RESONANT SCATTERING OF ELECTRONS IN THE PRESENCE OF COUPLING TO PHONONS

We consider the resonant scattering of an electron from a localized object, in the presence of coupling to a spectrum of phonons. The discussion is carried out within the framework of the Friedel model of a virtual level; the electron couples to the phonons while it resides in this level. Within a certain approximation (the residence time of the electron in the virtual level is short compared to the period of vibration motion in the lattice), we obtain an expression for the cross section for elastic scattering off the center in the presence of electron-phonon coupling, and for scattering off the center with multiphonon emission. The results are compared with an earlier analysis of the problem by the present author, based on a semiclassical picture.