A study of the electronic and ionic structure, for competing states of fully and partially ionized hydrogen, using the neutral pseudo-atom method as well as a classical map for the electron subsystem

Prof. 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, as reflected in this festschrift. Here we review the theoretical methods available for these systems where traditional small-parameter methods fail. We use the neutral-pseudo atom (NPA) method, and a classical map for quantum electrons to study hydrogen plasmas. We show that {\it both} fully-ionized and partially-ionized hydrogen phases can exist with the same nominal density and temperature, at pressures and temperatures of interest to planetary physics. The mean ionization $\bar{Z}$, pair-distribution functions, free energies, pressures and conductivities are calculated for the competing phases. Here $\bar{Z}$ is also a measure of the miscibility of fully ionized and un-ionized hydrogen. 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 inexpensively evaluated using classical-map schemes for fully ionized plasmas, and more generally, using one-atom (average-atom) DFT methods for partially ionized systems.