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Full-Text Articles in Physical Sciences and Mathematics
Resummation Of The Divergent Perturbation Series For A Hydrogen Atom In An Electric Field, Ulrich D. Jentschura
Resummation Of The Divergent Perturbation Series For A Hydrogen Atom In An Electric Field, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
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, …
Electron Self-Energy For The K And L Shells At Low Nuclear Charge, Ulrich D. Jentschura, Peter J. Mohr, Gerhard Soff
Electron Self-Energy For The K And L Shells At Low Nuclear Charge, Ulrich D. Jentschura, Peter J. Mohr, Gerhard Soff
Physics Faculty Research & Creative Works
A nonperturbative numerical evaluation of the one-photon electron self-energy for the K- and L-shell states of hydrogenlike ions with nuclear charge numbers Z =1 to 5 is described. Our calculation for the 1S1/2 state has a numerical uncertainty of 0.8 Hz in atomic hydrogen, and for the L-shell states (2S1/2 , 2P1/2 , and 2P3/2) the numerical uncertainty is 1.0 Hz. The method of evaluation for the ground state and for the excited states is described in detail. The numerical results are compared to results based on known terms in the expansion of the self-energy …