Three-Body and One-Body Channels of the Auger Core-Valence-Valence decay: Simplified Approach

TL;DR

This paper introduces a simplified computational model for Auger decay line shapes in open-band solids, effectively capturing core-hole screening effects and providing insights into spectral behaviors of transition metals.

Contribution

It presents a practical approach to compute two-hole and three-body Green's functions, including a novel summation method for the series, improving understanding of Auger spectra in transition metals.

Findings

The model accurately describes Auger spectra of transition metals.

It explains negative-U behavior in early transition metals.

The approach interpolates between weak and strong coupling regimes.

Abstract

We propose a computationally simple model of Auger and APECS 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 $G^{(2)}_{\omega}$, 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 $G^{(2)}_{\omega}$ 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.