Granularity

The gamma rays and positrons of --- this is approximately the energy of the 's from pion beta and decays and 's from as explained in chapter 4 --- were thrown into the apparatus according to the stopping distributions and tracked throughout the detector volumes, keeping track of the location of the energy deposition at each step.

  
Figure: Profiles of the electromagnetic shower spreading in the calorimeter. Shown here are the histograms of the means and FWHM's of the energy deposited by the shower inside a conical fiducial subvolume of the calorimeter. The conical subvolumes are defined by the half-opening angles, . Showers were initiated by photons (solid curves) and positrons (dashed curves) using the Geant simulation package.

The energy deposited was then histogrammed into one degree conical bins concentric with the direction of the original particle's momentum. From figure , it is concluded that:

• The mean of the deposited energy as well as the full width half maximum approach saturation within a cone of half-angle .
• The shower profiles initiated by 's are similar to that initiated by 's particularly in the saturation region of the deposited energy: this is important in controlling the systematic errors which result from the normalization of pion beta events to decays.
• As indicated by the arrow marked 1, if hit centrally, a detector module will receive of the shower energy. At most three detector modules will receive significant portions of the shower. As shown by the arrow marked 7, clusters of 7 detectors constitute excellent trigger elements since almost all of the shower energy is contained within the conical fiducial volumes of seven modules. However, clusters of three are also satisfactory.

Therefore, the building blocks of the two main data triggers, and , are overlapping clusters of seven crystals. To each cluster, there corresponds a symmetric one in the opposite hemisphere. The determination of the clusters and their efficiency in detecting the gamma rays and positrons (of ) which indeed deposit over in the calorimeter, have been thoroughly investigated. The threshold of is selected so as to discriminate against the Michel 's whose spectrum extends up to as explained in chapter 4. 's and 's were thrown into the apparatus and the energy deposited into each cluster was recorded. A total of 100,000 shower histories were collected for each type of particles. The vetoes, due to their role as shower vetoes, are not included in the clustering scheme. In addition, a given module cannot belong to more than three clusters: this avoids the degradation of the PMT signals due to excessive splittings. The efficiency of the clustering scheme in detecting the particles whose shower energies exceed the threshold was defined as follows:

• The total energy deposited into the entire calorimeter is greater than the threshold but none of the clusters receive an energy greater than the threshold.
• The total number of events for which the above condition is true divided by the total number of events with energies above the threshold, determines the efficiency of the clusters.
• The energy distribution of the events which satisfy the above condition was displayed in a text histogram similar to that of figure 6.4 except that the names of the modules were replaced by the actual values of the energy deposited in each of the crystals on an event by event basis. By studying the pattern of the shower spreadings, it was possible to make modifications in the clusters. The new clustering scheme was tested in the same manner.
• After several iterations, the average number of elements per cluster was increased from 7 to 9 and the following results were arrived at: with the threshold at 50 MeV, the clustering scheme was and efficient for 70 MeV photons and positrons respectively. This suggests that, with the present cluster configuration, about seven out of one thousand pion beta decay events will not be detected although these events will deposit more than the threshold energy in the calorimeter.

    
  Figure: The efficiency of the clustering scheme as a function of the trigger threshold. An optimum value for the threshold is .
  

• The clustering method was also tested against Michel decays. The expected efficiency for suppressing these events in a single arm trigger is at 50 MeV. A small fraction () of Michel events will deposit more than 50 MeV in the calorimeter and fire at least one cluster. The performance of the clustering method as a function of trigger threshold is displayed in figure .