  The generation of narrow beams of high-energy positrons (electrons) in the
process of resonant photogeneration of ultrarelativistic electron-positron
pairs by high-energy gamma quanta in the field of the nucleus and a strong
electromagnetic wave is theoretically predicted. It is shown that if the energy
of the initial gamma quanta significantly exceeds the characteristic energy of
the process, then ultrarelativistic positrons (for channel A) or electrons (for
channel B) are emitted with energies very close to the energy of gamma quanta.
Moreover, the resonant differential cross-section of such processes can exceed
the corresponding differential cross-section without an external field by
thirteen orders of magnitude. This effect makes it possible to obtain narrow
beams of ultrarelativistic positrons (electrons) in strong electromagnetic
fields with high probability.
