Approximate scaling formula for collisional angular-momentum mixing of Rydberg atoms

An approximate scaling formula has been determined that permits the rapid estimation of cross sections for angular-momentum-changing collisions of Rydberg atoms with a variety of targets, using information about low-energy-electron scattering from the target. The formula is obtained by fitting the results of coupled-channel and Born-approximation calculations to functions of reduced parameters. Application to $\mathrm{Na}\mathrm{}\left(\mathrm{nd}\right)\mathrm{}$ + He, Ne, Ar, ${\mathrm{N}}_2$, C${\mathrm{H}}_4$, ${\mathrm{C}}_3$ ${\mathrm{H}}_8$; $\mathrm{Rb}\mathrm{}\left(\mathrm{nf}\right)\mathrm{}$ + He, Ar, Xe; and $\mathrm{Xe}\mathrm{}\left(\mathrm{nf}\right)\mathrm{}$ + C${\mathrm{O}}_2$, suggests that the accuracy is about a factor of 2.