Dynamical Shift and Broadening of Core Excitons in Semiconductors

A non-Hermitian eigenvalue equation is proposed to determine binding energies and widths of core excitons in semiconductors, taking into account the time dependence of screening effects through the dielectric matrix ${\epsilon }^{-1\mathrm{}}(\overrightarrow{\mathrm{r}}, {\overrightarrow{\mathrm{r}}}^{\prime };\omega )$. Deviations from static screening contribute both an increase of the binding energy and a narrowing of the Auger width. Numerical estimates of both effects for the Si $2p$ transition give qualitative agreement with experimental data when the exciton size is reduced by band-structure effects.