Interplay of correlation and electron-phonon interaction in strongly correlated systems

A contribution to the on-site electron-phonon (EP) interaction arising from the covalent one is derived. This term, under certain conditions, is similar to the residual electron-phonon interaction term derived from the normal interacting electron-phonon system. We treat the correlation problem using slave-Boson (SB) formalism. On going over to the momentum representation the on-site interaction takes a form where momentum is not conserved. The phonon self-energy for on-site electron-phonon interaction gives a non-zero contribution even when the phonon wave vector vanishes. (orig.)