Impact-parameter dependence of the total probability for electromagnetic electron-positron pair production in relativistic heavy-ion collisions

We calculate the impact-parameter-dependent total probability ${\mathit{P}}_{\mathrm{total}}$(b) for the electromagnetic production of electron-positron pairs in relativistic heavy-ion collisions in lowest order. We study expecially impact parameters smaller than the Compton wavelength of the electron, where the equivalent-photon approximation cannot be used. Calculations with and without a form factor for the heavy ions are done; the influence is found to be small. The lowest-order results are found to violate unitarity and are used for the calculation of multiple-pair production probabilities with the help of the approximate Poisson distribution already found in earlier publications.