herring_1986
============

G\. C\. Herring, M\. J\. Dyer and W\. K\. Bischel, "Temperature and density dependence of the linewidths and line shifts of the rotational Raman lines in N2 and H2", Phys\. Rev\. A 34, 1944 \(1986\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/herring_1986.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/PhysRevA\.34\.1944 <https://doi.org/10.1103/PhysRevA.34.1944>`__

**Source kind:** measurement

**Recorded technique:** Quasi\-cw stimulated Raman gain spectroscopy \(pp\. 1\-2\)\: a single\-mode Kr\-ion probe at 568 nm \(\< 30 MHz\) and a pulse\-amplified single\-mode cw dye pump near 565 nm \(10 ns, 100 MHz linewidth\), crossed at 1\.0 degree in a sample cell \(80, 195 or 295 K\) and a room\-temperature reference cell; Stokes S\-branch lines\. Densities 0\.01\-2\.0 amagat \(N2\) and up to 3 amagat \(H2\), from a Baratron gauge and a thermocouple by the perfect\-gas law \(the virial correction is below 1 %, p\. 2\)\. Line shapes fitted with Voigt profiles, the Gaussian part being the pump\-laser width \(about 100 MHz\); the Lorentzian FWHM against density gives B\.

**Materials in structured entries:** H2, N2

**Dataset quantities:** raman\_line\_shift, raman\_linewidth, raman\_shift

**Contents:** 21 datasets; 5 formulas.

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

Identity checked against the first page\. Page numbers are pdf pages \(1\-8 = journal pp\. 1944\-1951\)\. Materials\: 14N2 and H2 \(normal, ortho\:para 3\:1, Table IV caption\); no other isotopologue is measured\. Odd\-J N2 lines were not studied \(p\. 3\)\.

WIDTH CONVENTION\. Every width and coefficient is a FULL width\: Fig\. 3's axis 'FWHM RAMAN LINEWIDTH \(MHz\)' for the N2 S\(10\) data from which B is fitted; for H2, Eq\. \(1\), p\. 5\: 'the Raman line\-shape function is Lorentzian with a FWHM linewidth Delta nu that can be expressed as Delta nu = A/rho \+ B rho'\. B in MHz per perfect\-gas amagat \(p\. 2\)\. N2\: the law is linear in density, no Dicke term \('Doppler broadening \(5 MHz\), and hence the Dicke narrowing, is negligible', p\. 2\)\. H2\: the law INCLUDES the Dicke term A/rho \(A in MHz amagat\), but A was NOT fitted\: it was computed by Eq\. \(2\) from the self\-diffusion coefficients D\_0 of Bischel and Dyer's Q\-branch study \(Ref\. 18 = bischel\_1986, Table III\) and held fixed, B being the one free parameter \(p\. 5\); 'the maximum correction to the linewidth due to including the collisional narrowing term \.\.\. is on the order of 5\-10 %' \(p\. 5\)\.

UNCERTAINTIES \(p\. 3\)\. N2 Table I\: 'For S\(4\) through S\(12\), the specified uncertainties are one standard deviation for the least\-squares fit\. For S\(0\), S\(2\), S\(14\), and S\(16\), data were obtained at only one density, and the uncertainties shown \.\.\. represent the error in the linewidth determination of a single\-line profile\.' 'Systematic errors, due to uncertainty in the dye\-laser scan width, are about 1 % or less\.' H2 Table V\: 'one standard deviation for the one\-parameter linear least\-squares fit' \(p\. 5\)\. Tables III and VI\: not stated\.

TABLE I against TABLE II\. The 'Present work' column of Table II repeats Table I's 295 K values except S\(6\), 3570 \+\- 30 \(Table I 3560 \+\- 30\), and S\(10\), 3070 \+\- 60 \(Table I 3060 \+\- 60\); both images checked\. Table VII's B\_0 are Table I's \(3560, 3060\)\. Unresolved; Table I is the primary\.

