Electron correlations in metal nanoparticles with spin-orbit scattering

The combined effect of electron-electron interactions and spin-orbit scattering in metal nanoparticles can be studied by measuring splitting of electron levels in magnetic field ($g$ factors) in tunneling spectroscopy experiments. Using random matrix theory to describe the single-electron states in the metal particle, we find that even a relatively small electron-electron interaction strength (ratio of exchange constant $J$ and mean level spacing $\spacing$ $\simeq 0.3$) significantly increases $g$-factor fluctuations for not-too-strong spin-orbit scattering rates (spin-orbit time $\tau_{\rm so} \gtrsim 1/\spacing$). In particular, $g$-factors larger than 2 could be observed. (This is a manifestation of the many-body correlation effects in nanoparticles). While so far measurements only on noble metal (Cu, Ag, Au) and Al samples have been done for which the effects of electron-electron interactions are negligible, we discuss the possibility of observing interaction effects in nanoparticles made of other metals.