th / 0 10 10 24 v 1 1 2 Ja n 20 01 Coulomb corrections to e + e − production in ultra - relativistic nuclear collisions

The purpose of this paper is to explain the discrepancies existing in the literature relative to e + e − pair production in peripheral heavy ion collisions at ultra-relativistic energies. A controversial issue is the possible cancellation of Coulomb corrections to the Born term in the pair production cross-section. Such a cancellation is observed in a recent approach based on finding retarded solutions of the Dirac equation, but does not seem to hold in a perturbative approach. We show in this paper that the two approaches are in fact calculating different observables: the perturba-tive approach gives the exclusive cross-section of single pair production, while the other method gives the inclusive cross-section. We have also performed a thorough study of the electron propagator in the non-static background field of the two nuclei, the conclusion of which is that the retarded propagator is in the ultra-relativistic limit a much simpler object than the Feynman propagator, and can be calculated exactly.