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Energy-conserving, angular momentum-changing collisions between protons andhighly excited Rydberg hydrogen atoms are important for precise understandingof atomic recombination at the photon decoupling era, and the elementalabundance after primordial nucleosynthesis. Early approaches to $\ell$-changingcollisions used perturbation theory for only dipole-allowed ($\Delta \ell=\pm1$) transitions. An exact non-perturbative quantum mechanical treatment ispossible, but it comes at computational cost for highly excited Rydberg states.In this note we show how to obtain a semi-classical limit that is accurate andsimple, and develop further physical insights afforded by the non-perturbativequantum mechanical treatment.

On the treatment of $\ell$-changing proton-hydrogen Rydberg atom collisions