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

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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 a small- q peak structure, parametrized by a cut-off qc, 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 qc in the whole U-n space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permit to understand some anomalous features of the Quantum Monte Carlo data.