Statistic Ensemble Theory of Small Superconducting Grains

We apply random matrix theory to small metallic grains in different spin-states of S=0, 1/2, 1, 3/2, 2, 5/2, ..., and find that there exist theoretical critical level spacings d_c at which the superconductivity would break down. We also find that the higher the spin-state, the smaller the critical level spacing, and for the state of S = 0 there actually exists the superconducting enhancement.