Atom-to-solid core-level shifts for the rare-earth elements

Shifts of the lanthanide $2p$, $3d$, $4f$, and $5s$ core-level binding energies from the free atom to the metallic phase are reported. The shifts are obtained directly from relativistic Hartree-Fock calculations of the individual atomic and solid-state binding energies. Results for the $4f$ levels compare favorably with estimates derived from available photoemission and spectroscopic data. For Pr—Sm and Tb—Tm, elements which undergo a valence change on formation of the solid, the shifts are smaller and depend significantly on the $\mathrm{nl}$ core-state quantum numbers. One-electron analogs of the shifts share these attributes. Consequently, a unique shift characterizing all core states cannot be assumed when a configuration change involving the $4f$ electrons occurs on formation of the solid. The impact of the valence change is assessed by means of calculations for atoms having metal-like configurations.