Abstract
The method for the evaluation of the self-energy of bound electron is proposed. The integration over four-momenta of virtual photons is done in a way that preserves manifest Lorentz invariance.
The resulting expression can then be decomposed into high-and low-energy parts in a Lorentz invariant fashion. The high-energy part depends only on the behavior of the wave function of the reference state in the immediate vicinity of the nucleus and can be calculated analytically.
The low-energy part depends on further details of the atomic structure and has to be calculated numerically. The results accurate at least up to alpha(Z alpha)(6) are obtained for non-S states and normalized difference n(3)Delta E-n - Delta E-1 of the S states.
The method is applied to the states with the principal quantum number n ranging from 2 to 10, with the orbital quantum number l ranging from 0 to 3 and with the nuclear charges Z ranging from 1 to 30. In the cases that were already considered in literature a very good agreement with previous calculations is found, especially for the atoms with lower nuclear charges.
The advantages of the present method over the previous ones are pointed out.