Observing the onset of pressure-driven K-shell delocalization.

The gravitational pressure in many astrophysical objects exceeds one gigabar (one billion atmospheres)1-3, creating extreme conditions where the distance between nuclei approaches the size of the K shell. This close proximity modifies these tightly bound states and, above a certain pressure, drives them into a delocalized state4. Both processes substantially affect the equation of state and radiation transport and, therefore, the structure and evolution of these objects. Still, our understanding of this transition is far from satisfactory and experimental data are sparse. Here we report on experiments that create and diagnose matter at pressures exceeding three gigabars at the National Ignition Facility5 where 184 laser beams imploded a beryllium shell. Bright X-ray flashes enable precision radiography and X-ray Thomson scattering that reveal both the macroscopic conditions and the microscopic states. The data show clear signs of quantum-degenerate electrons in states reaching 30 times compression, and a temperature of around two million kelvins. At the most extreme conditions, we observe strongly reduced elastic scattering, which mainly originates from K-shell electrons. We attribute this reduction to the onset of delocalization of the remaining K-shell electron. With this interpretation, the ion charge inferred from the scattering data agrees well with ab initio simulations, but it is significantly higher than widely used analytical models predict6.

Erratum: Using Diffuse Scattering to Observe X-Ray-Driven Nonthermal Melting [Phys. Rev. Lett. 126, 015703 (2021)].

This corrects the article DOI: 10.1103/PhysRevLett.126.015703.

Using Diffuse Scattering to Observe X-Ray-Driven Nonthermal Melting.

We present results from the SPring-8 Angstrom Compact free electron LAser facility, where we used a high intensity (∼10^{20} W/cm^{2}) x-ray pump x-ray probe scheme to observe changes in the ionic structure of silicon induced by x-ray heating of the electrons. By avoiding Laue spots in the scattering signal from a single crystalline sample, we observe a rapid rise in diffuse scattering and a transition to a disordered, liquidlike state with a structure significantly different from liquid silicon. The disordering occurs within 100 fs of irradiation, a timescale that agrees well with first principles simulations, and is faster than that predicted by purely inertial behavior, suggesting that both the phase change and disordered state reached are dominated by Coulomb forces. This method is capable of observing liquid scattering without masking signal from the ambient solid, allowing the liquid structure to be measured throughout and beyond the phase change.

The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation.

The study of matter at extreme densities and temperatures as they occur in astrophysical objects and state-of-the-art experiments with high-intensity lasers is of high current interest for many applications. While no overarching theory for this regime exists, accurate data for the density response of correlated electrons to an external perturbation are of paramount importance. In this context, the key quantity is given by the local field correction (LFC), which provides a wave-vector resolved description of exchange-correlation effects. In this work, we present extensive new path integral Monte Carlo (PIMC) results for the static LFC of the uniform electron gas, which are subsequently used to train a fully connected deep neural network. This allows us to present a representation of the LFC with respect to continuous wave-vectors, densities, and temperatures covering the entire warm dense matter regime. Both the PIMC data and neural-net results are available online. Moreover, we expect the presented combination of ab initio calculations with machine-learning methods to be a promising strategy for many applications.

Ab initio Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter.

The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor S(q,ω) constitutes a key quantity as it is directly measured in x-ray Thomson scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first ab initio results for S(q,ω) by carrying out extensive path integral Monte Carlo simulations and developing a new method for the required analytic continuation, which is based on the stochastic sampling of the dynamic local field correction G(q,ω). In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for S(q,ω) over substantial parts of the warm dense matter regime.

Liquid Structure of Shock-Compressed Hydrocarbons at Megabar Pressures.

We present results for the ionic structure in hydrocarbons (polystyrene, polyethylene) that were shock compressed to pressures of up to 190 GPa, inducing rapid melting of the samples. The structure of the resulting liquid is then probed using in situ diffraction by an x-ray free electron laser beam, demonstrating the capability to obtain reliable diffraction data in a single shot, even for low-Z samples without long range order. The data agree well with ab initio simulations, validating the ability of such approaches to model mixed samples in states where complex interparticle bonds remain, and showing that simpler models are not necessarily valid. While the results clearly exclude the possibility of complete carbon-hydrogen demixing at the conditions probed, they also, in contrast to previous predictions, indicate that diffraction is not always a sufficient diagnostic for this phenomenon.

