We propose a simple model of core-valence-valence Auger and APECS intensities from open-band solids to account for the alleged negative-U behavior of the spectra of early transition metals. In these systems the maximum of the line shape is shifted by the interaction to lower binding energy, which is the contrary of what happens in closed band materials where the two-hole Green's function Gω(2) allows to understand the phenomenology of the spectra in terms of the U/W ratio of the on-site repulsion U to the band width W. Actually, for open-band solids, only part of the intensity comes from the decay of unscreened core-holes and is obtained by the two-body Green's function Gω(2), as in the case of filled bands. The rest of the intensity which arises from screened core-holes here is derived using a variational description of the relaxed ground state; this involves the two-holes-one-electron propagator Gω, that also contains one-hole contributions. We propose a practical scheme to calculate the three-body Green function by a summation of the perturbation 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 and interpolates well between weak and strong coupling, as we demonstrate by test model calculations. © 2002 Elsevier Science B.V. All rights reserved.
Marini, A., & Cini, M. (2002). One, two and three-body channels of the core-valence-valence Auger photoelectron coincidence spectra of early transition metals. Journal of Electron Spectroscopy and Related Phenomena, 127(1–2), 17–28. https://doi.org/10.1016/S0368-2048(02)00168-8