murray_1972#
J. R. Murray and A. Javan, “Effects of collisions on Raman line profiles of hydrogen and deuterium gas”, J. Mol. Spectrosc. 42, 1 (1972)
Source record · Catalogue · Review register
DOI: 10.1016/0022-2852(72)90139-7
Source kind: measurement
Recorded technique: Spontaneous vibrational Raman scattering, forward and backward (pp. 5, 11-16): a frequency-stabilised single-mode argon-ion laser at 488.0 nm (50 mW; long-term linewidth 0.003 cm-1), a 30 cm grazing-incidence fused-quartz capillary cell (0.5 mm bore) collecting light scattered within 0.05 rad of the forward or backward direction, a pressure-scanned Fabry-Perot (free spectral range 0.787 cm-1, finesse 25-30; instrumental width 0.025-0.036 cm-1 for H2, 0.053 cm-1 for D2), a tandem monochromator isolating one line, photon counting on a chart recorder; Lorentzians fitted by eye to the recordings (p. 16). Line shifts from two cells recorded together, one held at 35 amagat, the other at 5-90 amagat (p. 10). Pressures from Bourdon gauges (2 %), reduced to densities with the NBS tables; D2 assumed to follow H2’s equation of state (p. 16). Room temperature, 25 +- 2 C. Gases: Airco prepurified H2 (> 99.95 %), Matheson D2 (99.5 %, 0.5 % H2).
Materials in structured entries: D2, H2
Dataset quantities: raman_line_shift, raman_linewidth
Contents: 10 datasets; 1 formula.
Curation notes#
Identity checked against the first page. Page numbers are journal pages (pdf page n = p. n). Materials: H2 and D2 as supplied (normal; the ortho:para ratio is not discussed). Lines: the Q_1(n) lines of the 1-0 band, v = 0 -> 1 (n = J). Wavenumbers ‘where 1 cm-1 = 30 GHz’; densities in amagat, ‘rho amagat = (density/density at 1 atm pressure and 0 C)’ (p. 3).
WIDTH CONVENTION: FULL WIDTHS. ‘Figure 1 shows the predicted behavior of the line width (full width at half-maximum) of the Q_1(1) Raman scattering line’ (p. 2); ‘In this figure and in the remainder of the paper linewidths are expressed in wavenumbers’ (p. 3); ‘Figure 5 shows the measured full width at half maximum of the Q_1(1) line of hydrogen, with instrumental linewidth subtracted’ (p. 7), and ‘A least-mean-squared deviation fit of the forward-scattering data of Figure 5 to a straight line gives a collision-broadening coefficient for the Q_1(1) line of 1.5 x 10^-3 cm-1/amagat with an estimated error in the coefficient of less than 0.1 x 10^-3 cm-1/amagat’ (p. 7): the Table II value. Confirmed from Fig. 5 itself: its marked forward and backward Doppler widths, about 0.037 and 0.32 cm-1, are the FWHM Doppler widths of H2 Q_1(1) at 298 K (0.036 and 0.320 cm-1 computed), and its forward line reaches 0.153 cm-1 at 100 amagat. Fig. 8 (the other lines, forward) plots the widths on the same axis, instrument width retained (0.025 cm-1 for H2, 0.053 cm-1 for D2, p. 10). The appendix’s ‘halfwidth’ (Eqs. A.14 and the broadening Lorentzian, pp. 20, 25) is the HWHM of the model profiles, not the tabulated coefficients. So Table II’s coefficients are FWHM per amagat. The forward widths were fitted with a straight line (the Dicke term, small in forward scattering, not modelled).
DOUBT: THE D2 COEFFICIENTS (a finding for review). As FWHM, this paper’s H2 values agree with later FWHM measurements within about 15 % (bischel_1986’s 298 K Q(1) 52.2 MHz/amagat = 1.74e-3 cm-1/amagat against 1.5; Q(0) 76.6 = 2.56e-3 against 2.2), but its D2 values (1.4, 2.2, 2.6 for Q_1(1)-Q_1(3)) are half of the later FWHM ones (russell_1987 2.63, 3.91, 4.11; ottusch_1988 Q(2) 120 MHz/amagat = 4.0e-3) and equal to the later HWHM ones (smyth_1987 1.33, 2.06, 2.13). smyth_1987 prints these D2 values as HWHM and russell_1987 as FWHM (‘deviate almost 100 %’). The paper itself treats all its widths alike as FWHM; no statement singles out D2. Either the D2 coefficients are low by a factor 2 or they are half widths despite the paper’s convention: not settled here. Recorded as FWHM, the paper’s words.
