On the other hand, the disadvantage of the stopped pion technique is that one accepts into the detectors all the Michel positrons from muon decays in the target. In addition, one measures the branching ratio for pion beta decay. Then the decay rate is obtained from the measured branching ratio using the pion life time.
Clearly, the design of the apparatus, especially the size and the cost of
the detectors, is affected by the decay method used. The design of the pion
beta calorimeter stems from a decay at rest method which relies on the
similarity between the and
decays in terms of their systematic
uncertainties. This enables a relative measurement of the pion beta decay rate
without the absolute knowledge of acceptances and conversion
efficiencies for both processes as required in the in-flight technique.
Furthermore, the relative stopped pion technique finds its justification in the
drawbacks to the in-flight technique, particularly the difficulty in
controlling the systematic uncertainties with accuracy in an absolute
measurement of the pion beta decay which occurs with a probability of