3 (Bridge and Buckingham), taken for CH4 by symmetry (p. 14). 15 % below the n-based value, which the authors cannot explain (p. 14).
sneep_2005/rayleigh_N2O#
{
"id": "rayleigh_N2O",
"material": "N2O",
"file": "N2O/sneep_2005__rayleigh_N2O.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"king_factor": 1.225
}
}
Table 2, measured extinction cross section at 18 788.4 +- 0.4 cm^-1 (532.2 nm), the total over all scattering channels (absorption assumed absent), averaged over the pressure ramps; +- in parentheses is one sigma. king_factor is Table 2’s F_k (1.225), the factor of the n-based comparison: from the authors’ Eq. (19) fit of Alms et al.’s depolarization ratios.
sneep_2005/rayleigh_SF6#
{
"id": "rayleigh_SF6",
"material": "SF6",
"file": "SF6/sneep_2005__rayleigh_SF6.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"king_factor": 1.0
}
}
Table 2, measured extinction cross section at 18 788.4 +- 0.4 cm^-1 (532.2 nm), the total over all scattering channels (absorption assumed absent), averaged over the pressure ramps; +- in parentheses is one sigma. king_factor is Table 2’s F_k (1.000), the factor of the n-based comparison: unity: rho_p < 0.2e-3 (Bridge and Buckingham, p. 14).
sneep_2005/n_based_Ar#
{
"id": "n_based_Ar",
"material": "Ar",
"file": "Ar/sneep_2005__n_based_Ar.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "check",
"parameters": {
"king_factor": 1.0
}
}
Table 2, n-based cross section: Eq. (2) with N = 25.47e18 cm^-3, F_k = 1 and Eq. (9) (Peck and Fisher). Not a measurement.
sneep_2005/n_based_N2#
{
"id": "n_based_N2",
"material": "N2",
"file": "N2/sneep_2005__n_based_N2.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "check",
"parameters": {
"king_factor": 1.035
}
}
Table 2, n-based cross section: Eq. (2) with N = 25.47e18 cm^-3, F_k = 1.035 and Eq. (10) (Peck and Khanna). Not a measurement.
sneep_2005/n_based_CO#
{
"id": "n_based_CO",
"material": "CO",
"file": "CO/sneep_2005__n_based_CO.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "check",
"parameters": {
"king_factor": 1.016
}
}
Table 2, n-based cross section: Eq. (2) with N = 25.47e18 cm^-3, F_k = 1.016 and n - 1 = 325e-6 from Eq. (17) (the authors’ fit to Smith et al. 1976, extrapolated to 532 nm; see co_eq17). Not a measurement.
sneep_2005/n_based_CO2#
{
"id": "n_based_CO2",
"material": "CO2",
"file": "CO2/sneep_2005__n_based_CO2.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "check",
"parameters": {
"king_factor": 1.145
}
}
Table 2, n-based cross section: Eq. (2) with N = 25.47e18 cm^-3, F_k = 1.145 and Eq. (13) (Bideau-Mehu et al. 1973, as corrected by the authors; see co2_eq13). Not a measurement.
sneep_2005/n_based_CH4#
{
"id": "n_based_CH4",
"material": "CH4",
"file": "CH4/sneep_2005__n_based_CH4.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "check",
"parameters": {
"king_factor": 1.0
}
}
Table 2, n-based cross section: Eq. (2) with N = 25.47e18 cm^-3, F_k = 1.000 and Eq. (18) (the authors’ fit to Hohm 1993). Not a measurement.
sneep_2005/n_based_N2O#
{
"id": "n_based_N2O",
"material": "N2O",
"file": "N2O/sneep_2005__n_based_N2O.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "check",
"parameters": {
"king_factor": 1.225
}
}
Table 2, n-based cross section: Eq. (2) with N = 25.47e18 cm^-3, F_k = 1.225 and Eq. (20) (the authors’ fit to Alms et al.). Not a measurement.
sneep_2005/n_based_SF6#
{
"id": "n_based_SF6",
"material": "SF6",
"file": "SF6/sneep_2005__n_based_SF6.csv",
"table": "tbl_f4af3ec06557",
"quantity": "rayleigh_cross_section",
"unit": "cm2",
"scale": 1e-27,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "check",
"parameters": {
"king_factor": 1.0
}
}
Table 2, n-based cross section: Eq. (2) with N = 25.47e18 cm^-3, F_k = 1.000 and Eq. (21) (the authors’ two-point fit to Vukovic et al.). Not a measurement.
