Mean-free path of electrons in rare-gas solids derived from vacuum-uv photoemission data

Abstract

The energy distributions of photoelectrons of solid Ar, Kr, and Xe films with thicknesses between 10 and 300 \AA{} have been measured in the photon energy range of 10 to 30 eV using the synchrotron radiation of Deutsches Elektronen Synchrotron (DESY). By varying the photon energy and the film thickness the dependence of the electron-electron scattering length on the electron kinetic energy has been determined. The mean-free path for inelastic electron-electron scattering decreases monotonically from values of the order of 1000 \AA{} at the scattering threshold to values between 1 and 5 \AA{} for electron energies 10 eV above threshold. The observed energy dependence can be understood by a simplified band structure and a scattering probability described by a product of the density of states. The threshold energy for electron-electron scattering lies between twice the energy of the $n=1$ excitons and the sum of band-gap and exciton energy.