Radiative Energy Shifts Induced by Local Potentials
We study a specific correction to the Bethe logarithm induced by potentials which are proportional to a Dirac-δ function in coordinate space ('local potentials'). Corrections of this type occur naturally in the calculation of various self-energy corrections to the energy of bound states. Examples include logarithmic higher-order binding corrections to the two-loop self-energy, vacuum-polarization induced corrections to the self-energy and radiative corrections induced by the finite size of the nucleus. We obtain results for excited S and P states and find that the dependence of the corrections on the principal quantum number is remarkable. For the ground state, we find a small modification as compared to previously reported results. Our results are based on mathematical techniques for the treatment of quantum electrodynamic bound states introduced discussed previously by Jentschura and Pachucki (2002 J. Phys. A: Math. Gen. 35 1927).
U. D. Jentschura, "Radiative Energy Shifts Induced by Local Potentials," Journal of Physics A: Mathematical and General, vol. 36, no. 15, pp. L229-L236, IOP Publishing, Apr 2003.
The definitive version is available at https://doi.org/10.1088/0305-4470/36/15/103
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