bischel_1986
============

W\. K\. Bischel and M\. J\. Dyer, "Temperature dependence of the Raman linewidth and line shift for the Q\(1\) and Q\(0\) transitions in normal and para\-H2", Phys\. Rev\. A 33, 3113 \(1986\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/bischel_1986.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/PhysRevA\.33\.3113 <https://doi.org/10.1103/PhysRevA.33.3113>`__

**Source kind:** measurement

**Recorded technique:** cw stimulated Raman gain spectroscopy \(SRGS, p\. 2\)\: a single\-frequency argon\-ion probe at 488 nm \(the Stokes wave; drift \< 10 MHz per scan\) and an electronically tunable single\-frequency ring dye pump at 612 nm \(\< 1 MHz\), amplitude modulated at 100 kHz, in a multipass cell \(up to 50 passes\) at 77\-500 K and up to 500 psi, followed by a double\-pass reference cell at 298 K for the line shifts\. Forward scattering\. Density from a Baratron gauge and a thermocouple by the perfect\-gas law \('the density calculated using the second virial coefficient deviates from this calculation by less than 1 % at the maximum density of 12 amagats', p\. 2\)\. Lorentzian fits give FWHM widths; widths at each temperature fitted to Eq\. \(1\) over densities above the cutoff rho\_c \(Table III\), about 1\-25 amagat\. Normal H2 \(ortho\:para 3\:1\) and para\-enriched H2 \(1\:7\.7, stored boil\-off from liquid H2\)\.

**Materials in structured entries:** H2

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

**Contents:** 27 datasets; 6 formulas.

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

Identity checked against the first page\. Page numbers are pdf pages \(1\-11 = journal pp\. 3113\-3123\)\. Material H2 is the main isotopologue; the paper has no other\.

WIDTH CONVENTION \(the key hazard\)\. All widths are FULL widths\: p\. 3, 'A Lorentzian line\-shape function was used to determine the full width at half maximum \(FWHM\) Raman linewidth'; Eq\. \(1\), p\. 3\: 'Delta nu\_FWHM = A/rho \+ B rho, where A is a coefficient proportional to the self\-diffusion coefficient, rho is density, and B is the density\-broadening coefficient'; Table I's A in MHz amagat and B in MHz/amagat; Eq\. \(8\), p\. 8\: 'B is the FWHM linewidth in MHz/amagat given in Table I'; Figs\. 3 and 4 are labelled FWHM\. The law INCLUDES the Dicke \(collisional\-narrowing\) term A/rho, A in MHz amagat, valid above the cutoff density rho\_c \(Table III, about 1 amagat\); below it the hard\-collision model applies \(Fig\. 7\)\. The amagat densities are perfect\-gas densities \(p\. 2\), i\.e\. rho = \(p/p0\)\(273\.15/T\) with the gas at T, not a real\-gas amagat\. The coefficients are self\-broadening of H2 by H2 of the stated ortho\:para ratio\.

ORTHO\:PARA\. 3\:1 is normal H2 \(the room\-temperature equilibrium mixture\), the material H2; the 81 K data at 3\:1 are normal H2 cooled without conversion\. 1\:7\.7 is a para\-enriched mixture \(not normal H2\)\: the datasets that use it say so in parameters\.ortho\_para\. n\(J,T\) of Table IV is the relative population of level J\.

TABLE I \(p\. 4\)\: Q\(0\) and Q\(1\), T = 81, 298, 474 K\. 'We believe that the current value is correct to better than 5 % due to the high resolution afforded by our experimental technique' \(p\. 4, of the 298 K Q\(1\) value\)\. The \+\- are not otherwise described \(level not stated\)\. The 'Previous work' column \(the Q\(1\) measurements 'at 295 K', p\. 4, printed in the 298 K rows\)\: Owyoung \(Ref\. 9, SRGS\) A 302 \+\- 9, B 51\.3 \+\- 0\.6; Murray and Javan \(Ref\. 22, murray\_1972\) B 66\.0 \+\- 5\.0 \(Q\(0\)\), 45\.0 \+\- 3 \(Q\(1\)\); Allin et al\. \(Ref\. 6\) 70, 42; Hunt et al\. \(Ref\. 8\) 83\.0 \+\- 3\.0, 55\.0 \+\- 2\.0; Foltz et al\. \(Ref\. 5\) 53\.1 \(Q\(1\)\); Lallemand and Simova \(Ref\. 7\) 63 \(Q\(1\)\)\: reproduced datasets\. The authors\: 'our measurements agree almost exactly with the data of Owyoung \.\.\. those measurements of the other authors differ by 15\-20 %'; Lallemand and Simova's 'linewidths are 30 % larger than ours' \(p\. 4\)\.

