thalman_2014
============

R\. Thalman, K\. J\. Zarzana, M\. A\. Tolbert and R\. Volkamer, J\. Quant\. Spectrosc\. Radiat\. Transfer 147, 171 \(2014\); erratum J\. Quant\. Spectrosc\. Radiat\. Transfer 189, 281 \(2017\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/thalman_2014.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1016/j\.jqsrt\.2014\.05\.030 <https://doi.org/10.1016/j.jqsrt.2014.05.030>`__

**Source kind:** measurement

**Recorded technique:** Two cavity methods at Boulder \(630 Torr ambient\), room temperature\. \(1\) Cavity ring\-down spectroscopy \(CRDS\) of N2 at 405\.8 and 532\.2 nm \(mirrors R = 0\.99993 and 0\.99998\)\: the loss rate 1/\(tau c\) against density over pressure steps of 80\-100 % of ambient, whose slope is the absolute cross section; 'a limited number of sets of data' \(p\. 5\)\. \(2\) Broadband cavity\-enhanced spectroscopy \(BBCES\), 350\-700 nm, six mirror sets \(365, 405, 455, 532, 580, 630 nm\), 87 cm cavity, LED sources, Acton 2300i spectrometer\: the mirror reflectivity from the N2\-He difference \(Eq\. 3\) with the n\-based N2 cross section and Washenfelder's He fit, then Ar, O2 and air against N2 \(Eq\. 4\), each at a single density\. O2 and air only between the O4 \(O2\-O2\) bands\.

**Materials in structured entries:** Ar, N2, O2

**Dataset quantities:** rayleigh\_cross\_section

**Contents:** 9 datasets; 0 formulas.

Curation notes
--------------

The PDF in the library carries the paper \(pp\. 171\-177, PDF pages 1\-7\) and the authors' erratum \(JQSRT 189, 281\-282 \(2017\), PDF pages 8\-10\); both are cited here, the erratum's corrections applied as \[\[errata\]\] \(TC\-711\)\.

Cross sections per molecule, from Eq\. \(1\), sigma = 24 pi^3 nu^4 / N^2 \(\(n^2 \- 1\)/\(n^2 \+ 2\)\)^2 F\_k\(nu\), as Sneep & Ubachs\. Table 2 \(tbl\_576e4a7df80e\) prints, at 370\.0, 405\.8, 532\.2 and 660\.0 nm \('selected wavelengths' of the continuous BBCES data\), the n\-based \('Theory'\) and measured \('Exp'\) values of N2, Ar, O2 and air in 10^\-27 cm^2 \(the caption's 'cm^\-3 x 10^27' is corrected to cm^2 by the erratum\)\. Note c\: 'Number in \(\) is the 1\-sigma error in the reported value of the last digit for BBCES and the range for CRDS'\. Wavelengths are vacuum\: Table 2's corrected Theory values are reproduced to the printed digits from Table 1 with nu = 1/lambda\(vacuum\) \(with standard\-air wavelengths they would be 0\.1 % lower\)\.

Uncertainty \(pp\. 4, 6\-7\)\: BBCES 'measurement uncertainty of \+\-1\.3 % at the center of the mirror and \+\-2 % at the far extremes' \(pressure 0\.1 %, temperature 0\.3 %, cavity length 87 \+\- 0\.1 cm, the N2 \(\+\-1 %\) and He \(\+\-5 %\) reference cross sections\); the Ar data agree with n\-based theory to 0\.2 \+\- 0\.4 % \(the mean over all cavities, Fig\. 5; the per\-cavity biases UV \-0\.64 %, near\-UV \+0\.865 %, blue \+0\.3 %, red, amber, green within 0\.2 %, p\. 5\); O2 within 1 % outside the O4 bands \(370\-420 nm, 660 nm\), \< 4 % between adjacent bands; air within 1 %\. The BBCES values are relative to the n\-based N2 cross section \(Table 1\), not independent absolute measurements \(p\. 3\)\: Ar, O2 and air share that scale\.

