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The effects of spin-orbit scattering on discrete electronic energy levels arestudied in copper, silver, and gold nanoparticles. Level-to-level fluctuationsof the effective $g$-factor for Zeeman splitting are characterized, and thestatistics are found to be well-described by random matrix theory predictions.The strength of spin-orbit scattering increases with atomic number and alsovaries between nanoparticles made of the same metal. The spin-orbit scatteringrates in the nanoparticles are in order-of-magnitude agreement with bulkmeasurements on disordered samples.Comment: 4 pages, 3 figures, 1 in colo

Studies of Spin-Orbit Scattering in Noble-Metal Nanoparticles Using Energy-Level Tunneling Spectroscopy