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Auger spectra of transition metals: a solution for the multi-band model

A solution for two-body Green function relevant to the calculation of Auger spectra in the case of systems described by a multi-band Hubbard Hamiltonian with partially filled bands is presented. In order to obtain the correct atomic limit the formalism of atomic operators is employed. Equations of motion for double-time Green functions are solved using a two-step decoupling scheme. First, the authors restrict themselves to contributions from hopping processes in two bands containing the two studied particles. Second, to cut the hierarchy of equations they replace the local number operators by their average values. The obtained solution has the character of an effective-medium theory for the scattering of a pair of particles. Interpolating between the band and atomic limit yields exact results. It is also correct in the limit of completely filled bands. As an example, the case of five degenerate bands is studied numerically.