Formulas#
sneep_2005/ar_eq9#
{
"id": "ar_eq9",
"material": "Ar",
"equation": "Eq. (9), p. 8",
"printed": "(n - 1) x 10^8 = 6432.135 + 286.06021 x 10^12 / (14.4 x 10^9 - (nu/cm^-1)^2)",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "real",
"range": "5000-33000 cm^-1 (as stated)",
"coefficients": {
"A": "6432.135",
"B": "286.06021e12",
"C": "14.4e9"
},
"reproduced_from": [
"peck_1964"
],
"check": "Identical to peck_1964's 15 C formula (643.2135 + 286060.21/(144 - sigma^2), x 10^-7) rewritten in cm^-1; gives (n - 1) = 267.97e-6 at 18 788.4 cm^-1 (Table 2: 268). Checked 2026-09-25."
}
Peck and Fisher’s formula is for the real gas at 15 C; the authors use it with the ideal-gas N = 25.47e18 cm^-3 (a 0.1 % inconsistency in n - 1).
sneep_2005/n2_eq10#
{
"id": "n2_eq10",
"material": "N2",
"equation": "Eq. (10), p. 10",
"printed": "(n - 1) x 10^8 = 6498.2 + 307.43305 x 10^12 / (14.4 x 10^9 - (nu/cm^-1)^2), 4860 cm^-1 < nu < 21360 cm^-1",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "4860-21360 cm^-1 (468-2058 nm)",
"coefficients": {
"A": "6498.2",
"B": "307.43305e12",
"C": "14.4e9"
},
"reproduced_from": [
"peck_1966"
],
"check": "It is Peck and Khanna's 0 C formula (peck_1966 eq4: 6855.200, 3243157.0) scaled by the ideal-gas ratio 273.15/288.15: B = 307.43305e12 exactly, A = 6498.34 (printed 6498.2). Gives 283.84e-6 at 18 788.4 cm^-1 (Table 2: 284). Checked 2026-09-25."
}
‘after scaling to 15 C and 1013 hPa’ (p. 10): the scaling is the ideal-gas one from 0 C, so the formula is for the ideal-gas density 25.47e18 cm^-3, not Peck and Khanna’s own (real-gas) 15 C formula eq3.
sneep_2005/n2_eq11#
{
"id": "n2_eq11",
"material": "N2",
"equation": "Eq. (11), p. 10",
"printed": "(n - 1) x 10^8 = 5677.465 + 318.81874 x 10^12 / (14.4 x 10^9 - (nu/cm^-1)^2), 21360 cm^-1 < nu < 39370 cm^-1",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "21360-39370 cm^-1 (254-468 nm)",
"coefficients": {
"A": "5677.465",
"B": "318.81874e12",
"C": "14.4e9"
},
"reproduced_from": [
"D. R. Bates, Planet. Space Sci. 32, 785 (1984)"
],
"check": "Not used for Table 2 (outside its range); also quoted by he_2021 and wilmouth_2020 (N2_table1)."
}
Bates’s interpolation between Peck and Khanna and Abjean et al.’s ultraviolet data.
sneep_2005/n2_king_eq12#
{
"id": "n2_king_eq12",
"material": "N2",
"equation": "Eq. (12), p. 10",
"printed": "F_k(nu) = 1.034 + 3.17 x 10^-12 (nu/cm^-1)^2",
"variable": "nu: vacuum wavenumber in cm^-1",
"range": "not stated",
"coefficients": {
"a": "1.034",
"b": "3.17e-12"
},
"reproduced_from": [
"D. R. Bates, Planet. Space Sci. 32, 785 (1984)"
],
"check": "Gives 1.0352 at 18 788.4 cm^-1 (Table 2: 1.035). Checked 2026-09-25."
