Number of populated electronic configurations in a hot dense plasma

In hot dense plasmas of intermediate or high-Z elements in the state of local thermodynamic equilibrium, the number of electronic configurations contributing to key macroscopic quantities such as the spectral opacity and equation of state can be enormous. In this work we present systematic methods for the analysis of the number of relativistic electronic configurations in a plasma. While the combinatoric number of configurations can be huge even for mid-Z elements, the number of configurations which have non-negligible population is much lower and depends strongly and nontrivially on temperature and density. We discuss two useful methods for the estimation of the number of populated configurations: (i) using an exact calculation of the total combinatoric number of configurations within superconfigurations in a converged super-transition-array (STA) calculation, and (ii) by using an estimate for the multidimensional width of the probability distribution for electronic population over bound shells, which is binomial if electron exchange and correlation effects are neglected. These methods are analyzed, and the mechanism which leads to the huge number of populated configurations is discussed in detail. Comprehensive average-atom finite-temperature density functional theory (DFT) calculations are performed in a wide range of temperature and density for several low-, mid-, and high-Z plasmas. The effects of temperature and density on the number of populated configurations are discussed and explained.