Search for the lepton-family-number nonconserving decay μ^{+}→e^{+}γ

The MEGA experiment, which searched for the muon- and electron-number violating decay ${\\ensuremath{\\mu}}^{+}\\ensuremath{\\rightarrow}{e}^{+}\\ensuremath{\\gamma},$ is described. The spectrometer system, the calibrations, the data taking procedures, the data analysis, and the sensitivity of the experiment are discussed. The most stringent upper limit on the branching ratio, $\\mathcal{B}({\\ensuremath{\\mu}}^{+}\\ensuremath{\\rightarrow}{e}^{+}\\ensuremath{\\gamma})l1.2\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}11}$ with $90%$ confidence, is derived from a likelihood analysis.