Statistic ensemble theory of small superconducting grains

We apply the random matrix theory to small metallic grains in different spi n states of S = 0, 1/2, 1, 3/2, 2, 5/2, (...), and find that there exist th eoretical critical level spacings d(c) at which the superconductivity would break down. We also find that the higher the spin state, the smaller the c ritical level spacing, and for the state of S = 0 superconducting enhanceme nt actually exists.