musulin_1964#

B. Musulin and S. T. Epstein, Phys. Rev. 136, A966 (1964)

Source record · Catalogue · Review register

Source kind: theory

Recorded technique: Shielding approximation (Dalgarno and Stewart) extended to the dynamic polarizability: first-order corrections to two independent hydrogenic electrons of effective charge zeta, zeta fixed by making the first-order correction vanish; the result is a power series in omega through omega^4 (pp. A966-A967).

Materials in structured entries: He

Dataset quantities: None recorded.

Contents: 0 datasets; 1 formula.

Curation notes#

No tabulated values: the paper gives one formula (below) and a figure comparing it with Cuthbertson and Cuthbertson (1932), Wheeler (1933) and Karplus and Kolker (1963). Stated accuracy ‘about 10%’ (abstract). Hartree atomic units, with lambda (A) = 456/omega (footnote 11); zeta runs from 1.641 at omega = 0 to 1.629 at omega = 0.456. No dataset is extracted. mansfield_peck_1969 (Table IV) quotes 2.983e-5 for this theory at 5462 A, but the formula gives 3.130e-5 there (checked 2026-09-24): the quoted value does not come from this formula as printed.

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#

musulin_1964/shielding#

{
  "id": "shielding",
  "material": "He",
  "equation": "unnumbered, p. A967",
  "printed": "(n^2 - 1) x 10^4 = 0.50064 {zeta^-4 (9 + b0/zeta) + omega^2 zeta^-8 (319/6 + b2/zeta) + omega^4 zeta^-12 (297541/864 + b4/zeta)}, b0 = 207/16 + 36 (zeta - Z), b2 = 3983/24 + (1276/3)(zeta - Z), b4 = 4673097941/2764800 + (297541/72)(zeta - Z); zeta from b0 + omega^2 b2/zeta^4 + omega^4 b4/zeta^8 = 0 (solved through omega^4)",
  "variable": "omega: photon energy in hartree (lambda in A = 456/omega); Z = 2 for helium",
  "state": "1atm_0C",
  "density": "ideal",
  "range": "low frequencies, well below the first resonance ('it seemed reasonable to confine our attention to low frequencies', p. A967)",
  "coefficients": {
    "prefactor": "0.50064",
    "c0": "9",
    "c2": "319/6",
    "c4": "297541/864",
    "b0": "207/16 + 36 (zeta - Z)",
    "b2": "3983/24 + (1276/3)(zeta - Z)",
    "b4": "4673097941/2764800 + (297541/72)(zeta - Z)"
  },
  "check": "At omega = 0 the zeta equation gives zeta = 1.640625, the printed 1.641; n - 1 = 3.110e-5 static and 3.130e-5 at 5462 A, 10 % below experiment, as the paper says. The prefactor 0.50064e-4 is 4 pi N0 a0^3 with N0 = 2.689e19 cm^-3 (Loschmidt's number, 0 degrees C, 1 atm). Checked 2026-09-24."
}

The check solved the zeta equation numerically in full, not truncated at omega^4 as the paper did; at 5462 A the difference is far below the method’s 10 %.

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.