Resonant Production of an Ultrarelativistic Electron-Positron Pair by a Gamma Quantum in the Field of a Nucleus and a Laser Wave

The resonant photoproduction of electron-positron pairs (PPP) on nucleus in the field of laser is studied theoretically for intensities
$I\lesssim 10^{16}\mathrm{W}/\mathrm{cm}^{2}$
. In resonant conditions intermediate virtual electron (positron) becomes real particle in the laser field. As a result, the initial process of the second order in the fine structure constant in the laser field effectively splits into two successive processes of the first order: Single-photoproduction of electron-positron pair in a laser field (laser-stimulated Breit-Wheeler process) and laser-assisted scattering of electron (positron) on nucleus. Resonant kinematics of PPP was studied in details. It is shown that for the considered laser intensities the resonance is possible only for the energies of the initial photon more than the characteristic threshold energy. At the same time, ultrarelativistic electrons and positrons fly out in a narrow cone along the direction of the initial photon's momentum. It is important to emphasize that the resonance of this process can occur in two channels. The first channel is single-photoproduction of positron and intermediate electron in a laser field (laser-stimulated Breit-Wheeler process), and then the scattering of the intermediate electron on the nucleus (laser-assisted Mott process). The second channel is single-photoproduction of electron and intermediate positron in a laser field (laser-stimulated Breit-Wheeler process), and then the scattering of the intermediate positron on nucleus (laser-assisted Mott process). It is important to note that the resonant energy of a positron (electron) can have two values for each angle of escape, which varies from zero to some maximum value, determined by the energy of the initial photon and the threshold energy. Resonant differential cross section of the studied process is obtained. It is shown that the resonant differential cross section of the PPP in external field can significantly exceed the corresponding cross section of the PPP without an external field. The project calculations may be experimentally verified by the scientific facilities of pulsed laser radiation (SLAC, FAIR, XFEL, ELI, XCELS).