TABLE II \(p\. 5\)\: line shift nu\_R\(rho\) = nu\_R\(0\) \+ C rho \+ D rho^2 \(Eq\. \(3\)\); C only, except at 474 K where the quadratic term was fitted \(D = 0\.51 \+\- 0\.07 MHz/amagat^2\)\. The 81, 298 and 474 K Q\(1\) and the 81 K para Q\(0\) shifts are from the two\-cell technique; the others from successive scans \(p\. 5\)\. Previous work\: May et al\. / Looi et al\. \(Ref\. 11\), Murray and Javan \(Ref\. 22\), Lallemand and Simova \(Ref\. 7\)\. The sign\: negative C is a shift to lower Raman frequency with density \(Fig\. 2\: the 81 K line lies 2 GHz above the 298 K reference in the dye\-laser frequency, i\.e\. at lower Raman shift\)\. Zero\-density position 4155\.25 cm\-1 \(Fig\. 2 caption\); the text \(p\. 5\) quotes Stoicheff 4155\.207 \(stoicheff\_1957's Q\_1\(1\) 4155\.201 at 1\-2 atm, extrapolated to zero density with this paper's Eq\. \(4\)\), Foltz et al\. 4155\.259 and Brannon et al\. 4155\.240 \+\- 0\.02 cm\-1 \(reproduced values, not extracted; the note added in proof says FT\-Raman now fixes them to better than 0\.001 cm\-1\)\. 'The ratio of the shift coefficient \.\.\. to the broadening coefficient \.\.\. reaches a maximum value of 7\.3 at 77 K' \(p\. 6; 81 K in the abstract and Fig\. 2\)\.

TABLE III \(p\. 6\)\: Doppler FWHM for forward scattering \(Eq\. \(5\), with k\_e = 2 pi nu\_R, Eq\. \(6\)\), the self\-diffusion coefficient D\_0 \(cm2 amagat s\-1\) from A by Eq\. \(7\), Delta nu\_FWHM = D\_0 k\_e^2/\(pi rho\), and the cutoff density rho\_c \(amagat\) at X = 3\.33\. D\_0 and rho\_c have no quantity; as printed\: 81 K Q\(0\) 3\:1 D\_0 0\.871, rho\_c 1\.10; 81 K Q\(0\) 1\:7\.7 0\.350, 0\.45; 81 K Q\(1\) 3\:1 0\.493, 0\.63; 298 K Q\(0\) 3\:1 1\.19, 0\.79; 298 K Q\(1\) 3\:1 1\.42, 0\.92; 474 K Q\(1\) 3\:1 2\.34, 1\.23\. D\_0 of Q\(1\) follows T^0\.92 \(p\. 9\) against the theoretical T^0\.72 above 65 K\.

TABLE IV \(p\. 8\)\: at 81 K both theories print '\< 2' MHz/amagat for all three rows \(not extracted\: upper bounds\)\. n\_J as printed\: 81 K 0\.25 \(Q\(0\), 3\:1\), 0\.89 \(Q\(0\), 1\:7\.7\), 0\.75 \(Q\(1\)\); 298 K 0\.130, 0\.658, 0\.117, 0\.090 \(J = 0\-3\)\. The 'Vibrational contribution' column \(Table IV minus Van Kranendonk's beta, Eq\. \(8\)\) as printed\: 81 K 29\.0 \+\- 1\.0, 45\.4 \+\- 0\.8, 41\.5 \+\- 0\.6; 298 K '0\-9', '28\-34', '0\-2 \+\- 11', '21\-29 \+\- 28' \(ranges; notes only\)\.

TABLE V \(p\. 9\)\: formulas eq8\_\* and eq9\_\* below\. The 81 K alpha\_i is printed '23 \+\-' with no number after the sign \(image checked; the text, p\. 8, gives 'alpha\_i = 23 MHz/amagat and alpha\_c = 25 MHz/amagat'\)\. Previous line\-shift coefficients \(Eq\. \(9\)\) as printed, reproduced and not extracted\: May et al\. \(Ref\. 11\) experiment a\_i \-261 \(81 K\), \-60 \(298 K\), a\_c \-42, \-51; their theory a\_i \-260, \-60, a\_c \-63, \-63; Lallemand and Simova \(Ref\. 7\) experiment 298 K a\_i \-45, a\_c \-68\. Gray and Welsh \(Ref\. 35\) proposed alpha\_c = 42 MHz/amagat\.

solprop\: its H2 vibrational linewidth \(FWHM in Hz = 309e6/n \+ 52\.2e6 n, n in amagat\) is exactly Table I's Q\(1\), 298 K, 3\:1 A = 309 MHz amagat and B = 52\.2 MHz/amagat\.

