Muon decay

The techniques of u.SR and p-LCR are based on the fact that parity is violated in weak interactions. Consequently, when a positive muon is created from stationary pion decay its spin is directed opposite to its momentum. This makes it possible to form a beam of low energy (4 MeV) positive muons with nearly 100% spin polarization at high intensity particle accelerators such as TRIUMF in Canada, the PSI in Switzerland, LAMPF and BNL in the USA, KEK in Japan, and RAL in England. Furthermore the direction of position emission from muon decay is positively correlated with the muon spin polarization direction at the time of decay. This allows the time evolution of the muon spin polarization vector in a sample to be monitored with a sensitivity unparalleled in conventional magnetic resonance. For example, only about 101 7 muon decay events are necessary to obtain a reasonable signal. Another important point is that //.SR is conventionally done such that only one muon is in the sample at a time, and for p,LCR, even with the highest available incident muon rates, the 2.2 fis mean lifetime of the muon implies that only a few muons are present at a given time. Consequently, muonium centers are inherently isolated from one another. 

Fig. 1. Schematic for /zSR and fiLCR experiments. For pSR the muon spin polarization vector starts off in the x direction (open arrow). It then precesses about an effective field (the vector sum of the external field and the internal hyperfine field), which is normally approximately the z direction. The muons are detected in the M counter, and positrons from muon decay are detected in the L or R counters. For pLCR, the muon spin polarization is initially along the external field or t axis (solid arrow). The positron rates in the F and B counters are measured as a function of external field. A sharp decrease in the asymmetry of the F and B counting rates signifies a level crossing.

The work on muonium in Si is distinguished from that on other semiconductors in several respects. Not only was Si the first semiconductor studied, and it is the best understood semiconductor from a muonium point of view, but the importance of hydrogen and hydrogen complexes in Si, to which the muonium studies are relevant, is greatest. Much of the early work on Si predates the new spectroscopic methods described in the previous section. Since most of this early work, along with muon-decay channeling, has been reviewed by Patterson (1988), only the essential points will be included here to put into context the more recent spectroscopic developments. 

Figure 1. Muonium spin precession signal for a ZnO powder sample at 5 K. The upper plot is the raw time-domain spectrum (corrected for the muon decay) while the lower plot is the corresponding frequency spectrum. The central line corresponds to the Larmor frequency of the bare muon (ionized muonium) and the two symmetrically disposed satelhtes are associated with muonium. The dotted curve is a theoretical fit using a powder-pattern hneshape.

Figure 2 shows some time-histograms of both raw and fitted data. The data is computer fitted using MINUIT, a x minimization program, to a nine parameter function. Equation (3) shows that function with two parameters, background and muon decay, subtracted out. 

See the Note on Muon Decay Parameters in the p Particle Listings for definitions and details. 

While in the sample, the muon decays, emitting a positron (which is detected in the experiments), a neutrino, and an antineutrino ... 

The first approximation that is made for this description is that B = 0 that is, that there is no time-independent background of events unrelated to muon decay. Since experimental values of B are usually less than a few percent, this is a tolerable approximation, especially for early times. The raw histogram bins can therefore be represented as... 

Fig. 3. Polar diagram of the angular distribution of positrons from muon decay. The pattern with Oq 1 results if only positrons near are counted the pattern Oq = when aU positron energies are sampled with equal probability. The distributions are rotationally symmetric around the muon spin direction (z-axis).

Let us first assume that the external field is switched off. Furthermore, we have assumed that internal fields do not exist (nonmagnetic sample). Thus, no magnetic interaction works on Sy, which remains stationary. Under those circumstances Nf(t) simply reflects the muon decay process ... 

Elementary Particles ), in decay (O 28.1) of positive pions, the outgoing muons are polarized against the direction of their momentum and in the muon decay reaction. 

Typical xSR spectrum (number of detected positrons against muon lifetime). The exponential muon decay is superposed upper spectrum) by a signal oscillating with the muon precession frequency v (x B. The lower spectrum shows the slowly relaxing asymmetry curve with the exponential removed... 

Another method of orientating an emitter in its initial state and then observing the angular correlation of the subsequent radiation is used in /tSR spectroscopy. First a pion decays into a muon and a mesonic neutrino. This process determines the spin polarisation of the muon at the time of its creation. Subsequently after a mean lifetime of approximately 2.2 x 10 s the muon decays into a positron, a leptonic neutrino and a mesonic antineutrino. 

G i) by taking into account the electromagnetic corrections to muon decay, in the Fermi model, using the formula (Behrends et ai, 1956 Kinoshita and Sirlin 1959) ... 

We will return to the latter diagrams when discussing in detail the eflfect of weak radiative corrections in muon decay. 

Again, at present, it may be better to use the relation (8.5.26) coming from muon decay, so that... 

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