  The pulse intensity from X-ray free-electron lasers (FELs) can create extreme
excitation densities in solids, entering the regime of non-linear X-ray-matter
interactions. We show L3-edge absorption spectra of metallic nickel thin films
with fluences entering a regime where several X-ray photons are incident per
absorption cross-section. Main features of the observed non-linear spectral
changes are described with a predictive rate model for electron population
dynamics during the pulse, utilizing a fixed density of states and tabulated
ground-state properties.
