2003/04/02 by Ulrich D. Jentschura, Ulrich D Jentschura · 2 citations
Physics and Astronomy · #Bound state #Energy (signal processing) #Function (biology) #Logarithm #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Radiative transfer #Space (punctuation) #Upper and lower bounds #hep-ph
paper · pdf · doi:10.1088/0305-4470/36/15/103
published as J.Phys. A36 (2003) L229-L236 · 10 pages, LaTeX, with hyperref
openalex publication_date 2003/04/02 · arxiv created 2003/05/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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).