Spectrally resolved X-ray scattering

The Bethe surface represents the X-ray scattering cross section as a function of momentum transfer and energy loss, mapping the electronic spectrum of the target via the inelastic transition matrix elements. By effectively merging spectroscopy and scattering, a time-resolved measurement of the molecular Bethe surface during a chemical reaction could reveal details of the reaction path through the manifolds of electronic states and conical intersections. However, conventional imaging detectors used for X-ray scattering lack energy resolution. We demonstrate here how the Bethe surface can be measured with the help of a spectral filter in the form of a thin zinc metal foil inserted between the target and the detector. Harnessing the inherent stochasticity of X-ray pulses generated by self-amplified spontaneous emission at X-ray free-electron lasers (XFELs), we demonstrate how the double-differential X-ray scattering cross section can be reconstructed using a novel ghost-imaging algorithm. Corrections for fluorescence from the metal filter need to be applied. The method requires excellent signal levels that can be obtained for molecules with large scattering cross sections, but advances in XFEL technology promise opportunities for a wide range of applications.