russell_1987 ============ D\. A\. Russell and W\. B\. Roh, "High\-resolution CARS measurement of Raman linewidths of deuterium", J\. Mol\. Spectrosc\. 124, 240 \(1987\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1016/0022\-2852\(87\)90139\-1 `__ **Source kind:** measurement **Recorded technique:** High\-resolution cw CARS \(p\. 240\)\: a single\-mode Ar\-ion pump at 514\.5 nm \(effective linewidth about 0\.0003 cm\-1, which limits the resolution\) and a single\-mode ring\-dye Stokes beam at 608 nm, collinear, focused into a cell of D2; anti\-Stokes detection by photon counting; frequency markers from an etalon, calibration with a wavemeter and an iodine cell\. D2 Q\(0\)\-Q\(4\) of the fundamental band at room temperature, 0\.3\-18 amagat \(Q\(4\) below 10 amagat\); each point the average of three measurements\. Linewidth against density fitted with the Dicke \(diffusion\) law, Eq\. \(1\), by linear least squares for a and D\_0\. **Materials in structured entries:** D2 **Dataset quantities:** raman\_linewidth **Contents:** 3 datasets; 1 formula. Curation notes -------------- Identity checked against the first page\. Page numbers are journal pages \(pdf pages 1\-3 = pp\. 240\-242\)\. Material\: D2 as supplied \(normal, ortho\:para not stated; at room temperature\)\. 'room temperature' is the only temperature given \(Fig\. 1 caption, p\. 241\); no value in K\. 1 amagat 'is equal to the number density of gas at 1 atm at 273 K' \(p\. 240\)\. WIDTH CONVENTION\. FULL widths\. Eq\. \(1\), p\. 240\: 'Delta nu = \(4 pi nu^2/c\)\(D\_0/rho\) \+ a rho, where Delta nu is the linewidth \(FWHM in cm\-1\), nu is the frequency of the vibrational Raman transition \(in cm\-1\), rho is the gas density \(in amagat\), c is the speed of light \(in cm/sec\), a is the pressure broadening coefficient \(in cm\-1/amagat\), and D\_0 is the self\-diffusion coefficient at 1 amagat\.' Table I note\: 'a in \[10^\-3 cm\-1/amagat\]; D\_0 in \[cm2\-amagat/sec\]; delta\: rms error of the fit in \[10^\-3 cm\-1\]'\. The law INCLUDES the Dicke term, \(4 pi nu^2/c\) D\_0/rho \(FWHM, cm\-1\), fitted \(D\_0 per J, formula eq1\_dicke\)\. Independent confirmation of FWHM\: Smyth et al\. \(smyth\_1987, Table III, HWHM\) print 'Roh \(Ref\. 33\)' values 2\.90 \+\- 0\.04, 1\.32 \+\- 0\.02, 1\.96 \+\- 0\.02, 2\.06 \+\- 0\.04, 1\.94 \+\- 0\.04 for Q\(0\)\-Q\(4\), which are this table's a and errors halved and rounded \(5\.79/2 = 2\.895, 2\.63/2 = 1\.315, 3\.91/2 = 1\.955, 4\.11/2 = 2\.055, 3\.87/2 = 1\.935\)\. UNCERTAINTIES\. The \+\- on a and D\_0 are the least\-squares fit errors \('the fitting errors for the present measurement are more than five times smaller than those associated with Murray and Javan's measurements', p\. 241\); level not stated\. delta, the rms error of the fit \(10^\-3 cm\-1\)\: 0\.6, 1\.2, 1\.1, 1\.1, 0\.8 for Q\(0\)\-Q\(4\)\. Q\(4\) is 'somewhat less reliable' \(smaller density range, poor S/N, p\. 241\)\. THE COMPARISON COLUMNS \(p\. 241, reproduced\)\. Murray and Javan \(J\. R\. Murray and A\. Javan, J\. Mol\. Spectrosc\. 42, 1 \(1972\), curated as murray\_1972 since 2026\-09\-27; it calls its widths full widths\)\: a = 1\.4 \+\- 0\.15, 2\.2 \+\- 0\.2, 2\.6 \+\- 0\.5 \(Q\(1\)\-Q\(3\)\), D\_0 = 0\.952 for each, delta 7, 7, 8\. The paper says 'the present pressure\-broadening coefficients deviate almost 100 % from those of Murray and Javan' and blames Murray and Javan's 0\.053 cm\-1 instrument width\. But Smyth et al\. 