  We analyze the structure of the Coulomb and unitarity corrections to the
single pair production as well as the cross section for the multiple pair
production. In the external field approximation we consider the probability of
$e^+e^-$ pair production at fixed impact parameter $\rho$ between colliding
ultra-relativistic heavy nuclei. We obtain the analytical result for this
probability at large $\rho$ as compared to the electron Compton wavelength. We
estimate also the unitary corrections to the total cross section of the
process.
