Abstract
The ionization of hydrogen can be treated by classical theory when the initial quantum number is large and the photon energy is small. Classically, the electron motion is stochastic for high intensities and the resulting diffusion can lead to ionization. However, Casati et al. [Phys. Rev. Lett. 57, 823 (1986)] have found that the ionization threshold is often higher than the threshold for classical stochasticity. We present here a heuristic explanation: classical stochasticity will be suppressed when the phase-space area escaping through classical cantori each period of the electric field is small compared to Planck’s constant. We obtain a scaling law which agrees remarkably well with the numerical results of Casati et al.