Dynamical screening effects on AugerCVVline shapes of solids

The current theory of Auger $\mathrm{CVV}$ spectra of solids takes solid-state polarization effects into account by a statically screened hole-hole repulsion parameter $U$. Here we include dynamical screening effects by considering a plasmon field coupled to final-state holes interacting through the bare repulsion $U_0$. We sum the series of diagrams that dominate the two-hole Green's function when the plasma frequency ${\omega }_p$ is large compared with the hopping parameter $V$ between nearest neighbors. Moreover, we show that in this case the theory reduces to a Cini model or a Sawatzky model plus the interaction with a single effective plasmon. This is solved exactly and provides an understanding of various features of the system. Split-off two-hole resonances occur at higher kinetic energies than predicted by the statically screened theory, and under certain resonance conditions they are broadened due to the presence of a preferential decay channel. Bandlike spectra are also significantly modified and the transition between bandlike and atomiclike behavior is characterized by the occurrence of broadened resonances within the band continuum.