Multiple electromagnetic electron-positron pair production in relativistic heavy-ion collisions

We calculate the cross sections for the production of one and more electron-positron pairs due to the strong electromagnetic fields in relativistic heavy-ion collisions. We derive the N-pair amplitude using the generating functional of fermions in an external field and the path-integral formalism. The N-pair production probability is found to be an approximate Poisson distribution. We calculate total cross sections for the production of one pair in lowest order, including corrections from the Poisson distribution up to third order. Furthermore, we calculate cross sections for the production of up to five pairs including corrections from the Poisson distribution.