Calculation of secondary electron bremsstrahlung in the binary encounter approximation using Dirac–Hartree–Fock–Slater velocity distributions

Abstract

One of the main factors that determine the detection limit in particle-induced X-ray emission (PIXE) spectrometry is the continuous X-ray background. In the case of impinging protons, a complete description requires five radiative processes. Among them, secondary electron bremsstrahlung (SEB) is one of the largest contributions and describes the bremsstrahlung radiated by the electrons ejected from the target atoms by proton impact. The calculation of SEB cross sections in the binary encounter approximation (BEA) entails knowledge of the velocity distributions (VDs) of the atomic electrons. For this purpose, analytical hydrogenic VDs are currently used for all the (sub)shells. In the present work, numerical VDs calculated from Dirac–Hartree–Fock–Slater (DHFS) wave functions are employed. Additionally, a compact equation for the SEB differential cross section is derived. Results for the ionisation and SEB cross sections of Al, Ag, and Au calculated from the DHFS and hydrogenic VDs are compared in detail.