Highly compressed spin-singlet Be at a million Kelvin

Experiments at the U.S. National Ignition Facility (NIF) [Döppner et al., Nature (London) 618, 270 (2023)0028-083610.1038/s41586-023-05996-8] have created highly compressed hot hydrogenlike Be plasmas. Published analyses of the the NIF experiment have used finite-T multiatom density-functional theory with Molecular dynamics, and Path-Integral Monte Carlo simulations. These methods are very expensive to implement and often lack physical transparency. Here we (i) relate their results to simpler first-principles average-atom results, (ii) establish the feasibility of rapid data analysis, with good accuracy and gain in physical transparency, and (iii) show that the NIF experiment reveals high-T spin-singlet pairing of hydrogenlike Be ions with near neighbors. Our analysis predicts such stabilization over a wide range of compressed densities for temperatures close to two million Kelvin. Calculations of structure factors S(k) for electrons or ions, the Raleigh weight and other quantities of interest to x-ray Thomson scattering are presented. We find that the NIF data at the scattering wave vector k_{sc} of 7.89Å^{-1} are more consistent with a density of 20±2g/cm^{3}, mean ionization Z[over ¯]=3.25, at a temperature of ≃ 1 800 000 K than the 34g/cm^{3},Z[over ¯]=3.4 proposed by the NIF team. The relevance of ion-electron coupled-modes in studying small k_{sc} data is indicated.