Numerical Method for Inverting 1s2p Resonant Inelastic X-ray Scattering Spectra: Interpretation of Hidden Electronic Excitations in CuO

Direct inversion of resonant inelastic x-ray scattering spectra (RIXSS) has been carried out using a numerical method for solving first-kind Fredholm integral equations. Hereby, the oscillator strength distribution (OSD), which is proportional to the empty density of states at the absorption edge, has been obtained from the experimental Cu 1s2p RIXSS of CuO. In particular, the inversion of RIXSS measured at incident energies below the K level threshold provides OSD having a better resolution than it can be achieved with one of the customary x-ray absorption near-edge structure spectroscopies. This can be explained by the virtual character of the intermediate states at low energy excitation. By means of the presented method a so-called 'hidden electronic excitation' of CuO has been identified as a very weak core excitation. Furthermore, numerical interpretation of polarized spectra has revealed the py-like character of the excited states in a suitable local reference frame. The obtained results are promising for further applications of the method, preferred in the field of strongly correlated materials.