[Paper Review] Model-free Rayleigh weight from x-ray Thomson scattering measurements

Tobias Dornheim, Hannah M. Bellenbaum+17 more|arXiv (Cornell University)|Sep 13, 2024

Seismic Imaging and Inversion Techniques4 citations

TL;DR

This paper presents a model-free method to extract the Rayleigh weight $ W_R(\mathbf{q}) $ directly from x-ray Thomson scattering (XRTS) data, bypassing reliance on theoretical models or simulations. Using experimental XRTS data from strongly compressed beryllium at the National Ignition Facility, the authors demonstrate that $ W_R(\mathbf{q}) $—a measure of electronic localization—can be determined from the inelastic-to-elastic scattering ratio, yielding a density of $ \rho = (22 \pm 2)\ \text{g/cm}^3 $, significantly lower than prior model-based estimates.

ABSTRACT

X-ray Thomson scattering (XRTS) has emerged as a powerful tool for the diagnostics of matter under extreme conditions. In principle, it gives one access to important system parameters such as the temperature, density, and ionization state, but the interpretation of the measured XRTS intensity usually relies on theoretical models and approximations. In this work, we show that it is possible to extract the Rayleigh weight -- a key property that describes the electronic localization around the ions -- directly from the experimental data without the need for any model calculations or simulations. As a practical application, we consider an experimental measurement of strongly compressed Be at the National Ignition Facility (NIF) [Döppner \emph{et al.}, extit{Nature} extbf{618}, 270-275 (2023)]. In addition to being interesting in their own right, our results will open up new avenues for diagnostics from \emph{ab initio} simulations, help to further constrain existing chemical models, and constitute a rigorous benchmark for theory and simulations.

Motivation & Objective

• To develop a method for extracting the Rayleigh weight $ W_R(\mathbf{q}) $ from XRTS measurements without relying on theoretical models or simulations.
• To provide a rigorous, model-independent benchmark for ab initio simulations and chemical models of warm dense matter.
• To improve the accuracy of equation-of-state measurements in extreme conditions by eliminating model-dependent assumptions in XRTS data interpretation.
• To enable high-precision diagnostics in inertial confinement fusion and planetary science using experimental XRTS data.
• To validate the method using experimental data from strongly compressed beryllium at the National Ignition Facility (NIF).

Proposed method

• The method extracts $ W_R(\mathbf{q}) $ directly from the measured XRTS intensity by analyzing the ratio of inelastic to elastic scattering components.
• It uses the f-sum rule to determine the static structure factor $ S_{ee}(\mathbf{q}) $, which is required for normalization but not for $ W_R(\mathbf{q}) $ itself.
• The Rayleigh weight is computed as $ W_R(\mathbf{q}) = \frac{1}{S_{ee}(\mathbf{q})} \int_{-\infty}^{\infty} S_{ee}(\mathbf{q}, \omega)\, d\omega $, derived from the inelastic scattering spectrum.
• The approach avoids assumptions about electron binding or ionization states, circumventing limitations of the Chihara model.
• The method is validated against ab initio simulations (PIMC and DFT-MD) and shows good agreement with reference data.
• The technique is applicable at any temperature and is particularly suited for high-resolution XRTS at XFEL facilities where the source and instrument function $ R(E) $ is well characterized.

Experimental results

Research questions

• RQ1 Can the Rayleigh weight $ W_R(\mathbf{q}) $ be extracted from XRTS data without relying on theoretical models or simulations?
• RQ2 How does the model-free determination of $ W_R(\mathbf{q}) $ compare to results from ab initio simulations such as PIMC and DFT-MD?
• RQ3 What is the inferred mass density of strongly compressed beryllium using this model-free approach compared to prior model-based estimates?
• RQ4 How sensitive is the extracted $ W_R(\mathbf{q}) $ to uncertainties in the source-and-instrument function $ R(E) $, and can it be reliably measured at modern XFELs?
• RQ5 Can this method serve as a benchmark for validating chemical models and ab initio simulations in warm dense matter?

Key findings

• The Rayleigh weight $ W_R(\mathbf{q}) $ is successfully extracted from experimental XRTS data on strongly compressed beryllium at the NIF without any theoretical model input.
• The inferred mass density from the model-free method is $ \rho = (22 \pm 2)\ \text{g/cm}^3 $, significantly lower than the previously reported value of $ \rho = (34 \pm 4)\ \text{g/cm}^3 $ based on the Chihara chemical model.
• The model-free $ W_R(\mathbf{q}) $ shows good agreement with both path-integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) simulations.
• The average-atom model overestimates the density, highlighting the importance of accurate quantum many-body effects in XRTS-based diagnostics.
• The method is robust and applicable at any temperature, with potential for high-precision measurements at modern XFEL facilities where $ R(E) $ is known with high accuracy.
• The approach enables the creation of unambiguous reference data sets when applied to isochorically heated samples with known $ T $ and $ \rho $, providing a gold standard for benchmarking simulations and models.