keijser_1974 ============ R\. A\. J\. Keijser, J\. R\. Lombardi, K\. D\. Van den Hout, B\. C\. Sanctuary and H\. F\. P\. Knaap, "The pressure broadening of the rotational Raman lines of hydrogen isotopes", Physica 76, 585 \(1974\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1016/0031\-8914\(74\)90160\-8 `__ **Source kind:** measurement **Recorded technique:** Pure rotational Raman scattering at 293 K \(pp\. 586\-590\)\: a single\-mode argon\-ion laser at 514\.5 nm \(600 mW\), polarisation vertical to the scattering plane, 90 degree scattering from a cell at up to 125 atm; a Glan\-Thompson prism passing only the depolarised component; a 25 cm monochromator \(6 or 15 A slit\) isolating one Stokes line, resolved by a pressure\-scanned Fabry\-Perot interferometer \(0\.198 cm spacer, free spectral range 75\.6 GHz, instrumental width 1\.9 GHz, finesse 40\) with photon counting\. The instrument deconvolved by Fourier transform, Eqs\. \(1\)\-\(5\); the lines are Lorentzian \(ln F\_R\(t\) linear in t\), Eq\. \(6\), and the half width is taken from the slope; the broadening coefficient Delta nu\_1/2/rho from the slope of Delta nu\_1/2 against density \(pp\. 591\-594\)\. HD at 25\-75 atm, normal H2 at 75\-125 atm, normal D2 at about 65\-90 amagat \(Fig\. 13; not stated in the text\); para\-H2 \(\> 96 %\) converting in the cell at 124\.5 atm for the ortho\-para series \(p\. 598\)\. Gases\: commercial H2 and D2 \(purity better than 99 %\); HD made from D2O and LiAlH4 \(96\.5 % HD, 3 % H2, 0\.5 % D2\)\. **Materials in structured entries:** D2, H2 **Dataset quantities:** raman\_linewidth **Contents:** 4 datasets; 0 formulas. Curation notes -------------- Identity checked against the first page\. PAGES\: pdf page n is journal p\. 584 \+ n \(Table I on p\. 595\)\. This is the Leiden group's room\-temperature paper \(Communication No\. 408c\); knaap\_1979 \(Phil\. Trans\. 1979\) extends the same measurements to 25\-300 K in figures only, and van\_den\_hout\_1980 gives the low\-temperature tables\. MATERIALS\. Normal H2 \('3/4 ortho \(odd j\) and 1/4 para \(even j\)'\) and normal D2 \('2/3 ortho \(even j\) and 1/3 para \(odd j\)'\), p\. 596\. HD is not a material\: its values are in these notes\. Only the Stokes lines S\_o\(J\) \(J \-\> J \+ 2, v = 0\) were measured\. WIDTH CONVENTION\: HALF WIDTHS\. Eq\. \(6\), p\. 592\: F\_R\(t\) = exp\(\-2 pi Delta nu\_1/2 t\), 'where Delta nu\_1/2 is the half\-width \(half the width at half intensity\) of the associated lorentzian line profile' \(p\. 593\), R\(nu\) = \(I\_0/pi\) Delta nu\_1/2 / \(nu^2 \+ Delta nu\_1/2^2\), Eq\. \(7\)\. The appendix repeats it\: 'The half\-width \(at half intensity\) for the S\_o\(j\) Raman lines' \(p\. 605\)\. Table I\: 'Delta nu\_1/2/rho in GHz/amagat' \(p\. 595\), a frequency \(not angular\); 'A density of 1 amagat corresponds approximately to 2\.687 x 10^19 molecules/cm3' \(the 0 C amagat\)\. The coefficients are HWHM per amagat\. DICKE\. The footnote on p\. 594\: 'The translational motion of the molecules gives rise to a contribution with a different density dependence\. For the hydrogen isotopes this effect has been shown to be unimportant at pressures above 25 atm' \(Refs\. 16\-18\)\: all measurements are above 25 atm, and the coefficients are the slope of Delta nu\_1/2 against density \(no Dicke term fitted or removed; Figs\. 