Muon lifetime

For the case of muonium, nonresonant spin precession in a magnetic field provides a copious source of information about its crystallographic sites and the associated unpaired electron distribution around them (see Chapter 15). Here, the concentration of muons is always too low for molecule formation, and migration to impurities and implantation defects can be kept small by the short muon lifetime and use of pure material and low temperature. 

In high purity silicon below T = 140 K the Mu center is stable on the time scale of the muon lifetime (2.2 ps). However, in electron irradiated silicon Westhauser et al. (1986) have reported that Mu is metastable and makes a thermally induced transition to Mu at a temperature of 15 K. A similar transition between Mu and Mu was first discovered in diamond (Holz-schuh et al., 1982, Odermatt et al., 1988) and will be discussed in Sec-... 

But one can ask the question why normal muonium is observed at all if the global energy minimum (i.e., the stable site) is really at the bond center (anomalous muonium). On the time scale of the muon lifetime, relaxations of the Si atoms may be sufficiently slow to effectively trap the muon in the low-density regions of the crystal, where relaxation of the host atoms is... 

For obtaining (8) it was assumed that the Avtl lifetime is determined by the pion and muon lifetimes. 

A relatively new technique which is being increasingly applied to the study of magnetic materials is that of muon spin rotation [jliSR also known as muon spin relaxation or resonance (Schenck 1985)]. In the most common arrangement a beam of spin polarized muons ju,+ (say) is directed towards and stopped in a target. The anisotropy in the ju, - e decay rate (e.g., from a comparison of the rate in backward and forward directions) is monitored as a function of elapsed muon lifetime for a large number of stopped muons. The basic equation on which the technique is based is... 

Long-time deviations from exponential decay have also been sought in particle physics. For a review of experiments up to 1968, see Nikolaev [9]. More recent attempts have similarly failed to detect any deviation. Tomono et al. [109] made precise measurements of the muon lifetime. Their experiment stopped at 17 /xs, around 8 muon lifetimes, whereas theoretical models predict deviations to occur only at times beyond 200 /xs. Novkovic et al. [110] have measured the decay of Au up to 25 lifetimes, also finding no evidence for nonexponential decay. 

D. Tomono, S.N. Nakamura, Y. Matsuda, M. Iwasaki, G. Mason, K. Ishida et al.. Precise muon lifetime measurement at RIKEN-RAL and prospects at a high intensity muon source, Nucl. Inst. Meth. A 503 (2003) 283. 

The "raw" time spectrum obtained in a SR experiment is not yet in a form suitable for input to a Fourier transform, as explained in the previous Section. The original time spectrum, except for a time-independent background fraction B, is weighted by a normalization factor whose initial value is Nq, but which decays exponentially with the muon lifetime Although these uninteresting factors are... 

This procedure is nothing more than application of a digital filter with an exponential time constant equal to twice the muon lifetime. Figure 7 shows the effect of this transformation on the data of Figure 6. Shorter time constants for the exponential filter may be appropriate for short-lived signals, in order to discriminate against noise at later times however, broadening of the peaks in the Fourier spectrum is an unavoidable and undesirable consequence. 

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... 

The measurement of absolute beam velocities, or the calibration of voltages, is already quite sensitive to the relativistic quadratic term in the Doppler shift formula (7). In fact, this transverse Doppler shift, caused by the time dilatation factor y = (1 - j8 )" , was first observed in the spectral lines of fast-moving hydrogen atoms from a 30-keV beam of H2 ions, viewed along and opposite the direction of propagation. Comparable accuracy in the percent range was also achieved in Mossbauer experi-ments, and more recently the time dilatation factor on the muon lifetime was determined to 1 x 10". ... 

To this end, G is defined from the very accurate measurement of the muon lifetime n —> e + Ue + for this reason it is sometimes labelled... 

The very precise measurement of the muon lifetime (Particle Data Group, 1992) gives... 

Historically, G was defined from the muon lifetime as calculated in the Fermi current-current model together with photonic radiative corrections, so that the amplitude is given by the Feynman diagrams following eqn (4.2.33). 

Higher order effects can be evaluated by using renormalization group arguments (Marciano, 1979) which lead to the replacement 1 + Ar — 1/(1-Ar) so that (7.4.2) for the muon lifetime becomes... 

A similar phenomenon occurs in a non-minimal model when considering the muon lifetime. Consistency with the Fermi theory will lead once again to (4.2.32)... 

The muon lifetime of 2.2 ps sets a natural limit of 0.45 MHz on the widths of, aSR lines. The nominal frequency resolution is given by the inverse length of the histogram. Using pulsed machines it is not uncommon to observe the FID over a time window of 20 ps, which leads to a nominal resolution of 0.05 MHz. 

The muon lifetime is long compared to the atomic time scale so that experiments in bound atomic systems can be carried out just as in "normal" atoms. 

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