Extended chemical picture of ionization balance to extremely dense plasmas

Understanding the ionization balance of extremely dense plasmas still remains a scientific challenge for both theory and experiment, which is very important in many research fields such as the equation of state, radiative opacity, and thermal and electrical conductivities. In a most recent experiment at the National Ignition Facility, the onset of pressure-driven K-shell delocalization was observed in hot dense Be plasmas [T. Döppner et al., Nature (London) 618, 270 (2023)0028-083610.1038/s41586-023-05996-8]. However, all the referenced widely used ionization models can only reproduce part of the experimental data on the ionization state. It is generally regarded that the normal Saha equation is difficult to be applied to the dense plasma regime of, for instance, above a mass density of 10g/cm^{3} when the interactions between the charged particles and the pressure ionization start to dominate the ionization balance. Herein, we show that the chemical picture of the ionization balance can be extended to an even denser regime up to a density of, for example, 100g/cm^{3} or higher when the nonideal effects due to the interactions between the electrons and ions and among the electrons themselves and the pressure-induced ionization can be properly considered in a modified Saha equation. An accurate prediction of the ionization potential depression is crucial to depict the transition of the pressure-induced ionization with increasing plasma density. Comparison of our calculated average degree of ionization with the above-mentioned experiment shows good agreement for all the experimental data before and after the K-shell delocalization transition.