Relaxation and atom-solid energy shift of multiple-hole levels and Auger spectra

The authors present a simple, approximate scheme for multiple-vacancy energies and energy differences, e.g. Auger energies and X-ray satellite energies. The method is based on knowledge of single-hole relaxation shifts and of the bare hole-hole Coulomb repulsion from the no-hole ground-state configuration. This leads to a formulation in terms of the screened hole-hole repulsion which, to lowest order, is independent of chemical shifts and only depends on intra- and extra-atomic relaxation. In the case of 4d vacancies in atomic Xe they examine the accuracy of the method as a function of the number of holes, by comparing with Delta SCF calculations. They improve the linear response approximation by including non-linear effects: the variation of the effective hole-hole interaction with respect to the number of holes becomes important when the number of holes increases. Finally, they present a simple, approximate scheme for atom-solid energy shifts of multiple vacancies.