H, He-like recombination spectra IV; H, He-like recombination spectra IV: clarification and refinement of methodology for $l$-changing collisions

TL;DR

This paper refines the methodology for calculating $l$-changing collision rates in hydrogen and helium recombination spectra, improving accuracy and computational efficiency for astrophysical spectral modeling.

Contribution

It clarifies and improves the modified Pengelly & Seaton formulae, correcting misinterpretations and providing efficient algorithms for quantum mechanical rate calculations.

Findings

Corrected the usage of the Pengelly & Seaton formulae.

Developed efficient numerical algorithms for rate coefficient calculations.

Demonstrated improved modeling of hydrogen recombination spectra.

Abstract

Precise spectral diagnostic modelling of H~{\sc i} and He~{\sc ii} recombination spectra can constrain theoretical models which describe many astrophysical environments. Simple analytic expressions are of interest for collisional $l$-changing rate coefficients that are used by large-scale population modelling codes. We review, clarify and improve-upon the modified Pengelly \& Seaton formulae of Guzm\'an \etal We show that the recent poor results for it shown by Vrinceanu \etal are due to their misinterpretation of its usage. We also detail efficient numerical algorithms which should enable the full quantum mechanical expression for such rate coefficients to be used much more routinely by modelling codes. We illustrate with some collisional-radiative population modelling for hydrogen.