Muon spin rotation for $\mu ^{+}$

Precession of the muon in a weak and variable magnetic field can introduce a time dependant modulation of the time distribution of the measured muon decay, if there is any efficiency for the detection system that varies with the electron decay angle. The distortion depends on the muon spin polarization coefficent and the decay asymmetry. We have observed this effect and we have empirically corrected the time spectrum to minimize the resulting $\chi^2$ with an excellent fit. To first order the cylindrical symmetry of our detector eliminates this effect, however we wish to reduce it further by actually measuring both the polarization and the residual detection assymetries within our detector.

We will apply a uniform 70 Gauss field perpendicular to the beam direction with the coils described previously. This field precesses the remaining free muon polarization at 1 MHz causing an easily fittable sinusoid on top of our decay spectrum. Both the amount of polarization and the decay of that polarization will be fit and removed from the decay curve. In the case that there is a small transverse polarization or our coils are not perfectly aligned we will also rotate the coil set by 90$^0$ to fully resolve the polarization vector and correct for it. One other reason for rotating the field is to spin the polarization past the other half of the detector so we can measure the differential efficiencies of each opposing element of our detector.

Little or no polarization should exist in the $\mu^-$ experiment. However, we will look for polarization effects in both $\mu^-$ and $\mu^+$. The primary plan is to use the magnetic field to allow us to check the $\mu^+$ lifetime reference with the same setup used for the $\mu^-$ capture experiment. Though the magnet is not necessary for the $\mu$ capture part we intend to leave the magnet in place for both runs so that the experiments would have been done in identical situations. In the outer position scattering in the magnet materials will not significantly affect our traceback resolution.