Theoretical line strengths for the4d10S1−4d94fPo1resonance transition in the palladium isoelectronic sequence

Abstract

Theoretical line strengths for the $4d^{10}{}_{}{}^1{}_{}{}^{}S-4\mathrm{}{d}^{9}4f{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ resonance transition in the palladium isoelectronic sequence have been computed in three approximations: configuration-averaged Hartree-Fock, term-dependent Hartree-Fock, and many-body perturbation theory. The Hartree-Fock $4f$ state exhibits pronounced term dependence in the intermediate ionization stages III-XV, with the configuration-averaged radial orbital collapsing more rapidly with $Z$ than the $4f{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ term-dependent orbital due to the large repulsive exchange interaction with the $4d^9$ subshell in the latter. The $4d-4f$ oscillator strength is small for low ionization stages, and does not reach a maximum until Ba XI. Contracted orbital many-body perturbation theory calculations confirm that, as expected for this closed-shell ground-state system, most of the correlation effects are concentrated in the $4d^{8}4f^2{}_{}{}^1{}_{}{}^{}S$ configuration mixing with the ground state. As a comparison, Hartree-Fock data are also given for the transition $4d^{10}{}_{}{}^1{}_{}{}^{}S-4\mathrm{}{d}^{9}5p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$. For $Z<\mathrm{}60\mathrm{}$ the $5p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ state is the lowest-lying ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ in the Pd I sequence.