Plasma Theory of Electron-Phonon Interaction in Metals

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Abstract
The transport theory of an electron gas recently developed is extended to include the interaction with the ions in a metal. The perturbation of the lattice vibrations induced by an anistropy of the electron distribution is calculated. Subsequently the ionic degrees of freedom are eliminated from the transport equation of the electrons in favor of a long-range electron correlation term. The influence of this term becomes important at long wavelengths (in the far infrared) but constitutes a small perturbation for the eigenfrequencies of collective motion of the electron gas. Nevertheless the dispersion relation for the collective oscillations shows that the contributions due to the phonon interaction are of the same order of magnitude as the influence of thermal agitation.