High precision variational calculations for the 1s 21S state of H − and the 1s 21s, 1s2s 1s and 1s2s 3s states of helium

Abstract

High precision variational eigenvalues are presented for the 1s 21S state of H −, and the 1s 2 1S, 1s2s 1S and 1s2s 3S helium, together with relativistic, mass polarization and relativistic recoil corrections. In addition to the nonrelativistic energy, all corrections of order α 2, μ M ( μ M ) 2 and α 2 M are calculated to an accuracy of better than 10 −6 cm −1. Previous results of similar accuracy are available for the 1 sn d 1 D and 3 D states up to n = 8. A comparison with the high precision 1 s2 s 3 S 1−1 sn d 3 D 1 transition frequency measurements of Hlousek et al. indicates that the known quantum electrodynamic (Lamb shift) contribution of − 0.13488 cm −1 to the ionization energy of the 1s2s 3S 1 state is too small in magnitude by 0.00048(6) cm −1. A discrepancy of this size can reasonably be accounted for by as yet uncalculated contributions to the two-electron Lamb shift.