On Coster-Kronig Line Shapes of Solids

We propose the foundations of an extended Auger line-shape analysis of solids aiming to include three-hole features such as the ones due to core-valence-valence Auger decays following Coster-Kronig transitions. In transition metals, such features show up as intense high binding energy satellites of the diagrammatic core-valence-valence lines. Our theory is grounded on the full one-step approach, but to keep the complications to a minimum, in the present exploratory paper, the valence band is assumed fully below the Fermi level. In this way, explicit model calculations can be confidently based on a three-step approach. The line-shape analysis then amounts to compute a three-body Green’s function, which, however, is much less known than one- and two-body ones. Our treatment covers the whole range between weak and strong correlations. Furthermore, we show that the relevant physics can be captured by a transparent, computationally simple closed formula. We find that, in general, the satellites cover separated spectral regions with three-hole multiplets, shifted and broadened two-hole features, and distorted bandlike continua.