Fluctuating spin g-tensor in small metal grains

In the presence of spin-orbit scattering, the splitting of an energy level epsilon(mu) in a generic small metal grain due to the Zeeman coupling to a magnetic field (B) over right arrow depends on the direction of (B) over ri ght arrow, as a result of mesoscopic fluctuations. The anisotropy is descri bed 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 stat istical distribution of G and find that the anisotropy is enhanced by eigen value repulsion between the g(j).