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** Up:** 3.2 Measuring the Internal
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Now consider the complete set of four positron counters in Fig. 3.1.
Ignoring geometric misalignments and differences in counter efficiency,
the *x*-component of the muon polarization *P*_{x}(*t*)
[monitored by the *L* and *R* counters]
differs from the *y*-component of the muon polarization *P*_{y}(*t*)
[monitored by the *U* and *D* counters] by a phase of .
The two components of the muon polarization can be combined to form a
``complex'' polarization function

| |
(25) |

where
| |
(26) |

and

The complex asymmetry for the four-counter setup is defined as

where *A*_{x}(*t*) and *A*_{y}(*t*) are the real and imaginary
parts of the complex asymmetry, respectively. The number of counts
per second in the *i*^{th} counter (*i* = *L*, *R*, *U* or *D*) is
| |
(27) |

where is the asymmetry function
for the *i*^{th} raw histogram. Rearranging Eq. (3.29)
gives
| |
(28) |

In terms of the individual counters, the real asymmetry
*A*_{x}(*t*) and the imaginary asymmetry *A*_{y}(*t*) are

In this thesis the real and imaginary parts of the asymmetry were
fit simultaneously, assuming a phase difference of between
them.

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** Up:** 3.2 Measuring the Internal
** Previous:** 3.2.3 The Relaxation Function