Muonium Lamb shift

Figure 20 Experimental apparatus used in the LAMPF muonium Lamb shift experiment.

Table Ila. Theoretical value of muonium Lamb shift for n=2 state.

As in the case of the Lamb shift, QED provides the framework for systematic calculation of numerous corrections to the Fermi formula for hyperfine splitting (see the scheme of muonium energy levels in Fig. 8.3). We again... 

A number of data are available for Is and 2s hfs intervals in hydrogen, deuterium and the helium-3 ion. The potential of this difference for the hfs intervals in the helium-3 ion [21] with respect to testing bound state QED is compatible with the ground state hfs in muonium both values are sensitive to fourth-order perturbative contributions. The difference of the Lamb shift plays an important role in the evaluation of optical data on the hydrogen and deuterium spectrum [22]-... 

Metastable muonium atoms in the 2s state have been produced with a beam foil technique at LAMPF and at the Tri University Meson Physics Facility (TRI-UMF) at Vancouver, Canada. Only moderate numbers of atoms could be obtained. The velocity resonance nature of the electron transfer reaction results in a muonium beam at keV energies. Very difficult and challenging experiments using electromagnetic transitions in excited states, particularly the 2 Si/2 2 Pi/2 classical Lamb shift and 2 Si/2-2 P3/2 splitting could be induced with microwaves. However, the achieved experimental accuracy at the 1.5 % level [18,19,20], does not represent a severe test of theory yet. 

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... 

The Lamb shift and the fine structure of the n=2 state of muonium has been measured by microwave spectroscopy in experiments at LAMPF(31) and TRIUMF(32) very similar to the classical measurement of the Lamb shift in hydrogen. However, the muonium experiments suffer from a dramatically smaller number of atoms--a factor of at least lO and consequentially the accuracy achieved is much poorer. 

Spectroscopy of Positronium and Muonium Table Ilb. Experimental values of Lamb shift and fine structure. 

The 1S-2S transition in muonium has also been measured by laser spectroscopy. The transition is induced by a two-photon Doppler-free process and detected through the subsequent photoionization of the 2S state in the laser field. The key to success in this experiment was the production of muonium into vacuum from the surface of heated W or of Si02 powder. The discovery experiment(33) was done at the KEK facility in Japan with a pulsed muon beam and an intense pulsed laser system. A subsequent experiment(34) done with the pulsed beam at RAL and a similar pulsed laser has improved the signal substantially and has achieved a a precision of about lO" in the 1S- 2S interval, thus determining the Lamb shift in the IS state to about 1% accuracy (Fig. 22). The precision of this experiment should be greatly improved in a new experiment now underway at RAL. This experiment will provide a precise... 

Although measurements of the ground state hfs splitting and the n=2 Lamb shift have been made, the analogous two-photon laser experiment (ls-2s) to that in hydrogen has only recently been comtemplated because of developments in the production of slow muonium atomsl. It should be noted that both positronium and muonium are pure leptonic systems and therefore do not suffer from any uncertainty in nuclear size in the case of hydrogen the present error in the proton size determination is 4 (see equation (5)). 

In connection with this discussion of hindamental interactions we note that, besides hydrogen, there are numerous simple systems for which precision spectroscopic measurements can provide accurate tests of the QED theory and reveal effects beyond the Standard Model [9.367]. Positronium (e "-e ) and muonium (jil -e ) are hydrogen-like systems for which precise Lamb-shift and g-2 experiments have been performed. Precision spectroscopic studies on anti-hydrogen (antiproton-positron), once achievable, would certainly be extremely interesting in revealing possible asymmetries between the world and an anti-world [9.368]. 

The fact that y e can now be studied in vacuum is very important for a number of fundamental experiments. One is the measurement of the Lamb shift in the first excited state of muonium (Fig.5). The beam-foil method produces not only the n=l state but excited states as well l with a probability roughly as l/n. We expect that 15% of the muonium formed is in the 2S state. 

The major motivation for measuring the Lamb shift is that it is a pure QED test. In hydrogen the uncertainty in the proton size limits the accuracy in the theory to lOppm, which is the same as for the experimental valued. This uncertainty does not exist in muonium. Because of the difference in the masses of the proton and the muon different recoil corrections must be taken into account ... 

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