Separate muon, electron, and tau numbers are conserved in the minimal standard model of electroweak interactions with massless neutrinos. However, in many extensions to the standard model, separate lepton numbers are not expected to be conserved quantities. A new search for muon number non-conserving processes has been undertaken at the Los Alamos Meson Physics Facility (LAMPF), specifically to look for three neutrinoless decay modes of the muon. The search for the decay of a muon to an electron and a photon is discussed here. A new detector facility, located in the LAMPF stopped muon channel, was developed for this experiment. This Crystal Box detector consists of a cylindrical drift chamber surrounded by a plastic scintillator hodoscope and a large solid angle, modularized, NaI(Tl) calorimeter. The apparatus measures the trajectories, relative timing, and energies of charged particles and photons from the decays of positive muons stopped in a central target. The assembly and calibration of the detector are described, and the procedure for taking data is discussed. The sample of 1.3 million candidate events, from the first data run of the Crystal Box, was analyzed using a maximum-likelihood method. The upper limit on the branching ratio, relative to normal muon decay, for a muon decaying to an electron and a photon is found to be consistent with previous measurements. With 90% confidence, the branching ratio for this neutrinoless decay is observed to be less than 2.8 x 10/sup 10/.
