Fluctuating spin g-tensor in small metal grains

In the presence of spin-orbit scattering, the splitting of an energy level 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_j^2 (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.