Muonium in vacuum

The very precise measurement of the ground state hyperfine structure (hfs) is described. A new successful technique for producing muonium in vacuum has been developed and possible future experiments using this technique are presented in the second part. 

The observation of muonium in vacuum makes it possible to do experiments on muonium which require a collision-free environment. 

Attempts to find thermal muonium in vacuum failed An early experiment at the Space Radiation Effects Laboratory (SREL) seemed to show that y" " stopped in thin gold foils emerges as muonium at thermal energies. But more sensitive experiments at LAMPF and SIN observed no muonium formation. 

However with a technique similar to beam neutralization in proton beam-foil spectroscopy energetic muonium in vacuum was observed 5. 

Fig. 5. The /rSR spectra from fused quartz at room temperature and silicon at 77 K, each in a magnetic field of 10 mT. For quartz, the two high-frequency lines result from muonium with a hyperfine parameter close to that in vacuum. The two high-frequency lines in Si result from Mu, and their larger splitting arises because the hyperfine parameter is less than the vacuum value (0.45 Afree). The lowest line in each sample comes from muons in diamagnetic environments. The lines from 40 to 50 MHz in Si arise from Mu. From Brewer et al. (1973).

An unambiguous identification of anomalous muonium with the bond-center site became possible based on pseudopotential-spin-density-functional calculations (Van de Walle, 1990). For an axially symmetric defect such as anomalous muonium the hyperfine tensor can be written in terms of an isotropic and an anisotropic hyperfine interaction. The isotropic part (labeled a) is related to the spin density at the nucleus, ip(0) [2 it is often compared to the corresponding value in vacuum, leading to the ratio i7s = a/Afee = j i (O) Hi/) / (O) vac- The anisotropic part (labeled b) describes the p-like contribution to the defect wave function. 

In diamond, Sahoo et al. (1983) investigated the hyperfine interaction using an unrestricted Hartree-Fock cluster method. The spin density of the muon was calculated as a function of its position in a potential well around the T site. Their value was within 10% of the experimental number. However, the energy profiles and spin densities calculated in this study were later shown to be cluster-size dependent (Estreicher et al., 1985). Estreicher et al., in their Hartree-Fock approach to the study of normal muonium in diamond (1986) and in Si (1987), found an enhancement of the spin density at the impurity over its vacuum value, in contradiction with experiment this overestimation was attributed to the neglect of correlation in the HF method. 

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... 

The time window can be extended to even shorter times if there is a muonium precursor state. Evolution of spin polarization in Mu occurs partly at frequencies near the Mu hyperfine frequency (4463 MHz in vacuum, broken arrows in Figure 2), which sets the timescale for loss of phase coherence during formation of the observed muonated species. The formation process can be studied indirectly in transverse fields by interpretation of shifts in the initial phase and concomitant loss of amplitude. Thus, processes occurring on a timescale down to 10 ps can be analysed, but the results rely on the validity of the underlying model. 

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. 

An important point is that the difference is sensitive to 4th order corrections and so is competitive with the muonium hfs as a test of the QED. The difference between the QED part of the theory and the experiment is an indication of higher-order corrections due to the QED and the nuclear structure, which have to be studied in detail. In particular, we have to mention that while we expect that we have a complete result on logarithmic corrections and on the vacuum-... 

---