Measurement of the Gamma-Ray Spectrum from Radiative Muon Decay

The energy spectrum of the gamma rays emitted by inner bremsstrahlung in the muon decay process, ${\mu }^{+}\to e^{+}+\nu +\overline{\nu }+\gamma$, has been measured by means of a large sodium iodide crystal. Only those gamma rays which were time-coincident with the decay electrons were recorded. These decay electrons were detected in a scintillation counter telescope adjoining the crystal counter. The counter geometry permitted detection of events with angles between the electron and gamma ray in the range from 0° to 26°. The muons were obtained by stopping a positive pion beam in a block of material. By measuring the gamma-ray spectra from muons originating first in carbon and then aluminum, a correction could be made for bremsstrahlung externally produced by the decay electrons. The measured spectrum is in agreement with that predicted by the theory with an average ratio of 1.02±0.10.