THE NUCLEAR-SPIN RELAXATION RATE FOR CLEAN QUASI-2-DIMENSIONAL SUPERCONDUCTORS IN THE VICINITY OF H-C2

We calculate the nuclear spin relaxation rate of clean quasi-two-dimen sional (2D) superconductors with s-wave pairing in high magnetic field s using the BCS model and the Brandt, Pesch and Tewordt approximation for the single-particle propagator. The calculation is valid in the vi cinity of H-c2(T). Thermal fluctuations of vortices are not taken into account. We evaluate numerically our results in the case of high-T-c materials and organic superconductors. In a perpendicular field the He bel-Slichter coherence peak is suppressed depending on the variation o f the quasi-particle lifetime below T-c. We also describe the magnetic held dependence of the nuclear spin relaxation rate. Using the experi mentally determined value of the quasi-particle lifetime, the model re produces the experimental initial variations of T-1(-1) versus T/T-c a t different magnetic fields. However, the Hebel-Slichter peak is conse rved in the low-field limit, or when the applied magnetic field is par allel to the superconducting planes.