# Efficient computation of collisional $\ell$-mixing rate coefficients in astrophysical plasmas

## TL;DR

This paper introduces analytical formulas and a software tool for efficiently calculating collisional $\, ext{l}$-mixing rate coefficients in hydrogen atom collisions, with validation through astrophysical radio recombination line data.

## Contribution

It provides new analytical expressions and a software package for rapid, accurate computation of $\, ext{l}$-mixing rate coefficients in astrophysical plasmas, improving upon previous approximation methods.

## Key findings

- Validated rate coefficients against radio recombination lines.
- Highlighted the validity range of various approximation methods.
- Provided efficient computational tools for astrophysical plasma modeling.

## Abstract

We present analytical expressions for direct evaluation of $\ell$-mixing rate coefficients in proton-excited hydrogen atom collisions and describe a software package for efficient numerical evaluation of the collisional rate coefficients. Comparisons between rate coefficients calculated with various levels of approximation are discussed, highlighting their range of validity. These rate coefficients are benchmarked via radio recombination lines for hydrogen, evaluating the corresponding departure coefficients from local thermal equilibrium.