Isotope effect in the hubbard model for d-wave 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 , and the resitivity with different models for the phonon interaction ²F(q, ). The smallest T_c supression and the largest values are obtained for interactions which are enhanced atq = 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.