Ionization of Rydberg atoms by an electric-field kick

We provide a rigorous lower bound for the ionization probability of a Rydberg atom under the perturbation by a time-dependent electric field in the form of an ultrashort pulse idealized as a Dirac δ function. This estimate is of the form 1-O(${\mathit{F}}_0^{\mathrm{-}4}$) for large values of the electric field ${\mathit{F}}_0$. For the hydrogen atom we also prove the scaling behavior ${\mathit{F}}_0$∼${\mathit{n}}^{\mathrm{-}1}$, predicted recently by Reinhold et al. [Phys. Rev. Lett. 70, 4026 (1993); J. Phys. B 26, L659 (1993)], for the electric field required to ionize a given percentage of states with principal quantum number n.