The number of populated electronic configurations in a hot dense plasma

TL;DR

This paper introduces systematic methods to estimate the number of populated electronic configurations in hot dense plasmas, revealing that the actual number is much lower than the total combinatoric possibilities and depends on temperature and density.

Contribution

The work presents two novel methods for estimating the number of populated configurations in plasmas, combining combinatoric calculations and probability distribution estimates.

Findings

Number of populated configurations is significantly lower than total possible configurations.

Temperature and density strongly influence the number of populated configurations.

Methods are validated with comprehensive DFT calculations across various plasma conditions.

Abstract

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 non-trivially 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.