The direct optical transition line shape function from the equilibrium density projection operator technique

Using the equilibrium density projection operator technique (EDPT), we calc ulate the lineshape function for the magneto-optical direct interband trans ition in an electron-phonon system. We present the calculation processes fo r obtaining the scattering factor using the EDPT. We introduce two useful i dentities necessary to expand the elements of the scattering factor. We der ive a cancellation relation which simplifies the expansion of the scatterin g factor. We obtain the lineshape function in the case of a weak interactio n and compared our results with those of other theories.