Ionization Cross Sections for Rydberg-Atom-Rydberg-Atom Collisions

A classical-trajectory Monte Carlo method has been applied to collisions of two Rydberg atoms. Numerical calculations were made for velocities $v=0.01{v}_{e} \mathrm{to} 10{v}_{e}$, where the Rydberg electron's velocity ${v}_{e}(\mathrm{a}.\mathrm{u}.)=\frac{1}{n}$ and $n$ is the principal quantum number of the Rydberg atom. The total ionization cross sections scale as ${n}^{4}$ and show a ${v}^{\ensuremath{-}0.65}$ dependence at low $v$, a slight maximum around ${v}_{e}$, and a rapid decrease at high $v$. The cross sections are almost an order of magnitude larger than $\ensuremath{\pi}{n}^{4}{{a}_{0}}^{2}$ at thermal energies.