  We derive general expressions for resonant inelastic x-ray scattering (RIXS)
operators for $t_{2g}$ orbital systems, which exhibit a rich array of
unconventional magnetism arising from unquenched orbital moments. Within the
fast collision approximation, which is valid especially for 4$d$ and 5$d$
transition metal compounds with short core-hole lifetimes, the RIXS operators
are expressed in terms of total spin and orbital angular momenta of the
constituent ions. We then map these operators onto pseudospins that represent
spin-orbit entangled magnetic moments in systems with strong spin-orbit
coupling. Applications of our theory to such systems as iridates and ruthenates
are discussed, with a particular focus on compounds based on $d^4$ ions with
Van Vleck-type nonmagnetic ground state.
