Quasi-zero dimensional CuB$_{2}$O$_{4}$ as an archetype for resonant inelastic X-ray scattering

We explore the general phenomenology of resonant inelastic scattering (RIXS) using CuB$_{2}$O$_{4}$, a network of CuO$_{4}$ plaquettes electronically isolated by B$^{+3}$ ions. Spectra show a small number of well-separated features, and we exploit the simple electronic structure to explore RIXS phenomenology by developing a calculation allowing for intermediate-state effects ignored in standard approaches. These effects are found to be non-negligible and good correspondence between our model and experiment leads to a simple picture of such phenomenology as the genesis of d$\to $d excitations at the K edge and intermediate-state interference effects.