  High-resolution resonant inelastic X-ray scattering (RIXS) at the oxygen
K-edge has been used to study the orbital excitations of Ca2RuO4 and Sr2RuO4.
In combination with linear dichroism X-ray absorption spectroscopy, the
ruthenium 4d-orbital occupation and excitations were probed through their
hybridization with the oxygen p-orbitals. These results are described within a
minimal model, taking into account crystal field splitting and a spin-orbit
coupling \lambda_{so}=200~meV. The effects of spin-orbit interaction on the
electronic structure and implications for the Mott and superconducting ground
states of (Ca,Sr)2RuO4 are discussed.