}
A King correction factor, not a refractive index. Based on Alms et al. (alms_1975), Bridge and Buckingham (1966) and Oddershede and Svendsen (1982).
sneep_2005/co2_eq13#
{
"id": "co2_eq13",
"material": "CO2",
"equation": "Eq. (13), p. 10",
"printed": "(n - 1) = 1.1427 x 10^6 (5799.25/((128908.9)^2 - (nu/cm^-1)^2) + 120.05/((89223.8)^2 - (nu/cm^-1)^2) + 5.3334/((75037.5)^2 - (nu/cm^-1)^2) + 4.3244/((67837.7)^2 - (nu/cm^-1)^2) + 0.1218145 x 10^-4/((2418.136)^2 - (nu/cm^-1)^2))",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "the ultraviolet and visible (Bideau-Mehu et al. 1973; not stated here)",
"coefficients": {
"scale": "1.1427e6",
"B1": "5799.25",
"nu1": "128908.9",
"B2": "120.05",
"nu2": "89223.8",
"B3": "5.3334",
"nu3": "75037.5",
"B4": "4.3244",
"nu4": "67837.7",
"B5": "0.1218145e-4",
"nu5": "2418.136"
},
"reproduced_from": [
"A. Bideau-Mehu, Y. Guern, R. Abjean and A. Johannin-Gilles, Opt. Commun. 9, 432 (1973)"
],
"check": "As printed (1.1427 x 10^6, page image checked) it gives n - 1 = 0.428 at 18 788.4 cm^-1, 1000 times too large. With 1.1427 x 10^3 it gives 427.79e-6 (Table 2: 427) and, with F_k = 1.145, sigma = 13.31e-27 cm^2 (Table 2: 13.29). The scale factor is misprinted: read 10^3 (427.79e-6 rounds to 428, not Table 2's 427: Sneep's own n - 1 was about 427.5e-6; He et al. 2021's 1.1427 x 10^11 on (n - 1) x 10^8 and all 22 of Ityaksov's CO2 values confirm the 10^3 reading, (second reading, 2026-09-25; TC-157)). Checked 2026-09-25."
}
‘Their article contains a typographical error, and the corrected formula, scaled to 15 C and 1013 hPa, yields’ (p. 10): the authors’ correction of the 1973 formula, itself misprinted here in the power of ten. The 2418.136 cm^-1 term is CO2’s infrared bands. A second misprint (found against the 1973 original, bideau_mehu_1973; TC-167): the infrared numerator 0.1218145 x 10^-4 should be 1000 times the 1973 numerator, about 0.128 (the 1973 paper prints 1.218145e-4 for Old et al.’s 1.28154e-4). As printed here the infrared term vanishes; with 0.128154 it is -0.42e-6 at 18 788.4 cm^-1 and -5.1e-6 at 1.69 um (computed 2026-09-25). With it the formula gives 427.37e-6 at 18 788.4 cm^-1, which rounds to Table 2’s 427 where the printed form’s 427.79e-6 does not (see check): Sneep and Ubachs computed with the term, and only their printed copy lost it. ityaksov_2008_co2 copies this form.
sneep_2005/co2_king_eq14#
{
"id": "co2_king_eq14",
"material": "CO2",
"equation": "Eq. (14), p. 10",
"printed": "F_k(nu) = (1.1364 +- 0.0005) + (25.3 +- 1.5) x 10^-12 (nu/cm^-1)^2",
"variable": "nu: vacuum wavenumber in cm^-1",
"range": "the range of Alms et al.'s depolarization ratios (4579-6471 A)",
"coefficients": {
"a": "1.1364",
"b": "25.3e-12"
},
"check": "Gives 1.1453 at 18 788.4 cm^-1 (Table 2: 1.145). 'The differences between (Eq. 14) and the measured King correction factors are less than 0.5%' (p. 10). Checked 2026-09-25."
