wilmouth_2020#
D. M. Wilmouth and D. S. Sayres, J. Quant. Spectrosc. Radiat. Transfer 255, 107224 (2020)
Source record · Catalogue · Review register
DOI: 10.1016/j.jqsrt.2020.107224
Source kind: measurement
Recorded technique: Broadband cavity-enhanced spectroscopy (BBCES), 264-297 nm: laser-driven Xe arc lamp, 35 cm cavity of two plano-concave mirrors (peak reflectivity 0.996655 at 289.6 nm), 0.3 m spectrograph calibrated on Hg lines. Cavity filled with the pure gas at 1020-1060 hPa, static. Mirror reflectivity from N2 against He (N2 n-based cross section, +-1 %), then the sample’s Rayleigh extinction against He (Eqs. 2-3). Purity 99.999 % (He, N2, Ar), 99.99 % (CO2, CH4), 99.8 % (SF6).
Materials in structured entries: Ar, CH4, CO2, He, N2, SF6
Dataset quantities: None recorded.
Contents: 0 datasets; 8 formulas.
Curation notes#
The measured quantity is the Rayleigh scattering cross section (cm^2 per molecule), not the refractive index; it relates to n through Eq. (1), sigma = 24 pi^3 nu^4 / N^2 ((n^2 - 1)/(n^2 + 2))^2 F_k, with the King factor F_k. The measured cross sections are shown only in figures (Figs. 1-3: 238 points per gas over 264-297 nm, and the authors’ 2019 UV-A data), never tabulated, so no dataset is extracted. The text gives the mean ratio of measured to n-based cross sections over 264-297 nm (p. 5): Ar 1.008, CO2 0.990, SF6 0.959, CH4 0.775 (the n-based values from Table 1 of Wilmouth & Sayres 2019 and Sneep & Ubachs 2005); mean 1-sigma uncertainty 3.1 % (Ar), 2.1 % (CO2), 1.9 % (SF6), 2.1 % (CH4), including 1.5 % from the path length (N2 reference cross section), 0.3 % temperature and 0.1 % pressure (p. 3). There is no vocabulary quantity for a Rayleigh cross section; one would be needed to curate such data (the He et al. 2021 values are tabulated).
The paper’s own results are four dispersion formulas for SF6 and CH4 (Eqs. 4-7), derived by inverting Eq. (1) with F_k = 1 and fitting (n - 1) x 10^8 = A + B/(C - nu^2), nu the vacuum wavenumber in cm^-1, ‘n is defined at 288.15 K and 101,325 Pa’ with N = 2.5469e19 cm^-3 (Table 1 note a): an ideal-gas density. Eqs. 4 and 5 fit only the UV data (264-297 and 333-363 nm); Eqs. 6 and 7 also weight visible refractive-index measurements (Vukovic et al. 1996 for SF6; Watson & Ramaswamy 1936 and Cuthbertson & Cuthbertson 1920 for CH4) and are the recommended ones (Table 1, 250-650 nm). F_k = 1 for SF6 and CH4 (spherical tops) is an assumption, not a measurement.
Table 1 (tbl_02ae1202ecac, image checked) also reproduces the He, N2, Ar and CO2 formulas used for the reference and n-based cross sections; they are recorded as reproduced formulas. The library’s CSV of Table 1 mangles the CO2 cell (its 4.3244/(67837.7^2 - nu^2) term is rendered as a denominator); the image shows five additive terms inside the bracket, as recorded below, identical to He et al. (2021)’s Table 1.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
No datasets are recorded.
Formulas#
wilmouth_2020/SF6_uv#
{
"id": "SF6_uv",
"material": "SF6",
"equation": "Eq. (4), p. 5",
"printed": "(n - 1) x 10^8 = 25850.9 + 7.8229 x 10^14 / (1.680 x 10^10 - nu^2)",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "264-363 nm (the BBCES data of this work and Wilmouth & Sayres 2019)",
"coefficients": {
"A": "25850.9",
"B": "7.8229e14",
"C": "1.680e10"
},
"check": "Against Eq. (6) the Rayleigh cross sections differ by 0.23-0.26 % on average and 0.46 % at most over 264-363 nm (the paper: 0.25 % and 0.49 %) (checked 2026-09-24)."
