The electron-phonon interaction, according to the adiabatic approximation

The interaction of conduction electrons with a vibrating metallic lattice has been considered by Ziman in terms of non-adiabatic perturbations to the adiabatic approximation of the Born-Oppenheimer theory. This programme is continued to calculate the self-energy of the electrons. When account is taken of the dependence of the energy levels of the adiabatic Hamiltonian itself upon the electron configuration, the final result is the same as the standard one.