wheeler_1933 ============ J\. A\. Wheeler, Phys\. Rev\. 43, 258 \(1933\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physrev\.43\.258 `__ **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 Superseded by later theory \(liu\_1997, stone\_2004\)\.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 ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.