UNCERTAINTIES. Table II and III +- not described beyond the Q_1(1) ‘estimated error’ (level not stated); delta = the rms deviation of the points from the fit (10^-3 cm-1), in printed. The Q_1(1) forward coefficient is 10 % below what the backward data need (‘a 10 % increase in the broadening coefficient as determined for forward scattering gives a much better fit to the backward-scattering data’, p. 9), unexplained.
SHIFT SIGN. Table III, ‘Frequency shift with density’: a negative a is taken to lower the Raman shift (the paper gives no sign convention in words; the H2 values have the sign of May et al.’s and of bischel_1986’s C = -96 MHz/amagat, a shift to lower Raman frequency). Quadratic term b positive.
NARROWING (Table I, Figs. 1-7; notes only). The backward Q_1(1) widths show Dicke narrowing to below the Doppler width; three strategies (Table I, p. 8) fit the hard- and soft-collision models with D_0 fixed at the gas-kinetic 1.36 (Table I; 1.346 in the text, p. 16) or free: ‘the data lie between the hard- and soft-collision models ... The hard-collision model gives a better fit under all strategies’ (p. 8). The fitted D_0 of strategy c is shown only in Figs. 6-7 (not digitised). The diffusion constants are in formula diffusion_D0.
REPRINTS (re-pointed 2026-09-27 to this record): bischel_1986 Table I B (66.0, 45.0 MHz/amagat = 2.2, 1.5 x 29.98) and Table II C and D (-65, -90 MHz/amagat and 0.174, 0.135 MHz/amagat^2 = the QUADRATIC fit’s a and b of Q_1(0), Q_1(1) converted), and Table IV’s average; bischel_1986b’s D = 0.174 MHz/amagat^2, which is the Q_1(0) b (the Q_1(1) b is 0.0045e-3 cm-1 = 0.135 MHz): Bischel and Dyer’s H2 Q(1) shift law uses the Q(0) coefficient; ottusch_1988 (the same 0.17 for Q(1), and D2 Q(2) -50 MHz/amagat = the linear -1.7e-3 cm-1 = -51.0 MHz/amagat); russell_1987 and smyth_1987 (the D2 coefficients, digit-identical); hanna_1986’s D2 Q(2) 70 MHz/atm does not follow from 2.2e-3 cm-1/amagat (66.0 MHz/amagat, 60.4 MHz/atm at 25 C).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
murray_1972/table2_H2#
{
"id": "table2_H2",
"material": "H2",
"file": "H2/murray_1972__table2_H2.csv",
"table": "tbl_cab7e16264ae",
"quantity": "raman_linewidth",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"width": "fwhm",
"perturber": "self",
"temperature_k": 298.15
}
}
Table II (p. 11), ‘This work’: FWHM density broadening coefficients of H2 Q_1(0)-Q_1(3), 10^-3 cm-1 per 0 C amagat at 25 C, from forward scattering (Q_1(1) from Fig. 5 over 0-100 amagat, the others from Fig. 8, single runs). FWHM: the paper’s ‘full width at half maximum’ (pp. 2, 7). No Dicke term modelled (forward scattering). The rms deviation delta (5, 1.5, 8, 10 x 10^-3 cm-1) in printed. Q_1(3) (5.5 +- 1) is well above May et al.’s 3.66 and the theory’s 3.6.
murray_1972/table2_D2#
{
"id": "table2_D2",
"material": "D2",
"file": "D2/murray_1972__table2_D2.csv",
"table": "tbl_cab7e16264ae",
"quantity": "raman_linewidth",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"width": "fwhm",
"perturber": "self",
"temperature_k": 298.15
}
}
Table II (p. 11), ‘This work’: density broadening coefficients of D2 Q_1(1)-Q_1(3), 10^-3 cm-1 per amagat at 25 C, forward scattering (Fig. 8; instrument width 0.053 cm-1). FWHM by the paper’s convention, but half of the later FWHM measurements and equal to smyth_1987’s HWHM (see the source notes’ DOUBT): these should not be used as FWHM without resolving it.
