Fluctuations of g-factors in metal nanoparticles: Effects of electron-electron interaction and spin-orbit scattering

We investigate the combined effect of spin-orbit scattering and electron-electron interactions on the probability distribution of $g$-factors of metal nanoparticles. Using random matrix theory, we find that even a relatively small interaction strength %(ratio of exchange constant $J$ and mean level %spacing $\text{spacing}$ $\simeq 0.3$) significantly increases $g$-factor fluctuations for not-too-strong spin-orbit scattering (ratio of spin-orbit rate and single-electron level spacing $1\mathrm{/}{\tau }_{\mathrm{s}\mathrm{o}}\text{spacing}\lesssim 1$), and leads to the possibility to observe $g$-factors larger than two.