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

Datasets
--------

bischel\_1986/table1\_B\_Q1\_normal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_Q1_normal",
     "material": "H2",
     "file": "H2/bischel_1986__table1_B_Q1_normal.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(1)",
       "width": "fwhm",
       "perturber": "self",
       "ortho_para": "3:1"
     }
   }

Table I \(p\. 4\), B of Eq\. \(1\), 'This work'\: the FWHM density\-broadening coefficient of Q\(1\) in normal H2 \(3\:1\), MHz per \(perfect\-gas\) amagat, fitted with the Dicke term A/rho \(dataset table1\_A\_Q1\_normal\)\. 298 K 'correct to better than 5 %' \(p\. 4\)\.

bischel\_1986/table1\_A\_Q1\_normal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_A_Q1_normal",
     "material": "H2",
     "file": "H2/bischel_1986__table1_A_Q1_normal.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz amagat",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(1)",
       "width": "fwhm",
       "perturber": "self",
       "term": "A/rho (Dicke narrowing) of Eq. (1)",
       "ortho_para": "3:1"
     }
   }

Table I \(p\. 4\), A of Eq\. \(1\), 'This work'\: the coefficient of the Dicke \(collisional\-narrowing, diffusion\-model\) term A/rho of the FWHM, MHz amagat, Q\(1\), normal H2 \(3\:1\)\. Not a broadening coefficient\: the width is A/rho \+ B rho\. Valid above rho\_c \(Table III\)\.

bischel\_1986/table1\_B\_Q0\_normal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_Q0_normal",
     "material": "H2",
     "file": "H2/bischel_1986__table1_B_Q0_normal.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(0)",
       "width": "fwhm",
       "perturber": "self",
       "ortho_para": "3:1"
     }
   }

Table I \(p\. 4\), B of Eq\. \(1\), 'This work'\: FWHM density\-broadening coefficient of Q\(0\) in normal H2 \(3\:1\)\. The Q\(0\) signal\-to\-noise was 'somewhat worse' than Q\(1\)'s \(p\. 4\)\.

bischel\_1986/table1\_A\_Q0\_normal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_A_Q0_normal",
     "material": "H2",
     "file": "H2/bischel_1986__table1_A_Q0_normal.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz amagat",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(0)",
       "width": "fwhm",
       "perturber": "self",
       "term": "A/rho (Dicke narrowing) of Eq. (1)",
       "ortho_para": "3:1"
     }
   }

Table I \(p\. 4\), A of Eq\. \(1\) \(the Dicke term A/rho of the FWHM, MHz amagat\), Q\(0\), normal H2 \(3\:1\)\.

bischel\_1986/table1\_B\_Q0\_para
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_Q0_para",
     "material": "H2",
     "file": "H2/bischel_1986__table1_B_Q0_para.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(0)",
       "width": "fwhm",
       "perturber": "self",
       "ortho_para": "1:7.7"
     }
   }

Table I \(p\. 4\), B of Eq\. \(1\), 'This work'\: FWHM density\-broadening coefficient of Q\(0\) at 81 K in PARA\-ENRICHED H2 \(ortho\:para 1\:7\.7\), not normal H2\: broadened by that mixture\.

bischel\_1986/table1\_A\_Q0\_para
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_A_Q0_para",
     "material": "H2",
     "file": "H2/bischel_1986__table1_A_Q0_para.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz amagat",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(0)",
       "width": "fwhm",
       "perturber": "self",
       "term": "A/rho (Dicke narrowing) of Eq. (1)",
       "ortho_para": "1:7.7"
     }
   }

Table I \(p\. 4\), A of Eq\. \(1\) \(Dicke term, MHz amagat\), Q\(0\) at 81 K in para\-enriched H2 \(1\:7\.7\)\. The authors have 'no current explanation' for A's factor\-2\.5 dependence on the ortho\:para ratio \(p\. 10\)\.

bischel\_1986/table1\_A\_owyoung
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_A_owyoung",
     "material": "H2",
     "file": "H2/bischel_1986__table1_A_owyoung.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "A. Owyoung, Opt. Lett. 2, 91 (1978)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "term": "A/rho (Dicke narrowing) of Eq. (1)",
       "temperature_k": 295
     }
   }