}
The authors’ fit of Bates’s N2 model function to King factors computed with Eq. (7) from Alms et al.’s depolarization ratios (alms_1975, Table I; Fig. 7).
sneep_2005/co_eq17#
{
"id": "co_eq17",
"material": "CO",
"equation": "Eq. (17), p. 12",
"printed": "(n - 1) x 10^8 = (22 851 +- 200) + (0.456 +- 0.01) x 10^12 / ((71 427 +- 200)^2 - (nu/cm^-1)^2)",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "168-288 nm (Smith et al.'s data); extrapolated to 532 nm for Table 2, 'rather far outside the range of the measurements' (p. 12)",
"coefficients": {
"A": "22851",
"B": "0.456e12",
"C": "71427"
},
"reproduced_from": [
"smith_1976"
],
"check": "As printed (equation image checked) it gives n - 1 = 229.5e-6 at 18 788.4 cm^-1, not Table 2's 325e-6, and 231.5e-6 at 167.2 nm against Smith's 532.0e-6 (scaled to 15 C): the numerator is 100 times too small. With 0.456 x 10^14 it gives 324.53e-6 at 18 788.4 cm^-1 (Table 2: 325) and follows smith_1976's experiment_CO, scaled from 0 C to 15 C by 273.15/288.15, to within -0.83 % to +0.26 % over 167-288 nm (within the stated ~2 %). Read the numerator as 0.456 x 10^14. The n-based 6.82e-27 needs n - 1 = 325.1e-6; 324.53e-6 gives 6.80e-27, a 0.3 % gap within the rounding of the printed coefficients. Checked 2026-09-25."
}
The authors’ fit of the N2/Ar functional form to Smith et al.’s 38 CO values (Fig. 6), ‘scaled to 15 C and 1013 hPa, or a density of 25.47e18 cm^-3’ (p. 12): an ideal-gas rescaling of Smith’s real-gas 0 C values, as for Eq. (10). ‘Within the range of the measurements, the accuracy of n - 1 is estimated to be ~2%’; the authors note that Smith et al. did not fit a dispersion relation themselves. Not independent of smith_1976 (which includes the Lagrange-interpolated cells among the 38).
sneep_2005/ch4_eq18#
{
"id": "ch4_eq18",
"material": "CH4",
"equation": "Eq. (18), p. 14",
"printed": "(n - 1) x 10^8 = (46662 +- 13) + (4.02 +- 0.03) x 10^-6 (nu/cm^-1)^2",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "325-633 nm (Hohm's data)",
"coefficients": {
"a": "46662",
"b": "4.02e-6"
},
"reproduced_from": [
"U. Hohm, Mol. Phys. 78, 929 (1993)"
],
"check": "Gives 480.81e-6 at 18 788.4 cm^-1 (Table 2: 481). Checked 2026-09-25."
}
The authors’ fit to Hohm’s polarizabilities (Fig. 6), converted to n - 1 at N = 25.47e18 cm^-3. ‘The accuracy of this equation is estimated to be better than 4%’ (p. 14). Not independent of Hohm 1993 (not in the library).
sneep_2005/n2o_rho_eq19#
{
"id": "n2o_rho_eq19",
"material": "N2O",
"equation": "Eq. (19), p. 14",
"printed": "rho_p = (0.0577 +- 0.0007) + (11.8 +- 2) x 10^-12 (nu/cm^-1)^2",
"variable": "nu: vacuum wavenumber in cm^-1",
"range": "4579-6471 A (Alms et al.)",
"coefficients": {
"a": "0.0577",
"b": "11.8e-12"
},
"check": "Gives rho_p = 0.06187 at 18 788.4 cm^-1 and, with Eq. (7), F_k = 1.2248 (Table 2: 1.225). Checked 2026-09-25."
}
The depolarization ratio for polarized light, fitted to Alms et al. (alms_1975); F_k = (3 + 6 rho_p)/(3 - 4 rho_p) (Eq. 7).
sneep_2005/n2o_eq20#
{
"id": "n2o_eq20",
"material": "N2O",
"equation": "Eq. (20), p. 14",
"printed": "(n - 1) x 10^8 = (46890 +- 85) + (4.12 +- 0.2) x 10^-6 (nu/cm^-1)^2",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "4579-6471 A (Alms et al.)",
"coefficients": {
"a": "46890",
"b": "4.12e-6"
},
"reproduced_from": [
"alms_1975"
],
"check": "Gives 483.44e-6 at 18 788.4 cm^-1 (Table 2: 483). Checked 2026-09-25."
