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 $β$. Both free-free and bound-free $e^{+}e^{-}$ pair production is considered. The parameters $η_{A,B}=Z_{A,B}α$ are assumed to be small compared to unity but arbitrary compared to $β$ ($Z_{A,B}$ 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 $η_{A,B}\gtrsim β$. The effect of a finite nuclear mass is discussed. In contrast to the result obtained in the infinite nuclear mass limit, the terms $\propto M^{-2}$ are not suppressed by the high power of $β$ and may easily dominate at sufficiently small velocities.

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