Table I \(p\. 4\), A 'Previous work', note d \(Ref\. 9, SRGS\), printed in the 298 K row; the text \(p\. 4\) says the previous Q\(1\) measurements were at 295 K\. Normal H2\.

bischel\_1986/table1\_B\_owyoung
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_owyoung",
     "material": "H2",
     "file": "H2/bischel_1986__table1_B_owyoung.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "A. Owyoung, Opt. Lett. 2, 91 (1978)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table I \(p\. 4\), B 'Previous work', note d \(Ref\. 9\), 298 K row \(the text\: 295 K\)\. FWHM as Bischel and Dyer tabulate it\.

bischel\_1986/table1\_B\_murray\_javan
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_murray_javan",
     "material": "H2",
     "file": "H2/bischel_1986__table1_B_murray_javan.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "murray_1972"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table I \(p\. 4\), B 'Previous work', note a \(Ref\. 22\), Q\(0\) and Q\(1\) in the 298 K rows \(the text\: 295 K\)\. FWHM as Bischel and Dyer tabulate it\. Re\-pointed to murray\_1972 \(2026\-09\-27\)\: its Table II \(p\. 11\) prints 2\.2 \+\- 0\.15 and 1\.5 \+\- 0\.1 x 10^\-3 cm\-1/amagat at 25 C, FULL widths in its own words \('full width at half maximum', its pp\. 2, 7\); x 29\.98 GHz/cm\-1 = 65\.95 and 44\.97 MHz/amagat, errors 4\.5 and 3\.0\: these values \(66\.0 \+\- 5\.0, 45\.0 \+\- 3\), the Q\(0\) error rounded up\.

bischel\_1986/table1\_B\_allin
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_allin",
     "material": "H2",
     "file": "H2/bischel_1986__table1_B_allin.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "E. J. Allin, A. D. May, B. P. Stoicheff, J. C. Stryland and H. L. Welsh, Appl. Opt. 6, 1597 (1967)"
     ],
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table I \(p\. 4\), B 'Previous work', note b \(Ref\. 6\), Q\(0\) and Q\(1\), no uncertainty printed; 298 K rows \(the text\: 295 K\)\.

bischel\_1986/table1\_B\_hunt
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_hunt",
     "material": "H2",
     "file": "H2/bischel_1986__table1_B_hunt.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "R. H. Hunt, W. L. Barnes and P. J. Brannon, Phys. Rev. A 1, 1570 (1970); P. J. Brannon, J. Quant. Spectrosc. Radiat. Transfer 8, 1615 (1968)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table I \(p\. 4\), B 'Previous work', note c \(Ref\. 8\), Q\(0\) and Q\(1\); 298 K rows \(the text\: 295 K\)\.

bischel\_1986/table1\_B\_foltz
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_foltz",
     "material": "H2",
     "file": "H2/bischel_1986__table1_B_foltz.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "J. V. Foltz, D. H. Rank and T. A. Wiggins, J. Mol. Spectrosc. 21, 208 (1966)"
     ],
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table I \(p\. 4\), B 'Previous work', note e \(Ref\. 5\), Q\(1\), no uncertainty printed; 298 K row \(the text\: 295 K\)\.

bischel\_1986/table1\_B\_lallemand
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_lallemand",
     "material": "H2",
     "file": "H2/bischel_1986__table1_B_lallemand.csv",
     "table": "tbl_64d6921655d1",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "P. Lallemand and P. Simova, J. Mol. Spectrosc. 26, 262 (1968)"
     ],
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self",
       "temperature_k": 295
     }
   }

Table I \(p\. 4\), B 'Previous work', note f \(Ref\. 7\), Q\(1\), no uncertainty printed; 298 K row\. Stimulated Raman; 'their linewidths are 30 % larger than ours' \(p\. 4\)\.

bischel\_1986/table2\_C\_Q1\_normal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_C_Q1_normal",
     "material": "H2",
     "file": "H2/bischel_1986__table2_C_Q1_normal.csv",
     "table": "tbl_9778e6276a73",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(1)",
       "perturber": "self",
       "ortho_para": "3:1"
     }
   }

Table II \(p\. 5\), C of Eq\. \(3\), 'This work'\: the linear density shift of Q\(1\) in normal H2 \(3\:1\), MHz per perfect\-gas amagat; two\-cell technique\. At 474 K the quadratic term was fitted too \(table2\_D\_Q1\_normal\); elsewhere a linear fit below 25 amagat\.

bischel\_1986/table2\_C\_Q0\_normal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_C_Q0_normal",
     "material": "H2",
     "file": "H2/bischel_1986__table2_C_Q0_normal.csv",
     "table": "tbl_9778e6276a73",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(0)",
       "perturber": "self",
       "ortho_para": "3:1"
     }
   }

