Characteristic Energy Loss of Electrons Passing Through Metal Foils: Momentum-Exciton Model of Plasma Oscillations

Abstract

Previous work is extended so as to obtain a unified theory of collective and individual electron effects in the excitation of a degenerate electron gas by fast incident electrons. The two characteristically collective features of the characteristic energy loss, the relatively large magnitude and the sharpness of the energy, are shown to follow from a straightforward quantum-mechanical treatment of one-electron excitations, provided only that the interactions of the electrons are taken into account. The interaction causes the excitation to be transferred from one excited configuration to another, resulting in an exciton in momentum space. This "momentum-exciton" is a discrete state which separates from the continuum of one-electron excitations and rises to higher energy, in accordance with Hund's rule. Correlation is taken into account by means of Feynman graphs in which the excitation makes a "jog" and travels backwards in time, as well as forwards. With this refinement the identification of the momentum-exciton with the Bohm-Pines plasma oscillation is completed.