Re-entrant spin susceptibility of a superconducting grain

We study the spin susceptibility chi of a small, isolated superconducting g rain. Because of the interplay between parity effects and pairing correlati ons, the dependence of chi on temperature T is qualitatively different from the standard BCS result valid in the bulk limit. If the number of electron s on the grain is odd, chi shows a re-entrant behavior as a function of tem perature. This behavior persists even in the case of ultrasmall grains wher e the mean level spacing is much larger than the BCS gap. If the number of electrons is even, chi(T) is exponentially small at low temperatures. PACS numbers: 74.20.Fg, 73.23.Hk, 74.80.Bj.