Emission of real phonons due to electron's self-dressing in a covalent crystal

A slow monoelectronic excitation in a covalent crystal at the temperature T=0 is analyzed. The interaction with zero-point longitudinal acoustic phonons leads to the formation of a dressed electronic state at an energy level lower than that of the initial bare state. This aspect of the dressing process is described here by hypothesizing that the excess of energy is released with the emission of real phonons. Specifically, this paper considers the transition probability from the bare monoelectronic state to a dressed state of the electron accompanied by real phonons and a deformation field. The spectrum of the real phonons emitted during the electronic self-dressing is calculated by applying nonperturbative techniques based on the resolvent method. The present analysis indicates that the transition between the bare monoelectronic state and the asymptotic dressed state is accompanied, at the lowest order, by the appearance of two real phonons.