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