sneep_2005
==========

M\. Sneep and W\. Ubachs, J\. Quant\. Spectrosc\. Radiat\. Transfer 92, 293 \(2005\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/sneep_2005.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1016/j\.jqsrt\.2004\.07\.025 <https://doi.org/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
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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 :doc:`review register </register>` for the checks and decisions.