ABSTRACTNonresonant inelastic x-ray scattering (NIXS) measurements probing the 5d → 5f electronic transitions at the uranium O_4,5 edges in a localized electron system such as UO₂ show a good agreement with many-electron atomic spectral calculations. The higher multipole spectra are split into two peaks that can be assigned as the 5d_5/2 and 5d_3/2 structures, despite the large electrostatic interactions. A new sum rule for the branching ratio of spin-orbit split core levels in electric multipole spectra, which generalizes the sum rule for dipole transitions in x-ray absorption spectroscopy, allows for a systematic analysis of the NIXS spectra. The branching ratio is linearly proportional to the expectation value of the angular part of the spin-orbit interaction in the initial state, where the rank of the multipole determines the coefficient of the linear dependence. This spin-orbit sum rule can be an important diagnostic tool for high-energy spectroscopies.