A relativistic optical-data model for inelastic scattering of electrons and positrons in condensed matter

A relativistic optical-data model for the calculation of non-radiative inelastic scattering of electrons and positrons in condensed matter is presented. The scattering is described within the first Born approximation, in terms of longitudinal and transverse interactions. Differential cross sections are determined by a generalized oscillator strength density, which is generated by extending a semi-empirical optical oscillator strength density to non-zero momentum transfers using a modified δ-oscillator as the extension algorithm. The Fermi density-effect correction is obtained from the optical oscillator strength and a simple approximation is proposed to account for its effect on the cross section differential in energy loss. The differential cross sections take relatively simple analytical forms, and various quantities of interest, such as total cross section, stopping power, straggling parameter and restricted inelastic transport cross section are evaluated by a single quadrature. Results are presented for electron and positron energies between 10 eV and 1 GeV.