Comparison of two forms of the S-matrix element of strong-field photoionization

Abstract

We numerically compare ionization rates and photoelectron energy spectra resulting from the so-called length gauge (LG) and velocity gauge (VG) forms of the Keldysh–Faisal–Reiss (KFR) theory for a circularly polarized laser field. To this end, we use the well-known analytical formulae for the ground state of a hydrogen atom and we derive analogous formulae for its first excited (degenerate) state. It appears that both forms of the KFR theories show qualitatively different behaviour of ionization rate as a function of frequency and intensity of the laser field. In the LG KFR theory, one obtains much smaller stabilization of the hydrogen atom than in the VG KFR theory. Unlike the latter one, the LG KFR theory shows that for sufficiently strong laser field (in the non-relativistic and dipole approximations) ionization rate from a given initial state is only a function of intensity, but not of frequency of the laser field. We also find substantial differences in the shape of photoelectron energy spectra for both theories. In contrast to the VG KFR theory, the LG one shows a minimum in photoelectron energy spectra for some initial states of the hydrogen atom. We discuss our results by comparing them, where possible, to other theoretical calculations.