  A strong laser field and the Coulomb field of a nucleus can produce
e^{+}e^{-} pairs. It is shown for the first time that there is a large
probability that electrons and positrons created in this process collide after
one or several oscillations of the laser field. These collisions can take place
at high energy resulting in several phenomena. The quasielastic collision
e^{+}e^{-} -> e^{+}e^{-} allows acceleration of leptons in the laser field to
higher energies. The inelastic collisions allow production of high energy
photons e^{+}e^{-}-> 2 gamma and muons, e^{+}e^{-} -> mu^{+}mu^{-}. The yield
of high-energy photons and muons produced via this mechanism exceeds
exponentially their production through conventional direct creation in laser
and Coulomb fields. A relation of the phenomena considered with the
antenna-mechanism of multiphoton absorption in atoms is discussed.
