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

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.