Measuring the kernel of time-dependent density functional theory with X-ray absorption spectroscopy of 3d transition metals

The 2p-3d core-hole interaction in the L2,3 absorption spectra of the 3d transition metals is treated within time-dependent density functional theory. A simple three-level model explains the origin of the strong deviations from the one-particle branching ratio and yields matrix elements of the unknown exchange-correlation kernel directly from experiment.