The t-J model and nuclear magnetic relaxation in high T sub c materials.

We obtain the fermi contact term of the electron-nuclear effective Hamiltonian describing the coupling between the planar Cu (2) nucleus and the O(2,3) nucleii on the one hand, and the effective degrees of freedom of the one band t-J (or Heisenberg Hubbard) model on the other. The details of the resulting couplings suggest that the copper and oxygen relaxation rates are sensitive to antiferromagnetic correlations in different degree. In the insulating phase we predict that the effective dynamical critical exponent for oxygen (2,3) is reduced by two from that of copper (2).