LINE SHIFTS \(p\. 6\)\. N2\: self and O2\-induced shifts 'in the range 50\-150 MHz/amagat' with no consistent J or T dependence, disturbed by an unexplained line asymmetry; the paper gives only an upper limit, 'the density line shifts are less than 150 MHz/amagat' \(not extracted\)\. H2\: Table VI, delta nu = nu\_R\(rho\) \- nu\_R\(0\) \(Eq\. \(5\); a negative shift lowers the Raman frequency\)\. At 80 K the Q\(1\) shift is 13 times the S\(1\) shift \(p\. 6\)\.

TABLE IV \(p\. 5\), ortho\:para 3\:1\: nu\_R \(354 and 587 cm\-1, rounded\), the Doppler FWHM by Eq\. \(4\), A by Eq\. \(2\), and, not extracted \(no quantity\), D\_0 \(cm2 amagat s\-1, note a 'Reference 18'\: bischel\_1986 Table III, whose 81 and 298 K Q\(0\) and Q\(1\) values are reused here at 80 and 295 K for S\(0\) and S\(1\)\) and rho\_c \(amagat, Eq\. \(3\)\)\: 80 K S\(0\) D\_0 0\.871, rho\_c 0\.095; 80 K S\(1\) 0\.493, 0\.088; 295 K S\(0\) 1\.19, 0\.068; 295 K S\(1\) 1\.42, 0\.134\.

TEMPERATURE LAWS \(Table VII, p\. 7\)\. Eq\. \(9\) B = B\_0 \(T/295\)^gamma is a law for the per\-density coefficient; the paper notes \(p\. 7\) that 'gamma \.\.\. is related to eta by gamma = 1 \- eta, where eta is the exponent of the temperature for pressure\-broadening coefficients'\. In the vocabulary's form gamma\(T\) = gamma\(T0\)\(T0/T\)^N, N = \-gamma for B per amagat and N = eta = 1 \- gamma for a coefficient per unit pressure\. Recorded as formulas \(not as broadening\_temperature\_exponent datasets, whose N is not the printed gamma\)\.

solprop\: its N2 rotational FWHM density coefficient, 3\.3e9 Hz/amagat, cites this paper without a J\: Table I at 295 K runs from 4160 \(S\(2\)\) to 2660 \(S\(14\)\) MHz/amagat; 3\.3e9 is S\(8\) \(3270\) rounded\. Its H2 rotational law, 6\.15e6/n \+ 114e6 n Hz \(n in amagat, 'Tables IV/V\: S\(1\), 295 K'\), is Table IV's A = 6\.15 MHz amagat and Table V's B = 114 MHz/amagat for S\(1\) at 295 K exactly\. Ref\. 4 is 'G\. V\. Milahailov \[sic\], Zh\. Eksp\. Teor\. Fiz\. 36, 1368 \(1959\) \[Sov\. Phys\.\-JETP 9, 974 \(1959\)\]', the paper in the library as Mikhailov\_1959 \(see mikhailov\_1959\)\.

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

Datasets
--------

herring\_1986/table1\_295K
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_295K",
     "material": "N2",
     "file": "N2/herring_1986__table1_295K.csv",
     "table": "tbl_efca0dbdd612",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table I \(p\. 3\), 295 K\: FWHM self\-broadening coefficient B of the S\(J\) rotational Raman lines \(v = 0, Stokes\), MHz per perfect\-gas amagat\. S\(0\) and S\(16\) are blank at 295 K\. S\(2\) and S\(14\)\: one density only \(the error of a single profile\); S\(4\)\-S\(12\)\: 1 sigma of the linear fit \(p\. 3\)\.

herring\_1986/table1\_195K
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_195K",
     "material": "N2",
     "file": "N2/herring_1986__table1_195K.csv",
     "table": "tbl_efca0dbdd612",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 195
     }
   }

