knaap_1979 ========== H\. F\. P\. Knaap, K\. D\. van den Hout and P\. W\. Hermans, "Dynamic aspects of light scattering by gases", Phil\. Trans\. R\. Soc\. Lond\. A 293, 407 \(1979\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1098/rsta\.1979\.0107 `__ **Source kind:** measurement **Recorded technique:** Pure rotational Raman \(Stokes, Delta j = 2\) and depolarised Rayleigh spectroscopy of H2, D2 and HD \(p\. 409\)\: Ar\-ion laser, horizontally polarised, 90 degree scattering through a polariser, a small monochromator selecting one Raman line and a Fabry\-Perot interferometer resolving it; photon counting; a scattering cell for 5\-300 K in an optical cryostat \(the room\-temperature apparatus of Keijser et al\. 1974\)\. Lorentzian lines after correction for the instrumental width; the collisional half width against density gives the broadening coefficient; measured against ortho\-para composition \(linear, extrapolated to the pure modifications\), 25\-300 K\. **Materials in structured entries:** None recorded. **Dataset quantities:** None recorded. **Contents:** 0 datasets; 0 formulas. Curation notes -------------- Identity checked against the first page \(the JSTOR copy includes the discussion by A\. D\. Buckingham\)\. This IS the paper edwards\_1991 cites as Ref\. 10 \('Knaap, van der Hout \[sic\] and Hermans, Philos\. Trans\. R\. Soc\. London, Ser\. A 293, 407 \(1979\)'\)\. Page numbers are journal pages \(pdf page 1 is the JSTOR cover; pdf pages 2\-7 = pp\. 407\-412; the pages also carry the proceedings numbers \[197\]\-\[202\]\)\. NOTHING IS TAKEN\: the paper prints no table and no numerical linewidth in its text\. The results are figures only \(not digitised\)\: \- Fig\. 3 \(p\. 409\)\: collisional half widths of n\-H2 S\(0\), S\(1\), S\(2\) against density at 77\.8 K\. \- Fig\. 4 \(p\. 409\)\: Delta nu\_1/2/rho \(MHz m3 mol\-1\) of H2 against the p\-H2 fraction at 77\.8 K\. \- Figs\. 5\-7 \(pp\. 410\-411\)\: the line\-broadening cross sections sigma\_rR \(10^\-20 m2\) of n\-H2 \(lines 0\-2 to 4\-6\), n\-D2 \(0\-2 to 5\-7\) and HD \(0\-2 to 4\-6\) against temperature, 25\-300 K\. \- Fig\. 8 \(p\. 411\)\: p\-H2 and o\-H2 \(the pure\-modification limits\) against temperature, with distorted\-wave Born calculations \(Coombe and Kohler, 'to be published'\)\. WIDTH CONVENTION\: HALF widths\. Eq\. \(1\) \(p\. 407\)\: I\(nu\) = \(I\_0/pi\) Delta nu\_1/2\(rho\) / \[\(nu \- nu\_R\)^2 \+ Delta nu\_1/2\(rho\)^2\], 'Delta nu\_1/2 is the halfwidth of the line'\: the half width at half maximum\. Fig\. 3's caption\: 'The collisional halfwidths'\. The broadening coefficient is Delta nu\_1/2/rho \(p\. 409\)\. The cross section, Eq\. \(3\) \(p\. 411\)\: sigma\_rR = 2 pi Delta nu\_1/2 / \(n \\_0\), with \\_0 = \(8 k\_B T/pi mu\)^1/2, Eq\. \(4\), mu the reduced mass of the pair, n the number density\: Delta nu\_1/2 in Hz \(not angular frequency, hence the 2 pi\)\. THE COMPARISON WITH edwards\_1991 \(TC\-483\), checked 2026\-09\-27\. The cross sections below were READ APPROXIMATELY from the 300\-dpi page images of Figs\. 5 and 6 at the highest\-temperature points \(about 295 K; \+\-0\.03e\-20 m2\) for this comparison only; they are not data\. Converted by Eqs\. \(3\)\-\(4\) at 295 K with 1 amagat = 2\.6868e25 m\-3\: Delta nu\_1/2/rho = sigma \\_0 / 2 pi, i\.e\. 3\.551e\-3 \(H2\) and 2\.512e\-3 \(D2\) cm\-1/amagat HWHM per 1e\-20 m2\. \- D2 \(Fig\. 6\)\: sigma about 1\.13, 0\.91, 0\.85, 0\.69, 0\.56, 0\.39 for S0\(0\)\-S0\(5\), i\.e\. HWHM 2\.84, 2\.29, 2\.14, 1\.73, 1\.41, 0\.98 e\-3 cm\-1/amagat\. Keijser et al\.'s printed 293 K HWHM, as quoted by smyth\_1987 \(p\. 