Theory of resonant x-ray scattering with ultrafast intense pulses

We present a time-dependent Schr\"odinger equation (TDSE) approach within a non-relativistic quantum electrodynamics (QED) framework to investigate resonant x-ray scattering under intense x-ray pulses. This method enables us to explore how coherent x-ray electron dynamics affect scattering signals from Ne$^+$. We account for both resonant fluorescence and elastic scattering channels, while also considering competing photoionization and inner-shell decay processes. By computing the angular distribution and energy spectrum of scattered photons, we uncover the interference effects between elastic scattering and resonant fluorescence pathways. Notably, our results reveal a small asymmetry in the energy spectrum as a result of this interference. We discuss the experimental potential for detecting signatures of interference. Our findings demonstrate that the x-ray Rabi dynamics can be used to control scattering responses and offer new insights into interference mechanisms and scattering efficiency in high-intensity x-ray regimes.