2.1.1 Properties of $\mu^+$

For later reference, a brief summary of the properties of the muon is included at this point.

The positive muon ($\mu^+$) is a lepton, the heavier analogue of the positron. It is unstable, and decays via the weak interaction with lifetime $\tau_\mu$ into a positron and two neutrinos:

The branching ratios to other decay channels are less than 2%. Some properties of $\mu^+$ are given in Table 2.3.

$$\mu^+$$ e^- p^{+ 13}C

$$\mu s \gt 4.3\times10^{23} \gt 1.6\times10^{25}$$ Lifetime stable

Type lepton lepton baryon nucleus

Mass [MeV/c²] 105.65839(4) 0.5109991(2) 938.2723(3) 12100

Mass [m_e] 207 1 1836 23700

$$5.5\times 10^{-4}$$ Mass [u] 0.113 1.007 13.0

Charge [e] +1 -1 +1 +6

$$\hbar$$ 1/2 1/2 1/2 1/2

$$\mu \mu_B \times 10^{-3} \times 10^{-3} \times 10^{-3}$$ 1.001165923(8)

$$\mu \mu_N$$ 9.021 1838 2.79284739(6) 0.702199

$$\mu \times 10^{-14} \times 10^{-11} \times 10^{-14} \times 10^{-14}$$

$$\mu/k$$ 3.3 672 1.0 0.26

$$\gamma/2\pi$$ 13.554 2802 4.25759 1.07054

caption

[Selected Properties of The Muon and Other Particles] Selected properties of $\mu^+$ and other particles which are important in various magnetic resonance techniques.

Because of the parity violation of the weak interaction, the positron emitted in a $\mu^+$ decay is correlated with the direction of the muon spin at the instant it decays. In detail, the average rate (probability per time) that a positron of energy within $d\epsilon$ of $\epsilon$ is emitted within $d\theta$ of $\theta$, the angle with respect to the $\mu^+$ spin at the time of decay, is

It is this correlation that allows the direction of the spin to be monitored in a $\mu {\cal SR}$ experiment by angle-resolved (often crude) observation of their decay positrons. Typically, no energy resolved measurements are done. All decay positrons (down to some low energy threshold) are treated equally in the data acquisition, effectively causing an average over the range of emitted positron energies (0-52.8MeV).

The technique of $\mu {\cal SR}$ was born with the discovery of the parity violation in muon decay by Garwin, Ledermann, and Weinrich[81]. The discovery of this parity violation has recently been recounted in [82].