Resonant production of electron-positron pairs by a hard gamma-ray on a nucleus in an external electromagnetic field

The resonant production of electron-positron pairs by a hard gamma-ray on nucleus in an external electromagnetic field is studied theoretically. The main property of this process is that the initial process of the second order in the fine structure constant in an external field effectively splits into two successive processes of the first order due to the fact that in resonant conditions intermediate virtual electron (positron) becomes a real particle. One of these processes is a single-photoproduction of electron-positron pair in a laser field (laser-stimulated Breit-Wheeler process) another is a laser-assisted scattering of electron (positron) on nucleus (laser-assisted Mott scattering). It is shown that the resonances are possible only for the energies of the initial hard gamma-ray more than the characteristic threshold energy. Resonant differential cross section of this process is obtained. It is shown that the resonant differential cross section can significantly exceed the corresponding cross section without an external field. The obtained results may be experimentally verified using the facilities of pulsed laser radiation (SLAC, FAIR, XFEL, ELI, XCELS).