Statistical inference of electron-ion collision rates from simulated X-ray Thomson scattering spectra

Electron-ion collisions play an important role in the free electron dynamics in high energy density states, which are often probed with X-ray Thompson scattering (XRTS) diagnostics. The inclusion of dynamic collision rates or frequencies in free electron models goes beyond the typical uniform electron gas approximation and improves the predictions of spectra, or dynamic structure factors (DSFs), from XRTS in warm dense matter (WDM). However, without experimental data or ab initio calculations of collision rates, current collision rate theories applicable to WDM are typically indirectly validated, for example, by finding the collisional model that, when input into a specific free electron DSF model, yields the best fit to experimental DSF data. We illustrate that this inversion process suffers from instabilities, where large variations in collision frequencies can correspond to approximately the same DSF output. By using ideas from statistical inference, we demonstrate how we can extract reliable confidence intervals for collision frequencies from DSF data. Our approach provides the means for direct validation of collisional theories in the WDM regime, and can help guide improvements to these models.