Electron-positron pair production in ion collisions at low velocity beyond Born approximation

We derive the spectrum and the total cross section of electromagnetic e(+)e(-) pair production in the collisions of two nuclei at low relative velocity beta. Both free-free and bound-free e(+)e(-) pair production is considered. The parameters eta(A,B), = Z(A),(B) alpha are assumed to be small compared to unity but arbitrary compared to beta (Z(A,B) are the charge numbers of the nuclei and alpha is the fine structure constant). Due to a suppression of the Born term by high power of beta, the first Coulomb correction to the amplitude appears to be important at eta(A),(B) greater than or similar to beta. The effect of a finite nuclear mass is discussed. In contrast to the result obtained in the infinite nuclear mass limit, the terms. alpha M-2 are not suppressed by the high power of beta and may easily dominate at sufficiently small velocities. (C) 2016 The Author(s). Published by Elsevier B.V.