# Integrated cross sections of high-energy $e^+e^-$ electroproduction by an electron in an atomic field

## TL;DR

This paper investigates the high-energy electron-positron pair production cross sections in atomic fields, emphasizing the significant role of Coulomb corrections and their impact on differential and integrated cross sections.

## Contribution

It provides a detailed analysis of Coulomb corrections and interference effects in $e^+e^-$ electroproduction, highlighting their importance even for moderate atomic charge numbers.

## Key findings

- Coulomb corrections are crucial for both differential and integrated cross sections.
- Interference and virtual bremsstrahlung significantly affect the differential cross section over electron transverse momentum.
- Coulomb corrections to scattering are larger than interference effects but smaller than those in pair photoproduction amplitude.

## Abstract

The integrated cross sections of high-energy $e^+e^-$ electroproduction by an electron in an atomic field is studied. Importance of various contributions to these cross sections is discussed. It is shown that the Coulomb corrections are very important both for the differential cross section and for the integrated cross sections even for moderate values of the atomic charge number. This effect is mainly related to the interaction of the produced $e^+e^-$ pair with the atomic field. For the cross section differential over the electron transverse momentum the account for the interference of the amplitudes and the contribution of virtual bremsstrahlung is noticeable. The Coulomb corrections to scattering is larger than these two effects but essentially smaller than the Coulomb corrections to the amplitude of pair photoproduction by a virtual photon. However, in the cross section differential over the positron transverse momentum, there is a strong suppression of the effect of the Coulomb corrections to scattering.