Nonstationary theory for short-pulse near-threshold photoionization of inner atomic shells

A theoretical description of near-threshold ionization of inner atomic shells by short electromagnetic pulses is developed. It is based on a nonstationary approach to the Fano-Feshbach problem of photoexcitation with simultaneous Auger decay of the produced vacancy. We suggest a method of solving the system of time-dependent Schr\"odinger equations describing a resonant state embedded into continuum. The method gives a nonstationary description of the post-collision interaction in near-threshold photoionization including the recapture of the slow photoelectron in high Rydberg states. As an example, $1s$ photoionization in Ne with the following $\mathit{KLL}$ Auger decay is considered. The influence of the duration of the pulse on the recapture probability and shape of the emitted electron peak is studied.