Multiple lepton pair production in relativistic ion collisions

We apply the Sudakov technique to description of the multiple production of lepton pairs in peripheral collisions of ultrarelativistic heavy ions. For heavy ions with $Z_1\alpha\sim Z_2\alpha\ll 1$ one needs a careful treatment of the multiple Coulomb exchange between colliding ions and screening effects, whereas interaction of real or virtual lepton pairs with colliding ions can be neglected. We demonstrate that while the inclusive spectra are modified by multiple Coulomb exchange between the colliding ions, the Coulomb corrections to the momentum integrated multiplicity distributions do vanish. After transformation to the impact parameter representation the probability of $n$ lepton pair production is shown to obey the Poisson distribution. The relevant cross section is obtained.