Breaking the Vicious Cycle of Warm Dense Matter Diagnostics: From X-ray Scattering to Ab-initio Simulations

Matter at extreme densities and temperatures displays a complex quantum behavior that is characterized by
Coulomb interactions, thermal excitations, and partial ionization. Such warm dense matter (WDM) is
ubiquitous throughout the universe and occurs in a host of astrophysical objects such as giant planet
interiors and white dwarf atmospheres. A particularly intriguing application is given by inertial confinement
fusion, where both the fuel capsule and the ablator have to traverse the WDM regime in a controlled way to
reach ignition. In practice, rigorously understanding WDM is highly challenging both from experimental
measurements and numerical simulations [1]. On the one hand, interpreting and diagnosing experiments with
WDM requires a suitable theoretical description. One the other hand, there is no single method that is
capable of accurately describing the full range of relevant densities and temperatures, and the interpretation
of experiments is, therefore, usually based on a number of de-facto uncontrolled approximations. The result
is the vicious cycle of WDM diagnostics: making sense of experimental observations requires theoretical
modeling, whereas theoretical models must be benchmarked against experiments to verify their inherent
assumptions. In this work, we outline a strategy to break this vicious cycle by combining the X-ray Thomson
scattering (XRTS) technique [2] with new ab initio path integral Monte Carlo (PIMC) capabilities [3,4,5]. As
a first step, we have proposed to interpret XRTS experiments in the imaginary-time (Laplace) domain, which
allows for the model-free diagnostics of the temperature [6] and normalization [7]. Moreover, by switching
to the imaginary-time, we can directly compare our quasi-exact PIMC calculations with the experimental
measurement [5]. This opens up novel ways to diagnose the experimental conditions, as we have recently
demonstrated for the case of strongly compressed beryllium at the National Ignition Facility. Our results
open up new possibilities for improved XRTS set-ups that are specifically designed to be sensitive to
particular parameters of interest [8]. Moreover, the presented PIMC capabilities are important in their own
right and will allow for a gamut of applications, including equation-of-state calculations and the
estimation of structural properties and linear response functions.