Decay of negative muons bound in ${}^{27}\mathrm{Al}$

We present the first measurement of the energy spectrum up to 70 MeV of electrons from the decay of negative muons after they become bound in ${}^{27}\mathrm{Al}$ atoms. The data were taken with the TWIST apparatus at TRIUMF. We find a muon lifetime of $(864.6\pm 1.2)\mathrm{ns}$, in agreement with earlier measurements. The asymmetry of the decay spectrum is consistent with zero, indicating that the atomic capture has completely depolarized the muons. The measured momentum spectrum is in reasonable agreement with theoretical predictions at the higher energies, but differences around the peak of the spectrum indicate the need for $\mathcal{O}(\alpha )$ radiative corrections to the calculations. The present measurement is the most precise measurement of the decay spectrum of muons bound to any nucleus.

Figure 1

Side view of the TWIST spectrometer planar chambers and support structures. Muons stopped in the target foil, which also served as a chamber cathode. The spectrometer is symmetric about the target foil, immersed in a uniform 2.0 T solenoidal field aligned with the beam axis.

Figure 2

Reconstructed muon decay time spectrum. The decay time binning is 10 ns and the fit range 500 to 7500 ns (error bars not shown).

Figure 3

Decay energy spectrum. For comparison, the appropriately normalized TWIST ${\mu }^{+}$ spectrum is shown as well as the spectrum calculated by Watanabe et al. [23]. Most error bars are smaller than the symbols and are not displayed. The inset shows the high-energy tail of the spectrum on a logarithmic scale (with error bars). The numerical values are tabulated in Table 1. An overall energy scale error of $2\times {10}^{-3}$ is not included.

Figure 4

Relative spectrum differences. The difference between the measured and calculated spectrum is normalized to the theoretical spectrum. The $\mathcal{O}(\alpha )$ radiative corrections [49] are normalized to the free muon decay spectrum with an end point of $\approx 52.8\mathrm{MeV}$.