Effects of dynamical screening on resonances at inner-shell thresholds in semiconductors

A theory of core excitons in semiconductors is formulated, taking into account the frequency dependence of the dielectric matrix which screens the electron-hole attraction. The present approach combines standard many-body techniques (which reduce the Bethe-Salpeter equation for the two-particle Green's function to an effective eigenvalue problem) with elements drawn from Fano's formalism for discrete states interacting with continuum channels. The positions and the widths of core-exciton resonances are affected by dynamical screening, which increases the binding energy above its value for static screening and decreases its Auger width below its value for a core hole. The latter effect is peculiar to a dynamical theory and has recently been confirmed experimentally.