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−e+e− pair production in the collisions of two nuclei at low relative velocity β  . Both free–free and bound-free e+e−e+e− pair production is considered. The parameters ηA,B=ZA,BαηA,B=ZA,Bα are assumed to be small compared to unity but arbitrary compared to β   (ZA,BZA,B are the charge numbers of the nuclei and α is the fine structure constant). Due to a suppression of the Born term by high power of β  , the first Coulomb correction to the amplitude appears to be important at ηA,B≳βηA,B≳β. The effect of a finite nuclear mass is discussed. In contrast to the result obtained in the infinite nuclear mass limit, the terms ∝M−2∝M−2 are not suppressed by the high power of β and may easily dominate at sufficiently small velocities.