Consider the pair of counters *i* and *j* in Fig. 3.11,
analogous to counters *R* and *L* respectively in Fig. 3.10.
In a real experiment
one can define the *raw asymmetry*
*A*_{ij} (*t*) of the appropriately
paired histograms *N*_{i} (*t*) and *N*_{j} (*t*) defined by
Eq. (3.16) as [77]:

where

so that

The motivation behind introducing
*A*_{ij} (*t*) is the elimination of the
muon lifetime (which is a well known quantity)
and the random backgrounds
and
.
In the ideal situation,
the two counters in question are identical
to one another so that the SR histograms recorded by each differ
only by an initial phase. Because the muons travel for some time in the
applied field before reaching the sample, their initial
direction of polarization at the time of arrival in the sample
is field dependent. However,
the difference in phase between histograms is due solely to the geometry
of the positron counters with respect to the sample.
This situation is illustrated in Fig. 3.11.
In the presence of a constant magnetic flux density *B*, the
time evolution of the
muon spin polarization vector
is given in general by

where is the muon spin precession frequency and is the initial phase of the muon spin polarization vector. For counters

(22) |

(23) |

Since then,

(24) |

With the counters

(25) |

Thus Eq. (3.17) becomes:

If and then Eq. (3.26) reduces to:

If , then using Eqs. (3.17), (3.18), (3.19) and (3.27) the

(28) |

2001-09-28