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

TL;DR

This paper derives the spectrum and cross section for electron-positron pair production in low-velocity ion collisions, highlighting the importance of Coulomb corrections and finite nuclear mass effects beyond the Born approximation.

Contribution

It provides a detailed analysis of Coulomb corrections and finite mass effects in pair production at low velocities, extending previous infinite mass models.

Findings

Coulomb corrections become significant when ,B rac{ ext{Z} ext{A,B} ext{ extalpha}}{ ext{1}} rac{eta}{}.

Finite nuclear mass effects can dominate at very low velocities, contrary to infinite mass assumptions.

The derived formulas account for both free-free and bound-free pair production processes.

Abstract

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 $\eta_{A,B}\gtrsim \beta$. 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 $\beta$ and may easily dominate at sufficiently small velocities.