Self-energy of a bound electron for excited states

摘要

The method for the evaluation of the self-energy of bound electron is proposed. The integration over fourmomentanof virtual photons is done in a way that preserves manifest Lorentz invariance. The resulting expressionncan then be decomposed into high- and low-energy parts in a Lorentz invariant fashion. The high-energy partndepends only on the behavior of the wave function of the reference state in the immediate vicinity of the nucleusnand can be calculated analytically. The low-energy part depends on further details of the atomic structure andnhas to be calculated numerically. The results accurate at least up to α(Zα)6 are obtained for non-S states andnnormalized difference n3u0003En − u0003E1 of the S states. The method is applied to the states with the principalnquantum number n ranging from 2 to 10, with the orbital quantum number l ranging from 0 to 3 and withnthe nuclear charges Z ranging from 1 to 30. In the cases that were already considered in literature a veryngood agreement with previous calculations is found, especially for the atoms with lower nuclear charges. Thenadvantages of the present method over the previous ones are pointed out.