Relativistic calculations of2pexcitation energies in the rare-earth metals

Abstract

We report a systematic investigation of $2p$-electron excitation energies in the rare-earth metals. Crystal potentials are constructed via the renormalized atom method, and level positions are obtained from differences between total band energies. Calculations have been performed for the principal excitations, which involve conduction-electron screening of the $2p$ core hole, as well as for satellite levels associated with $4f$ screening in the final state. For the five lanthanides (Ce, Sm, Eu, Tm, Yb) known to form valence-fluctuation compounds, we also calculate the change in $2p$ excitation energy accompanying a change in the $4f$ occupation number; these replicate splittings are 8-9 eV, comparable to analogous splittings for the $3d$ and $4d$ states. For $2p$ and other core states we show that the replicate splitting is equal to the energy by which the $4{f}^{n+1}$ level is lowered by a core hole. The energies associated with conduction-band and $4f$-electron screening of a $2p$ core hole are estimated and found to be related to the position of the $4{f}^{n+1}$ level in the $2p$ hole state.