About 
following the pion stop, a time window known as the
delayed pion gate (DPG), of 
is
opened. The pion gate is delayed in order to avoid prompt interaction
processes such as elastic scatterings or pion charge exchanges. Within this
time window, pion beta decay is registered as a detection
in coincidence in the shower calorimeter, of the two gamma rays (with energies
exceeding the Michel endpoint) which originate from the decay of the neutral
pion. Following the delayed pion gate, another time window is opened; however,
this time window is mostly sensitive to Michel events as shown in
figure 
and can be used to understand their rate and the energy
distribution.
Figure: Time
spectra of Michel and 
events. The
Delayed Pion Gate (DPG) is opened 
ns after a valid 
stop in
order to avoid Prompt (P) interaction processes.
and 
events are
registered during the DPG. Following the DPG, the DPG Prime (DPG') is mostly
sensitive to Michel decays. The accurate branching ratios are not taken into
account in these pictures. The temporal distribution of
event is similar to that of the
events, the only difference being in the
branching ratios of both decays.
Normalization is performed with the 
events registered
within the DPG as the detection in the calorimeter of the single arm showers with
total energy exceeding that of the Michel positrons. The relative measurement of the
pion beta decay is possible because of the similarity between the showers produced by
photons from 
and by positrons from 
as shown in
figure . As a result, the detector acceptance and response to the
events are very similar to those of the
events so that the differences in systematic uncertainties are small and
manageable. To account for the difference in the branching ratios the
events need to be prescaled.
Figure: Simulated calorimeter responses to 
photons and
positrons. The similarity of the responses can be used to do a relative
measurement of the pion beta decay rate by normalizing to
events and accounting for the differences in
the acceptances and the branching ratios.
Experimentally, the pion beta decay rate is given as the ratio:
where 
is the pion lifetime, the N's represent
the respective numbers of good 
and 
events and
is the prescale factor for the 
trigger. The above corrections
include ratios of the following quantities for the two triggers respectively:
events are due to the fact the
two gamma rays from a pion beta event are not collinear. As explained in
chapter 4, the deviation from collinearity reflects the spread in the recoil
energy of the original 
.
's from 
decay which did not
deposit any energy in the calorimeter. A fraction of the gamma rays traversing
the shower calorimeter escape detection because they do not convert and
therefore do not initiate showers.
decays loose some energy in the
target and suffer net defections from their original directions via multiple
scatterings. The energy losses and the deflections depend on the points of
origin of the positrons, i.e., the stopping distributions. This results in
further differences in the acceptances for pion beta and
decays.
