Karshenboim, Savely G.; Ivanov, Vladimir G.
(2018):
The g factor of the bound muon in mediumZ muonic atoms.
In: Physics Letters B, Vol. 786: pp. 485490

Abstract
We consider a theory of the g factor of a bound muon in a threebody atomic system, which consists of a spinless nucleus, a muon, and an electron in the medium range of Z = 1030. We show that the calculation at the oneppm level of accuracy can be separated into a consideration of an internal subsystem mu  N (with a muon at the ground state) and an external subsystem with an electron and a compound mu  N nucleus. We discuss the most important contributions to the g factor of the bound muon in the mu  N system in the mediumZ approximation. In this range the list of relevant contributions contains kinematic pure Coulomb contributions, the finitenuclearsize ones, and muonicatomspecific contributions with closed electron loops. In the case of the medium Zone can apply a double limit Z alpha << 1 and Z alpha m(mu)/m(e) >> 1, at which a number of specific contributions is simplified. Special attention is paid to nonpotential contributions, i.e., those which cannot be expressed in terms of an effective potential. We also consider the electron shielding of the magnetic moment of the compound nucleus, focusing on the corrections which are enhanced or suppressed comparing to the shielding of ordinary nuclei. In conclusion we discuss a generalization of our result for muonic atoms with a few electrons.