1987 \(smyth\_1987 Table III, 'half\-width at half\-maximum'\) print the same three numbers, 1\.4 \+\- 0\.15, 2\.2 \+\- 0\.2, 2\.6 \+\- 0\.5, as HWHM, in agreement with their own HWHM \(1\.33, 2\.06, 2\.13\)\: the 'almost 100 %' deviation is the factor of 2 between a half width and a full width\. The original \(murray\_1972\) says its widths are FWHM, so they are recorded as 'fwhm' \(the original's word; this paper tabulates them under its FWHM a too, and Smyth et al\. call them HWHM\)\: the factor of 2 is then between Murray and Javan's D2 widths and every later D2 measurement, unresolved \(murray\_1972's notes\)\. Robertson and Hunt \(C\. W\. Robertson and R\. H\. Hunt, J\. Chem\. Phys\. 55, 4149 \(1971\); electric\-field\-induced infrared absorption at 10\-30 amagat, no D\_0\)\: 5\.77 \+\- 0\.2, 2\.59 \+\- 0\.10, 4\.00 \+\- 0\.10, 4\.22 \+\- 0\.10, 4\.14 \+\- 0\.15, within 3 % of this study for Q\(0\)\-Q\(3\) \(p\. 240\); smyth\_1987 prints exactly half of them as HWHM \(2\.89 \+\- 0\.10, 1\.30 \+\- 0\.05, 2\.00 \+\- 0\.05, 2\.11 \+\- 0\.05, 2\.07 \+\- 0\.08\), so Robertson and Hunt's are FWHM, consistent with this table\. NOTE ADDED IN PROOF \(p\. 242\)\: Rosasco's group's stimulated Raman gain widths 'appear to be in agreement with ours within approximately 6 %' \(smyth\_1987\)\. What this bears on\: the D2 Q\-branch width law in use is Ottusch and Rockwell's, FWHM = 101/rho \+ 120 rho MHz \(rho in amagat\) for Q\(2\), cited to this paper and to smyth\_1987 \(ottusch\_1988 linewidth\_D2\)\. Its 101 MHz amagat is this paper's Q\(2\) Dicke term, \(4 pi nu^2/c\) D\_0 with D\_0 = 0\.901 and nu = 2987 cm\-1 \(Hanna et al\.'s Q\(2\) shift\)\: 3\.370e\-3 cm\-1 amagat = 101\.0 MHz amagat\. Its 120 MHz/amagat is the mean of this paper's a\(Q\(2\)\) = 3\.91e\-3 cm\-1/amagat = 117\.2 MHz/amagat and smyth\_1987's 2 x 2\.06e\-3 = 123\.5 MHz/amagat \(mean 120\.4\)\: an inference from the numbers, not stated by Ottusch and Rockwell\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- russell\_1987/table1\_a ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_a", "material": "D2", "file": "D2/russell_1987__table1_a.csv", "table": "tbl_99029db61edc", "quantity": "raman_linewidth", "unit": "cm-1/amagat", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "Q(J), v = 0 -> 1, per row", "width": "fwhm", "perturber": "self" } } Table I \(p\. 241\), 'This Study', a\: the FWHM pressure\-broadening coefficient of Eq\. \(1\) \(Dicke term fitted separately\) of the D2 Q\(0\)\-Q\(4\) lines \(v = 0 \-\> 1\), 10^\-3 cm\-1 per amagat, room temperature \(no value in K\)\. The \+\- is the fit error \(level not stated\)\. smyth\_1987 quotes these halved as HWHM \('Roh \(Ref\. 33\)'\)\. russell\_1987/table1\_murray\_javan\_a ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_murray_javan_a", "material": "D2", "file": "D2/russell_1987__table1_murray_javan_a.csv", "table": "tbl_99029db61edc", "quantity": "raman_linewidth", "unit": "cm-1/amagat", "scale": 0.001, "abscissa": "label", "use": "reproduced", "reproduced_from": [ "murray_1972" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "Q(J), v = 0 -> 1, per row", "width": "fwhm", "perturber": "self" } } Table I \(p\. 241\), 'Murray & Javan', a, Q\(1\)\-Q\(3\) \(Q\(0\), Q\(4\) printed '\-'\); spontaneous Raman with a 0\.053 cm\-1 instrument width \(p\. 