}
Fitted to Alms et al.’s polarizabilities, which are themselves Landolt-Bornstein’s refractive indices (see alms_1975): not an independent refractive-index source.
sneep_2005/sf6_eq21#
{
"id": "sf6_eq21",
"material": "SF6",
"equation": "Eq. (21), p. 14",
"printed": "(n - 1) x 10^8 = 71517 + 4.996 x 10^-6 (nu/cm^-1)^2",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "633-1300 nm (two points); 'an extrapolation to short wavelength only provides a crude approximation' (p. 14)",
"coefficients": {
"a": "71517",
"b": "4.996e-6"
},
"reproduced_from": [
"vukovic_1996"
],
"check": "Gives 732.81e-6 at 18 788.4 cm^-1 (Table 2: 733). Checked 2026-09-25."
}
Two constants from Vukovic et al.’s 632.99 and 1300 nm values, rescaled to 15 C (how is not stated).
sneep_2005/o2_eq23#
{
"id": "o2_eq23",
"material": "O2",
"equation": "Eq. (23), p. 16",
"printed": "(n - 1) x 10^8 = 20564.8 + 24.80899 / (4.09 x 10^9 - (nu/cm^-1)^2), 546 > lambda_vac > 288 nm",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_0C",
"density": "ideal",
"range": "288-546 nm (vacuum)",
"coefficients": {
"A": "20564.8",
"B": "24.80899",
"C": "4.09e9"
},
"reproduced_from": [
"D. R. Bates, Planet. Space Sci. 32, 785 (1984)"
],
"check": "As printed (page image checked) the second term is negligible (7e-9); the numerator lacks a factor 10^12: he_2021 quotes the same formula with 2.480899 x 10^13, which gives n - 1 = 272.0e-6 at 18 788.4 cm^-1. Neither version reproduces the n-based oxygen cross section the paper prints ('4066 x 10^-27', i.e. 4.066e-27 cm^2): with Eq. (24) and N = 25.47e18 they give 2.96e-27 (as printed) and 5.18e-27 (with 10^12), and 4.66e-27 with he_2021's N = 2.68678e19 at 0 C. Not resolved. Checked 2026-09-25."
}
The paper does not say to what state Eq. (23) refers; he_2021 records Bates’s oxygen formula at 273.15 K and 1013.25 hPa, which is taken here.
sneep_2005/o2_king_eq24#
{
"id": "o2_king_eq24",
"material": "O2",
"equation": "Eq. (24), p. 16",
"printed": "F_k(nu) = 1.096 + 1.385 x 10^-11 (nu/cm^-1)^2 + 1.448 x 10^-20 (nu/cm^-1)^2",
"variable": "nu: vacuum wavenumber in cm^-1",
"range": "not stated",
"coefficients": {
"a": "1.096",
"b": "1.385e-11",
"c": "1.448e-20"
},
"reproduced_from": [
"D. R. Bates, Planet. Space Sci. 32, 785 (1984)"
],
"check": "The third term's exponent is printed 2 (page image checked); a second nu^2 term would merge with the first, so it is presumably nu^4 (he_2021 quotes nu^4, with a leading 1.09). With nu^4: F_k = 1.1027 at 18 788.4 cm^-1. Checked 2026-09-25."
}
sneep_2005/ar_power_exp#
{
"id": "ar_power_exp",
"material": "Ar",
"equation": "Eq. (15) with Table 1, p. 11",
"printed": "sigma = sigma_bar (nu/cm^-1)^(4 + delta); sigma_bar_exp/10^-47 = 14.21(8), delta_exp = 0.0968(5)",
"variable": "nu: vacuum wavenumber in cm^-1; sigma in cm^2",
"range": "the measured frequencies, 15 400-21 400 cm^-1",
"coefficients": {
"sigma_bar": "14.21e-47",
"delta": "0.0968"
},
"check": "With the printed 10^-47 it gives 4.6e-29 cm^2 at 18 788.4 cm^-1, 100 times Table 2 (4.45e-27): the unit must be 10^-45 cm^2 (every sigma_bar of Table 1 fits Table 2 only so). With 10^-45: 4.59e-27 at 18 788.4 cm^-1. Checked 2026-09-25."
