Effects of a finite band width on the spin-fluctuation and the phonon coupling constant

We have investigated effects of a finite band width on the electron-spin-fluctuation coupling constant λ_sf and the electron-phonon coupling constant λ_ph in the Hubbard Hamiltonian system. We have found that both λ_ph and λ_sf are reduced a lot in overall magnitudes by an effect of the finite band width. From the phonon self-energy, we have obtained the renormalized phonon frequency, which becomes hardened with increasing the Coulomb correlation. In particular, λ_ph becomes larger than λ_sf for a system with a nearly filled band, which indicates that a phonon mediated BCS superconductivity may be possible in correlated systems.