Ground-state configurations and theoretical soft-x-ray emission of highly charged actinide ions

Abstract

It is well known that the lanthanide and actinide elements are formed by the filling of $4f$ and $5f$ subshells which occurs after the filling of $5d$ and $6d$ subshells, respectively, has begun. With increasing ionization one expects the energy levels to eventually regroup to their hydrogenic ordering, i.e., in terms of principal quantum number. In the lanthanides, the $4f$ electron binding energy overtakes that of $5p$ near the 6th or 7th ion stage and $5s$ near the 14th or 15th ion stage, leading to dramatic rearrangements of ground-state configurations. In this paper we report on the results of a study to explore the effects of increasing ionization on the ground-state configurations of actinide ions as a result of $5f$ and $6p$ or $6s$ level crossings. It is seen that the effects generally occur later and are more strongly influenced by spin-orbit splitting than in the lanthanides. The near degeneracies of $5f$ and $6l$ energies in these stages lead to configuration interaction (CI) amongst configurations with variable numbers of $5f$ and $6p$ electrons. The effects of CI on the level complexity are explored for ions along the Rn I sequence and are found to lead to the formation of ``compound states'' as predicted for the lanthanides. The extreme ultraviolet and soft x-ray spectra of medium and highly charged lanthanides are dominated by emission from unresolved transition arrays (UTAs) of the type $\mathrm{\ensuremath{\Delta}}n=0$, $4{p}^{6}4{d}^{N+1}\ensuremath{-}4{p}^{5}4{d}^{N+2}+4{p}^{6}4{d}^{N}4f$, which, in general, overlap in adjacent ion stages of a particular element. Here, the corresponding $\mathrm{\ensuremath{\Delta}}n=0$, $5{p}^{6}5{d}^{N+1}\ensuremath{-}5{p}^{5}5{d}^{N+2}+5{p}^{6}5{d}^{N}5f$ UTAs have been studied theoretically with the aid of Hartree-Fock with configuration interaction calculations. As well as predicting the wavelengths and spectral details of the anticipated features, the calculations show that the effects of configuration interaction are quite different for the two different families of $\mathrm{\ensuremath{\Delta}}n=0$ transitions and, once more, spin-orbit interactions play a major role.