Light Muonic Atoms

The current surge of interest in muonic hydrogen is mainly inspired by the desire to obtain a new more precise value of the proton charge radius as a result of measurement of the 2P — 25 Lamb shift [64]. As we have seen 

The natural linewidth of the 2P states in muonic hydrogen and respectively of the 2P — 2S transition is determined by the linewidth of the 2P — IS transition, which is equal hP = 0.077 meV. It is planned [64] to measure 2P — 2S Lamb shift with an accuracy at the level of 10% of the natural linewidth, or with an error about 0.008 meV, which means measuring the 2P — 2S transition with relative error about 4 x 10 . 

The total 2P — 2S Lamb shift in muonic hydrogen calculated according to the formulae in Table 7.1 for = 0.895 (18) fm, is 

We can write the 2P — 25 Lamb shift in muonic hydrogen as a difference of a theoretical number and a term proportional to the proton charge radius squared 

We see from this equation that when the experiment achieves the planned accuracy of about 0.008 meV [64] this would allow determination of the proton charge radius with relative accuracy about 0.1% which is about an order of magnitude better than the accuracy of the available experimental results. 

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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. 

Electron-loop radiative corrections to the leading nuclear finite size contribution in light muonic atoms were considered in [60, 20]. Two diagrams in Fig. 7.15 give contributions of order a Za) m r ). The analytic expression for the first diagram up to a numerical factor coincides with the expression for the mixed electron and muon loops in (7.48), and we obtain... 

J. L. Friar, Nuclear Finite-Size Effects in Light Muonic Atoms, Ann. Phys (N. Y.) 122 (1979) 151-196. 

The decay of the exotic atom can be a simple decay of the exotic particle in the case of light muonic atoms however, due to the strong nuclear interaction in hadronic atoms, the negative hadron can be absorbed by the nucleus leading to nuclear reaction (O Fig. 28.5). 

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-... 

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