2000/10/31 by U. D. Jentschura, Ulrich D. Jentschura · 1 citation
Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Spectroscopy and Quantum Chemical Studies #hep-ph #physics.atom-ph #quant-ph
paper · pdf · doi:10.1103/physreva.64.013403
published as Phys.Rev. A64 (2001) 013403 · 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results enhanced; one section and one appendix added and some minor changes and additions; to appear in phys. rev. a
arxiv created 2001/04/23 · openalex publication_date 2001/05/31 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric-field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented that appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pad'e resummation method, with an additional improvement due to utilization of the leading renormalon poles, and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pad'e approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.