Explaining the x-ray nonlinear susceptibility of diamond and silicon near absorption edges

We report the observation and the theoretical explanation of the parametric down-conversion nonlinear susceptibility at the K-absorption edge of diamond and at the L23-absorption edge of a silicon crystal. Using arguments similar to those invoked to successfully predict resonant inelastic x-ray spectra, we derive an expression for the renormalization term of the nonlinear susceptibility at the x-ray edges, which can be evaluated by using first-principles calculations of the atomic scattering factor f1. Our model is shown to reproduce the observed enhancement of the parametric down-conversion at the diamond K and the Si L23 edges rather than the suppression previously claimed.