Abstract
The theory of Bardeen for the electron shielding of the perturbation potential arising from lattice vibrations is extended to cover exchange and correlation effects. The method is to set up a self-consistent set of one-electron equations, and calculate the effect of the perturbation in the charge densities. The exchange term is corrected to conform to the results of the Bohm-Pines theory, but the plasma wave function is assumed not to be disturbed by the lattice. With this approximate model, a solution to the problem can be obtained. For small-angle scattering, the results do not return to the original Bardeen values. The interaction potential matrix element depends on the initial electron wave vector k as well as on the difference between initial and final state wave vectors. Hence, to use the results an average over k must be made, and we make an average over the Fermi surface. The general effect of the exchange hole is to increase the scattering.
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