Table I \(p\. 3\), 195 K\: FWHM self\-broadening coefficient of N2 S\(J\), MHz per perfect\-gas amagat\. S\(0\), S\(2\), S\(14\), S\(16\)\: one density only; S\(4\)\-S\(12\)\: 1 sigma of the fit \(p\. 3; S\(4\) and S\(12\) carry about 10 % errors at 195 K although they are fitted rows\)\.

herring\_1986/table1\_80K
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_80K",
     "material": "N2",
     "file": "N2/herring_1986__table1_80K.csv",
     "table": "tbl_efca0dbdd612",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 80
     }
   }

Table I \(p\. 3\), 80 K\: FWHM self\-broadening coefficient of N2 S\(J\), MHz per perfect\-gas amagat\. S\(0\), S\(2\)\: one density only; S\(4\)\-S\(12\)\: 1 sigma of the fit \(p\. 3\)\. S\(14\) and S\(16\) blank\.

herring\_1986/table2\_present
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_present",
     "material": "N2",
     "file": "N2/herring_1986__table2_present.csv",
     "table": "tbl_f0f74c352efe",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table II \(p\. 3\), 'Present work'\: Table I's 295 K column repeated, except S\(6\) 3570 \(Table I 3560\) and S\(10\) 3070 \(Table I 3060\) \(images checked; unresolved\)\. A duplicate of table1\_295K, kept as printed\.

herring\_1986/table2\_jammu
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_jammu",
     "material": "N2",
     "file": "N2/herring_1986__table2_jammu.csv",
     "table": "tbl_f0f74c352efe",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "jammu_1966"
     ],
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self"
     }
   }

Table II \(p\. 3\), Ref\. 3 \(Jammu, St\. John and Welsh 1966\), room temperature, as Herring et al\. print it \(in MHz/amagat, FWHM; converted from Jammu's own units by Herring et al\.\: compare jammu\_1966\)\. Spontaneous Raman at 1\-100 amagat with overlapping lines \(p\. 3\)\.

herring\_1986/table2\_pinter
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_pinter",
     "material": "N2",
     "file": "N2/herring_1986__table2_pinter.csv",
     "table": "tbl_f0f74c352efe",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "F. Pinter, Opt. Spectrosc. 17, 428 (1964)"
     ],
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self"
     }
   }

Table II \(p\. 3\), Ref\. 6 \(Pinter\), room temperature, as Herring et al\. print it\.

herring\_1986/table2\_edwards
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_edwards",
     "material": "N2",
     "file": "N2/herring_1986__table2_edwards.csv",
     "table": "tbl_f0f74c352efe",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "H. G. M. Edwards, D. A. Long and S. W. Webb, Self- and Foreign-Gas Broadening of the Pure Rotational Raman Lines of Oxygen and Nitrogen, Proceedings of the 9th International Conference on Raman Spectroscopy, 1984 (unpublished), p. 760"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self"
     }
   }

Table II \(p\. 3\), Ref\. 7 \(Edwards, Long and Webb 1984, a conference proceedings\), room temperature, as Herring et al\. print it; 'our current measurement is consistent with that of Ref\. 7' \(p\. 3\)\.

herring\_1986/table3\_O2\_295K
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table3_O2_295K",
     "material": "N2",
     "file": "N2/herring_1986__table3_O2_295K.csv",
     "table": "tbl_27787ea84e18",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "O2",
       "temperature_k": 295
     }
   }

Table III \(p\. 4\), 295 K\: FWHM broadening coefficient of the N2 S\(J\) lines by O2 \(foreign gas\), MHz per amagat of O2; 'typically 85\-90 % of the self\-broadening' \(p\. 5\)\. How the mixture was prepared is not stated beyond 'foreign\-gas' measurements\.

herring\_1986/table3\_O2\_195K
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table3_O2_195K",
     "material": "N2",
     "file": "N2/herring_1986__table3_O2_195K.csv",
     "table": "tbl_27787ea84e18",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "O2",
       "temperature_k": 195
     }
   }

