Cluster size definition

  In order to study efficiently the effect of cluster size on the above three items, the algorithm allows for convenient cluster size variation. A cone of opening angle  is defined, with its apex at the center of the detector (See Fig. 6.1).

  
Figure 6.1: Cone of opening angle  to define size of cluster.

The cone opens from the center to intersect a solid angle segment of the calorimeter, centered around the previously reconstructed origin of the electromagnetic shower. This shower origin is found through an iterative combination of the shower reconstruction process discussed in Chapter 5, and the cone algorithm discussed in this chapter. The steps to reach the final cluster definition, beginning with the shower reconstruction algorithm, are as follows:

1. The CsI crystal detectors with the highest three ADC values of the array are identified.
2. Using only the ADC values from these three crystals, the shower origin is calculated according the procedure described in Chapter 5.
3.   A cone of opening angle  is placed around the shower origin, in order to select a cluster of crystals.
4.   Using the ADC values from the cluster in step 3, the shower origin is reconstructed again.
5. Finally, the cone of opening angle  is placed around the shower origin from step 4, which defines the cluster of crystals which is used to complete the optimization study.

By implementing this algorithm, and recording the number of CsI crystals which are intercepted by the solid angle cone for each opening angle , one can see the characteristic number of crystals selected for various cluster sizes. Figure 6.2 shows the number of crystals included in three cones of differing opening angles .

  
Figure 6.2: Number of crystals intersected by the cone used for cluster definition, for three different opening angles  of the cone.