  For complete development of quantum electrodynamics in the presence of a
strong external field, the proper understanding of resonant processes and all
their peculiarities is essential. We present our attempt to analytically
investigate the resonant case of laser-assisted electron-positron pair
photoproduction on a nucleus. Due to the presence of 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 section was obtained.
We established that the resonant energies of produced particles ambiguously
depend on the positron (channel A) or electron (channel B) outgoing angle, and
the certain minimal amount of absorbed wave photons are required for resonance
to happen. Furthermore, the resonant cross section significantly exceeds the
corresponding one in the absence of the external field within the particular
kinematic regions and consequently, the considered process can be used qua a
marker for probing theoretical predictions of quantum electrodynamics with
strong background field.
