The electron-phonon interaction, according to the adiabatic approximation

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Abstract
The behaviour of the conduction electrons in a vibrating metallic lattice is treated by the Born-Oppenheimer method. Non-adiabatic processes, due to certain terms usually neglected, are shown to correspond to scattering of electrons by the lattice vibrations, as in Bloch's theory of electrical resistivity, but the matrix elements are not the same as Bloch's except when energy is conserved in the process. This may have important consequences in Fröhlich's theory of superconductivity.