Higher-order processes in the electromagnetic production of electron-positron pairs in relativistic heavy-ion collisions

We study higher-order effects in the electromagnetic production of electron-positron pairs in relativistic heavy-ion collisions. Treating the field of the heavy ions as an external field and neglecting the interaction among electrons and positrons, we show that the N-pair creation amplitude is the antisymmetrized product of N one-pair creation amplitudes and the vacuum amplitude. Neglecting contributions coming from exchange terms, we show that the total probability for N pairs is approximately a Poisson distribution. We investigate further the structure of the reduced one-pair amplitude, concentrating especially on multiple-particle corrections. We calculate the first of these corrections in second-order Magnus theory based on our previous result [Phys. Rev. A 49, 1584 (1994)] in the second-order Born approximation for impact parameter b zero. Explicit calculations show that the total probability is increased up to 10% by this correction for realistic collider parameters. The calculations can also be used to confirm the use of the Poisson distribution for the total probability.