}
From Rayleigh cross sections with F_k = 1 (UV only). The equation image was checked.
wilmouth_2020/CH4_uv#
{
"id": "CH4_uv",
"material": "CH4",
"equation": "Eq. (5), p. 5",
"printed": "(n - 1) x 10^8 = 16873.2 + 2.2970 x 10^14 / (9.270 x 10^9 - nu^2)",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "264-363 nm (the BBCES data of this work and Wilmouth & Sayres 2019)",
"coefficients": {
"A": "16873.2",
"B": "2.2970e14",
"C": "9.270e9"
},
"check": "Against Eq. (7) the cross sections differ by 0.40-0.47 % on average and 0.85 % at most over 264-363 nm (the paper: 0.44 % and 0.91 %) (checked 2026-09-24)."
}
From Rayleigh cross sections with F_k = 1. Extrapolated to the visible it lies above every direct refractive-index measurement beyond about 500 nm (3.7 % in cross section at 600 nm, p. 7).
wilmouth_2020/SF6#
{
"id": "SF6",
"form": "dn_wavenumber2",
"terms": {
"scale": "1e-8",
"A": "18611.4",
"B": [
"8.9566e14"
],
"C": [
"1.680e10"
]
},
"range_nm": [
250.0,
650.0
],
"material": "SF6",
"equation": "Eq. (6), p. 6; Table 1 (tbl_02ae1202ecac)",
"printed": "(n - 1) x 10^8 = 18611.4 + 8.9566 x 10^14 / (1.680 x 10^10 - nu^2)",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "approximately 250-650 nm (Table 1 note c: 40000 > nu > 15385 cm^-1)",
"coefficients": {
"A": "18611.4",
"B": "8.9566e14",
"C": "1.680e10"
},
"check": "Reproduces He et al. (2021)'s n-based SF6 cross sections (their Table 2, computed from this formula) to 0.1 % (checked 2026-09-24)."
}
The UV BBCES data plus Vukovic et al.’s (1996) refractive index at 633 nm (+-5e-7 in n), weighted in the fit (p. 6). Recommended over Eq. (4) for 250-650 nm.
wilmouth_2020/CH4#
{
"id": "CH4",
"form": "dn_wavenumber2",
"terms": {
"scale": "1e-8",
"A": "4869.8",
"B": [
"4.1023e14"
],
"C": [
"1.133e10"
]
},
"range_nm": [
250.0,
650.0
],
"material": "CH4",
"equation": "Eq. (7), p. 8; Table 1 (tbl_02ae1202ecac)",
"printed": "(n - 1) x 10^8 = 4869.8 + 4.1023 x 10^14 / (1.133 x 10^10 - nu^2)",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "approximately 250-650 nm (Table 1 note c)",
"coefficients": {
"A": "4869.8",
"B": "4.1023e14",
"C": "1.133e10"
},
"check": "Reproduces He et al. (2021)'s n-based CH4 cross sections (their Table 2) to 0.15 % (checked 2026-09-24)."
}
The UV BBCES data plus Watson & Ramaswamy (1936) and Cuthbertson & Cuthbertson (1920) in the visible, equally weighted with each other and less than the UV data (p. 8). Recommended over Eq. (5) for 250-650 nm.
wilmouth_2020/He_table1#
{
"id": "He_table1",
"material": "He",
"equation": "Table 1 (tbl_02ae1202ecac), p. 8",
"printed": "(n - 1) x 10^8 = 2283 + 1.8102 x 10^13 / (1.5342 x 10^10 - nu^2)",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "not stated here (He et al. 2021 give 14285-33333 cm^-1)",
"coefficients": {
"A": "2283",
"B": "1.8102e13",
"C": "1.5342e10"
},
"reproduced_from": [
"R. Thalman, K. J. Zarzana, M. A. Tolbert and R. Volkamer, J. Quant. Spectrosc. Radiat. Transfer 147, 171 (2014)",
"R. Abjean, A. Mehu and A. Johannin-Gilles, C. R. Acad. Sci. B 271, 835 (1970)",
"leonard_1974",
"cuthbertson_1932"
],
"check": "Not checked against an original."
