Muonic

Multimetallic fullerene adducts, 44 24, 26-28 Multinuclear metalloenzymes, 44 247-258 nt Multiple bonds, 33 260 structure of and proofs for, 33 256 Muonic radical, formation and reactions of, 28 122-130... 

Theoretically, light muonic atoms have two main special features as compared with the ordinary electronic hydrogenlike atoms, both of which are connected with the fact that the muon is about 200 times heavier than the electron First, the role of the radiative corrections generated by the closed electron loops is greatly enhanced, and second, the leading proton size contribution becomes the second largest individual contribution to the energy shifts after the polarization correction. 

Discussing light muonic atoms we will often speak about muonic hydrogen but almost ah results below are valid also for another phenomenologically interesting case, namely muonic helium. In the Sections on light muonic atoms, m is the muon mass, M is the proton mass, and rUe is the electron mass. 

The effects connected with the electron vacuum polarization contributions in muonic atoms were first quantitatively discussed in [4]. In electronic hydrogen polarization loops of other leptons and hadrons considered in Subsect. 3.2.5 played a relatively minor role, because they were additionally suppressed by the typical factors (mg/m). In the case of muonic hydrogen we have to deal with the polarization loops of the light electron, which are not suppressed at all. Moreover, characteristic exchange momenta mZa in muonic atoms are not small in comparison with the electron mass rUg, which determines the momentum scale of the polarization insertions m Za)jme 1.5). We see that even in the simplest case the polarization loops cannot be expanded in the exchange momenta, and the radiative corrections in muonic atoms induced by the electron loops should be calculated exactly in the parameter m Za)/me-... 

Numerically, contribution to the 2P — 2S Lamb shift in muonic hydrogen is equal to... 

The uncertainty here is due to the unknown nonlogarithmic terms. Calculation of these nonlogarithmic terms is one of the future tasks in the theory of muonic hydrogen. 

Contributions of order a Za) m in muonic hydrogen generated by the two-loop muon form factors have almost exactly the same form as the respective contributions in the case of electronic hydrogen. The only new feature is connected with the contribution to the muon form factors generated bj insertion of one-loop electron polarization in the radiative photon in Fig. 7.9. Respective insertion of the muon polarization in the electron form factors in electronic hydrogen is suppressed as (mg/m), but insertion of a light loop in the muon case is logarithmically enhanced. 

In the case of muonic hydrogen rur in (3.30) is the muon-proton reduced mass. 

All corrections to the energy levels obtained above in the case of ordinary hydrogen and collected in the Tables 3.2, 3.3, 3.7, 3.8, 3.9, 4.1, 5.1 are still valid for muonic hydrogen after an obvious substitution of the muon mass instead of the electron mass in all formulae. These contributions are included in Table 7.1. 

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