Table III \(p\. 4\), 195 K\: FWHM broadening coefficient of N2 S\(J\) by O2, MHz/amagat\.

herring\_1986/table4\_shift
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table4_shift",
     "material": "H2",
     "file": "H2/herring_1986__table4_shift.csv",
     "table": "tbl_0e34a8d11d00",
     "quantity": "raman_shift",
     "unit": "cm-1",
     "abscissa": "label",
     "use": "check",
     "parameters": {
       "transition": "S(J), per row"
     }
   }

Table IV \(p\. 5\), nu\_R of S\(0\) and S\(1\), rounded to 1 cm\-1 \(printed twice, at 80 and 295 K; the 295 K row is taken\)\: the frequencies used in Eqs\. \(2\) and \(4\), not a measurement\.

herring\_1986/table4\_doppler
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table4_doppler",
     "material": "H2",
     "file": "H2/herring_1986__table4_doppler.csv",
     "table": "tbl_0e34a8d11d00",
     "quantity": "raman_linewidth",
     "unit": "MHz",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "check",
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm"
     }
   }

Table IV \(p\. 5\)\: the FWHM Doppler width for forward scattering, calculated by Eq\. \(4\), Delta nu\_D = 7\.15e\-7 nu\_R \(T/m\)^\(1/2\), nu\_R in MHz, m in amu\. Reproduced by formula eq4\_doppler to 0\.5 MHz with m = 2 amu\.

herring\_1986/table4\_A
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table4_A",
     "material": "H2",
     "file": "H2/herring_1986__table4_A.csv",
     "table": "tbl_0e34a8d11d00",
     "quantity": "raman_linewidth",
     "unit": "MHz amagat",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "check",
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "term": "A/rho (Dicke narrowing) of Eq. (1)",
       "ortho_para": "3:1"
     }
   }

Table IV \(p\. 5\)\: A of Eq\. \(1\), the Dicke \(diffusion\-model\) term A/rho of the FWHM, MHz amagat, CALCULATED by Eq\. \(2\) from D\_0 of Bischel and Dyer \(Ref\. 18 = bischel\_1986 Table III, Q\-branch values\) and held fixed in the fits of Table V\: an input of this paper, not a measurement\. The printed values follow A = 4 pi nu\_R^2 D\_0, not Eq\. \(2\)'s printed 4 pi^2 \(see formula eq2\_A\)\. Normal H2\.

herring\_1986/table5\_295K
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table5_295K",
     "material": "H2",
     "file": "H2/herring_1986__table5_295K.csv",
     "table": "tbl_bc667320a0be",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295,
       "ortho_para": "3:1"
     }
   }

Table V \(p\. 5\), 295 K, 'This work'\: FWHM self\-broadening coefficient B of H2 S\(0\) and S\(1\), MHz per perfect\-gas amagat, normal H2 \(3\:1\), fitted with Eq\. \(1\) including the fixed Dicke term A/rho \(table4\_A\); 1 sigma of the one\-parameter fit \(p\. 5\)\.

herring\_1986/table5\_80K
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table5_80K",
     "material": "H2",
     "file": "H2/herring_1986__table5_80K.csv",
     "table": "tbl_bc667320a0be",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 80,
       "ortho_para": "3:1"
     }
   }

Table V \(p\. 5\), 80 K, 'This work'\: FWHM self\-broadening coefficient of H2 S\(0\), S\(1\) \(normal H2, 3\:1, cooled\), with the Dicke term fixed; 1 sigma of the fit\.

herring\_1986/table5\_van\_den\_hout\_295K
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table5_van_den_hout_295K",
     "material": "H2",
     "file": "H2/herring_1986__table5_van_den_hout_295K.csv",
     "table": "tbl_bc667320a0be",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "keijser_1974"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table V \(p\. 5\), 295 K, Ref\. 20, as Herring et al\. print it \(FWHM MHz/amagat\)\.

