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For a complete development of quantum electrodynamics in the presence of a strong external field, proper understanding of the resonant processes and all their peculiarities is essential. We present our attempt to analytically investigate the resonant case of laser-assisted ultrarelativistic electron-positron pair photoproduction on a nucleus. The initial gamma quantum with energy ₈100 GeV and external field with intensity up to I10^24 W/cm^2 are considered. Due to the presence of the external field, the intermediate virtual particle may become real, herewith the second order process in the fine structure constant effectively reduces into the two successive first order processes. All inherent kinematics features were discussed in details and the resonant differential cross sections with simultaneous registration of the produced particle (positron for channel A or electron for channel B) energy and its outgoing angle were obtained. We established that the resonant energies of produced particles acquire two different values with respect to the positron (channel A) or electron (channel B) outgoing angle. Additionally, the certain minimal amount of absorbed wave photons is required for resonance to happen. Wherein, the resonant differential cross section significantly exceeds the corresponding one without the external field within the particular kinematic regions. Consequently, the considered process can be used as a marker for probing theoretical predictions of quantum electrodynamics with strong background electromagnetic field.
Roshchupkin et al. (Fri,) studied this question.