Studies of threshold effects in the interaction of protons, electrons, and positrons in matter using dielectric models

Abstract

A review of the behavior of the energy loss, mean-free path and straggling of protons, positrons, and electrons in an electron gas is performed using different dielectric models which represent the case of metals (Lindhard model for a free electron gas and wave-packet model or extended wave-packet model for bound states contributions) and the cases of semiconductors and insulators (Levine and Louie model, Brandt and Reinheimer model, and extended wave-packet model for systems with a band gap). 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. In particular, inner-shell contributions are described for protons and correlated protons with a corresponding comparison with experimental results. Analytical expressions for the high-energy limit are displayed for all the cases using the plasmon-pole approximation.