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 `__ · :doc:`Catalogue ` · :doc:`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. 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 :doc:`review register ` for the checks and decisions.