murray_1972/table2_may_H2#
{
"id": "table2_may_H2",
"material": "H2",
"file": "H2/murray_1972__table2_may_H2.csv",
"table": "tbl_cab7e16264ae",
"quantity": "raman_linewidth",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"A. D. May, G. Varghese, J. C. Stryland and H. L. Welsh, Can. J. Phys. 42, 1058 (1964); E. J. Allin, A. D. May, B. P. Stoicheff, J. C. Stryland and H. L. Welsh, Appl. Opt. 6, 1597 (1967)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"width": "fwhm",
"perturber": "self"
}
}
Table II (p. 11), ‘May, et al. (11)’: H2 Q_1(0)-Q_1(3) broadening from measurements ‘at higher densities’ (up to about 500 amagat, p. 10), in the table’s FWHM convention as this paper presents them. bischel_1986 prints Allin et al.’s Q(0), Q(1) as 70 and 42 MHz/amagat FWHM (2.33, 1.40e-3 cm-1): consistent.
murray_1972/table2_theory_H2#
{
"id": "table2_theory_H2",
"material": "H2",
"file": "H2/murray_1972__table2_theory_H2.csv",
"table": "tbl_cab7e16264ae",
"quantity": "raman_linewidth",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"J. Fiutak and J. Van Kranendonk, Can. J. Phys. 40, 1085 (1962); 41, 21 (1963); J. Van Kranendonk, Can. J. Phys. 41, 433 (1963); C. G. Gray and J. Van Kranendonk, Can. J. Phys. 44, 2411 (1966)"
],
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"width": "fwhm",
"perturber": "self"
}
}
Table II (p. 11), ‘Theoretical (32)’: Van Kranendonk et al.’s calculated H2 Q_1(0)-Q_1(3) broadening, as this paper tabulates it (FWHM convention). Theory: a check, not a measurement. Q_1(1) 0.6 against the measured 1.5.
murray_1972/table3_linear_H2#
{
"id": "table3_linear_H2",
"material": "H2",
"file": "H2/murray_1972__table3_linear_H2.csv",
"table": "tbl_ca64e120ea87",
"quantity": "raman_line_shift",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 298.15
}
}
Table III (p. 11), ‘This work Linear fit w = a rho’: the line-shift coefficient a of H2 Q_1(0)-Q_1(3), 10^-3 cm-1 per amagat at 25 C, forward scattering over 5-90 amagat against a 35 amagat reference cell (p. 10). Q_1(3) printed without an error. Negative: to lower Raman shift (source notes). The quadratic fit is table3_quadratic_a_H2 and _b_H2; ‘the improvement in the fit over a simple linear fit is insignificant for our limited density range’ (p. 10). rms deviation delta in printed.
murray_1972/table3_linear_D2#
{
"id": "table3_linear_D2",
"material": "D2",
"file": "D2/murray_1972__table3_linear_D2.csv",
"table": "tbl_ca64e120ea87",
"quantity": "raman_line_shift",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 298.15
}
}
Table III (p. 11), ‘This work Linear fit’: the line-shift coefficient a of D2 Q_1(1)-Q_1(3), 10^-3 cm-1 per amagat at 25 C; Q_1(3) without an error. ottusch_1988’s D2 Q(2) shift, -50 MHz/amagat, is this Q_1(2) value (-1.7e-3 cm-1 = -51.0 MHz/amagat).
murray_1972/table3_quadratic_a_H2#
{
"id": "table3_quadratic_a_H2",
"material": "H2",
"file": "H2/murray_1972__table3_quadratic_a_H2.csv",
"table": "tbl_ca64e120ea87",
"quantity": "raman_line_shift",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 298.15,
"term": "a rho of w = a rho + b rho^2"
}
}
Table III (p. 11), ‘This work Quadratic fit w = a rho + b rho^2’: a of H2 Q_1(0), Q_1(1), 10^-3 cm-1/amagat, no errors printed (rms deviation 5.8 and 6.3 against 8 and 7 for the linear fit). A second fit of the same data: check, beside table3_linear_H2. bischel_1986 reproduces these (with b) as C = -65 and -90 MHz/amagat.
murray_1972/table3_quadratic_b_H2#
{
"id": "table3_quadratic_b_H2",
"material": "H2",
"file": "H2/murray_1972__table3_quadratic_b_H2.csv",
"table": "tbl_ca64e120ea87",
"quantity": "raman_line_shift",
"unit": "cm-1/amagat2",
"scale": 0.001,
"abscissa": "label",
"use": "check",
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"perturber": "self",
"temperature_k": 298.15,
"term": "b rho^2 of w = a rho + b rho^2"
}
}
Table III (p. 11), quadratic fit: b of H2 Q_1(0), Q_1(1), ‘10^-3 cm-1 amagat^-2’. In MHz/amagat^2: 0.174 (Q_1(0)) and 0.135 (Q_1(1)); bischel_1986b and ottusch_1988 use 0.174 (or 0.17) for the Q(1) line, which is the Q_1(0) value.