herring\_1986/table5\_cooper\_295K
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table5_cooper_295K",
     "material": "H2",
     "file": "H2/herring_1986__table5_cooper_295K.csv",
     "table": "tbl_bc667320a0be",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "V. G. Cooper, A. D. May and B. K. Gupta, Can. J. Phys. 48, 725 (1970)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table V \(p\. 5\), 295 K, Ref\. 21, as Herring et al\. print it\.

herring\_1986/table5\_van\_den\_hout\_80K
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table5_van_den_hout_80K",
     "material": "H2",
     "file": "H2/herring_1986__table5_van_den_hout_80K.csv",
     "table": "tbl_bc667320a0be",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "van_den_hout_1980"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "S(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 80
     }
   }

Table V \(p\. 5\), 80 K, Ref\. 20, as Herring et al\. print it\.

herring\_1986/table6\_295K
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table6_295K",
     "material": "H2",
     "file": "H2/herring_1986__table6_295K.csv",
     "table": "tbl_e8a79c044c46",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "S(J), per row",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table VI \(p\. 6\), 295 K, 'This work'\: density shift delta nu = nu\_R\(rho\) \- nu\_R\(0\) of H2 S\(0\), S\(1\) per perfect\-gas amagat \(Eq\. \(5\)\), normal H2; fitted against the density difference between the sample and reference cells \(Fig\. 7\)\.

herring\_1986/table6\_80K
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table6_80K",
     "material": "H2",
     "file": "H2/herring_1986__table6_80K.csv",
     "table": "tbl_e8a79c044c46",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "S(J), per row",
       "perturber": "self",
       "temperature_k": 80
     }
   }

Table VI \(p\. 6\), 80 K, 'This work'\: density shift of H2 S\(0\), S\(1\) \(Eq\. \(5\)\)\.

herring\_1986/table6\_cooper\_295K
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table6_cooper_295K",
     "material": "H2",
     "file": "H2/herring_1986__table6_cooper_295K.csv",
     "table": "tbl_e8a79c044c46",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "V. G. Cooper, A. D. May and B. K. Gupta, Can. J. Phys. 48, 725 (1970)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "S(J), per row",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table VI \(p\. 6\), 295 K, Ref\. 21, as Herring et al\. print it; 'consistent with the combined uncertainties' \(p\. 6\)\.

herring\_1986/table6\_van\_den\_hout\_80K
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table6_van_den_hout_80K",
     "material": "H2",
     "file": "H2/herring_1986__table6_van_den_hout_80K.csv",
     "table": "tbl_e8a79c044c46",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "van_den_hout_1980"
     ],
     "parameters": {
       "transition": "S(J), per row",
       "perturber": "self",
       "temperature_k": 80
     }
   }

Table VI \(p\. 6\), 80 K, Ref\. 20, as Herring et al\. print it \(no uncertainty\)\.

Formulas
--------

herring\_1986/eq9\_power\_law
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq9_power_law",
     "material": "N2",
     "equation": "Eq. (9), p. 7; Table VII (tbl_b2bf3ef501ad), p. 7",
     "printed": "B = B_0 (T/295)^gamma",
     "variable": "T: temperature in K; B: FWHM self-broadening coefficient of N2 S(J) in MHz per perfect-gas amagat; B_0 its 295 K value (Table I)",
     "state": "pure N2, self-broadening",
     "density": "ideal",
     "range": "80-295 K (the three measured temperatures); S(2)-S(12)",
     "coefficients": {
       "B0_S2": "4160",
       "gamma_S2": "0.33",
       "gamma_S2_error": "0.02",
       "B0_S4": "3580",
       "gamma_S4": "0.28",
       "gamma_S4_error": "0.01",
       "B0_S6": "3560",
       "gamma_S6": "0.26",
       "gamma_S6_error": "0.04",
       "B0_S8": "3270",
       "gamma_S8": "0.33",
       "gamma_S8_error": "0.004",
       "B0_S10": "3060",
       "gamma_S10": "0.35",
       "gamma_S10_error": "0.002",
       "B0_S12": "2870",
       "gamma_S12": "0.39",
       "gamma_S12_error": "0.03"
     },
     "check": "Against Table I at 195 and 80 K (scratch, 2026-09-26): within 2.1 % except S(6) 195 K (+4.1 %: 3197 against 3070) and S(12) 195 K (+4.4 %: 2442 against 2340); the paper says 'Both Eqs. (9) and (10) can be used to predict B to better than 3 % over the range of 80-300 K' (p. 7), which these two rows exceed. A log-linear refit through B_0 gives gamma = 0.335, 0.276, 0.273, 0.331, 0.348, 0.414 (J = 2-12), within 0.025 of the printed values."
   }

