Equivalence between pressure- and structure-defined ionization in hot dense carbon

The determination of the ionization of a system in the hot dense regime is a long standing issue. Recent studies have shown inconsistencies between standard predictions using average atom models and evaluations deduced from electronic transport properties computed with quantum molecular dynamics simulations [Bethkenhagen et al., Phys. Rev. Res. 2, 023260 (2020)]2643-156410.1103/PhysRevResearch.2.023260. Here, we propose a definition of the ionization based on its effect on the plasma structure as given by the pair distribution function (PDF), and on the concept of effective one-component plasma (eOCP). We also introduce a definition based on the total pressure and on a modelization of the electronic pressure. We show the equivalence of these definitions on two studies of carbon along the 100 eV isotherm and the 10 g/cm^{3} isochor. Simulations along the 100 eV isotherm are obtained with the newly implemented Ext. First principles molecular dynamics (Fpmd) method in Abinit for densities ranging from 1 to 500 g/cm^{3}and along the 10 g/cm^{3} isochor with the recently published Spectral quadrature DFT (Sqdft) simulations, between 8 and 860 eV. The resulting ionizations are compared to the predictions of the average-atom code Qaam which is based on the muffin-tin approximation. A disagreement between the eOCP and the actual PDFs (non-OCP behavior) is interpreted as the onset of bonding in the system.