Table 1 \(tbl\_e8dbeaabf242; the erratum's reprint tbl\_03101fb7ffc0\) gives the \(n \- 1\) x 10^8 = A \+ B/\(C \- nu^2\) and F\_k formulas behind the Theory columns\: Sneep & Ubachs's \(sneep\_2005 n2\_eq10, n2\_eq11 \(Bates\), ar\_eq9 \(Peck & Fisher\), o2\_eq23 with Bates's F\_k\), N = 2\.546899e19 cm^\-3 for N2, Ar and He, 2\.68678e19 cm^\-3 for O2; air from Bodhaine et al\. \(1999\) at 288\.15 K and 1013\.25 hPa with 360 ppm CO2\. Not recorded as formulas\: they are sneep\_2005's\. The erratum corrects them \(p\. 9\)\: the second N2 branch's B is 307\.43305 x 10^12 \(printed 307\.4335 x 10^13\), and both N2 King factors are 1\.034 \+ 3\.17 x 10^\-12 nu^2 \(printed '\.\.\. nu'\); the reprint also prints the O2 King factor's constant 1\.096 \(the 2014 table\: 1\.09\) without saying so, and adds, for nu \< 18315 cm^\-1, the O2 branch A = 21351\.1, B = 2\.18567 x 10^13 \(Bates\)\. With these \(and only these\) the corrected Theory column reproduces\: N2 23\.7092, 16\.1455, 5\.2998, 2\.2099; Ar 20\.3614, 13\.8807, 4\.5633, 1\.9038; O2 21\.2685, 14\.3728, 4\.6600, 1\.9378 \(computed 2026\-09\-29\)\.

Air \(not a registered material; not extracted\)\: Theory 23\.183, 15\.765, 5\.159, 2\.148 and BBCES 23\.0\(3\), 15\.7\(2\), \-, 2\.15\(3\) at 370\.0, 405\.8, 532\.2, 660\.0 nm \(1 sigma\)\.

Not extracted\: the continuous BBCES spectra \(Figs\. 3\-5, figures only; Table 2 prints the selected values\) and the He comparison \(Fig\. 4A, literature only\)\.

**Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

thalman\_2014/crds\_N2\_405
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "crds_N2_405",
     "material": "N2",
     "file": "N2/thalman_2014__crds_N2_405.csv",
     "table": "tbl_576e4a7df80e",
     "quantity": "rayleigh_cross_section",
     "unit": "cm2",
     "scale": 1e-27,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "bound"
     },
     "parameters": {
       "king_factor": 1.03593
     }
   }

Table 2, CRDS at 405\.8 nm\: the slope of the loss rate against density, absolute\. The parenthesis is 'the range' of the repeat runs \(note c\); taken as a bound \(half\-width\), which may overstate it if the printed number is the full range\. king\_factor\: Bates's F\_k = 1\.034 \+ 3\.17e\-12 nu^2 of the corrected Table 1 at nu = 1e7/405\.8 cm^\-1 \(1\.035925\), the factor of the paper's n\-based comparison\.

thalman\_2014/crds\_N2\_532
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "crds_N2_532",
     "material": "N2",
     "file": "N2/thalman_2014__crds_N2_532.csv",
     "table": "tbl_576e4a7df80e",
     "quantity": "rayleigh_cross_section",
     "unit": "cm2",
     "scale": 1e-27,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "bound"
     },
     "parameters": {
       "king_factor": 1.03512
     }
   }

Table 2, CRDS at 532\.2 nm \(Fig\. 2 shows the loss\-rate fit\)\: absolute\. The parenthesis is 'the range' of the repeat runs \(note c\); taken as a bound \(half\-width\)\. king\_factor\: Bates's F\_k = 1\.034 \+ 3\.17e\-12 nu^2 at nu = 1e7/532\.2 cm^\-1 \(1\.035119\)\.

thalman\_2014/bbces\_Ar
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "bbces_Ar",
     "material": "Ar",
     "file": "Ar/thalman_2014__bbces_Ar.csv",
     "table": "tbl_576e4a7df80e",
     "quantity": "rayleigh_cross_section",
     "unit": "cm2",
     "scale": 1e-27,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "king_factor": 1.0
     }
   }

