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Resummation in the Doubly-Cut Borel Plane: The LoSurdo-Stark Effect

Published

Author(s)

U Jentschura

Abstract

The divergent perturbation series for the LoSurdo--Stark effect has purely real coefficients. By contrast, the energy eigenvalue of the quasistationary states is complex (the imaginary part corresponds to the autoionization width). Two different resummation prescriptions are compared: (I) a contour-improved resummation method based on a combination of Borel and Pad\'e} techniques and (ii) a combination of the Borel method with an analytic continuation by conformal mapping. With both methods, the complex energy eigenvalue can be reconstructed from the purely real perturbation series. The performance of both methods is compared, calculational difficulties at strong field are addressed, and the connection to divergent perturbative expansions in quantum field theory is discussed.
Citation
Physical Review A (Atomic, Molecular and Optical Physics)

Keywords

asymptotic problems and properties, general properties of perturbation theor, line shapes, numerical algorithum, numerical analysis, special functions, widths, and Shifts, Zeeman and Stark Effects

Citation

Jentschura, U. (2008), Resummation in the Doubly-Cut Borel Plane: The LoSurdo-Stark Effect, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed November 29, 2023)
Created October 16, 2008