Two-body corrections to the g factors of the bound muon and nucleus in light muonic atoms

  • Savely G. KarshenboimEmail author
  • Vladimir G. Ivanov
Open Access
Regular Article


A nonrelativistic (NR) theory of recoil corrections to the magnetic moments of bound particles is revisited. A number of contributions can be described within an NR theory with the help of various potentials. We study those potential-type contributions for two-body atomic systems. We have developed an approach, that allows us to find the g factor for an electron or muon in a two-body bound system for an arbitrary electrostatic interaction together with the m/M recoil corrections, as well as the binding corrections to the g factor of the nucleus. We focus our attention on light muonic two-body atoms, where the recoil effects are enhanced. Both mentioned kinds of contributions have been previously known only for the pure Coulomb effects. We have applied the here-obtained master equations to a few particular cases of perturbations of the Coulomb potential. In particular, the results on the recoil corrections to the finite-nuclear-size (FNS) and Uehling-potential contributions to the g factor of the bound muon are obtained. The Uehling-potential and FNS contributions to the g factor of the bound nucleus have been found as well together with the related recoil corrections. We have generalized the results for the case of the g factor of a bound muon in a three-body atomic system consisting of an electron, a muon, and a spinless nucleus.

Graphical abstract


Atomic Physics 



Open access funding provided by Max Planck Society.


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© The Author(s) 2019

Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Ludwig-Maximilians-Universität, Fakultät für Physik80799MünchenGermany
  2. 2.Max-Planck-Institut für QuantenoptikGarchingGermany
  3. 3.Pulkovo ObservatorySt. PetersburgRussia

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