Classical Stark Mixing at Ultralow Collision Energies

Exact solutions of the time-dependent classical equations are obtained for the full array of angular momentum mixing transitions $n\ell \to n{\ell }^{\prime }$ in atomic hydrogen induced by collisions with charged particles at ultralow energies. A novel classical expression for the transition probability $P_{{\ell }^{\prime }\ell }$ is presented. The exact classical results for $P_{{\ell }^{\prime }\ell }\left(\alpha \right)$ as a function of $\ell ,{\ell }^{\prime }$ and the Stark parameter $\alpha$ agree exceptionally well with (exact) quantal results. They complement the quantal results by revealing essential characteristics which remain obscured in the quantal treatment.