QED Corrections to Atomic Wavefunctions in Highly Charged Ions

Abstract

Bound electron states in highly charged ions are strongly influenced by the effects of relativity and quantum electrodynamics (QED). These effects induce shifts of the binding energies as well as corrections to observables related to atomic processes. In this work a numerical procedure is described and implemented in which the QED effects are treated as corrections to relativistic bound-state wavefunctions. This approach, which is based on the recently developed covariant evolution-operator formalism, allows for a merging of QED with the standard methods of many-body perturbation theory. In particular, it enables an evaluation of the combined effect of QED and electron correlation in few-electron systems. Numerical results for this effect are presented for the ground state energy of heliumlike ions. A detailed analysis of the contribution from the electron self-energy is carried out in both the Feynman and Coulomb gauge. It is found that the Feynman gauge suffers from large numerical cancellations and aquires significant contributions from terms involving multiple interactions with the nuclear potential (the so-called many-potential terms), while the Coulomb gauge is well suited for an approximate treatment based on terms involving only freely propagating electrons (the zero-potential terms). With the help of QED-corrected wavefunctions it is also possible to compute corrections to observables in basic atomic processes. In this work some of the one-loop QED corrections (those derivable from perturbed wavefunctions and energies) to the differential cross section and distribution of polarization in radiative recombination of initially bare uranium nuclei are evaluated, as well as the corresponding corrections to the ratio of the electric dipole and magnetic quadrupole transition amplitudes in the 2p3/2 → 1s radiative decay of hydrogenlike uranium. The results from these calculations are all of the expected magnitude, namely on the order of the fine-structure contant.