Table II \(p\. 5\), C of Eq\. \(3\), 'This work', Q\(0\) in normal H2 \(3\:1\); successive\-scan technique \(p\. 5\)\.

bischel\_1986/table2\_C\_Q0\_para
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_C_Q0_para",
     "material": "H2",
     "file": "H2/bischel_1986__table2_C_Q0_para.csv",
     "table": "tbl_9778e6276a73",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(0)",
       "perturber": "self",
       "ortho_para": "1:7.7"
     }
   }

Table II \(p\. 5\), C of Eq\. \(3\), 'This work', Q\(0\) at 81 K in para\-enriched H2 \(1\:7\.7\), two\-cell technique\.

bischel\_1986/table2\_D\_Q1\_normal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_D_Q1_normal",
     "material": "H2",
     "file": "H2/bischel_1986__table2_D_Q1_normal.csv",
     "table": "tbl_9778e6276a73",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat2",
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(1)",
       "perturber": "self",
       "term": "D rho^2 of Eq. (3)",
       "ortho_para": "3:1"
     }
   }

Table II \(p\. 5\), D of Eq\. \(3\) \(the coefficient of rho^2, MHz/amagat^2\), 'This work', Q\(1\) at 474 K only, where 'the linear component in Eq\. \(3\) \[was\] small enough that we had to include the second\-order term'\.

bischel\_1986/table2\_C\_may
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_C_may",
     "material": "H2",
     "file": "H2/bischel_1986__table2_C_may.csv",
     "table": "tbl_9778e6276a73",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. D. May, G. Varghese, J. C. Stryland and H. L. Welsh, Can. J. Phys. 42, 1058 (1964)",
       "E. C. Looi, J. C. Stryland and H. L. Welsh, Can. J. Phys. 56, 1102 (1978)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), per row",
       "perturber": "self"
     }
   }

Table II \(p\. 5\), C 'Previous work', note a \(Ref\. 11, which cites both papers\), normal H2, rows by transition and temperature \(81 K as Table II prints it; Table V says their calculation is at 85 K\)\.

bischel\_1986/table2\_D\_may
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_D_may",
     "material": "H2",
     "file": "H2/bischel_1986__table2_D_may.csv",
     "table": "tbl_9778e6276a73",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat2",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "reproduced",
     "reproduced_from": [
       "A. D. May, G. Varghese, J. C. Stryland and H. L. Welsh, Can. J. Phys. 42, 1058 (1964)",
       "E. C. Looi, J. C. Stryland and H. L. Welsh, Can. J. Phys. 56, 1102 (1978)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), per row",
       "perturber": "self",
       "term": "D rho^2 of Eq. (3)"
     }
   }

Table II \(p\. 5\), D \(rho^2 coefficient\) 'Previous work', note a \(Ref\. 11\)\. The mark is extracted as a bare 'a' at 81 K \('0\.16±0\.02a'\); the image shows the superscript\.

bischel\_1986/table2\_C\_murray\_javan
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_C_murray_javan",
     "material": "H2",
     "file": "H2/bischel_1986__table2_C_murray_javan.csv",
     "table": "tbl_9778e6276a73",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "reproduced",
     "reproduced_from": [
       "murray_1972"
     ],
     "parameters": {
       "transition": "Q(J), per row",
       "perturber": "self"
     }
   }

Table II \(p\. 5\), C 'Previous work', note b \(Ref\. 22\), 298 K, normal H2\. Re\-pointed to murray\_1972 \(2026\-09\-27\)\: these are its Table III QUADRATIC\-fit a of Q\_1\(0\) and Q\_1\(1\), \-2\.15 and \-3\.0 x 10^\-3 cm\-1/amagat at 25 C \(x 29\.98 = \-64\.5, \-89\.9 MHz/amagat\), not its linear\-fit a \(\-1\.5, \-2\.5\)\.

bischel\_1986/table2\_D\_murray\_javan
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_D_murray_javan",
     "material": "H2",
     "file": "H2/bischel_1986__table2_D_murray_javan.csv",
     "table": "tbl_9778e6276a73",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat2",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "reproduced",
     "reproduced_from": [
       "murray_1972"
     ],
     "parameters": {
       "transition": "Q(J), per row",
       "perturber": "self",
       "term": "D rho^2 of Eq. (3)"
     }
   }

