  First correction to the high-energy asymptotics of the total $e^+e^-$
photoproduction cross section in the electric field of a heavy atom is obtained
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
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. The detailed
comparison of our results with experimental data is performed. This comparison
has justified the analytical result and allowed us to elaborate a simple ansatz
for the next-to-leading correction. Using this ansatz, good agreement with the
experimental data is obtained for photon energies above a few $MeV$. In the
region where both produced particles are relativistic, the corrections to the
high-energy asymptotics of the electron (positron) spectrum are obtained. In
addition, analogous corrections to the bremsstrahlung spectrum are derived
starting from the corresponding results for pair production.
