Semiempirical cross sections for the simulation of the energy loss of electrons and positrons in matter

Abstract

Differential cross sections (DCS) suitable for Monte Carlo simulation of the energy loss of fast electrons and positrons in matter are proposed. These DCSs are based on high-energy approximations, complemented with semiempirical ingredients which make them accurate for a wide energy range. The DCS for collision losses, including Fermi's density effect correction, is obtained from the Born approximation and a simple generalized oscillator strength model. Collision stopping powers, and also mean free paths and energy straggling parameters, can be evaluated in a purely analytical way. The DCS for bremsstrahlung emission is given in the form of the Bethe-Heitler DCS with exponential screening including a Coulomb correction. The described DCSs have moderately simple analytical expressions which allow random sampling of the energy loss in detailed Monte Carlo simulations by using purely analytical methods. Suitable sampling algorithms are also described.