Many-body effects in praesodymium core-level spectroscopies ofPrO2

The high-energy deep-core-level spectra of ${\mathrm{PrO}}_2$ have been studied. Pr 3d x-ray photoemission spectroscopy (XPS), Pr $M_4$,5 x-ray-absorption spectroscopy (XAS) and Pr $L_3$ XAS show many-body effects. The data are analyzed in the framework of the filled-band Anderson-impurity model. Starting from the many-body description of the ground-state, the final states of each core-level spectroscopy are predicted. The effective relaxation energy in the final state decreases going from 3d XPS to $L_3$ XAS to $M_4$,5 XAS because of the repulsive interaction between the excited electron and the 4f electron in XAS spectra. It is shown that the ground state exhibits mixing of many-body configurations 4$f^1$ and 4$f^2$L, where L denotes a hole in the oxygen 2p-derived valence band, separated by the energy ΔE=0.5 eV. A nonzero probability of the occupation of the 4$f^2$L configuration, giving a noninteger 4f count $n_f$=1.6, is found.