Total Born cross section of $e^+e^-$-pair production in relativistic ion collisions from differential equations

TL;DR

This paper uses the differential equation method to derive an explicit, exact expression for the total Born cross section of electron-positron pair production in relativistic ion collisions, accounting for the nuclei's relative velocity.

Contribution

It introduces a novel application of differential equations to compute an exact cross section in relativistic ion collision processes.

Findings

Derived an explicit formula for the cross section

Accounted for the relative velocity of nuclei

Provided a precise theoretical prediction

Abstract

We apply the differential equation method to the calculation of the total Born cross section of the process $Z_1Z_2\to Z_1Z_2e^+e^-$. We obtain explicit expression for the cross section exact in the relative velocity of the nuclei.