Ionization and recombination in attosecond electric field pulses

Based on the results of a previous communication [Dimitrovski et al., Phys. Rev. Lett. 93, 083003 (2004)], we study ionization and excitation of a hydrogenic atom from the ground and first excited states in short electric field pulses of several cycles. A process of ionization and recombination which occurs periodically in time is identified, for both small and extremely large peak electric field strengths. In the limit of large electric peak fields closed-form analytic expressions for the population of the initial state after single- and few-cycle pulses are derived. These formulas, strictly valid for asymptotically large momentum transfer from the field, give excellent agreement with fully numerical calculations for all momentum transfers.