Charge fluctuations and electron-phonon interaction in the finite-U Hubbard model

In this paper we employ a Gaussian expansion within the finite-U slave-bosons formalism to investigate the momentum structure of the electron-phonon vertex function in the Hubbard model as function of U and n. The suppression of large momentum scattering and the onset of a small-q peak structure, parametrized by a cut-off q(c), are shown to be essentially ruled by the band narrowing factor Z(MF) due to the electronic correlation. A phase diagram of Z(MF) and q(c) in the whole U-n space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permit one to understand some anomalous features of the quantum Monte Carlo data.