9, 11 and 13 draw the lines through the origin\)\. UNCERTAINTIES\. Table I prints '\+\-' per value \(0\.001 GHz/amagat for H2 and D2, 0\.01 for HD\); the paper does not say what they are \(level not stated\)\. The ortho\-para composition of each run 'within 2 %' \(p\. 590\)\. HD \(Table I, GHz/amagat HWHM, S\_o\(0\)\-S\_o\(4\)\)\: 0\.43, 0\.38, 0\.33, 0\.27, 0\.20, each \+\- 0\.01; an order of magnitude above H2 and D2 \(the P\_1 term of the loaded\-sphere potential, p\. 600\)\. TABLE II \(p\. 597\)\: fractional populations of H2 rotational levels at 293 K, j = 0\-6\: ortho \-, 0\.884, \-, 0\.115, \-, 0\.001, \-; normal 0\.132, 0\.662, 0\.115, 0\.086, 0\.004, 0\.001, 0\.000; para 0\.525, \-, 0\.460, \-, 0\.015, \-, 0\.000\. CROSS SECTIONS \(Tables III\-IV, notes\: no quantity\)\. Eq\. \(8\), p\. 599\: 2 pi Delta nu\_1/2 = n \\_0 S\_RR, \\_0 = \(8 k\_B T/pi mu\)^1/2 \(Eq\. 9, mu the reduced mass of the pair; 2485 m/s for H2 at 293 K\)\. Table III \(A^2\)\: HD 4\.9, 4\.4, 3\.8, 3\.1, 2\.3 \(\+\- 0\.1\); nH2 0\.40, 0\.49, 0\.35, 0\.36, 0\.22 \(\+\- 0\.01\); nD2 1\.12, 0\.89, 0\.83, 0\.68, 0\.57, 0\.37 \(\+\- 0\.01\)\. Checked \(scratch, 2026\-09\-27\)\: Table I with n = 2\.687e25 m\-3 per amagat and \\_0 = 2485 m/s x \(1 amu/mu\)^1/2 \(mu = 1, 1\.5, 2 amu for H2, HD, D2\) gives 0\.40 \(H2 S\_o\(0\)\), 4\.96 \(HD S\_o\(0\)\) and 1\.12 \(D2 S\_o\(0\)\) A^2\: Table III follows from Table I, confirming that the coefficients are per 0 C amagat and in cyclic frequency\. Table IV \(A^2\), the extrapolated limits of Fig\. 15 \(Delta nu\_1/2 against the para fraction at 124\.5 atm, linear\)\: pure oH2 0\.36, 0\.54, 0\.32, 0\.39, 0\.22; pure pH2 0\.49, 0\.31, 0\.43, 0\.25, 0\.23 \(\+\- 0\.01\), S\_o\(0\)\-S\_o\(4\)\. The 'contribution of \(exact\) resonance collisions for some of the lines exceeds 40 % of the total linewidth' \(p\. 599\)\. THEORY \(Tables V\-VI, pp\. 601\-604, notes only\)\. Van Kranendonk's quadrupole\-quadrupole impact theory, Eqs\. \(A\.1\)\-\(A\.12\), extended to ortho and para perturbers\: the elastic, resonance, quasi\-resonance and two nonresonance parts of S\_RR per line, with tau = d/v = 0\.96e\-13 s \(Table V\: total calc\. oH2 0\.52, 0\.54, 0\.52, 0\.34, 0\.29; pH2 0\.52, 0\.49, 0\.39, 0\.41, 0\.15\) and tau = 1\.18e\-13 s \(Table VI and its continuation tbl\_32991a1c3209\: oH2 0\.33, 0\.54, 0\.30, 0\.34, 0\.16; pH2 0\.46, 0\.27, 0\.36, 0\.21, 0\.14\)\. Table VI's caption prints 'tau = 1\.18 x 10^\-12 s' where Figs\. 19\-20 and the text \('a slightly larger value for tau \(by about 20 %\)', p\. 604\) give 1\.18 x 10^\-13 s\: a misprint in the caption \(no data affected\)\. The paper\: the sensitivity to tau 'indicates that a re\-evaluation of the approximations in this theory is required' \(p\. 604\)\. FIGURES \(not digitised\)\. Figs\. 9, 11, 13\: Delta nu\_1/2 \(GHz\) against density \(amagat\) for HD, nH2, nD2; Figs\. 10, 12, 14\: the coefficients against J \(Fig\. 12 with Cooper et al\. and Gupta and May\); Fig\. 15\: the H2 widths at 124\.5 atm against the para fraction 0\.25\-0\.96; Figs\. 16\-17, 19\-20\: theory against experiment\. WHO REPRINTS IT\. smyth\_1987's keijser\_S\_branch \(the D2 row, converted to 10^\-3 cm\-1/ amagat, p\. 1008 of that paper\) and edwards\_1991's 'Knaap et al\.' columns \(Tables 7\-8, which are this Table I doubled to full widths and converted to cm\-1, the unit printed there as per bar\) were re\-pointed here on 2026\-09\-27 \(see those records\)\. knaap\_1979 shows the same room\-temperature points in its Figs\. 