Rydberg atoms in electric fields

The Stark effect in one-electron atoms is investigated. The reliability of semiclassical approaches as a method to provide the field evolution of the complex resonance parameters is studied in detail. An expression for the asymptotic phase-shift is derived. From a Breit-Wigner parametrization of this phase-shift simple analytical expressions for the resonance parameters are obtained. As a byproduct of this work, we derive a general expression for the phase-shift for problems involving potentials diverging like -r at infinity. We also propose the use of Hadamard's concept of an improper integral as an efficient analytical way of treating the exceedingly complicated high-order semiclassical contributions. (orig.)