Table II \(p\. 5\), D 'Previous work', note b \(Ref\. 22\), 298 K\. Re\-pointed to murray\_1972 \(2026\-09\-27\)\: its Table III quadratic\-fit b of Q\_1\(0\) and Q\_1\(1\), 0\.0058 and 0\.0045 x 10^\-3 cm\-1/amagat^2 \(x 29\.98 = 0\.174, 0\.135 MHz/amagat^2\)\: the same values, each on its own line\.

bischel\_1986/table2\_C\_lallemand
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_C_lallemand",
     "material": "H2",
     "file": "H2/bischel_1986__table2_C_lallemand.csv",
     "table": "tbl_9778e6276a73",
     "quantity": "raman_line_shift",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "reproduced",
     "reproduced_from": [
       "P. Lallemand and P. Simova, J. Mol. Spectrosc. 26, 262 (1968)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), per row",
       "perturber": "self"
     }
   }

Table II \(p\. 5\), C 'Previous work', note c \(Ref\. 7\), Q\(1\) at 298 and 474 K\.

bischel\_1986/table3\_doppler
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table3_doppler",
     "material": "H2",
     "file": "H2/bischel_1986__table3_doppler.csv",
     "table": "tbl_ac118c75b5a0",
     "quantity": "raman_linewidth",
     "unit": "MHz",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "check",
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm"
     }
   }

Table III \(p\. 6\)\: the Doppler FWHM Delta nu\_D for forward scattering, calculated by Eq\. \(5\), Delta nu\_D = \(k\_e/pi\)\[2 ln2 kT/m\]^\(1/2\), k\_e = 2 pi nu\_R \(Eq\. \(6\), theta = 0\)\: the zero\-density Gaussian width, not a collisional one\. Rows name the transition, temperature and ortho\:para ratio\.

bischel\_1986/table4\_experiment
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table4_experiment",
     "material": "H2",
     "file": "H2/bischel_1986__table4_experiment.csv",
     "table": "tbl_b44c3eba642d",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self"
     }
   }

Table IV \(p\. 8\), 'Experiment \(this work\)'\: Table I's B repeated for comparison with theory, except that the 298 K values differ from Table I's\: Q\(0\) 77\.0 \+\- 1 \(Table I 76\.6 \+\- 0\.8\) and Q\(1\) 52\.4 \+\- 0\.6 \(Table I 52\.2 \+\- 0\.5\) \(both images checked; unexplained, Table I is the primary\)\. The 81 K Q\(0\) rows are 3\:1 and 1\:7\.7 \(n\_J 0\.25 and 0\.89\); the others normal H2\.

bischel\_1986/table4\_average
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table4_average",
     "material": "H2",
     "file": "H2/bischel_1986__table4_average.csv",
     "table": "tbl_b44c3eba642d",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "reproduced",
     "reproduced_from": [
       "E. J. Allin, A. D. May, B. P. Stoicheff, J. C. Stryland and H. L. Welsh, Appl. Opt. 6, 1597 (1967)",
       "R. H. Hunt, W. L. Barnes and P. J. Brannon, Phys. Rev. A 1, 1570 (1970); P. J. Brannon, J. Quant. Spectrosc. Radiat. Transfer 8, 1615 (1968)",
       "murray_1972"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self"
     }
   }

Table IV \(p\. 8\), 'Experiment' column for Q\(2\) and Q\(3\) at 298 K, note a\: 'Average of values in Refs\. 6, 8, and 22' \(formed by Bischel and Dyer from others' data\)\. Normal H2, FWHM\. Ref\. 22 is murray\_1972 \(re\-pointed 2026\-09\-27\)\: its Q\_1\(2\), Q\_1\(3\) are 2\.6 and 5\.5 x 10^\-3 cm\-1/amagat FWHM = 77\.9 and 164\.9 MHz/amagat \(murray\_1972 also prints Ref\. 6's as 2\.53 and 3\.66 = 75\.8 and 109\.7\)\.

bischel\_1986/table4\_theory\_van\_kranendonk
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table4_theory_van_kranendonk",
     "material": "H2",
     "file": "H2/bischel_1986__table4_theory_van_kranendonk.csv",
     "table": "tbl_b44c3eba642d",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "reproduced",
     "reproduced_from": [
       "J. Van Kranendonk, Can. J. Phys. 41, 433 (1963)"
     ],
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self"
     }
   }

Table IV \(p\. 8\), 'Theory, Ref\. 3'\: Van Kranendonk's calculated self\-broadening of the Q lines at 298 K, normal H2 \(rotationally inelastic collisions only; Q\(1\) a factor of 3 too low, p\. 7\)\. At 81 K the column prints '\< 2' for Q\(0\) and Q\(1\) \(not extracted\)\. A theory reprint, recorded as reproduced \(not fitted\)\.

