Longitudinal muon spin relaxation in high-purity aluminum and silver

The time dependence of muon spin relaxation has been measured in high-purity aluminum and silver samples in a longitudinal 2 T magnetic field at room temperature, using the time-differential muon spin relaxation technique. For times greater than 10 ns, the shape fits well to a single exponential with relaxation rates of ${\lambda }_{\text{Al}}=1.3\pm 0.2\hspace{0.5em}(\text{stat.})\pm 0.3\hspace{0.5em}(\text{syst.})\hspace{0.5em}{\text{ms}}^{-1}$ and ${\lambda }_{\text{Ag}}=1.0\pm 0.2\hspace{0.5em}(\text{stat.})\pm 0.2\hspace{0.5em}(\text{syst.})\hspace{0.5em}{\text{ms}}^{-1}$.

Figure 1

Schematic for the experiment. A collimated muon beam enters from the left and muon decays are recorded in one set of histograms if they are detected only by the first scintillator (TM1), stopping mostly in the Ag mask, or in another set of histograms if they are recorded by both scintillators (TM1 and TM2), mostly stopping in the target. The backward positron counter (B) is protected from the muon beam by a collimator. Materials such as the photomultiplier tubes and light guides are not shown.

Figure 2

Depolarization for the CS (Gd${}_2$Ti${}_2$O${}_7$). (a) Relative polarization and (b) normalized residuals. The fit is $P_{\mu }(t)/P_{\mu }(0)=\exp (-\lambda t)$ to data from set E, with $\lambda =(0.860\pm 0.004)\hspace{0.5em}\mu {\text{s}}^{-1}$ and the ${\chi }^2$/(number of degrees of freedom) $=$ 285.5/302.

Figure 3

Results for fits to the metal samples. (a) $\lambda$ for Al, (b) $\lambda$ for Ag, (c) $r$ for Al, and (d) $r$ for Ag. Sets F and G had multiple runs. The parameter $r$ is highly sensitive to target placement, which occurred at the beginning of each set.

Figure 4

Aluminum relative polarization vs time. (a) Full time range, (b) first 6 $\mu$s, and (c) normalized residuals from fit. The fit is $P_{\mu }(t)/P_{\mu }(0)=\exp (-\lambda t)$ to one run of set F, with $\lambda =(1.5\pm 0.5)\hspace{0.5em}{\text{ms}}^{-1}$ and the ${\chi }^2$/(number of degrees of freedom) $=$ 280.6/304.

Figure 5

Silver relative polarization vs time. (a) Full time range, (b) first 6 $\mu$s, and (c) normalized residuals from fit. The fit is $P_{\mu }(t)/P_{\mu }(0)=\exp (-\lambda t)$ to one run of set G, with $\lambda =(1.5\pm 0.5)\hspace{0.5em}{\text{ms}}^{-1}$ and the ${\chi }^2$/(number of degrees of freedom) $=$ 300.2/304.