Optimized recursion relation for the computation of partition functions in the superconfiguration approach

TL;DR

This paper introduces an optimized recursion relation for calculating partition functions in the superconfiguration approach, enhancing stability and efficiency by leveraging elementary symmetric polynomials.

Contribution

The authors improve a previously published recursion relation for partition functions, making it more practical and adaptable through the use of elementary symmetric polynomials.

Findings

Enhanced stability and efficiency in partition function calculations

Practical implementation guidelines provided

Potential for further improvements via elementary symmetric polynomials

Abstract

Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion relation for the calculation of such partition functions. In this paper, we propose an optimization of the latter method and explain how to implement it in practice. The formalism relies on the evaluation of elementary symmetric polynomials, which opens the way to further improvements.