Ab initio calculations of mean free paths and stopping powers

A method is presented for first-principles calculations of inelastic mean free paths and stopping powers in condensed matter over a broad energy range. The method is based on {\it ab initio} calculations of the dielectric function in the long wavelength limit using a real-space Green's function formalism, together with extensions to finite momentum transfer. From these results we obtain the loss function and related quantities such as optical-oscillator strengths and mean excitation energies. From a many-pole representation of the dielectric function we then obtain the electron self-energy and inelastic mean free paths (IMFP). Finally using our calculated dielectric function and the optical-data model of Fern\'andez-Varea {\it et al}., we obtain collision stopping powers (CSP) and penetration ranges. The results are consistent with semi-empirical approaches and with experiment.