Nonlinear light scattering in molecules triggered by an impulsive x-ray Raman process

The time- and frequency-resolved nonlinear light scattering (NLS) signals from a time- evolving charge distribution of valence electrons prepared by impulsive x-ray pulses are calculated using a superoperator Green's function formalism. The signal consists of a coherent similar to N-2-scaling difference-frequency-generation and an incoherent fluorescence similar to N-scaling component, where N is the number of active molecules. The former is given by the classical Larmor formula based on the time-dependent charge density. The latter carries additional information about the electronic structure and may be recast in terms of transition amplitudes representing quantum matter pathways.