Ab Initio Thermodynamic Results for the Degenerate Electron Gas at Finite Temperature.

The uniform electron gas at finite temperature is of key relevance for many applications in dense plasmas, warm dense matter, laser excited solids, and much more. Accurate thermodynamic data for the uniform electron gas are an essential ingredient for many-body theories, in particular, density-functional theory. Recently, first-principles restricted path integral Monte Carlo results became available, which, however, had to be restricted to moderate degeneracy, i.e., low to moderate densities with r_{s}=r[over ¯]/a_{B}≳1. Here we present novel first-principles configuration path integral Monte Carlo results for electrons for r_{s}≤4. We also present quantum statistical data within the e^{4} approximation that are in good agreement with the simulations at small to moderate r_{s}.

Observations of continuum depression in warm dense matter with x-ray Thomson scattering.

Detailed measurements of the electron densities, temperatures, and ionization states of compressed CH shells approaching pressures of 50 Mbar are achieved with spectrally resolved x-ray scattering. Laser-produced 9 keV x-rays probe the plasma during the transient state of three-shock coalescence. High signal-to-noise x-ray scattering spectra show direct evidence of continuum depression in highly degenerate warm dense matter states with electron densities ne>1024 cm-3. The measured densities and temperatures agree well with radiation-hydrodynamic modeling when accounting for continuum lowering in calculations that employ detailed configuration accounting.

Virial coefficients of the uniform electron gas from path-integral Monte Carlo simulations.

The properties of plasmas in the low-density limit are described by virial expansions. Analytical expressions are known from Green's function approaches only for the first three virial coefficients. Accurate path-integral Monte Carlo (PIMC) simulations have recently been performed for the uniform electron gas, allowing the virial expansions to be analyzed and interpolation formulas to be derived. The exact expression for the second virial coefficient is used to test the accuracy of the PIMC simulations and the range of validity of the interpolation formula of Groth et al. [Phys. Rev. Lett. 119, 135001 (2017)0031-900710.1103/PhysRevLett.119.135001], and we discuss the fourth virial coefficient, which is not exactly known yet. Combining PIMC simulations with benchmarks from exact virial expansion results would allow us to obtain more accurate representations of the equation of state for parameter ranges of conditions which are of interest, e.g., for helioseismology.

X-ray Thomson scattering absolute intensity from the f-sum rule in the imaginary-time domain.

We present a formally exact and simulation-free approach for the normalization of X-ray Thomson scattering (XRTS) spectra based on the f-sum rule of the imaginary-time correlation function (ITCF). Our method works for any degree of collectivity, over a broad range of temperatures, and is applicable even in nonequilibrium situations. In addition to giving us model-free access to electronic correlations, this new approach opens up the intriguing possibility to extract a plethora of physical properties from the ITCF based on XRTS experiments.

X-ray scattering measurements of strong ion-ion correlations in shock-compressed aluminum.

The strong ion-ion correlation peak characteristic of warm dense matter (WDM) is observed for the first time using simultaneous angularly, temporally, and spectrally resolved x-ray scattering measurements in laser-driven shock-compressed aluminum. Laser-produced molybdenum x-ray line emission at an energy of 17.9 keV is employed to probe aluminum compressed to a density of ρ>8 g/cm(3). We observe a well pronounced peak in the static structure factor at a wave number of k=4.0 Å(-1). The measurements of the magnitude and position of this correlation peak are precise enough to test different theoretical models for the ion structure and show that only models taking the complex interaction in WDM into account agree with the data. This also demonstrates a new highly accurate diagnostic to directly measure the state of compression of warm dense matter.

Probing the complex ion structure in liquid carbon at 100 GPa.

We present the first direct experimental test of the complex ion structure in liquid carbon at pressures around 100 GPa, using spectrally resolved x-ray scattering from shock-compressed graphite samples. Our results confirm the structure predicted by ab initio quantum simulations and demonstrate the importance of chemical bonds at extreme conditions similar to those found in the interiors of giant planets. The evidence presented here thus provides a firmer ground for modeling the evolution and current structure of carbon-bearing icy giants like Neptune, Uranus, and a number of extrasolar planets.

Dynamic ion structure factor of warm dense matter.

