Exchange and Correlation Corrections to the Electron-Phonon Interaction

Abstract

The method of Bardeen and Pines for treating electron-phonon interactions in normal metals is extended to include exchange and correlation effects. The interaction matrix element is found to depend not only on electron momentum transfer but also on the initial electron wave vector. An average over initial wave vector direction is therefore made; the average taken is discussed as being more reasonable than that of Bailyn in a previous treatment. Shielding is also introduced in a more physical manner than in Bailyn's paper—via the dielectric constant as it arises in the random phase approximation. An alternate method of treating the problem in the long wavelength limit—employing deformation potential techniques—verifies the results of the above method in this limit.