Fluctuating spin g-tensor in small metal grains.

In the presence of spin-orbit scattering, the splitting of an energy level varepsilon(&mgr;) in a generic small metal grain due to the Zeeman coupling to a magnetic field B--> depends on the direction of B-->, as a result of mesoscopic fluctuations. The anisotropy is described by the eigenvalues g(2)(j) ( j = 1,2,3) of a tensor G, corresponding to the (squares of) g-factors along three principal axes. We consider the statistical distribution of G and find that the anisotropy is enhanced by eigenvalue repulsion between the g(j).