A comparative study of threshold effects in the energy loss moments of protons,electrons and positrons using dielectric models for band-gap materials

A comparative study of the energy loss, mean free path and straggling of protons, positrons and electrons in an electron gas is performed using three dielectric models which represent the case of metals (Lindhard model for a free electron gas) and the cases of semiconductors and insulators (Levine and Louie model and Brandt and Reinheimer model for systems with a band gap). The properties of individual and collective contributions according to each model and for each of the particles are analyzed. In particular, the effects produced by the band gap of the material and by the properties of the incident particle are analyzed in detail. Significant differences related to the mass and to the indistinguishability (in the case of electrons) are described. Analytical expressions for the high-energy limit are derived in a simple way using the plasmon-pole approximation.