drake_1969#
G. W. F. Drake, G. A. Victor and A. Dalgarno, “Two-photon decay of the singlet and triplet metastable states of helium-like ions”, Phys. Rev. 180, 25 (1969)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Variational second-order perturbation theory of the spontaneous two-photon (2E1) decay of the 1s2s 2 1S0 and 2 3S1 metastable levels to the 1s2 1 1S0 ground level of the helium sequence, He I to Ne IX: the sums over intermediate 1P (and, for 2 3S1, spin-orbit mixed 1P1-3P1) states replaced by discrete pseudostate sets of correlated Hylleraas-type functions r1^i r2^j r12^k exp(-alpha r1 - beta r2) (Eqs. 6-8, 30-50 terms), the spin-orbit and spin-other-orbit matrix elements in closed form (Appendix). Nonrelativistic, infinite nuclear mass, length form; photon directions and polarisations averaged (Eqs. 1, 5).
Materials in structured entries: None recorded.
Dataset quantities: None recorded.
Contents: 0 datasets; 0 formulas.
Curation notes#
Phys. Rev. 180(1), 25-32 (5 April 1969) = PDF pages 1-8 (journal page = PDF page + 24); a scan with a text layer. Identity checked against the first page (journal, volume, number, date, title, authors).
NOTHING TAKEN. The paper gives spontaneous two-photon emission rates (s^-1) and their photon-energy distributions; no quantity of the vocabulary holds a decay rate, and the rates are not converted here into a two-photon transition strength or cross section (the conversion needs the paper’s matrix elements, which it does not print). The values are recorded below for reference.
HELIUM (the only registered material among the ions). Table I (p. 29, tbl_947449bbca88, image checked): 2 1S0 -> 1 1S0, He I, A = ‘5.13 x 10^1’ s^-1 (text, p. 27: ‘51.3 sec^-1’), lambda_max = 771 A (the peak of the distribution on a wavelength scale). Table III (p. 30, tbl_455db92a41b3, image checked): 2 3S1 -> 1 1S0, He I, A = ‘4.02 x 10^-9’ s^-1, lambda_max = 699 and 2400 A (two peaks). Tables II and IV (pp. 29, 30): A(y), the rate per unit y, at y = 0 to 0.5 in steps of 0.025, y the fraction of the transition energy carried by one photon; Figs. 1, 2, 5, 7 draw the He profiles (raster; not digitised). ‘The results converged to the number of figures quoted’ (p. 27).
CHECKED (computed 2026-10-09). Simpson’s rule over Table II’s He column (y = 0-0.5) gives 51.15 s^-1 against Table I’s 51.3 (-0.3 %), and over Table IV’s He column 4.04 x 10^-9 against Table III’s 4.02 x 10^-9 (+0.5 %): the tabulated A(y) count each photon of a pair, and the total is the integral over half the range (Eq. 2, the factor 1/2 ‘because only pairs of photons are counted’). The wavelength peaks follow from A(y) y^2 with lambda = lambda_T / y: with NIST’s 2 1S0 and 2 3S1 levels (166 277.44 and 159 855.97 cm^-1, data/external/nist_asd/He_I_levels.tsv) a spline through Table II peaks at 761 A (printed 771) and Table IV at 700 and 2344 A (printed 699, 2400); the singlet peak is so flat (A y^2 changes by less than 0.1 % between y = 0.78 and 0.79) that the three-figure table cannot place it closer. The paper does not print the transition energies it used.
COMPARISONS (p. 28). Dalgarno’s semi-empirical 45 s^-1 and Victor’s coupled Hartree-Fock 50 s^-1 for He 2 1S0 ‘compare well’; the uncoupled Hartree-Fock rate is about 60 % high. For 2 3S1 of He the value is consistent with Drake and Dalgarno’s bound (not above 10^-7 s^-1) but not with Bely’s (near 10^-10 s^-1). bondy_2020 recomputes the singlet rates to nine figures: see its record (this paper’s 51.3 s^-1 is 0.54 % above bondy_2020’s infinite-mass 51.0233 s^-1).
FURTHER TWO-PHOTON DATA CITED, NOT IN THE LIBRARY (two-photon decay rates, no absorption data): G. Breit and E. Teller, Astrophys. J. 91, 215 (1940); A. Dalgarno, Mon. Not. R. Astron. Soc. 131, 311 (1966); A. Dalgarno and G. A. Victor, Proc. Phys. Soc. 87, 371 (1966); G. A. Victor, Proc. Phys. Soc. 91, 825 (1967); G. W. F. Drake and A. Dalgarno, Astrophys. J. Lett. 152, L121 (1968); O. Bely, J. Phys. B 1, 718 (1968); G. A. Victor and A. Dalgarno, Phys. Rev. Lett. 18, 1105 (1967) (Li II).
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#
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.