Muonic hyperfine structure

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. 

Abstract. We consider the hyperfine structure of the Is and 2s states in muonic hydrogen and muonic deuterium. We put emphasis on two particular topics a possibility to measure the hfs interval in the ground state and a calculation of a specific difference. Ehfs(ls) — 8 Ehfa(2s). Such a measurement and the calculations are of interest in connection with an upcoming experiment at PSI in which different 2s — 2p transitions in muonic hydrogen shall be determined. Together all these investigations will improve the knowledge of the internal structure of proton and deuteron. 

QED can be considered to be one of the most precisely tested theories in physics at present. It provides an extremely accurate description of systems such as hydrogen and helium atoms, as well as for bound-leptonic systems, for example, positronium and muonium. Remarkable agreement between theory and experiment has been achieved with respect to the determination of the hyperfine structure and the Lamb shift. The same holds true for the electronic and muonic g-factors. The free-electron g-factor is determined at present as... 

Studies of the volmne effect yield information on the charge distribution in the nucleus. Hyperfine structure and isotopic shifts are of the same order of magnitude. Isotopic shifts can be studied in the visible region as weU as in the X-ray region. Particularly prominent isotopic shifts are obtained for muonic atoms, in which, for example, a p meson (m = 209me) has taken the place of an electron. The classical radius of the orbit is reduced by a factor of 209, and thus the nuclear influences are much greater than those pertaining to the electrons. Isotope shifts and their interpretation have been discussed m [2.57-2.59J. 

T. Fujita, A. Arima, Magnetic Hyperfine Structure of Muonic and Electronic Atoms, Nucl. Phys. A254 513 (1975). 

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