Level statistics in superconductivity in ultrasmall metallic grains

The effect of level statistics on critical level spacings <d(c)> of odd/eve n electrons are calculated by using the mean field self-consistency equatio n in three different Gauss ensembles (Gauss Orthogonal Ensemble, Gauss Unit ary Ensemble, and Gauss Symplectic Ensemble) according to Random Matrix The ory. We obtain the ratios of critical level spacings of even electrons to t hose of odd electrons in different spin-orbit coupling and magnetic fields quantitatively, and the relations of <(Delta)over cap>(0) and average level spacings <d(o)> in the odd case.