Many-body perturbation procedure for energy-dependent perturbation: Merging many-body perturbation theory with QED

A formalism for energy-dependent many-body perturbation theory (MBPT), previously indicated in our recent review articles (Lindgren et al., Phys.Rep. 389,161(2004), Can.J.Phys. 83,183(2005)), is developed in more detail. The formalism allows for a mixture of energy-dependent (retarded) and energy-independent (instantaneous) interactions and hence for a merger of QED and standard (relativistic) MBPT. This combination is particularly important for light elements, such as light heliumlike ions, where electron correlation is pronounced. It can also be quite significant in the medium-heavy mass range, as recently discussed by Fritzsche et al. (J.Phys. B38,S707(2005)), with the consequence that the effects might be significant also in analyzing the data of experiments with highly charged ions. A numerical procedure for treating the combined effect is described, and some preliminary numerical results are given for heliumlike ions. This represent the first numerical evaluation of effects beyond two-photon exchange involving a retarded interaction. It is found that for heliumlike neon the effect of one retarded photon (with Coulomb interactions of all orders) represents about 99% of the non-radiative effects beyond energy-independent MBPT.