The authors present a method for calculating the core-level X-ray photoemission (XPS), the 3d to 4f X-ray absorption (XAS), the valence photoemission, and the bremsstrahlung isochromat spectra in a slightly modified Anderson impurity model of a Ce compound at zero temperature. Both the spin and orbital degeneracies of the f level are included and the Coulomb interaction between the f electrons is taken into account. The spectra are expressed in terms of a resolvent operator. A many-electron basis set is introduced, and the resolvent is obtained from a matrix inversion. The particular form of the Anderson model allows the authors to find a small but sufficiently complete basis set, if the degeneracy Nf of the f level is large. In particular, they consider the limit Nf to infinity , and show that the method is exact for the XPS, XAS, and valence photoemission spectra in this limit. It is also demonstrated that for Nf>or approximately=6l, the method provides accurate spectra. Analytical results are obtained for the valence photoemission spectrum rho v( epsilon ). The spectrum has a sharp rise close to the Fermi energy epsilon F, which goes over to a 'Kondo peak' in the spin-fluctuation limit. An exact relation between rho v( epsilon F) and the f-level occupancy nf is shown to be satisfied to within 10\% for Nf>or=6. The authors discuss how core-level XPS spectra can be used to estimate the f-level occupancy nf and the coupling Delta between the f level and the conduction states. They find that the values of nf and Delta obtained from core-level XPS are basically consistent with the other spectroscopies and the static, T=0 susceptibility. It is, therefore, possible to describe these experiments in the Anderson model, using essentially the same set of parameters for all the experiments. Typically, they find nf>0.7 and Delta approximately 0.1 eV.
 

Physical Review B, 28 4315-41, 1983.