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The article presents a theoretical study of Oleinik resonances in the process of scattering a gamma quantum by an ultrarelativistic electron in the field of a strong electromagnetic wave. It is shown that under resonant conditions, the scattering channels of the reaction effectively split into two first-order processes according to a fine structure constant such as the external field-stimulated Compton effect. And the annihilation channel of the reaction effectively decays into direct and reverse the external field-stimulated Breit-Wheeler processes. The significant dependence of the resonant energy of final particles and resonant cross sections on the outgoing angles of the final gamma quantum, the number of absorbed and emitted photons of the wave, as well as the characteristic quantum parameters of the problem is shown. These quantum parameters are determined by the ratio of the initial particle energies to the characteristic energies of the Compton effect and the Breit-Wheeler process. An unambiguous relationship between the outgoing angles of final electrons and gamma quanta has been obtained, which qualitatively distinguishes the resonant process from the non-resonant one. The cases when the energy of the initial electrons significantly exceeds the energy of the initial gamma quanta have been studied. The conditions under which the energy of high-energy initial electrons is converted into the energy of final gamma quanta are obtained. At the same time, the resonant differential cross-section of such a process significantly (by several orders of magnitude) exceeds the corresponding non-resonant cross-section. This theoretical study predicts a number of new physical effects that may explain the high-energy fluxes of gamma quanta born near neutron stars and magnetars.
Roshchupkin et al. (Fri,) studied this question.