Self-consistent treatment ofthe frequency-independent Breit interaction in Dirac-Fockcalculations of atomic structures. II. He- and Be-like ions

Abstract

We systematically study the effect of the inclusion of thefrequency-independent Breit interaction - treated perturbativelyas well as variationally - on Dirac-Fock total energies and⟨rk⟩ expectation values for He- and Be-likeions using an algorithm recently described by Reiher andHinze. Fully numerical, highly accuratesolution methods are employed throughout for solving theDirac-Fock-Coulomb-Breit (DFCB) equations. These methods allow us to investigate the change of the wavefunction upon inclusion ofthe Breit interaction in the self-consistent field procedureof an atomic structure program.The dependence of expectation values on different finite-nucleusmodel (FNM) potentials for the electron-nucleus attraction is alsostudied. It is shown that, in general, the choice of theFNM for the electron-nucleus potential hardlyaffects the difference between Dirac-Fock-Coulomb (DFC) andDFCB expectation values. In the case ofpointlike nuclei one should treat the Breit interaction variationally instead of perturbatively.For energy eigenvalues, we find that the difference betweenthe Breit interaction treated self-consistently or perturbativelyis negligibly small - even for highly charged ions - if anextended nucleus model is used. The data given may serve as areference for more approximate treatments involving, for example,basis-set approaches with limited basis-set size. In thisextensive study of the SCF effect on the Breit interaction,highly accurate, variationally obtained DFCB total energies and⟨rk⟩ expectation values are given for differentmodels of the electron-nucleus interaction.