Table 2, BBCES at 370\.0, 405\.8, 532\.2 and 660\.0 nm, relative to the n\-based N2 cross section of Table 1 \(so on the N2 formula's scale, which is 0\.06\-0\.10 % above fit/N2 in alpha\); one sigma in parentheses \(note c\)\. king\_factor 1\: 'unity for mono\-atomic gases' \(p\. 2\)\.

thalman\_2014/bbces\_O2\_370
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "bbces_O2_370",
     "material": "O2",
     "file": "O2/thalman_2014__bbces_O2_370.csv",
     "table": "tbl_576e4a7df80e",
     "quantity": "rayleigh_cross_section",
     "unit": "cm2",
     "scale": 1e-27,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "king_factor": 1.11384
     }
   }

Table 2, BBCES at 370\.0 nm, relative to the n\-based N2 cross section; one sigma\. Between O4 bands, from a single density\: O4 absorption is not separated but avoided \(p\. 5\)\. king\_factor\: Bates's F\_k = 1\.096 \+ 1\.385e\-11 nu^2 \+ 1\.448e\-20 nu^4 \(the erratum's constant; the 2014 table prints 1\.09; the corrected Theory column needs 1\.096\) at nu = 1e7/370\.0 cm^\-1 \(1\.113844\)\.

thalman\_2014/bbces\_O2\_405
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "bbces_O2_405",
     "material": "O2",
     "file": "O2/thalman_2014__bbces_O2_405.csv",
     "table": "tbl_576e4a7df80e",
     "quantity": "rayleigh_cross_section",
     "unit": "cm2",
     "scale": 1e-27,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "king_factor": 1.10975
     }
   }

Table 2, BBCES at 405\.8 nm, relative to the n\-based N2 cross section; one sigma; between O4 bands\. king\_factor\: Bates's O2 F\_k \(constant 1\.096\) at nu = 1e7/405\.8 cm^\-1 \(1\.109752\)\.

thalman\_2014/bbces\_O2\_660
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "bbces_O2_660",
     "material": "O2",
     "file": "O2/thalman_2014__bbces_O2_660.csv",
     "table": "tbl_576e4a7df80e",
     "quantity": "rayleigh_cross_section",
     "unit": "cm2",
     "scale": 1e-27,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "king_factor": 1.09994
     }
   }

Table 2, BBCES at 660\.0 nm, relative to the n\-based N2 cross section; one sigma; between O4 bands \(the 630 nm band's edge; the B band of O2 is at 687 nm\)\. king\_factor\: Bates's O2 F\_k \(constant 1\.096\) at nu = 1e7/660\.0 cm^\-1 \(1\.099943\)\.

thalman\_2014/theory\_N2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_N2",
     "material": "N2",
     "file": "N2/thalman_2014__theory_N2.csv",
     "table": "tbl_576e4a7df80e",
     "quantity": "rayleigh_cross_section",
     "unit": "cm2",
     "scale": 1e-27,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 2 'Theory'\: n\-based from Table 1 \(Peck & Khanna / Bates formulas as Sneep & Ubachs, F\_k = 1\.034 \+ 3\.17e\-12 nu^2 varying with wavelength, so no single king\_factor\), N = 2\.546899e19 cm^\-3\. All four cells corrected by the erratum \(errata below\); corrected, they reproduce from Table 1 to the printed digits\.

thalman\_2014/theory\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_Ar",
     "material": "Ar",
     "file": "Ar/thalman_2014__theory_Ar.csv",
     "table": "tbl_576e4a7df80e",
     "quantity": "rayleigh_cross_section",
     "unit": "cm2",
     "scale": 1e-27,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "parameters": {
       "king_factor": 1.0
     }
   }

Table 2 'Theory'\: n\-based from Peck & Fisher's formula \(Table 1, as Sneep & Ubachs Eq\. 9\), N = 2\.546899e19 cm^\-3 \(15 C ideal\), F\_k = 1\. Reproduced to the printed digits \(20\.3614, 13\.8807, 4\.5633, 1\.9038\); unchanged by the erratum\. It lies 0\.11 % above fit/Ar in alpha\.

thalman\_2014/theory\_O2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_O2",
     "material": "O2",
     "file": "O2/thalman_2014__theory_O2.csv",
     "table": "tbl_576e4a7df80e",
     "quantity": "rayleigh_cross_section",
     "unit": "cm2",
     "scale": 1e-27,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 2 'Theory'\: n\-based from Bates's O2 formula \(Table 1, two branches split at 18315 cm^\-1\), N = 2\.68678e19 cm^\-3, F\_k = 1\.096 \+ 1\.385e\-11 nu^2 \+ 1\.448e\-20 nu^4 \(no single king\_factor\)\. The 532\.2 and 660\.0 nm cells are corrected by the erratum \(errata below\)\.

