ford_1973#

A. L. Ford and J. C. Browne, Phys. Rev. A 7, 418 (1973)

Source record · Catalogue · 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 Superseded for refraction by bishop_1980, rychlewski_1983 and raj_2018 (all about 0.5-1 % higher); everything here is kept as a check.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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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<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#

{
  "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#

{
  "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#

{
  "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#

{
  "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 review register for the checks and decisions.