wilmouth_2020 ============= D\. M\. Wilmouth and D\. S\. Sayres, J\. Quant\. Spectrosc\. Radiat\. Transfer 255, 107224 \(2020\) `Source record `__ · :doc:`Catalogue ` · :doc:`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 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.