Table VII's B\_0 are Table I's 295 K values\. The paper's gamma is the exponent of the per\-density coefficient; for a per\-pressure coefficient 'gamma = 1 \- eta' \(p\. 7\), so in the vocabulary's gamma\(T0\)\(T0/T\)^N form N = 1 \- gamma per atm and N = \-gamma per amagat\. The printed errors are presumably fit errors \(not described\)\. The abstract says 0\.25 \< gamma \< 0\.39, the text \(p\. 7\) 0\.26 \< gamma \< 0\.39 \(Table VII's smallest is 0\.26\)\.

herring\_1986/eq10\_linear
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq10_linear",
     "material": "N2",
     "equation": "Eq. (10) with D_0 = 0, p. 7; Table VII, p. 7",
     "printed": "B = B_0 + C_0 (T - 295) + D_0 (T - 295)^2, fitted with D_0 = 0",
     "variable": "T in K; B the FWHM self-broadening coefficient of N2 S(J) in MHz/amagat; C_0 in MHz amagat^-1 K^-1",
     "state": "pure N2, self-broadening",
     "density": "ideal",
     "range": "80-295 K; S(2)-S(12)",
     "coefficients": {
       "B0_S2": "4160",
       "C0_S2": "6.8",
       "C0_S2_error": "0.4",
       "B0_S4": "3580",
       "C0_S4": "5.1",
       "C0_S4_error": "0.7",
       "B0_S6": "3560",
       "C0_S6": "4.8",
       "C0_S6_error": "0.1",
       "B0_S8": "3270",
       "C0_S8": "5.4",
       "C0_S8_error": "0.7",
       "B0_S10": "3060",
       "C0_S10": "5.2",
       "C0_S10_error": "0.6",
       "B0_S12": "2870",
       "C0_S12": "5.4",
       "C0_S12_error": "0.1"
     },
     "check": "Against Table I (scratch, 2026-09-26): 80 K within 1.1 %; 195 K off by -2.2 (S(2)), -5.0 (S(4)), +0.3 (S(6)), -4.5 (S(8)), -4.5 (S(10)), -0.4 % (S(12)): not 'better than 3 %' at 195 K for S(4), S(8), S(10). A least-squares C_0 through B_0 gives 6.65, 4.79, 4.85, 5.13, 4.99, 5.45, close to the printed ones."
   }

Pack's \(Ref\. 26\) quadratic law; 'B\_0 is the broadening coefficient at 298 K \[same as in Eq\. \(9\)\]' \(p\. 7\)\: the text says 298 K where Eq\. \(10\) and Table VII use 295 K\.