5\-6\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- keijser\_1974/table1\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_H2", "material": "H2", "file": "H2/keijser_1974__table1_H2.csv", "table": "tbl_ef6959254514", "quantity": "raman_linewidth", "unit": "GHz/amagat", "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "S0(J), v = 0, J -> J + 2, per row", "width": "hwhm", "perturber": "self", "temperature_k": 293, "ortho_para": "3:1" } } Table I \(p\. 595\), nH2 'this exp\.'\: the HWHM self\-broadening coefficient Delta nu\_1/2/rho of the pure rotational S0\(0\)\-S0\(4\) lines of normal H2 at 293 K, GHz per 0 C amagat, from 75\-125 atm; no Dicke term \(negligible above 25 atm, p\. 594\)\. The paper\: 'Delta nu\_1/2 is the half\-width \(half the width at half intensity\)' \(p\. 593\)\. Per\-value \+\-0\.001 \(level not stated\)\. The odd lines are broader \(resonance collisions with the abundant j = 1, p\. 596\)\. In cm\-1/amagat\: 1\.401, 1\.735, 1\.234, 1\.268, 0\.767e\-3 HWHM\. keijser\_1974/table1\_H2\_cooper ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_H2_cooper", "material": "H2", "file": "H2/keijser_1974__table1_H2_cooper.csv", "table": "tbl_ef6959254514", "quantity": "raman_linewidth", "unit": "GHz/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": "S0(J), v = 0, J -> J + 2, per row", "width": "hwhm", "perturber": "self", "ortho_para": "3:1" } } Table I \(p\. 595\), nH2 'literature', note a \(Ref\. 17\)\: S0\(0\) and S0\(1\), HWHM per amagat as the column; 'in excellent agreement with the present results' \(p\. 594\)\. herring\_1986 \(Table V\) prints the same paper as 84 and 105 MHz/amagat FWHM, i\.e\. 0\.042 and 0\.0525 GHz/amagat HWHM\: consistent\. keijser\_1974/table1\_H2\_gupta\_may ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_H2_gupta_may", "material": "H2", "file": "H2/keijser_1974__table1_H2_gupta_may.csv", "table": "tbl_ef6959254514", "quantity": "raman_linewidth", "unit": "GHz/amagat", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "B. K. Gupta and A. D. May, Can. J. Phys. 50, 1747 (1972)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "S0(J), v = 0, J -> J + 2, per row", "width": "hwhm", "perturber": "self", "ortho_para": "3:1" } } Table I \(p\. 595\), nH2 'literature', note b \(Ref\. 18\)\: S0\(1\) only, HWHM per amagat as the column \(split from the same cell as Ref\. 17's value; see the script\)\. keijser\_1974/table1\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_D2", "material": "D2", "file": "D2/keijser_1974__table1_D2.csv", "table": "tbl_ef6959254514", "quantity": "raman_linewidth", "unit": "GHz/amagat", "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "S0(J), v = 0, J -> J + 2, per row", "width": "hwhm", "perturber": "self", "temperature_k": 293, "ortho_para": "2:1" } } Table I \(p\. 595\), nD2\: the HWHM self\-broadening coefficient of the pure rotational S0\(0\)\-S0\(5\) lines of normal D2 at 293 K, GHz per 0 C amagat, from about 65\-90 amagat \(Fig\. 13\); no Dicke term\. Per\-value \+\-0\.001 \(level not stated\)\. The even lines are broader, the reverse of H2 \(p\. 596\)\. In cm\-1/amagat\: 2\.802, 2\.235, 2\.068, 1\.701, 1\.434, 0\.934e\-3 HWHM, the values smyth\_1987 quotes \(2\.80, 2\.23, 2\.07, 1\.70, 1\.43, 0\.93\)\. Formulas -------- No formulas are recorded. 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.