Photoproduction of $e^+e^-$ pair in a Coulomb field near the threshold

TL;DR

This paper provides exact analytical results for electron-positron pair production by a photon in a Coulomb field near threshold, highlighting the limitations of previous approximation methods.

Contribution

It offers precise analytical formulas for the energy spectrum and angular distribution, improving upon earlier approximate approaches.

Findings

Furry-Sommerfeld-Maue approximation is insufficient near threshold.

Exact results differ significantly from previous approximations.

The study clarifies the behavior of pair production close to the energy threshold.

Abstract

We consider the electron-positron pair production by a photon in Coulomb field near threshold. We obtain the analytical results for the particle energy spectrum and angular distribution exactly in the parameter $Ze^2/\hbar v$. We show that Furry-Sommerfeld-Maue approximation for the wave functions used by Nishina, Tomonaga and Sakata is not sufficient and leads to wrong results.