Electron Exchange Correction to the Phonon Dispersion Relation in Metals

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Abstract
The statistical theory recently developed is applied in this paper to an investigation of the dispersion relation of sound waves in metals with special regard to contributions due to electron exchange. It is found that these contributions are by no means negligible in the long-wavelength limit, contrary to current belief. Furthermore it is shown that the temperature dependence of the renormalized sound frequencies is solely mediated by the temperature dependence of the Fermi-Dirac distribution of the electrons.