Coulomb corrections to the bremsstrahlung and electron pair production cross section of high-energy muons on extended nuclei

TL;DR

This paper provides precise calculations of Coulomb corrections to bremsstrahlung and electron pair production cross sections for high-energy muons interacting with extended nuclei, essential for accurate muon energy measurements.

Contribution

It introduces exact Coulomb correction calculations for these processes on extended nuclei, including an analytical parametrization of cross section dependence on nuclear charge and mass.

Findings

Coulomb corrections significantly affect cross section calculations.

Analytical parametrization simplifies the inclusion of nuclear effects.

Results improve the accuracy of muon energy loss modeling.

Abstract

The energy reconstruction of high-energy muons depends on the energy loss characteristics. Accurate knowledge of the cross sections of the energy loss processes is necessary for precise measurements of the energy spectrum of muons and muon-induced neutrinos. The cross sections of the two most dominant processes, electron pair production and bremsstrahlung are calculated exact in the coupling parameter $Z\alpha$ to the electromagnetic field of a nucleus for realistic extended screened nuclei. An analytical parametrization of the mass and nuclear-charge dependence of the cross section is given.