Measurement of the Polarization of the Muon Beam for the SMC Experiment.

A high energy muon beam polarimeter for the SMC experiment at CERN is described, as is the analysis of the beam polarization. The polarization is determined using the shape of the energy spectrum of the positrons from the decay mu^{+}--> e^{+}nu_{e}| nu_mu which is described by the Michel spectrum. The parent muon is tagged upstream of a field-free decay region and its momentum is measured. A 30 m long muon decay path is defined between a shower veto hodoscope which identifies the mu^ {+} and a dipole analyzing magnet. The spectrometer includes the dipole magnet and several multi -wire proportional chambers which measure the momentum of the e^{+}. Identification of decay positrons is based on the energy deposited in a lead glass calorimeter. Muon polarization can be determined with 60 hours of data-taking to a statistical accuracy of 0.03 and a systematic uncertainty of the same order. Hence the muon beam polarization of ~eq-0.8 is measured to 5% relative accuracy.