Complex energies from real perturbation series for the LoSurdo-Stark effect in hydrogen by Borel-Padé approximants

Abstract

The resonance energies for the hydrogen atom in an electric field, both the real and imaginary parts, have been calculated together from the real Rayleigh-Schr\"odinger perturbation series by Borel summation. Pad\'e approximants were used to evaluate the Borel transform. The numerical results compare well with values obtained by the complex-coordinate variational method and by sequential use of Pad\'e approximants.