  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.
