Phonon spectral function for an interacting electron-phonon system

Using exact diagonalization techniques, we study a model of interacting electrons and phonons. The spectral width of the phonons is found to be reduced as the Coulomb interaction U is increased. For a system with two modes per site, we find a transfer of coupling strength from the upper to the lower mode. This transfer is reduced as U is increased. These results give a qualitative explanation of differences between Raman and photoemission estimates of the electron-phonon coupling constants for ${A}_{3}{\mathrm{C}}_{60}(A=\mathrm{K},\mathrm{}\mathrm{Rb}).$