A fast approximation to supershell partition functions

TL;DR

This paper introduces a rapid approximation method for supershell partition functions, essential in radiative-opacity calculations, enabling efficient evaluations through an alternative expansion approach.

Contribution

It presents a new formula for supershell partition functions as a functional of energy distribution, facilitating quick approximations with truncated expansions.

Findings

Provides a functional formula for supershell partition functions.

Enables fast approximate evaluations with fewer terms.

Improves computational efficiency in radiative-opacity calculations.

Abstract

A formula for supershell partition functions, which play a major role in the Super Transition Array approach to radiative-opacity calculations, is derived as a functional of the distribution of energies within the supershell. It consists in an alternative expansion for an arbitrary number of electrons or holes which also allows for quick approximate evaluations with truncated number of terms in the expansion.