Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift

Abstract

We present a derivation of the last unknown part of the ${\alpha }^{7}m$ contribution to the Lamb shift of a two-electron atom, induced by the radiative QED effects beyond the Bethe logarithm. This derivation is performed in the framework of nonrelativistic quantum electrodynamics and is valid for the triplet (spin $S=1$) atomic states. The obtained formulas are free from any divergences and are suitable for a numerical evaluation. This opens a way for a complete numerical calculation of the ${\alpha }^{7}m$ QED effects in helium, which will allow an accurate determination of the nuclear charge radius from measurements of helium transition frequencies.

Comments: 28 pages, corrected numerous misprints