Screening effects in the core-level spectra of mixed-valence compounds

The effects of screening in the core-level photoemission spectra of mixed-valence compounds are studied with the use of an Anderson-model formulation. The mixed-valent ground-state properties and core-hole Green's function are calculated with the use of a decoupling approximation. The relative weights of peaks corresponding to two different configurations ($f^n$ and $f^{n+1\mathrm{}}$) are found to become appreciably different from the ground-state valence due to shakedown as the hybridization between the localized $f$-level and conduction electrons is increased. The discrepancy is estimated to be of the order of $\frac{V}{U_{\mathrm{df}}}$, where $U_{\mathrm{df}}$ is the correlation energy between the core hole and $f$ electron, and $V$ represents the hybridization between $f$ electron and conduction electrons. We also find a shakedown $f^{n+2\mathrm{}}$ peak in this limit. From a comparison of ground-state valence with the measured intensity of the shake-down peak for Ce${\mathrm{Pd}}_3$, the width of the $f$ level due to hybridization is estimated to be of the order of 1 eV, in agreement with a recent resonant photoemission measurement.