An α2( Zα) 5m correction to the Lamb shift from the radiative electron factor and Coulomb line polarization

Abstract

A radiative correction of order α 2( Zα) 5 m to the Lamb shift connected with a polarization insertion in one of the two external Coulomb lines is obtained. This correction arises from a gauge invariant set of diagrams which contain, besides the polarization insertion in the Coulomb leg, all one-loop radiative photon insertions in the electron line with two external Coulomb lines. A new contribution to the Lamb shift in an arbitrary hydrogen-like ion is equal to 0.611 [ α 2(Zα) 5 πn 3 ]m for any S-level with the principal quantum number n. For hydrogen itself we obtain a correction 3.31 kHz for the 2S state and 26.5 kHz for the 1S state. The contribution for the 2S state is larger than the accuracy of contemporary experiments while the contribution for the 1S state is comparable with the experimental error.