Role of Electron-Phonon Interaction in the Theory of Infrared Divergence in Metals

Abstract

correlation function are studied in the Born approximation. A new formulation is developed which relates the hole correlation function to the retarded polarization propagator of the electron gas. Previously obtained results for the free-electron gas at finite temperature are recovered. The Migdal approximation is employed to find an expression for the imaginary part of the polarization propagator and it is seen that although the strength of the singularity is potentially modified by a constant factor the time dependence is not changed. Inclusion of the electron-phonon interaction via the Migdal form for the electron spectral weight func­ tion has no effect on the hole correlation function if the one-electron density of states varies slowly on the scale of the width of the spectral weight function. Similarity of this behavior to that of the nuclear spin relaxation in electron-phonon system is pointed out.