Relation between low-energy-electron scattering andl-changing collisions of Rydberg atoms

Collisions of Rydberg atoms with other atoms may induce changes in the electronic orbital angular momentum of the Rydberg state. A theory is presented that expresses the cross section for this process in terms of the $s$-wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the $l$-mixing cross section at a particular $n$ is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on $n$. The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of $\mathrm{Na}\mathrm{}\left(\mathrm{nd}\right)+\mathrm{He}$, Ne, and Ar are treated as specific examples.