Plural Scattering of 20-kev Electrons in Aluminum

Abstract

The angular and energy distribution of 20-kev electrons, scattered at very small angles (${10}^{\ensuremath{-}2}$ rad) by transmission through aluminum foils, are compared with the theory of plural inelastic scattering, under the following assumptions: (a) The probability of elastic scattering at very small angles is negligibly small in comparison with the probability of inelastic scattering. (b) Inelastic scattering occurs predominantly through sharply defined "characteristic" energy losses, whose number follows a Poisson statistical distribution. (c) The angular distribution in each loss follows a simple law: $\ensuremath{\Phi}(\ensuremath{\theta})\ensuremath{\propto}{({{\ensuremath{\theta}}_{E}}^{2}+{\ensuremath{\theta}}^{2})}^{\ensuremath{-}1}$. (d) The cumulative angular distribution from plural inelastic scattering is obtained by repeated "folding" of $\ensuremath{\Phi}(\ensuremath{\theta})$ with the angular spread of the incident beam. The angular distribution of zero-loss electrons is found to be substantially independent of the foil thickness; the normalized angular distributions of the first- and second-loss peaks are accurately fitted by the "folding" calculation; Poisson statistics gives a good approximation to the observed numbers of energy losses. The value of $\ensuremath{\lambda}$ for five observations on foils of thicknesses 650-2580 A is approximately 810 A, independent of thickness; systematic errors in the method of observation may render this value up to 20% higher than the mean free path corresponding to the total cross section.