ford_1973 ========= A\. L\. Ford and J\. C\. Browne, Phys\. Rev\. A 7, 418 \(1973\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physreva\.7\.418 `__ **Source kind:** theory **Recorded technique:** Sum\-over\-states \(Dalgarno\-Epstein finite\-set resolvent\) calculation of the dynamic polarizability of H2\: configuration\-interaction wave functions for the X 1Sigma\_g\+ ground state \(14 and 24 configurations\) and the 1Sigma\_u\+ and 1Pi\_u manifolds \(26\-52 and 28\-40 configurations, including r times the ground state so that S\(0\) and S\(\-1\) are satisfied\), R = 0\.5\-8 a0; oscillator strengths averaged over the vibrational functions with explicit summation over the vibrational levels \(and the nuclear continuum\) of the B and C states; Eq\. \(7\) alpha\(omega\) = sum f/\(E^2 \- omega^2\), thermally averaged over rotational levels \(pp\. 418\-424\)\. **Materials in structured entries:** H2 **Dataset quantities:** cauchy\_moment, polarizability, rayleigh\_cross\_section **Contents:** 9 datasets; 0 formulas. Curation notes -------------- Units\: a0^3; wavelengths in angstroms \(vacuum\: omega and lambda are related for the computation\), the static limit printed as an infinity sign \(stored inf\)\. The 'set 1' and 'set 2' wave\-function sets give slightly different values \(Table II footnotes\: set 2 gives alpha\_00^00 = 5\.411 against set 1's 5\.3981\)\. Accuracy \(p\. 424\)\: 'The results are generally in agreement with experiment to approximately 1%' \(Table VII\: this work lies 0\.6\-1\.1 % below Victor & Dalgarno's experimental values\)\. Superseded for refraction by bishop\_1980, rychlewski\_1983 and raj\_2018 \(all about 0\.5\-1 % higher\); everything here is kept as a check\. Table VII \(p\. 424\)\: 'This work' \(footnote a\: set 1, 'thermal average \(T = 293 K\) over rotational levels', explicit vibrational summation for B and C\); the 'Semi\-empirical' and 'Expt\.' columns are Victor & Dalgarno's \(the text, p\. 423\: 'compared with semiempirical results of Dalgarno and Victor \[Ref\. 17\] and the experimental results \(also as compiled by Dalgarno and Victor\)'\)\. The table's footnote b reads 'Reference 20', which in the paper's list is Golden & Crawford\: the table notes' reference numbers do not match the list \(also c 'Reference 21' for the 12\.2 at 1215\.7 A, which the text attributes to Gill & Heddle, Ref\. 18, re\-reduced with Ford's rho\_u^T = 0\.0558\)\. The 'Expt\.' values are identical to bishop\_1980/victor\_dalgarno at its 16 wavelengths \(checked 2026\-09\-25\) and are not extracted again; the 12\.2 is derived from gill\_1963 and not extracted\. The semi\-empirical column is extracted as a reproduction \(22 wavelengths; bishop\_1980 has five of them, identical\)\. The gamma block and the '% diff\.' column are not extracted\. Table VII continued \(p\. 424\)\: Cauchy coefficients alpha\_k of alpha\(omega\) = sum\_k alpha\_k \(omega^2\)^k, k = 0\-3, 'This work' \(footnotes a, f\: 'Integration over nuclear continuum for B and C not included', hence alpha\_0 = 5\.379 against Table VII's static 5\.406\) and 'From experimental refractive index data' \(footnote g 'Reference 12', Nelissen, Reuss and Dymanus, a static anisotropy paper\: again a mismatched note; the origin of these coefficients is unresolved\)\. Since alpha\_k = S\(\-2k\-2\), they are stored as Cauchy moments of orders \-2, \-4, \-6, \-8\. Check\: this work's series at 6328 A gives 5\.4815, 0\.0275 below Table VII's 5\.509 \(the static offset 0\.027\); the refractive one gives 5\.5450 against Victor & Dalgarno's 5\.554 \(computed 2026\-09\-25\)\. Table II \(p\. 422\)\: static alpha\_00^JJ for J = 0\-4 and the thermal average at 300 K \(5\.4144\), 'This work' \(set 1\)\. The 'KW results' column \(Kolos & Wolniewicz, J\. Chem\. Phys\. 51, 5002 \(1969\), not in the library\) equals kolos\_1967's Table III for J = 0\-3, but prints 5\.4292 at J = 4, the value of its own 300 K average; kolos\_1967 has 5\.5096 \(image checked; a misprint in that column, which is not extracted\)\. Table XI \(p\. 425\)\: Lyman alpha \(1215\.7 A\), 'thermal average over rotational and vibrational states at 300 K', exact rather than approximate formulas\: alpha\_00 = 12\.538 \(Table VII's 293 K value is 12\.603, set 1 with the continuum; the difference is not explained\) and the cross sections Q\_00^c \(Rayleigh, elastic\) = 2\.129e\-24 cm^2 and Q\_00^T \(Rayleigh plus rotational Raman\) = 2\.265e\-24 cm^2\. Not extracted\: the depolarization ratios, alpha\_01, gamma, Q\_01^T\. Not extracted\: Table I \(sum rules at fixed R = 1\.4\), Tables III\-IV \(convergence of S\(1\), S\(2\) at fixed R\), Table V \(mean excitation energies\), Table VI \(alpha\(omega\) at fixed R = 1\.4, clamped nuclei, with other calculations\), Table VIII \(Raman alpha\_01\), Table IX \(depolarization\), Table X \(dispersion\-force coefficients\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- ford\_1973/thermal\_293K ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "thermal_293K", "material": "H2", "file": "H2/ford_1973__thermal_293K.csv", "table": "tbl_8218ee3b07f5", "quantity": "polarizability", "unit": "au", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "check", "uncertainty": { "relative": 0.01, "level": "not stated" }, "parameters": { "temperature_k": 293, "average": "thermal average over rotational levels (normal H2 not stated)" } } Table VII alpha\(omega\) 'This work'\: v = 0, thermal average over rotational levels at 293 K, 24 wavelengths 1215\.7 A to static \(image checked\)\. About 1 % below experiment \(p\. 