Relativistic calculations of3dexcitation energies in the rare-earth metals

Abstract

A systematic investigation of $3d$-electron excitation energies in the rare-earth metals is described. The $3d_{\frac{3}{2}}$ and $3d_{\frac{5}{2}}$ energy levels are calculated by a method based on the renormalized-atom approach which has proved successful in calculating $4f$ and $5s$ level positions in these materials. $3d-4f$ multiplet effects, which are small compared to the spin-orbit splittings, and satellite structures are not considered. Total energy differences obtained within the approximation of a completely screened final state, in which the atomic cell having a $3d$ hole is electrically neutral, lead to results in accord with available x-ray photoemission measurements; one-electron values are 20-33 eV larger. The impact of the complete screening assumption is examined by estimating excitation energies corresponding to ionized final states. The presence of a screening electron reduces the $3d$ binding energy by 4-5 eV, a value similar to that calculated for the $4f$ and $5s$ levels.