Classical theory ofl-changing transitions in collisions between Rydberg atoms and ions

The l-changing transitions in collisions of Rydberg atoms with ions, A(${\mathit{nl}}_0$)+${\mathit{B}}^{+}$→A(nl)+${\mathit{B}}^{+}$, are considered within the classical approximation for atomic electron motion. The elliptic orbit of the electron evolves slowly under the influence of the time-dependent electric field exerted by the incident ion. The quantum electron state is represented by an ensemble of classical trajectories. Within the dipole approximation extremely simple analytical formulas for the final-state l-distribution function are obtained for a fixed value of the impact parameter. The influence of the non-Coulomb core is taken into account approximately. The results of our calculations compare favorably with recent experimental data for the ${\mathrm{Na}}^{+}$(26d, 28d) Rydberg atom. The method can be extended to the calculation of distributions over various observables other than l.