241\)\. Tabulated under this paper's FWHM a, but smyth\_1987 \(Table III\) prints the same values as HWHM, and the 'almost 100 %' disagreement the paper reports is that factor of 2\. Their D\_0 is 0\.952 for every line\. Re\-pointed to murray\_1972 \(2026\-09\-27\)\: its Table II prints D2 Q\_1\(1\)\-Q\_1\(3\) 1\.4 \+\- 0\.15, 2\.2 \+\- 0\.2, 2\.6 \+\- 0\.5 x 10^\-3 cm\-1/amagat at 25 C \(digit\-identical, with delta 7, 7, 8 and D\_0 = 0\.952 from its p\. 16\), and calls all its widths FULL widths \('full width at half maximum', its pp\. 2 and 7; its Fig\. 5 marks the FWHM Doppler widths\)\: width is now 'fwhm', the original's convention \(was 'not stated'\)\. The factor\-of\-2 disagreement with this paper and with smyth\_1987 \(which reads them as HWHM\) is therefore unresolved\: murray\_1972's H2 widths agree with later FWHM measurements, its D2 widths with later HWHM ones \(see murray\_1972's DOUBT\)\. russell\_1987/table1\_robertson\_hunt\_a ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_robertson_hunt_a", "material": "D2", "file": "D2/russell_1987__table1_robertson_hunt_a.csv", "table": "tbl_99029db61edc", "quantity": "raman_linewidth", "unit": "cm-1/amagat", "scale": 0.001, "abscissa": "label", "use": "reproduced", "reproduced_from": [ "C. W. Robertson and R. H. Hunt, J. Chem. Phys. 55, 4149 (1971)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "Q(J), v = 0 -> 1, per row", "width": "fwhm", "perturber": "self" } } Table I \(p\. 241\), 'Robertson & Hunt', a, Q\(0\)\-Q\(4\)\: electric\-field\-induced infrared absorption at 10\-30 amagat \(no D\_0, no fit error reported, p\. 240\)\. FWHM, as this table's a; smyth\_1987 prints exactly half of each \(Robertson, Hunt and Brannon, same reference\) as HWHM\. Formulas -------- russell\_1987/eq1\_dicke ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq1_dicke", "material": "D2", "equation": "Eq. (1), p. 240; Table I (tbl_99029db61edc), p. 241", "printed": "Delta nu = (4 pi nu^2 / c) (D_0 / rho) + a rho", "variable": "Delta nu: the linewidth, FWHM in cm-1; nu: the frequency of the Q(J) transition in cm-1 (not printed in the paper); rho: density in amagat; c in cm/s; D_0: self-diffusion coefficient at 1 amagat in cm2 amagat/s; a: pressure-broadening coefficient in cm-1/amagat (Table I in 10^-3 cm-1/amagat, dataset table1_a)", "state": "pure D2, room temperature", "density": "unknown", "range": "0.3-18 amagat (Q(4) below 10 amagat)", "coefficients": { "a_Q0": "5.79", "a_Q0_error": "0.08", "D0_Q0": "1.084", "D0_Q0_error": "0.13", "a_Q1": "2.63", "a_Q1_error": "0.04", "D0_Q1": "0.873", "D0_Q1_error": "0.09", "a_Q2": "3.91", "a_Q2_error": "0.04", "D0_Q2": "0.901", "D0_Q2_error": "0.06", "a_Q3": "4.11", "a_Q3_error": "0.08", "D0_Q3": "1.083", "D0_Q3_error": "0.13", "a_Q4": "3.87", "a_Q4_error": "0.08", "D0_Q4": "0.913", "D0_Q4_error": "0.20" }, "check": "No width is printed to reproduce (Fig. 1 is a figure). Checked (scratch, 2026-09-27) against ottusch_1988's D2 Q(2) law: the Dicke term (4 pi nu^2/c) D_0 with D_0 = 0.901 and nu = 2987 cm-1 (hanna_1986's Q(2) shift) is 3.370e-3 cm-1 amagat = 101.0 MHz amagat, Ottusch and Rockwell's 101. The paper's D_0 are 'J dependent' (0.87-1.08); smyth_1987 finds no J dependence (0.984 and 0.967 cm2/s for Q(1), Q(2) at 298.5 K)." } The a\_ coefficients are as printed, in 10^\-3 cm\-1/amagat \(multiply by 1e\-3 for Eq\. \(1\) in cm\-1\)\. The D\_0 of Table I; Murray and Javan's D\_0 = 0\.952 \(all lines\) is in the source notes\. The paper's comparison\: 'the agreement between the present results and the infrared data is excellent, being within 3 % of each other for the Q\(0\)\-Q\(3\) lines' \(p\. 240\)\. 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 ` for the checks and decisions.