< How to detect spin polarization | Index | Transverse field >
Let us build the simplest possible experimental setup: we place two positron detectors in front of the sample, one in the muon spin direction (F for forward) and one in the opposite direction (B, for backward).
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With spin polarized muons the F detector will count more and the B detector less than with unpolarized muons. If we simply count events vs. the lifetimes of the individual muons, we shall record rates that follow an exponential decay with mean lifetime {$\tau_\mu=2.2\, \mu\mbox{S}$}
{$ (1) \qquad\qquad dN(t) = N_0\, e^{-t/\tau_\mu}\, (1+A \cos\theta) dt\,d\theta$}
The unpolarized muon rate, {$N_0\,e^-t/\tau_\mu$} is the black curve, the polarized F and B detectors are color coded. Note that the polar plot below is for the maximum asymmetry, {$ A(52.8MeV)=1$}, whereas the count rates on the right are shown for the average asymmetry {$\overline A = 0.33$}
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In order to obtain the count rates of a real experiment Eq. 1 must be integrated over a finite time bin and over the solid angle covered by the detector. Both integrations lead to an average, i.e a reduction of the observed asymmetry from the theoretical {$\frac 1 3 $} value.
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< How to detect spin polarization | Index | Transverse field >