herring\_1986/eq2\_A
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq2_A",
     "material": "H2",
     "equation": "Eq. (2), p. 5",
     "printed": "A = 4 pi^2 nu_R^2 D_0",
     "variable": "nu_R: the Raman frequency in cm-1; D_0: the self-diffusion coefficient in cm2 amagat s-1; A in Hz amagat (the Dicke term of Eq. (1), Table IV in MHz amagat), forward scattering",
     "state": "H2, forward scattering",
     "density": "ideal",
     "range": "densities above rho_c (Eq. (3))",
     "coefficients": {
       "prefactor": "4 pi^2"
     },
     "check": "With the printed 4 pi^2, Table IV's A would be 4.31, 6.71, 5.89, 19.32 MHz amagat (80 K S(0), S(1); 295 K S(0), S(1)); Table IV prints 1.37, 2.10, 1.87, 6.15, which 4 pi nu_R^2 D_0 reproduces (1.372, 2.135, 1.874, 6.149; the 80 K S(1) row 1.6 % low) (scratch, 2026-09-26).",
     "corrections": [
       {
         "term": "prefactor",
         "printed": "4 pi^2",
         "corrected": "4 pi",
         "reason": "Eq. (2) as printed is a factor pi larger than every A of Table IV, which the paper computes with it; 4 pi nu_R^2 D_0 reproduces Table IV to 0.3 % (three rows) and 1.6 % (80 K S(1)). It is also Bischel and Dyer's Eq. (7) (Ref. 18, Phys. Rev. A 33, 3113), Delta nu_FWHM = D_0 k_e^2/(pi rho) with k_e = 2 pi nu_R, i.e. A = 4 pi nu_R^2 D_0.",
         "evidence": "Eq. (2) on p. 5 (journal p. 1948; the pdf page image checked) prints 4 pi^2. Table IV (tbl_0e34a8d11d00, image checked): nu_R 354 and 587 cm-1, D_0 0.871, 0.493, 1.19, 1.42; A 1.37, 2.10, 1.87, 6.15 MHz amagat. bischel_1986 Eq. (7), p. 6."
       }
     ]
   }

Eq\. \(3\), rho\_c = 3\.33 A/Delta nu\_D, reproduces Table IV's rho\_c \(0\.095, 0\.087, 0\.068, 0\.134\); curated as eq3\_cutoff\.

herring\_1986/eq3\_cutoff
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq3_cutoff",
     "material": "H2",
     "equation": "Eq. (3), p. 5",
     "printed": "rho_c = 3.33 A/Delta nu_D",
     "variable": "A: the Dicke coefficient of Eq. (1), MHz amagat; Delta nu_D: the FWHM Doppler width for forward scattering, MHz (Eq. (4)); rho_c: the cutoff density, amagat",
     "state": "H2, forward scattering",
     "density": "ideal",
     "range": "any",
     "coefficients": {
       "factor": "3.33"
     },
     "check": "With Table IV's A and Delta nu_D it gives Table IV's rho_c 0.095, 0.087, 0.068, 0.134 amagat (80 K S(0), S(1); 295 K S(0), S(1)); Table IV prints 0.088 for 80 K S(1) (scratch, 2026-09-28, TC-688)."
   }

'There is a cutoff density, rho\_c, at which this model \[Eq\. \(1\), the diffusion model\] predicts a linewidth that is 10% larger than that predicted by the "hard collision" line\-shape theory' \(p\. 5\), from Bischel & Dyer \(Ref\. 18\); above it the line is Lorentzian with the width of Eq\. \(1\)\.

herring\_1986/eq4\_doppler
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq4_doppler",
     "material": "H2",
     "equation": "Eq. (4), p. 5",
     "printed": "Delta nu_D = 7.15 x 10^-7 nu_R (T/m)^(1/2)",
     "variable": "nu_R: the Raman frequency in MHz; T in K; m: the molecular mass in amu; Delta nu_D: the FWHM Doppler width in MHz for forward scattering",
     "state": "zero-density limit",
     "density": "unknown",
     "range": "any",
     "coefficients": {
       "k": "7.15e-7"
     },
     "check": "With m = 2 amu and nu_R = 354, 587 cm-1 x 29979.2458 MHz: 48.0, 79.6, 92.2, 152.8 MHz against Table IV's 48, 80, 92, 153 (80 and 295 K) (scratch, 2026-09-26); with m = 2.016 amu the S(1) rows come out 79.3 and 152.2."
   }

The standard Doppler FWHM constant \(8 k ln2/\(amu c^2\)\)^\(1/2\) = 7\.16e\-7\.

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.