  The effects of spin-orbit scattering on discrete electronic energy levels are
studied in copper, silver, and gold nanoparticles. Level-to-level fluctuations
of the effective $g$-factor for Zeeman splitting are characterized, and the
statistics are found to be well-described by random matrix theory predictions.
The strength of spin-orbit scattering increases with atomic number and also
varies between nanoparticles made of the same metal. The spin-orbit scattering
rates in the nanoparticles are in order-of-magnitude agreement with bulk
measurements on disordered samples.
