On the treatment of $\ell$-changing proton-hydrogen Rydberg atom
  collisions
  Energy-conserving, angular momentum-changing collisions between protons and
highly excited Rydberg hydrogen atoms are important for precise understanding
of atomic recombination at the photon decoupling era, and the elemental
abundance after primordial nucleosynthesis. Early approaches to $\ell$-changing
collisions used perturbation theory for only dipole-allowed ($\Delta \ell=\pm
1$) transitions. An exact non-perturbative quantum mechanical treatment is
possible, 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 and
simple, and develop further physical insights afforded by the non-perturbative
quantum mechanical treatment.
