Approximate recalculation of the [formula omitted] contribution to the self-energy effect on hydrogenic states with a multipole expansion

Abstract

A contribution of virtual electron states with large wave numbers to the self-energy of an electron bound in the weak Coulomb field is analyzed in the context of the evaluation method suggested in the previous paper. The contribution is of the order α(Zα)5. The same value for this contribution is found here as the one found in the previous calculations using different evaluation methods. When we add the remaining terms of the order α(Zα)5 to the calculation of the self-energy effect in hydrogen-like ions presented in the previous paper we find a very good agreement with numerical evaluations. The relative difference between present and numerical evaluations ranges from 2 parts in 106 for Z=1 up to 6 parts in 104 for Z=10.