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Abstract

Prof. Michael Bonitz and his collaborators have made seminal contributions to the study of the uniform electron fluid and the electron-proton fluid, viz., hydrogen, in using {\it ab initio} simulations. These studies provide essential inputs to astrophysics as well as high-energy density physics. This is reflected in the contributions to this festshrift in his honour. The electron-proton system becomes particularly difficult for theoretical modeling when the temperature becomes comparable to the Fermi energy $E_F$, when the warm-dense matter (WDM) state of hydrogen is reached. In this study we briefly review the theoretical methods available for the study of WDM systems, and use the neutral-pseudo atom (NPA) method, and a classical map for quantum electrons to study fully and partially ionized hydrogen. It is shown that {\it both} fully and partially ionized states can independently exist at the {\it same density and temperature} in many cases. Recent studies using path-integral Monte Carlo methods, and $N$-atom Density Functional Theory (DFT) simulations have provided essential structure data including the electron-electron structure factor $S_{ee}(k)$ that enters into interpretation of X-ray Thomson scattering and other diagnostics. We show that these structure data can be rapidly and inexpensively evaluated, with sufficient accuracy, using classical-map schemes for fully ionized plasmas, and more generally, using one-atom (average-atom) DFT methods for partially ionized systems.