Multiphonon Processes Occurring in First-Order Perturbation Theory

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Abstract
An estimate of the effect of the multiphonon processes in first-order perturbation theory on the electrical conductivity in metals is made, according to a simplified model of the electron-phonon interaction, and a correspondingly simple model of the electron wave functions (plane waves). A method for taking Umklapp processes into account is worked in detail and the calculation is set up in the framework of the variational principle. A sample computation of the effect of double-phonon processes on the conductivity of the alkali metals is performed using a nonisotropic phonon spectrum, the result being a decrease by less than four percent (1% being more characteristic for the lighter elements). The method is not restricted to long-wave phonons, but does not include the effects of higher-order perturbation theory or of interference terms, which may be considerable.

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