Relativistic many-body calculations of the energies ofn=4states along the zinc isoelectronic sequence

Abstract

The energies of the 44 even-parity and 40 odd-parity $(4l4{l}^{\ensuremath{'}})$ states of ions of the zinc isoelectronic sequence are determined through second order in relativistic many-body perturbation theory. Our calculations start from a Ni-like ${V}^{(N\ensuremath{-}2)}$ Dirac-Fock potential. Two alternative treatments of the Breit interaction are investigated. In the first approach, we omit Breit contributions to the Dirac-Fock potential and evaluate Coulomb and Breit-Coulomb corrections through second order perturbatively. This approach was used previously to evaluate the energies of Be-, B-, Mg-, and Yb-like systems. In the second approach, we include both Coulomb and Breit contributions to the Breit-Dirac-Fock potential and then treat the residual Breit and Coulomb interactions perturbatively. The results obtained from the two approaches are compared and discussed. Theoretical excitation energies are compared with critically evaluated experimental data and with results from other recent calculations. Trends of excitation energies including splitting of triplet terms as functions of nuclear charge $Z=34--100$ are illustrated graphically for some states. The resulting $Z$ dependence shows explicitly the effect of mixing of $[4{p}^{2}+4s4d]$, $[4{d}^{2}+4p4f]$, and $[4p4d+4s4f]$ configurations.