bondy_2020

A. T. Bondy, D. C. Morton and G. W. F. Drake, “Two-photon decay rates in heliumlike ions: Finite-nuclear-mass effects”, Phys. Rev. A 102, 052807 (2020)

Source record · Catalogue · Review register

DOI: 10.1103/PhysRevA.102.052807

Source kind: theory

Recorded technique: Nonrelativistic variational calculation of the spontaneous two-photon (2E1) decay rate of the 1s2s 2 1S0 level to the 1s2 1 1S0 ground level of 3He, 4He, 6Li+, 7Li+ and the most abundant isotopes of Be2+ to Ne8+ (and of three ‘heavy helium’ systems), with finite nuclear mass to all orders in mu/M (mass scaling, mass polarisation, and the motion of the nucleus in the centre-of-mass frame): doubled-basis Hylleraas wave functions and P-state pseudostates, extrapolated in the basis size; length and velocity forms agree to about one part in 10^8. The final rates (Table VI) add a relativistic correction estimated, after Drake 1986, as the mean of the unscreened and fully screened one-electron shifts, with the full range as its uncertainty.

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Phys. Rev. A 102, 052807 (published 10 November 2020), PDF pages 1-10 = pages 052807-1 to -10. Identity checked against the first page (journal, volume, article number, dates, title, authors). A born-digital PDF; every number below was checked against its table image or the PDF’s text.

NOTHING TAKEN. The paper gives spontaneous two-photon emission rates (s^-1, and in atomic units divided by alpha^6); 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. Only helium is a registered material; the values are recorded for reference.

HELIUM 2 1S0 -> 1 1S0. Table VI (p. 8, tbl_2e60d34395e6; its extracted text is scrambled, the image is clear), 4He, s^-1, scale x 10^1: w_inf = 5.102 332 10(5) (infinite nuclear mass), Delta w_mu/M = -0.001 561 748, Delta w_rel = -0.008(7), w_total = 5.093(7), Derevianko and Johnson (Ref. 10) 5.102, difference -0.009(7); 3He the same but Delta w_mu/M = -0.002 072 586 and w_total 5.093(7). Table IV (p. 7, tbl_1b8dc68d98fd), w/alpha^6 in au: 4He 8.170 693 021 30(21) x 10^-3, infinite mass 8.173 194 7151(20) x 10^-3, ratio 0.999 693 914 82(35); conversion alpha^6 / tau_e = 6242.763420(56) s^-1 (Table I caption, p. 6). Table II (unlabelled in the library, tbl_75d5c3ca48b0, p. 6; image read): 4He velocity 8.170 693 021 30(21) and length 8.170 693 117(8) x 10^-3, ratio 0.999 999 988(9). Table V (p. 7, tbl_83d92116af1b): 4He w_max = 7.256 232 28 x 10^1 s^-1 (the peak of the distribution per unit fraction y of the energy, counting pairs), Delta = 1.663 025 x 10^5 cm^-1 (the calculated 2 1S0 - 1 1S0 interval), peak lambda = 1.202 628 x 10^2 nm.

CHECKED (computed 2026-10-09). w_inf/alpha^6 x 6242.763420 = 51.023 321 s^-1 = Table VI’s w_inf; (w - w_inf)/alpha^6 x 6242.763420 = -0.015 617 5 (4He) and -0.020 725 9 (3He) = Table VI’s Delta w_mu/M; the peak wavelength is 2 / Delta (120.2628 nm) = half the transition frequency.

MISPRINTS IN THE TEXT (nothing taken, so no errata). (1) Sec. V (p. 8): ‘a total rate of 50.093 s^-1’ for helium; Table VI’s total is 50.93(7) s^-1. (2) Sec. V gives wavelengths in ‘um’ that are nm or angstrom: hydrogen’s two-photon continuum ‘from 121.9 um to a maximum at 243.1 um’ (Lyman alpha is 121.57 nm, and 243.1 nm is twice it), helium’s ‘from 601.40 um to a maximum at 120.28 um’ (1e8 / 166 277.44 cm^-1, NIST’s 2 1S0 level, is 601.40 angstrom; 120.28 nm is twice it, against Table V’s 120.2628 from the calculated interval). (3) p. 8: ‘Experimental lifetimes of 5.03(26) x 10^-4 s for both 4He and 3He [12] and 1.97(10) x 10^-2 s for 7Li+ [13] are entirely consistent with our respective calculations of 5.178(45) x 10^-4 and 1.9634(28) x 10^-2’: the attributions are swapped. 1/50.93 s^-1 = 1.9635 x 10^-2 s is helium’s lifetime and 1/1938.8 s^-1 = 5.158 x 10^-4 s that of 7Li+ (Van Dyck et al., Ref. 12, measured He; Prior and Shugart, Ref. 13, Li+). The printed 5.178(45) x 10^-4 s is not 1/1938.8(17) s^-1 (5.158(5) x 10^-4 s); unexplained.

COMPARISONS. drake_1969 (this paper’s Ref. 7) gives 51.3 s^-1 for He 2 1S0 in the same approximation (nonrelativistic, infinite mass): 0.54 % above w_inf = 51.0233 s^-1. Its three-figure rates for Li II to Ne IX differ from Table VI’s w_inf by +0.49, -0.39, +0.48, +0.23, -0.26, -0.14, +0.23 and -0.36 %: errors of a few units of the third figure, larger than drake_1969’s statement that its results ‘converged to the number of figures quoted’. The text (p. 7): drake_1969’s Table II ‘give[s] the helium rates over half the spectrum, but exclude[s] the factor of 1/2 due to double counting’; its He peak (y = 0.5), 1.45 x 10^2 s^-1, is twice Table V’s 72.562 within its rounding (145 / 2 = 72.5). The 2 3S1 two-photon rate is not calculated here; p. 1 quotes Derevianko and Johnson’s triplet-to-singlet ratio of 6.2 x 10^-11 at Z = 2 without saying which rates it divides (drake_1969’s 2 3S1 rate, 4.02 x 10^-9 s^-1, is 7.8 x 10^-11 of its 2 1S0 rate). The text (p. 8) calls the 0.09 +- 0.07 s^-1 difference from Derevianko and Johnson’s relativistic CI a ‘marginal disagreement’.

FURTHER TWO-PHOTON DATA CITED, NOT IN THE LIBRARY (decay rates and spectra): G. W. F. Drake, Phys. Rev. A 34, 2871 (1986); A. Derevianko and W. R. Johnson, Phys. Rev. A 56, 1288 (1997); R. S. Van Dyck, Jr., C. E. Johnson and H. A. Shugart, Phys. Rev. A 4, 1327 (1971) (the measured He 2 1S0 lifetime); M. H. Prior and H. A. Shugart, Phys. Rev. Lett. 27, 902 (1971); P. H. Mokler and R. W. Dunford, Phys. Scr. 69, C1 (2004); A. V. Volotka et al., Phys. Rev. A 83, 062508 (2011); D. Banas et al., Phys. Rev. A 87, 062510 (2013). Fig. 1 (the 4He profile, raster) is not digitised.

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

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Formulas

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Corrections

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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.