bischel\_1986/table4\_theory\_hunt
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table4_theory_hunt",
     "material": "H2",
     "file": "H2/bischel_1986__table4_theory_hunt.csv",
     "table": "tbl_b44c3eba642d",
     "quantity": "raman_linewidth",
     "unit": "MHz/amagat",
     "abscissa": "label",
     "columns": {
       "temperature": "K"
     },
     "use": "reproduced",
     "reproduced_from": [
       "R. H. Hunt, W. L. Barnes and P. J. Brannon, Phys. Rev. A 1, 1570 (1970); P. J. Brannon, J. Quant. Spectrosc. Radiat. Transfer 8, 1615 (1968)"
     ],
     "parameters": {
       "transition": "Q(J), per row",
       "width": "fwhm",
       "perturber": "self"
     }
   }

Table IV \(p\. 8\), 'Theory, Ref\. 8'\: Hunt et al\.'s calculation 'using his \[Van Kranendonk's\] basic theory' \(p\. 7\), 298 K, normal H2; '\< 2' at 81 K \(not extracted\)\. A theory reprint, recorded as reproduced \(not fitted\)\.

Formulas
--------

bischel\_1986/eq2\_linewidth
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq2_linewidth",
     "material": "H2",
     "equation": "Eq. (2), p. 4",
     "printed": "Delta nu(rho) = (309/rho)(T/298)^0.92 + [51.8 + 0.152 (T - 298) + 4.85 x 10^-4 (T - 298)^2] rho",
     "variable": "rho: density in amagat (perfect gas, p. 2); T: temperature in K; Delta nu: the FWHM Raman linewidth of Q(1) in MHz",
     "state": "normal H2 (ortho:para 3:1), self-broadened",
     "density": "ideal",
     "range": "77-500 K, 1-50 amagat, ortho:para 3:1 (p. 4)",
     "coefficients": {
       "A298": "309",
       "A_exponent": "0.92",
       "B0": "51.8",
       "B1": "0.152",
       "B2": "4.85e-4",
       "T0": "298"
     },
     "check": "Against Table I's Q(1), 3:1 (scratch, 2026-09-26): B(81) = 41.65 (table 41.5 +- 0.6), B(298) = 51.8 (52.2 +- 0.5), B(474) = 93.58 (94.0 +- 2.0); A(81) = 93.2 (107 +- 20), A(298) = 309 (309), A(474) = 473.6 (508 +- 29). B agrees to within the table's errors (0.4 MHz/amagat); A is the 'best power law that can be obtained for the three points' (T^0.92, p. 9) and misses 474 K by 1.2 sigma. FWHM."
   }

'a phenomenological second\-order fit to the Q\(1\) linewidth' \(p\. 4\) including the Dicke term; the Fig\. 4 solid line\. Eq\. \(2\) is FWHM in MHz \('Here Delta nu is the FWHM Raman linewidth in MHz'\)\.

bischel\_1986/eq4\_line\_shift
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq4_line_shift",
     "material": "H2",
     "equation": "Eq. (4), p. 5",
     "printed": "C = [nu_R(rho) - nu_R(0)] rho^-1 = [-96.1 + 0.777 (T - 298) - 8.82 x 10^-4 (T - 298)^2]",
     "variable": "T: temperature in K; C in MHz/amagat (perfect-gas amagat)",
     "state": "normal H2 (ortho:para 3:1), self-shift of Q(1)",
     "density": "ideal",
     "range": "77-480 K (Fig. 5)",
     "coefficients": {
       "C0": "-96.1",
       "C1": "0.777",
       "C2": "-8.82e-4",
       "T0": "298"
     },
     "check": "Against Table II's Q(1), 3:1 (scratch, 2026-09-26): C(81) = -306.2 (table -305 +- 10), C(298) = -96.1 (-96 +- 1), C(474) = +13.3 (9.5 +- 0.9; the 474 K table value is from a fit with the rho^2 term). C = 0 at T = 446.8 K, as the text's 'C = 0 at T = 446' (p. 9)."
   }

'a phenomenological fit to the data' \(p\. 5\), the Fig\. 5 solid line \(the Fig\. 5 caption calls it Eq\. \(3\)\)\.

