Atom-to-Solid Core-Level Shifts for the Lanthanides:nlDependence Introduced by Valence Changes

Free-atom-to-metal shifts of the rare-earth $2p$, $3d$, $4f$, and $5s$ core-level binding energies have been calculated. 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. Consequently, a unique shift characterizing all core levels of a given element cannot be assumed when a configuration change involving the $4f$ states occurs on solid formation.