  Resonant electron-positron pair production by a high-energy gamma quantum in
the field of a nucleus and a quasi-monochromatic laser wave was theoretically
studied. Under the resonant condition an intermediate virtual electron
(positron) in the laser field becomes a real particle. Due to that fact the
initial process of the second order in the fine structure constant in a laser
field effectively reduces into two successive processes of the first order: the
laser-stimulated Breit-Wheeler process and the laser-assisted process of an
intermediate electron (positron) scattering by a nucleus. It is shown that
there is a threshold energy for the initial gamma quantum, which significantly
depends on the number of absorbed photons of a wave. In the resonant condition
the electron-positron pair energy is determined by the outgoing angle of a
positron (for the channel A) or an electron (for the channel B) relative to the
initial gamma quantum momentum. The differential cross sections for the first
few resonances with simultaneous registration of the energy and the outgoing
angle of a positron or an electron were obtained. For the initial gamma quantum
energy ${\omega_i} = 125\;{\rm{GeV}}$ the resonant energies of an
electron-positron pair for the case of first three resonances can be measured
with a very high magnitude of the differential cross section: from $ \sim
{10^{13}}$ for the first resonance to $ \sim {10^8}$ (in the units of $\alpha
{Z^2}r_e^2$) for the third resonance.
