Muonic atom

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-... 

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... 

With the recent advances in atomic theories and experimental techniques, the value of the information obtained from studies of atoms that are different from but similar to atomic hydrogen have increased. These studies include atomic helium, muonic hydrogen, positronium, muonium, antihydrogen, moderate Z ions, high Z ions, antiprotonic atoms and muonic atoms. 

The list of simple atoms accessible now includes a broad range of very different natural and artificial systems hydrogen, helium, muonium, positronium, various few-electron ions, muonic atoms and exotic atomic systems containing a pion, antiproton etc. While hydrogen atoms form the essential part of our universe, the unstable atoms like muonium do not exist in nature at all. The investigation of simple atoms has provided us with important knowledge on fundamental interactions between the particles these atoms consist of. 

In the cases of muonium, positronium, muonic atoms and multiply-charged ions, the study implies the development of new sources and new detectors. The application of spectroscopic methods is very attractive for pionic and exotic atoms, because of an extremely high (for particle physics) level of accuracy. 

One can study muonic atoms [14,15,16]. The muon orbit lies lower and much more close to the nucleus and its energy levels are much more affected by the strong interactions. However, to determine the nuclear contributions (for e. g. the one for the Lamb shift, which is completely determined by the nuclear charge radius) it is not necessary to know the QED part with an accuracy as high as in the case of the hydrogen atom. As a result, one can try to determine the parameters due to the nuclear structure and apply them afterwards to normal atoms. 

Muonic Atoms and Nuclear Structure (see Part VIII)... 

The muon is about two hundred times heavier than the electron and its orbit lies 200 times closer to the nucleus. The nuclear structure effects scale with the mass of the orbiting particle as m3R2 (for the Lamb shift It is a characteristic value of the nuclear size) and as m R2 (for the hyperfine structure), while the linewidth is linear in m. That means, that from a purely atomic point of view the muonic atoms offer a way to measure the nuclear contribution with a higher accuracy than normal atoms. However, there are a number of problems with formation and thermalization of these atoms and with their collisions with the buffer gas. 

A major advantage of facilities with significantly increased muon fiux would be the possibility to use novel experimental techniques which could not be exploited so far [74] like, e.g. the use of cw lasers for optical spectroscopy or an old muonium approach for a new generation M-M search. Further, a wider class of muonic atoms would be become accessible for precision spectroscopy [75] beyond the already started laser investigations of muonic hydrogen [76]. 

A negative muon can participate in a variety of atomic and molecular processes. A muonic atom is formed when a muon stops in matter replacing an electron. A muonic atom interacting with ordinary atoms or molecules can form a muonic molecule. The latter in turn can result in fusion reactions between the nuclei if the target consists of hydrogen isotopes, a phenomenon known as muon catalyzed fusion (pCF) [6]. 

In the case of normal hydrogen [14] the difference is mainly determined by a relativistic contribution of order (Za)2Ep (so-called Breit term [15]). In muonic atoms the leading effect is due to vacuum polarization and it is of order aEp. 

In the range Z k. 2—10 and n 4 — 8, there is a window where in pionic and muonic atoms electrons are completely stripped off and the transition energies are accessible by X-ray spectroscopy. For the atomic states with maximum... 

At the ttE5 beam of the Paul-Scherrer-Institut (PSI), about 2% of the incoming pions (> 109/s) are stopped in the gas cell with a degrader set-up optimized for pionic atoms. Muons originating from pions decaying shortly before capture are slow enough to be stopped in the gas cell as well. With a set-up optimized for muons, the count rate for muonic atoms is about 4% of the one for pions. 

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