Low-energy valence photoemission in Ce compounds: Beyond the Anderson impurity model

Abstract

The valence level photoemission spectra in the Anderson impurity model for Ce compounds at zero temperature are studied as a function of the photon energy $\ensuremath{\omega}.$ Most of the former studies on Ce compounds are based on the sudden approximation, which is valid in the high energy region. For the photoemission in the adiabatic limit of the low-energy region, one should consider the dipole matrix elements and the dynamic photoelectron scattering potential. We can manage it by combining the time-evolution formalism and the ${1/N}_{f}$ scheme in a large f-level degeneracy ${N}_{f}.$ This gives the exact results as ${N}_{f}\ensuremath{\rightarrow}\ensuremath{\infty}.$ In view of experiments on the valence photoemission, two contributions of $4f$ and band emissions are mixed. We study the separate $4f$ and band contributions (from Ce $5d)$ and total emission including the interference between two on an equal footing with varying the photon energy. In the $4f$-emission case, we also explore the effects of dynamic scattering potential of the photoelectron with respect to $\ensuremath{\omega},$ for which the extended model is proposed. Its effects are found very similar to the core level photoemission in the shake down case with a localized charge transfer excitation. Additionally, we examine the adiabatic-sudden transition in valence level photoemission for the present localized system through the simplified two-level model.