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 · Catalogue · Review register
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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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 review register for the checks and decisions.