  We study the influence of a strong laser field on the Bethe-Heitler
photoproduction process by a relativistic nucleus. The laser field propagates
in the same direction as the incoming high-energy photon and it is taken into
account exactly in the calculations. Two cases are considered in detail. In the
first case, the energy of the incoming photon in the nucleus rest frame is much
larger than the electron's rest energy. The presence of the laser field may
significantly suppress the photoproduction rate at soon available values of
laser parameters. In the second case, the energy of the incoming photon in the
rest frame of the nucleus is less than and close to the electron-positron pair
production threshold. The presence of the laser field allows for the pair
production process and the obtained electron-positron rate is much larger than
in the presence of only the laser and the nuclear field. In both cases we have
observed a strong dependence of the rate on the mutual polarization of the
laser field and of the high-energy photon and the most favorable configuration
is with laser field and high-energy photon linearly polarized in the same
direction. The effects discussed are in principle measurable with presently
available proton accelerators and laser systems.