bischel\_1986/eq8\_81K
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq8_81K",
     "material": "H2",
     "equation": "Eq. (8), p. 8; Table V, p. 9",
     "printed": "B(J, T) = alpha_i + alpha_c n(J, T) + beta(J, T, R_o-p); 81 K: alpha_i = 23 +- [blank], alpha_c = 25 +- 1 MHz/amagat",
     "variable": "n(J, T): the relative population of rotational level J (Table IV's n_J); B the FWHM broadening coefficient in MHz/amagat; beta (rotationally inelastic part) about zero at 81 K",
     "state": "H2 at 81 K, ortho:para 3:1 and 1:7.7",
     "density": "ideal",
     "range": "81 K; Q(0) and Q(1)",
     "coefficients": {
       "alpha_i": "23",
       "alpha_c": "25",
       "alpha_c_error": "1"
     },
     "check": "Against Table I's 81 K B with beta = 0 (scratch, 2026-09-26): Q(0) 3:1 (n 0.25) 29.25 (table 29.0 +- 1.0), Q(0) 1:7.7 (n 0.89) 45.25 (45.4 +- 0.8), Q(1) 3:1 (n 0.75) 41.75 (41.5 +- 0.6): within 0.25 MHz/amagat."
   }

The 'vibrational dephasing' contribution\: alpha\_i, alpha\_c from the straight line of Fig\. 8\. The 81 K alpha\_i uncertainty is not printed \('23 \+\-', image checked\); the text \(p\. 8\) gives 23 and 25 without errors\.

bischel\_1986/eq8\_298K
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq8_298K",
     "material": "H2",
     "equation": "Eq. (8), p. 8; Table V, p. 9",
     "printed": "B(J, T) = alpha_i + alpha_c n(J, T) + beta(J, T, R_o-p); 298 K: alpha_i = 0 +- 5, alpha_c = 45 +- 5 MHz/amagat",
     "variable": "n(J, T) relative population; beta from Van Kranendonk (Table IV, Ref. 3); B FWHM in MHz/amagat",
     "state": "normal H2 at 298 K",
     "density": "ideal",
     "range": "298 K; Q(0)-Q(3)",
     "coefficients": {
       "alpha_i": "0",
       "alpha_i_error": "5",
       "alpha_c": "45",
       "alpha_c_error": "5"
     },
     "check": "alpha_c n for Q(1) (n 0.658) = 29.6 and Q(0) (n 0.130) = 5.9 MHz/amagat, within Table IV's 'vibrational contribution' ranges 28-34 and 0-9 (scratch, 2026-09-26). 'This analysis is only qualitative' (p. 8)."
   }

Gray and Welsh \(Ref\. 35\) proposed alpha\_c = 42 MHz/amagat \(Table V note a\)\.

bischel\_1986/eq9\_81K
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq9_81K",
     "material": "H2",
     "equation": "Eq. (9), p. 9; Table V, p. 9",
     "printed": "C = a_i(T) + a_c(T) n(J, T); 81 K: a_i = -225, a_c = -100 MHz/amagat",
     "variable": "n(J, T) relative population of level J; C the linear line-shift coefficient in MHz/amagat",
     "state": "H2 at 81 K",
     "density": "ideal",
     "range": "81 K; Q(0), Q(1)",
     "coefficients": {
       "a_i": "-225",
       "a_c": "-100"
     },
     "check": "Against Table II's 81 K C (scratch, 2026-09-26): Q(0) 3:1 (n 0.25) -250 (table -250 +- 10), Q(1) (n 0.75) -300 (-305 +- 10), Q(0) 1:7.7 (n 0.89) -314 (-336 +- 10): the para-enriched point misses by 2.2 of its errors; no uncertainty printed for a_i, a_c."
   }

Derived 'using Eq\. \(9\) from our data in Table II' \(p\. 9\)\. May et al\.'s values \(Ref\. 11\) are in the source notes; Table V's line\-shift theory rows are for 85 K per the text \('at 298 and 85 K', p\. 9\), printed in the 81 K row\.

bischel\_1986/eq9\_298K
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq9_298K",
     "material": "H2",
     "equation": "Eq. (9), p. 9; Table V, p. 9",
     "printed": "C = a_i(T) + a_c(T) n(J, T); 298 K: a_i = -58, a_c = -58 MHz/amagat",
     "variable": "n(J, T) relative population of level J; C in MHz/amagat",
     "state": "normal H2 at 298 K",
     "density": "ideal",
     "range": "298 K; Q(0), Q(1)",
     "coefficients": {
       "a_i": "-58",
       "a_c": "-58"
     },
     "check": "Against Table II's 298 K C (scratch, 2026-09-26): Q(0) (n 0.130) -65.5 (table -64 +- 5), Q(1) (n 0.658) -96.2 (-96 +- 1)."
   }

Two coefficients from two points; no uncertainty printed\.

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.