Resonant States in the Nonperturbative Regime: The Hydrogen Atom in an Intense Electric Field

I present the first results of a precise measurement of the intense-field Stark effect in highly excited states of atomic hydrogen, a prototype system for experimental and theoretical studies of resonant states in the nonperturbative regime. I show that the quantity ${n}^{4}F$ (in atomic units), known to be important for field ionization, also governs the divergence properties of the perturbation series for the energy shift.