  We use Ru $L_3$-edge (2838.5 eV) resonant inelastic x-ray scattering (RIXS)
to quantify the electronic structure of Ca$_2$RuO$_4$, a layered $4d$-electron
compound that exhibits a correlation-driven metal-insulator transition and
unconventional antiferromagnetism. We observe a series of Ru intra-ionic
transitions whose energies and intensities are well described by model
calculations. In particular, we find a $\rm{J}=0\rightarrow 2$ spin-orbit
excitation at 320 meV, as well as Hund's-rule driven $\rm{S}=1\rightarrow 0$
spin-state transitions at 750 and 1000 meV. The energy of these three features
uniquely determines the spin-orbit coupling, tetragonal crystal-field energy,
and Hund's rule interaction. The parameters inferred from the RIXS spectra are
in excellent agreement with the picture of excitonic magnetism that has been
devised to explain the collective modes of the antiferromagnetic state.
$L_3$-edge RIXS of Ru compounds and other $4d$-electron materials thus enables
direct measurements of interactions parameters that are essential for realistic
model calculations.
