Three-body and one-body channels of the Auger core-valence-valence decay: A simplified approach

We propose a computationally simple model of Auger and Auger photoelectron coincidence spectroscopy line shapes from open-band solids. Part of the intensity comes from the decay of unscreened core-holes and is obtained by the two-body Green’s function $G_{\omega }^{\mathrm{}\left(2\right)\mathrm{}},$ as in the case of filled bands. The rest of the intensity arises from screened core holes and is derived using a variational description of the relaxed ground state; this involves the two-holes–one-electron propagator $G_{\omega },$ which also contains one-hole contributions. For many transition metals, the two-hole Green’s function $G_{\omega }^{\mathrm{}\left(2\right)\mathrm{}}$ can be well described by the ladder approximation, but the three-body Green’s function poses serious further problems. To calculate $G_{\omega },$ treating electrons and holes on equal footing, we propose a practical approach to sum the series to all orders. We achieve that by formally rewriting the problem in terms of a fictitious three-body interaction. Our method grants non-negative densities of states, explains the apparent negative-U behavior of the spectra of early transition metals and interpolates well between weak and strong coupling, as we demonstrate by test model calculations.