The dynamics of the ion structure in warm dense matter is determined by molecular dynamics simulations using an effective ion-ion potential. This potential is obtained from ab initio simulations and has a strong short-range repulsion added to a screened Coulomb potential. Models based on static or dynamic local field corrections are found to be insufficient to describe the data. An extended Mermin approach, a hydrodynamic model, and the method of moments with local constraints are capable of reproducing the numerical results but have rather limited predictive powers as they all need some numerical data as input. The method of moments is found to be the most promising.

Inelastic x-ray scattering from shocked liquid deuterium.

The Fermi-degenerate plasma conditions created in liquid deuterium by a laser-ablation-driven shock wave were probed with noncollective, spectrally resolved, inelastic x-ray Thomson scattering employing Cl Ly(α) line emission at 2.96 keV. These first x-ray Thomson scattering measurements of the microscopic properties of shocked deuterium show an inferred spatially averaged electron temperature of 8±5 eV, an electron density of 2.2(±0.5)×10(23) cm(-3), and an ionization of 0.8 (-0.25, +0.15). Two-dimensional hydrodynamic simulations using equation-of-state models suited for the extreme parameters occurring in inertial confinement fusion research and planetary interiors are consistent with the experimental results.

Proton stopping measurements at low velocity in warm dense carbon.

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.

Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures.

We present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, [Formula: see text], also called mylar) shock-compressed to ([Formula: see text]) GPa and ([Formula: see text]) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

Ultrafast melting of carbon induced by intense proton beams.

Laser-produced proton beams have been used to achieve ultrafast volumetric heating of carbon samples at solid density. The isochoric melting of carbon was probed by a scattering of x rays from a secondary laser-produced plasma. From the scattering signal, we have deduced the fraction of the material that was melted by the inhomogeneous heating. The results are compared to different theoretical approaches for the equation of state which suggests modifications from standard models.

Demonstration of X-ray Thomson scattering as diagnostics for miscibility in warm dense matter.

The gas and ice giants in our solar system can be seen as a natural laboratory for the physics of highly compressed matter at temperatures up to thousands of kelvins. In turn, our understanding of their structure and evolution depends critically on our ability to model such matter. One key aspect is the miscibility of the elements in their interiors. Here, we demonstrate the feasibility of X-ray Thomson scattering to quantify the degree of species separation in a 1:1 carbon-hydrogen mixture at a pressure of ~150 GPa and a temperature of ~5000 K. Our measurements provide absolute values of the structure factor that encodes the microscopic arrangement of the particles. From these data, we find a lower limit of [Formula: see text]% of the carbon atoms forming isolated carbon clusters. In principle, this procedure can be employed for investigating the miscibility behaviour of any binary mixture at the high-pressure environment of planetary interiors, in particular, for non-crystalline samples where it is difficult to obtain conclusive results from X-ray diffraction. Moreover, this method will enable unprecedented measurements of mixing/demixing kinetics in dense plasma environments, e.g., induced by chemistry or hydrodynamic instabilities.

Measurements of ionic structure in shock compressed lithium hydride from ultrafast x-ray Thomson scattering.

We present the first ultrafast temporally, spectrally, and angularly resolved x-ray scattering measurements from shock-compressed matter. The experimental spectra yield the absolute elastic and inelastic scattering intensities from the measured density of free electrons. Laser-compressed lithium-hydride samples are well characterized by inelastic Compton and plasmon scattering of a K-alpha x-ray probe providing independent measurements of temperature and density. The data show excellent agreement with the total intensity and structure when using the two-species form factor and accounting for the screening of ion-ion interactions.

Ion structure in warm dense matter: benchmarking solutions of hypernetted-chain equations by first-principle simulations.

We investigate the microscopic structure of strongly coupled ions in warm dense matter using ab initio simulations and hypernetted chain (HNC) equations. We demonstrate that an approximate treatment of quantum effects by weak pseudopotentials fails to describe the highly degenerate electrons in warm dense matter correctly. However, one-component HNC calculations for the ions agree well with first-principles simulations if a linearly screened Coulomb potential is used. These HNC results can be further improved by adding a short-range repulsion that accounts for bound electrons. Examples are given for recently studied light elements, lithium and beryllium, and for aluminum where the extra short-range repulsion is essential.