On the number of atomic configurations in hot plasmas

TL;DR

This paper introduces formulas to estimate the number of electron configurations in hot plasmas, aiding opacity calculations, with one formula involving Bessel functions and an accuracy improvement method.

Contribution

It provides new approximate formulas for counting electron configurations in hot plasmas, including a novel approach using Bessel functions and series expansion for enhanced accuracy.

Findings

Derived formulas for configuration counts in hot plasmas.

Incorporated Bessel functions of fractional order into the formulas.

Outlined a series expansion method to improve accuracy.

Abstract

We propose approximate and accurate formulas for the number of electron configurations in hot plasmas. Such a quantity is an ingredient of algorithms devoted to the generation of configurations or superconfigurations, which is a pre-requisite of opacity calculations. One of the main formulas involves Bessel functions of fractional order and the procedure for improving the accuracy through a series expansion is explained.