}
Fit of Teillet’s power law to the measured Ar cross sections (Figs. 4, 5), one parameter at a time; ‘the correlation between the two parameters is very strong’. Delta_avg (measured minus n-based over measured, mean) 0.4 %.
sneep_2005/ar_power_n_based#
{
"id": "ar_power_n_based",
"material": "Ar",
"equation": "Eq. (15) with Table 1, p. 11",
"printed": "sigma_bar_n-based/10^-47 = 14.68(3), delta_n-based = 0.0930(2)",
"variable": "nu: vacuum wavenumber in cm^-1; sigma in cm^2",
"range": "fitted to Eq. (2) values over 10 000-25 000 cm^-1",
"coefficients": {
"sigma_bar": "14.68e-47",
"delta": "0.0930"
},
"check": "With 10^-45 (see ar_power_exp) it gives 4.568e-27 at 18 788.4 cm^-1 against Table 2's n-based 4.56. Checked 2026-09-25."
}
sneep_2005/n2_power_exp#
{
"id": "n2_power_exp",
"material": "N2",
"equation": "Eq. (15) with Table 1, p. 11",
"printed": "sigma_bar_exp/10^-47 = 18.83(9), delta_exp = 0.0817(5)",
"variable": "nu: vacuum wavenumber in cm^-1; sigma in cm^2",
"range": "the measured frequencies, 15 400-21 400 cm^-1",
"coefficients": {
"sigma_bar": "18.83e-47",
"delta": "0.0817"
},
"check": "With 10^-45 it gives 5.24e-27 at 18 788.4 cm^-1 (Table 2 measured 5.10 +- 0.24). Delta_avg -0.7 %. Checked 2026-09-25."
}
sneep_2005/n2_power_n_based#
{
"id": "n2_power_n_based",
"material": "N2",
"equation": "Eq. (15) with Table 1, p. 11",
"printed": "sigma_bar_n-based/10^-47 = 16.31(4), delta_n-based = 0.974(3)",
"variable": "nu: vacuum wavenumber in cm^-1; sigma in cm^2",
"range": "fitted to Eq. (2) values over 10 000-25 000 cm^-1",
"coefficients": {
"sigma_bar": "16.31e-47",
"delta": "0.974"
},
"check": "delta is printed 0.974 (image and pdf text checked), which gives 3e-23 cm^2 at 18 788.4 cm^-1; with 0.0974 (and 10^-45) it gives 5.300e-27, Table 2's n-based 5.30 exactly. Read delta_n-based = 0.0974(3). Checked 2026-09-25."
}
sneep_2005/co2_power_exp#
{
"id": "co2_power_exp",
"material": "CO2",
"equation": "Eq. (15) with Table 1, p. 11",
"printed": "sigma_bar_exp/10^-47 = 27.42(14), delta_exp = 0.1343(5)",
"variable": "nu: vacuum wavenumber in cm^-1; sigma in cm^2",
"range": "the measured frequencies, 17 400-21 400 cm^-1",
"coefficients": {
"sigma_bar": "27.42e-47",
"delta": "0.1343"
},
"check": "With 10^-45 it gives 12.81e-27 at 18 788.4 cm^-1 (Table 2 measured 12.4 +- 0.8). Delta_avg -3.9 %. Checked 2026-09-25."
}
sneep_2005/co2_power_n_based#
{
"id": "co2_power_n_based",
"material": "CO2",
"equation": "Eq. (15) with Table 1, p. 11",
"printed": "sigma_bar_n-based/10^-47 = 28.49(9), delta_n-based = 0.1343(3)",
"variable": "nu: vacuum wavenumber in cm^-1; sigma in cm^2",
"range": "fitted to Eq. (2) values over 10 000-25 000 cm^-1",
"coefficients": {
"sigma_bar": "28.49e-47",
"delta": "0.1343"
},
"check": "With 10^-45 it gives 13.31e-27 at 18 788.4 cm^-1 (Table 2's n-based 13.29). Checked 2026-09-25."
}
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.