Near-threshold excitation of Rydberg series by strong laser fields

We develop a theory describing laser excitation of a Rydberg series by an intense laser field. Our theory is based on the fact that the radiative coupling is restricted to a region around the atomic nucleus (the reaction zone) which is small in comparison with the extent of the excited Rydberg states. The physical processes inside the reaction zone are characterized by a few parameters which are slowly varying functions of energy across the Rydberg threshold. This finite range of the radiative coupling allows us to apply methods from quantum-defect theory and to treat the laser interaction with the Rydberg series and the adjoining electron continuum as a whole. Within this approach we derive analytical expressions for transition probabilities as a function of time in either a dressed-state representation which is appropriate as long as only a few Rydberg states are excited or a multiple-scattering expansion which is particularly suited for a description of the excitation process close to threshold. The physical picture emerging in this limit is one of a radial electronic wave packet which is generated within the reaction zone and moves in the Coulomb potential of the ionic core. Every time it returns to the inner turning point of its orbit, i.e., to the reaction zone, it is either deexcited back to the initial atomic state or is scattered by the ionic core.