The process of a resonant production of an ultrarelativistic electron–positron pair in the process of gamma-quantum scattering in the X-ray field of a pulsar is theoretically studied. This process has two reaction channels. Under resonant conditions, an intermediate electron (for a channel A) or a positron (for a channel B) enters the mass shell. As a result, the initial second-order process of the fine-structure constant in the X-ray field effectively splits into two first-order processes: the X-ray field-stimulated Breit–Wheeler process and the the X-ray field-stimulated Compton effect on an intermediate electron or a positron. The resonant kinematics of the process is studied in detail. It is shown that for the initial gamma quantum there is a threshold energy, which for the X-ray photon energy (1–102) keV has the order of magnitude (103–10) MeV. In this case, all the final particles (electron, positron, and final gamma quantum) fly in a narrow cone along the direction of the initial gamma quantum momentum. It is important to note that the energies of the electron–positron pair and the final gamma quantum depend significantly on their outgoing angles. The obtained resonant probability significantly exceeds the non-resonant one. The obtained results can be used to explain the spectrum of positrons near pulsars.
Resonant laser-assisted process of the ultrarelativistic electron-positron pair creation by a gamma quantum in the nucleus field