Hot electron in a polar crystal. I. The eikonal approximation

A quantum theory of the rates of momentum and energy loss by a fast electron to the optic modes of a polar crystal as a function of time elapsed since injection of the fast electron is developed. A nonequilibrium Green function technique is used to formulate the problem, and permits inclusion of quantum interference between the individual phonon processes. An approximation, which has been called the eikonal approximation in high energy scattering and is valid when the fractional electron energy loss in a single phonon collision is small, enables us to sum the resulting diagrams. The relationship of this method to a Boltzmann equation approach is discussed.