Formulas
--------

No formulas are recorded.

Corrections
-----------

.. code-block:: text

   [
     {
       "dataset": "theory_N2",
       "row": "370.0",
       "column": "value",
       "printed": "23.698",
       "corrected": "23.709",
       "reason": "The authors' erratum reprints Table 2 with the N2 Theory values recomputed; its text names only the 660 nm cell, but the reprint also changes 370.0, 405.8 and 532.2 nm. The corrected value is Eq. (1) with the corrected Table 1 (23.7092 computed); the printed 23.698 is 0.05 % lower and is not reproduced by either King-factor reading.",
       "evidence": "Erratum, JQSRT 189, 281 (2017), reprinted Table 2 (library tbl_c363d0a7b75b, PDF p. 9, image checked 2026-09-29): 23.709. Computed from Table 1 with nu = 1e7/370.0 cm^-1, N = 2.546899e19: 23.7092."
     },
     {
       "dataset": "theory_N2",
       "row": "405.8",
       "column": "value",
       "printed": "16.146",
       "corrected": "16.145",
       "reason": "Recomputed in the erratum's reprinted Table 2 (a last-digit rounding: 16.1455 computed from the corrected Table 1).",
       "evidence": "Erratum reprinted Table 2 (tbl_c363d0a7b75b, PDF p. 9, image checked 2026-09-29): 16.145. Computed: 16.1455."
     },
     {
       "dataset": "theory_N2",
       "row": "532.2",
       "column": "value",
       "printed": "5.302",
       "corrected": "5.300",
       "reason": "Recomputed in the erratum's reprinted Table 2 (5.2998 computed from the corrected Table 1).",
       "evidence": "Erratum reprinted Table 2 (tbl_c363d0a7b75b, PDF p. 9, image checked 2026-09-29): 5.300. Computed: 5.2998."
     },
     {
       "dataset": "theory_N2",
       "row": "660.0",
       "column": "value",
       "printed": "2.988",
       "corrected": "2.210",
       "reason": "The authors' erratum: 'the calculation at 660.0 nm is 2.21 x 10^-27 cm^2'. The printed 2.988 is larger than Ar's 1.904 by 57 %, where N2 exceeds Ar by 16 % at every other wavelength.",
       "evidence": "Erratum, JQSRT 189, 281 (2017), text p. 10 and reprinted Table 2 (tbl_c363d0a7b75b, PDF p. 9, image checked 2026-09-29): 2.210. Computed from the corrected Table 1: 2.2099."
     },
     {
       "dataset": "theory_O2",
       "row": "532.2",
       "column": "value",
       "printed": "4.740",
       "corrected": "4.660",
       "reason": "The authors' erratum: 'the O2 calculation at 532.2 nm is 4.66 x 10^-27 cm^2'.",
       "evidence": "Erratum, JQSRT 189, 281 (2017), text p. 10 and reprinted Table 2 (tbl_c363d0a7b75b, PDF p. 9, image checked 2026-09-29): 4.660. Computed from the corrected Table 1 (F_k constant 1.096): 4.6600."
     },
     {
       "dataset": "theory_O2",
       "row": "660.0",
       "column": "value",
       "printed": "1.935",
       "corrected": "1.938",
       "reason": "Recomputed in the erratum's reprinted Table 2, not named in its text: 1.9378 from Bates's low-wavenumber O2 branch (A = 21351.1, B = 2.18567e13, the erratum's added note) with F_k constant 1.096.",
       "evidence": "Erratum reprinted Table 2 (tbl_c363d0a7b75b, PDF p. 9, image checked 2026-09-29): 1.938. Computed: 1.9378."
     }
   ]

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.