Resummation of the divergent perturbation series for a hydrogen atom in anelectric field - art. no. 013403

We consider the resummation of the perturbation series describing the energ y displacement of a hydrogenic bound state in an electric field (known as t he Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric-field strength. The perturbation serie s exhibits a rich singularity structure in the Borel plane. Resummation met hods are presented that appear to lead to consistent results even in proble matic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescri ptions are compared: (i) a variant of the Borel-Pade resummation method, wi th an additional improvement due to utilization of the leading renormalon p oles, and (ii) a contour-improved combination of the Borel method with an a nalytic continuation by conformal mapping, and Pade approximations in the c onformal variable. The singularity structure in the case of the LoSurdo-Sta rk effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.