  X-ray absorption is the standard method to probe the unoccupied density of
states at a given edge. Here we show that polarized Resonant Inelastic X-Ray
Scattering in La2CuO4 at the Cu K-edge is extremely sensitive to the
environment of the Cu atom and the fine structure in the Cu 4p density of
states. Combined ab initio and many-body cluster calculations, used for the
first time in such a context, show remarkable agreement with experiment. In
particular we identify a non-local effect namely a transition to off-site Cu 3d
states.
