Stopping power and energy loss spectrum of a dense medium of bound electrons

Abstract

We have derived the dielectric function ϵ(k, ω) in the Lindhard approximation for a medium consisting of electrons individually bound by harmonic forces. This function is expressible in terms of a hypergeometric series and approaches well-known results in the limits of negligible binding, large momentum transfer, and long wavelength, respectively. The stopping power of the medium for a moving point charge scales very well with the shifted resonance frequency α0 = (ω02 + ωp2)12 (ω0 = oscillator frequency; ωp = plasma frequency) that follows from classical dispersion theory. The discrete excitation levels of an isolated harmonic oscillator are increasingly shifted and broadened with increasing density of the medium. The results for both the excitation spectrum and the stopping power differ noticeably from free-electron behavior even at a rather high electron density.