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


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.


Logarithmic Term Vacuum Polarization Lamb Shift Muonic System Muonic Hydrogen 
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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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