1008; keijser\_1974's Table I in cm\-1\), are 2\.80, 2\.23, 2\.07, 1\.70, 1\.43, 0\.93\: the same measurements, within the reading error \(\-2 to \+5 %\)\. \- H2 \(Fig\. 5\)\: sigma about 0\.41, 0\.50, 0\.355, 0\.37, 0\.235 for S0\(0\)\-S0\(4\), i\.e\. HWHM 1\.46, 1\.78, 1\.26, 1\.31, 0\.83 e\-3 cm\-1/amagat\. herring\_1986's 295 K FWHM 77 and 114 MHz/amagat for S\(0\), S\(1\) are HWHM 1\.28 and 1\.90e\-3 cm\-1/amagat \(\-12 %, \+7 %\)\. \- edwards\_1991's comparison columns 'Knaap et al\.' \(Table 7, H2\: 2\.8, 3\.5, 2\.5, 2\.5, 1\.5; Table 8, D2\: 5\.6, 4\.5, 4\.1, 3\.4, 2\.9; printed '10^3 cm\-1 bar\-1'\) are twice these half widths\: 0\.90\-0\.99 \(H2\) and 0\.96\-1\.03 \(D2\) of 2 x the figure's HWHM, and for D2 exactly twice Keijser et al\.'s printed HWHM \(2 x 2\.80 = 5\.60, 4\.46, 4\.14, 3\.40, 2\.86\)\. They are FULL widths PER AMAGAT \(not per bar\), and since this paper prints no numbers Edwards et al\. must have taken them from the Leiden group's tables \(Keijser et al\. 1974; van den Hout et al\. 1980\), not from this paper\. Confirmed 2026\-09\-27 against keijser\_1974 \(curated\)\: twice its Table I HWHM at 293 K \(GHz/amagat, converted to cm\-1\) rounds to Edwards's 'Knaap et al\.' columns in every row, H2 \(2\.802, 3\.469, 2\.468, 2\.535, 1\.534\) and D2 \(5\.604, 4\.470, 4\.136, 3\.402, 2\.869\); edwards\_1991's table7\_knaap and table8\_knaap now name keijser\_1974\. Keijser's H2 HWHM in cm\-1/amagat, 1\.401, 1\.735, 1\.234, 1\.268, 0\.767e\-3, lie 3\-8 % below the Fig\. 5 readings above \(1\.46, 1\.78, 1\.26, 1\.31, 0\.83\), within the reading error of a 295 K point on a 25\-300 K figure\. \- edwards\_1991's OWN coefficients, sigma 'FWHM' per bar at 293 K \(1 bar = 0\.9201 amagat\), against this paper's half widths per bar\: H2 S0\(0\), S0\(1\) 1\.19, 1\.48 = 0\.89, 0\.91 x HWHM \(0\.44, 0\.45 x FWHM\); H2 S0\(2\) 0\.58 = 0\.50 x HWHM; D2 S0\(0\)\-S0\(4\) 4\.05, 2\.69, 2\.46, 1\.22, 1\.14 = 1\.57, 1\.31, 1\.29, 0\.78, 0\.87 x Keijser's HWHM per bar \(0\.79, 0\.66, 0\.65, 0\.39, 0\.43 x FWHM\)\. \- VERDICT \(TC\-483\)\: as FWHM, edwards\_1991's widths are low by a factor 2\.2 for H2 S0\(0\)\-S0\(1\), 4\.0 for H2 S0\(2\), and 1\.3\-2\.6 for D2 S0\(0\)\-S0\(4\)\. For H2 S0\(0\)\-S0\(1\) and D2 S0\(3\)\-S0\(4\) the hypothesis that Edwards's sigma is a half width fits to 9\-22 %; for D2 S0\(0\)\-S0\(2\) it does not \(Edwards is 1\.3\-1\.6 x the HWHM\), nor for H2 S0\(2\) \(0\.5 x the HWHM\)\. No single factor reconciles the set\. The D2 S\(0\) width solprop takes from Edwards \(4\.05e\-3 cm\-1/bar as FWHM = 131\.96 MHz/amagat\) is 0\.79 of Keijser's FWHM at 293 K \(2 x 2\.80e\-3 cm\-1/amagat = 167\.9 MHz/amagat\); read as a HWHM it would be 1\.57 x too large\. The Leiden widths \(Keijser et al\., via smyth\_1987\) are the consistent room\-temperature D2 S\-branch set\: they agree with this paper's figure and with Edwards's own comparison column once that is read as FWHM per amagat\. OTHER CONTENT \(notes only\)\. HD's cross sections exceed those of H2 and D2 at higher temperatures \(the P1 term of the HD potential, p\. 412\)\. At the lowest temperatures only j = 0, 1 are populated, and the ortho\-para dependence of H2 at 20\-40 K tests the distorted\-wave Born calculations\. Collisional line shifts are mentioned \(abstract\) but not shown\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- No datasets are recorded. 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.