murray_1972/table3_may_a_H2#
{
"id": "table3_may_a_H2",
"material": "H2",
"file": "H2/murray_1972__table3_may_a_H2.csv",
"table": "tbl_ca64e120ea87",
"quantity": "raman_line_shift",
"unit": "cm-1/amagat",
"scale": 0.001,
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"A. D. May, G. Varghese, J. C. Stryland and H. L. Welsh, Can. J. Phys. 42, 1058 (1964); E. J. Allin, A. D. May, B. P. Stoicheff, J. C. Stryland and H. L. Welsh, Appl. Opt. 6, 1597 (1967)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"perturber": "self",
"term": "a rho of w = a rho + b rho^2"
}
}
Table III (p. 11), ‘May, et al. (11) Quadratic fit’: a of H2 Q_1(0)-Q_1(2), 10^-3 cm-1/amagat, from densities up to 500 amagat (p. 10).
murray_1972/table3_may_b_H2#
{
"id": "table3_may_b_H2",
"material": "H2",
"file": "H2/murray_1972__table3_may_b_H2.csv",
"table": "tbl_ca64e120ea87",
"quantity": "raman_line_shift",
"unit": "cm-1/amagat2",
"scale": 0.001,
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"A. D. May, G. Varghese, J. C. Stryland and H. L. Welsh, Can. J. Phys. 42, 1058 (1964); E. J. Allin, A. D. May, B. P. Stoicheff, J. C. Stryland and H. L. Welsh, Appl. Opt. 6, 1597 (1967)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "Q1(J), v = 0 -> 1, per row",
"perturber": "self",
"term": "b rho^2 of w = a rho + b rho^2"
}
}
Table III (p. 11), ‘May, et al. (11) Quadratic fit’: b of H2 Q_1(0)-Q_1(2), 10^-3 cm-1/amagat^2.
Formulas#
murray_1972/diffusion_D0#
{
"id": "diffusion_D0",
"material": "H2",
"equation": "Eq. (A.14), p. 20; Appendix 1f, p. 16; Table I, p. 8",
"printed": "S(omega) = K / [(omega - omega_0)^2 + (k_0^2 D)^2], a Lorentzian of halfwidth k_0^2 D; D_0 = D rho; D_0 = 1.346 cm2/amagat sec at 25 C (H2); D_0 for D2 = 0.952",
"variable": "omega in rad/s; k_0 the effective wavevector |k_e| of the Raman scattering in rad/cm (forward: k_r = 2 pi nu_Raman; backward: k_a + k_s); D the diffusion parameter in cm2/s; rho the density in amagat; the halfwidth k_0^2 D_0/rho is a HWHM in angular frequency (the diffusion, high-density limit of the narrowing)",
"state": "H2 and D2 at 25 C",
"density": "unknown",
"range": "the diffusion limit, mean free path << lambda/2 pi (above about 12 amagat in backward scattering, p. 16)",
"coefficients": {
"D0_H2": "1.346",
"D0_H2_table_I": "1.36",
"D0_D2": "0.952",
"D_harteck_schmidt": "1.396",
"D_harteck_schmidt_error": "0.0025",
"pressure_torr": "785",
"temperature_c": "20"
},
"check": "Scratch (2026-09-27): D_0(D2) = 1.346/sqrt(2) = 0.9518, the printed 0.952 (the reduced-mass scaling, p. 16). D_0(H2) from Harteck and Schmidt's D = 1.396 at 785 Torr and 20 C: rho = (785/760)(273.15/293.15) = 0.9624 amagat gives D_0 = 1.3436 at 20 C, and the stated T^(1/2) scaling to 25 C gives 1.355, not the printed 1.346 (nor Table I's 1.36): the text's number is not reproduced to its third digit. smyth_1987 used 0.950 (mass diffusion) for D2."
}
The diffusion constants are inputs, not measurements: H2’s from Harteck and Schmidt (Ref. 22, Z. Phys. Chem. B 21, 447 (1933), para into normal H2), D2’s by the reduced-mass scaling, ‘accurate to perhaps 10 %’ (Amdur and Beatty, p. 16). D_0 varies by 0.7 % over 25 +- 2 C (neglected, p. 16). The hard- and soft-collision line shapes (Eqs. A.23, A.27-A.29) reduce to this limit at high density.
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.