424\)\. ford\_1973/victor\_dalgarno\_semiempirical ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "victor_dalgarno_semiempirical", "material": "H2", "file": "H2/ford_1973__victor_dalgarno_semiempirical.csv", "table": "tbl_8218ee3b07f5", "quantity": "polarizability", "unit": "au", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "reproduced", "reproduced_from": [ "G. A. Victor and A. Dalgarno, J. Chem. Phys. 50, 2535 (1969)" ] } Table VII 'Semi\-empirical' column, 22 wavelengths \(none at 6943\.0 and 4880\.0 A\)\: Victor & Dalgarno's model\-spectrum values \(source notes on the table's footnote numbering\)\. Model values, not measurements; the five at 1300\-1700 A equal bishop\_1980/victor\_dalgarno\_semiempirical\. ford\_1973/cauchy\_this\_work ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cauchy_this_work", "material": "H2", "file": "H2/ford_1973__cauchy_this_work.csv", "table": "tbl_f90a64648330", "quantity": "cauchy_moment", "unit": "au", "abscissa": "order", "abscissa_unit": "1", "use": "check" } Table VII continued, alpha\_k 'This work' for k = 0\-3, stored as S\(\-2k\-2\) \(rows \-2, \-4, \-6, \-8\)\. Without the B and C nuclear continuum \(footnote f\)\: alpha\_0 = 5\.379 is 0\.027 below Table VII's static value\. ford\_1973/cauchy\_refractive ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cauchy_refractive", "material": "H2", "file": "H2/ford_1973__cauchy_refractive.csv", "table": "tbl_f90a64648330", "quantity": "cauchy_moment", "unit": "au", "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "'From experimental refractive index data', footnote g 'Reference 12' (the paper's Ref. 12 is L. Nelissen, J. Reuss, and A. Dymanus, Physica 42, 619 (1969), which does not fit; origin unresolved)" ] } Table VII continued, alpha\_k 'From experimental refractive index data' for k = 0\-3, stored as S\(\-2k\-2\) \(rows \-2, \-4, \-6, \-8\)\. Origin unresolved \(source notes\)\. ford\_1973/static\_states ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "static_states", "material": "H2", "file": "H2/ford_1973__static_states.csv", "table": "tbl_8a57694d1337", "quantity": "polarizability", "unit": "au", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "check", "parameters": { "rows": "rotational states J of v = 0, all static" } } Table II static alpha\_00^JJ 'This work' \(set 1\) for v = 0, J = 0\-4, rows J0\-J4, every row static \(wavelength inf\)\: each row is a different rotational state, not a wavelength series\. The J = 0 cell prints the unit a0^3 \(stripped\)\. ford\_1973/static\_300K ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "static_300K", "material": "H2", "file": "H2/ford_1973__static_300K.csv", "table": "tbl_8a57694d1337", "quantity": "polarizability", "unit": "au", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "check", "parameters": { "temperature_k": 300, "average": "thermal average over rotational levels" } } Table II 'thermal average over rotational levels for T = 300 K', static, 'This work' \(set 1\)\: 5\.4144\. ford\_1973/lyman\_alpha\_300K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "lyman_alpha_300K", "material": "H2", "file": "H2/ford_1973__lyman_alpha_300K.csv", "table": "tbl_31dd70cf3437", "quantity": "polarizability", "unit": "au", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "check", "parameters": { "temperature_k": 300, "average": "thermal average over rotational and vibrational states" } } Table XI alpha\_00 at Lyman alpha \(1215\.7 A\), thermal average over rotational and vibrational states at 300 K\: 12\.538 \(Table VII's 293 K value is 12\.603\)\. ford\_1973/rayleigh\_elastic\_lyman\_alpha ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "rayleigh_elastic_lyman_alpha", "material": "H2", "file": "H2/ford_1973__rayleigh_elastic.csv", "table": "tbl_31dd70cf3437", "quantity": "rayleigh_cross_section", "unit": "cm2", "scale": 1e-24, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "check", "parameters": { "king_factor": "not applicable: computed from alpha and gamma with exact rotational sums (Eq. (18)); elastic part only", "temperature_k": 300 } } Table XI Q\_00^c = 2\.129 x 10^\-24 cm^2 at Lyman alpha, 300 K\: the elastically scattered \(Rayleigh, Cabannes\) photons only, from Eq\. \(18\) with exact rotational sums\. ford\_1973/rayleigh\_total\_lyman\_alpha ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "rayleigh_total_lyman_alpha", "material": "H2", "file": "H2/ford_1973__rayleigh_total.csv", "table": "tbl_31dd70cf3437", "quantity": "rayleigh_cross_section", "unit": "cm2", "scale": 1e-24, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "check", "parameters": { "king_factor": "not applicable: computed from alpha and gamma with exact rotational sums (Eq. (18)); includes the rotational Raman lines", "temperature_k": 300 } } Table XI Q\_00^T = 2\.265 x 10^\-24 cm^2 at Lyman alpha, 300 K\: Rayleigh plus rotational Raman \(the total that a King\-factor formula describes\), exact rotational sums\. 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.