  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.

Strongly Correlated Electrons