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The European Physical Journal D

, Volume 65, Issue 3, pp 357–366 | Cite as

Semi-analytic approach to higher-order corrections in simple muonic bound systems: Vacuum polarization, self-energy and radiative-recoil

Regular Article Atomic Physics

Abstract

The current discrepancy of theory and experiment observed recently in muonic hydrogen necessitates a reinvestigation of all corrections to contribute to the Lamb shift in muonic hydrogen (μH), muonic deuterium (μD), the muonic \hbox{${}^3{\rm He}$} 3 He ion (denoted here as μ 3He+), as well as in the muonic \hbox{${}^4{\rm He}$} 4 He ion (μ 4He+). Here, we choose a semi-analytic approach and evaluate a number of higher-order corrections to vacuum polarization (VP) semi-analytically, while remaining integrals over the spectral density of VP are performed numerically. We obtain semi-analytic results for the second-order correction, and for the relativistic correction to VP. The self-energy correction to VP is calculated, including the perturbations of the Bethe logarithms by vacuum polarization. Subleading logarithmic terms in the radiative-recoil correction to the 2S–2P Lamb shift of order α()5 μ 3ln() / (m μ m N ) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.

Keywords

Logarithmic Term Vacuum Polarization Lamb Shift Muonic System Muonic Hydrogen 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of PhysicsMissouri University of Science and TechnologyRollaUSA
  2. 2.Institut für Theoretische PhysikUniversität HeidelbergHeidelbergGermany

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