Structure of the Coulomb and Unitarity Corrections in the e+e- Pair Production at Relativistic Nuclear Collisions

We analyze the structure of the Coulomb and unitarity corrections to the single e+e- pair production as well as the cross section σn for the multiple pair production in collision of ultra-relativistic nuclei. In the external field approximation we consider the probability of one pair production at fixed impact parameter ρ between colliding nuclei. We obtain the analytical result for this probability at ρ >> 1/me. The energy dependence of this probability as well as that of ρn differ essentially from widely cited but incorrect results. We present the Coulomb and unitary corrections to the total cross section of one pair production at the RHIC and LHC colliders. (author)