Isotope effect in the Hubbard model for d-waves superconductivity

We have solved the generalized Eliashberg equations for the 2D Hubbard model with interactions due to exchange of antiferromagnetic spin fluctuations and harmonic phonons. We calculate the supression of T-c for d-wave superconductivity, the isotope exponent alpha, and the resitivity rho with different models for the phonon interaction alpha(2)F(q,omega). The smallest T-c supression and the largest alpha values are obtained for interactions which are enhanced at q = 0. At lower temperatures the spin-fluctuation interaction is strongly reduced by the phonon interaction due to feed-back effects. We compare our results with the experimental data on high-T-c superconductors.