g-factors of discrete levels in nanoparticles

Spin-orbit scattering suppresses Zeeman splitting of individual energy levels in small metal particles. This suppression becomes significant when the spin-orbit scattering rate tau(so)(-1) is comparable to the quantum level spacing delta. At small delta tau(so) the g-factor exhibits strong mesoscopic fluctuations. We find the shape of their distribution function using the random matrix theory, and express its parameters in terms of physical characteristics: tau(so), delta, the electron mean free path l, and the particle size L. At delta tau(so) --> 0 the average g-factor levels off at a small value g similar to (l/L)(1/2). However, in 2D quantum dots the g-factor is strongly enhanced by spin-orbit coupling.