  First correction to the high-energy asymptotics of the total $e^+e^-$
photoproduction cross section in the electric field of a heavy atom is derived
with the exact account of this field. The consideration is based on the use of
the quasiclassical electron Green function in an external electric field. The
next-to-leading correction to the cross section is discussed. The influence of
screening on the Coulomb corrections is examined in the leading approximation.
It turns out that the high-energy asymptotics of the corresponding correction
is independent of the photon energy. In the region where both produced
particles are relativistic, the corrections to the high-energy asymptotics of
the electron (positron) spectrum are derived. Our results for the total cross
section are in good agreement with experimental data for photon energies down
to a few $MeV$. In addition, the corrections to the bremsstrahlung spectrum are
obtained from the corresponding results for pair production.

High Energy Physics - Phenomenology;Atomic Physics