Experiments at the U.S. National Ignition Facility (NIF) [Döppner et al., Nature (London) 618, 270 (2023)] 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 $S\left(k\right)$ 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 $7.89{\AA }^{-1}$ are more consistent with a density of $20\pm 2\mathrm{g}/{\mathrm{cm}}^3$, mean ionization $\overline{Z}=3.25$, at a temperature of $\simeq$ 1 800 000 K than the $34\mathrm{g}/{\mathrm{cm}}^3,\overline{Z}=3.4$ proposed by the NIF team. The relevance of ion-electron coupled-modes in studying small $k_{sc}$ data is indicated.

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• Inertial confinement fusion
• Plasma ionization
• Plasma thermodynamics
• Quantum statistical mechanics
• Spin-singlet pairing
• X-ray generation in plasmas