wheeler_1933#

J. A. Wheeler, Phys. Rev. 43, 258 (1933)

Source record · Catalogue · Review register

Source kind: theory

Recorded technique: Variational calculation of the oscillator strength of the helium resonance line (Hylleraas-type ground function, energy -1.8065 Rh against -1.8070) and of the continuum oscillator-strength density df/dE (Eq. 12), checked against the f sum rule and Cuthbertson and Cuthbertson’s (1932) refractive index (pp. 258-263).

Materials in structured entries: He

Dataset quantities: oscillator_strength

Contents: 2 datasets; 2 formulas.

Curation notes#

Energies are in Rydberg units (‘E is in units Rh’), E above the series limit (photon energy 1.807 + E Rh; lambda = 911/(1.807 + E) A). Results (pp. 261-262): resonance line f = 0.266 (max. error ‘of the order of 30 percent’; Vinti’s 0.349 is 31 % higher), continuum total 1.58, the rest of the 1s np series estimated by the 1/n^3 law as 0.159, total 2.00. Table I (tbl_302e1ef04d88) tabulates Eq. (12), df/dE at 20 energies E = 0-16 Rh: the format has no quantity for a differential oscillator strength, so the table is not extracted as data; Eq. (12) is recorded as a formula and checked against it. Table II (continuum strengths of H, Li, Na, K) holds no curated species beyond helium’s own 1.58 and 0.93.

The one-term formula (Eq. 14) is the theory’s equivalent of Cuthbertson’s (Eq. 13, reproduced from cuthbertson_1932, n0^2 = 3.83137e31, i.e. 38313.7e27) and differs from it by 3 %. Superseded by later theory (liu_1997, stone_2004).

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets#

wheeler_1933/f_resonance#

{
  "id": "f_resonance",
  "material": "He",
  "table": "text",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "uncertainty": {
    "relative": 0.3,
    "level": "bound"
  }
}

1 inline points in the source record.

1 1S -> 2 1P resonance line (row and index n = 2; E1 - E0 = 1.56 Rh), p. 261; ‘maximum error ... of the order of 30 percent’ (p. 262).

wheeler_1933/vinti_f_resonance#

{
  "id": "vinti_f_resonance",
  "material": "He",
  "table": "text",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "reproduced",
  "reproduced_from": [
    "J. P. Vinti, Phys. Rev. 42, 632 (1932)"
  ]
}

1 inline points in the source record.

‘Vinti obtains an f value of 0.349, 31 percent higher’ (p. 262), with a poorer ground function.

Formulas#

wheeler_1933/eq12#

{
  "id": "eq12",
  "material": "He",
  "equation": "Eq. (12), p. 261",
  "printed": "df/dE = Z0^2(E)(1.807 + E)/16 = (1.807 + E)(1 + E)^-1 (1 - e^{-2 pi E^-1/2})^-1 [(E + 3.31)^-5 (0.227 E^5 + 3.76 E^4 + 66.3 E^3 + 389 E^2 + 1250 E + 943) exp(-2 E^-1/2 arctan(E^1/2/1.82)) - (E + 31.8)^-3 (0.227 E^3 + 19.9 E^2 + 535 E + 3280) exp(-2 E^-1/2 arctan(E^1/2/5.64))]^2",
  "variable": "E: photoelectron energy above the He ionisation limit in Rydberg units (photon energy 1.807 + E Rh); df/dE per Rh",
  "state": "none (per atom)",
  "density": "none",
  "range": "E >= 0; 'inaccuracy ... of the order of 10 percent' at E = 0.01, decreasing with E; not below about 5 A",
  "coefficients": {
    "threshold": "1.807",
    "c1": "3.31",
    "c2": "31.8",
    "k1": "1.82",
    "k2": "5.64"
  },
  "check": "Agrees with Table I within 1.2 % up to E = 4 (0.935, 0.820, 0.467, 0.248, 0.0936 at E = 0, 0.2, 1, 2, 4 against the printed 0.93, 0.81, 0.47, 0.25, 0.093); at E = 10 and 16 it gives 0.0159 and 0.0054 against 0.015 and 0.0056 (6 % and 4 %), so the printed constants are probably rounded. Checked 2026-09-24."
}

Coefficients above are a selection; the full expression is the printed one. For large E, df/dE ~ 2.8e-8 lambda^3.5 (lambda in A, p. 262).

wheeler_1933/eq14#

{
  "id": "eq14",
  "material": "He",
  "equation": "Eq. (14), p. 263",
  "printed": "n - 1 = 1.38 x 10^27 / (3.865 x 10^31 - epsilon^2)",
  "variable": "epsilon: the light frequency in s^-1 (the paper's symbol; nu in Eq. 13)",
  "state": "1atm_0C",
  "density": "ideal",
  "range": "visible (matched in value and slope at 3644 A to the theoretical Eq. 1)",
  "coefficients": {
    "C": "1.38e27",
    "n0_squared": "3.865e31"
  },
  "check": "At 5462 A (nu = c/lambda, c = 3e10 cm/s) it gives 3.598e-5 against Eq. (13)'s 3.4885e-5, 3.1 % higher: the paper's '3 percent difference'. Checked 2026-09-24."
}

Effective electron number 1.27, effective frequency 1.89 Rh (482 A). The state is ‘standard pressure and temperature’ via N in Eq. (1).

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.