Compton scattering by a bound electron in the presence of a low-frequency electromagnetic field

Recently we derived a formula for Compton scattering of high-energy photons on a bound electron in the presence of a weak low-frequency laser field of circular polarization (Voitkiv et al 2003 J. Phys. B: At. Mol. Opt. Phys. 36 1907). However, numerical calculations were performed in the above study using a simplified expression for the parameter describing the coupling between the 'high-energy photon+target' subsystem and the laser field. In this paper we reconsider the field-assisted Compton scattering by using the full expression for the coupling parameter. We show that (i) the fully differential spectra of emitted electrons and scattered high-energy photons can be strongly influenced by the laser field (as was suggested in our earlier study although there may exist substantial deviations from the former predictions); (ii) the energy spectrum of the emitted electrons, integrated over all states of the scattered photons, can be profoundly modified by the field (only small deviations from our earlier predictions have been found); (iii) the energy spectrum of the scattered photons, integrated over all final electron states, turns out to be independent of the field, in contrast to our earlier predictions that this spectrum should be shifted to lower energies if the laser field is present. We also show that, despite the full coupling parameter containing a term which changes sign when one of the polarization vectors of the laser field is inverted, the so-called dichroism effect is absent in the field-assisted Compton scattering accompanied by emission of a high-energy electron