Spectral Weight Function and Electron Momentum Distribution in the Normal ElectronmPhonon System

A detailed calculation for the interacting electron-phonon system is carried out by using the double time Green's function method. The self-energy part and then the spectral weight function of the electron Green's function are given in detail to the second order of electron-phonon interaction. The effects of the interaction on the chemical potential of the electron and the Fermi momentum of the electron distribution are investigated. The average electron momentum distribution at zero temperature is evaluated in an approximation which may be considered as a simplification of the Migdal approximation. The amount of the discontinuity at the Fermi momentum is obtained and the numerical results show that there is a distinct modification of the electron distribution near the Fermi momentum due to the presence of the electron-phonon interaction