Radiative Decay of the Muon

The radiative decay of the muon, ${\mu }^{+}\to e^{+}+\gamma +{\nu }_e+{\overline{\nu }}_{\mu }$, has been measured using muons from the Columbia University Nevis synchrocyclotron. The decay products $e^{+}$ and $\gamma$ were observed at relative angles near 180°, using scintillation counters and two 9-in.×10-in. NaI crystals, which enabled simultaneous measurement of the positron and $\gamma$ energies. The pulses from the crystals were displayed on oscilloscopes and photographed, and the measured amplitudes of these pulses were calibrated using the positron spectrum of the nonradiative decay. The two-dimensional energy spectrum for positrons and $\gamma$'s was obtained for about 900 events, after subtraction of background. This spectrum and the measured rate, obtained by normalizing to the nonradiative decay, were compared with theoretical predictions for the radiative decay. The results were in good agreement with the theory, within statistics, for the case of pure $V-A$ coupling.