  The purpose of our research is to study the nuclear spin lattice relaxation
rate of impure d-wave superconductors. We use the Green function method to
derive the approximation equation of density of states including the impurity
scattering potential. We can get the analytic equation of the nuclear spin
lattice relaxation rate that contained the impurity scattering potential in
case of weak scattering potential and strong scattering potential in the simple
form as the power series of order parameter and temperature . The numerical
calculations show that there is coherence peak in the weak impurity scattering
potential but there is no peak in the strong impurity scattering potential.