}
Reproduced (refs. 2, 21-23): the reference gas of the measurement, F_k = 1.
wilmouth_2020/N2_table1#
{
"id": "N2_table1",
"material": "N2",
"equation": "Table 1 (tbl_02ae1202ecac), p. 8",
"printed": "(n - 1) x 10^8 = 5677.465 + 3.1881874 x 10^14 / (1.44 x 10^10 - nu^2); F_k = 1.034 + 3.17 x 10^-12 nu^2",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "not stated here (He et al. 2021 give 21360-39370 cm^-1, the UV branch of Bates's two-branch formula)",
"coefficients": {
"A": "5677.465",
"B": "3.1881874e14",
"C": "1.44e10"
},
"reproduced_from": [
"M. Sneep and W. Ubachs, J. Quant. Spectrosc. Radiat. Transfer 92, 293 (2005)",
"peck_1966",
"R. Abjean, A. Mehu and A. Johannin-Gilles, C. R. Acad. Sci. B 271, 411 (1970)",
"D. R. Bates, Planet. Space Sci. 32, 785 (1984)"
],
"check": "Not checked against an original."
}
Reproduced (refs. 5, 18-20); used for the mirror-reflectivity calibration.
wilmouth_2020/Ar_table1#
{
"id": "Ar_table1",
"material": "Ar",
"equation": "Table 1 (tbl_02ae1202ecac), p. 8",
"printed": "(n - 1) x 10^8 = 6432.135 + 2.8606021 x 10^14 / (1.44 x 10^10 - nu^2)",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "validated by this work for 264-363 nm (Table 1 note b)",
"coefficients": {
"A": "6432.135",
"B": "2.8606021e14",
"C": "1.44e10"
},
"reproduced_from": [
"M. Sneep and W. Ubachs, J. Quant. Spectrosc. Radiat. Transfer 92, 293 (2005)",
"peck_1964"
],
"check": "Algebraically identical to Peck & Fisher (1964)'s formula, (n - 1)10^7 = 643.2135 + 286060.21/(144 - sigma^2), sigma in um^-1, at 15 C and 760 Torr (their abstract, Peck_1964_DispersionArgon), rewritten in cm^-1 (checked 2026-09-24)."
}
Reproduced; F_k = 1. Measured/n-based cross-section ratio 1.008 over 264-297 nm (p. 5).
wilmouth_2020/CO2_table1#
{
"id": "CO2_table1",
"material": "CO2",
"equation": "Table 1 (tbl_02ae1202ecac), p. 8",
"printed": "(n - 1) x 10^8 = 1.1427 x 10^11 (5799.25/(128908.9^2 - nu^2) + 120.05/(89223.8^2 - nu^2) + 5.3334/(75037.5^2 - nu^2) + 4.3244/(67837.7^2 - nu^2) + 1.218145 x 10^-5/(2418.136^2 - nu^2)); F_k = 1.1364 + 2.53 x 10^-11 nu^2",
"variable": "nu: vacuum wavenumber in cm^-1",
"state": "1atm_15C",
"density": "ideal",
"range": "validated by this work for 264-363 nm (Table 1 note b); He et al. (2021) give the original range 39417-55340 cm^-1",
"coefficients": {
"scale": "1.1427e11",
"B1": "5799.25",
"C1": "128908.9",
"B2": "120.05",
"C2": "89223.8",
"B3": "5.3334",
"C3": "75037.5",
"B4": "4.3244",
"C4": "67837.7",
"B5": "1.218145e-5",
"C5": "2418.136"
},
"reproduced_from": [
"M. Sneep and W. Ubachs, J. Quant. Spectrosc. Radiat. Transfer 92, 293 (2005)",
"A. Bideau-Mehu, Y. Guern, R. Abjean and A. Johannin-Gilles, Opt. Commun. 9, 432 (1973)",
"G. R. Alms, A. K. Burnham and W. H. Flygare, J. Chem. Phys. 63, 3321 (1975)"
],
"check": "Structure read from the table image (the library CSV is mangled); identical to He et al. (2021)'s Table 1, whose n-based CO2 cross sections it reproduces to 0.15 % (checked 2026-09-24)."
}
Reproduced; measured/n-based cross-section ratio 0.990 over 264-297 nm (p. 5).
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.