The Direct Optical Transition Line Shape Function from the Equilibrium Density Projection Operator Technique

Abstract

Using the equilibrium density projection operator technique (EDPT), we calculate the lineshape function for the magneto-optical direct interband transition in an electron-phonon system. We present the calculation processes for obtaining the scattering factor using the EDPT. We introduce two useful identities necessary to expand the elements of the scattering factor. We derive a cancellation relation which simplifies the expansion of the scattering factor. We obtain the lineshape function in the case of a weak interaction and compared our results with those of other theories.