  Mott insulators with strong spin-orbit coupling have been proposed to host
unconventional magnetic states, including the Kitaev quantum spin liquid. The
4$d$ system $\alpha$-RuCl$_3$ has recently come into view as a candidate Kitaev
system, with evidence for unusual spin excitations in magnetic scattering
experiments. We apply a combination of optical spectroscopy and Raman
scattering to study the electronic structure of this material. Our measurements
reveal a series of orbital excitations involving localized total angular
momentum states of the Ru ion, implying that strong spin-orbit coupling and
electron-electron interactions coexist in this material. Analysis of these
features allows us to estimate the spin-orbit coupling strength, as well as
other parameters describing the local electronic structure, revealing a
well-defined hierarchy of energy scales within the Ru $d$ states. By comparing
our experimental results with density functional theory calculations, we also
clarify the overall features of the optical response. Our results demonstrate
that $\alpha$-RuCl$_3$ is an ideal material system to study spin-orbit coupled
magnetism on the honeycomb lattice.
