Shower Clusters Reconstruction

The purpose of the shower clusters reconstruction in each of Preshower and Shower of the shower detector is:

• Define all clusters of fired blocks, which belong to the showers, registered in the detector;
• Calculate parameters of showers in the detector: energy deposition of showers, $X$ and $Y$ coordinates of the shower center;
• Set parameters and identifier of the, so called, ``main'' cluster.

Cluster in the shower detector is determined as follows:

• Cluster is a group of continuous blocks;
• Cluster can occupy maximum 6 ($2\; \times 3$) blocks in the case of Preshower and 9 ($3\; \times 3$) blocks in the case of Shower;
• Central block is defined as block that has maximum energy deposition.

The ``main'' cluster in Preshower/Shower is the cluster with the biggest energy, which is coincident with the ``golden track'', or coincident with some Shower/Preshower cluster. Coincidence of cluster with ``golden track'' means, that distance between the shower cluster center and crossing point of ``golden track'' with detector plane is less than a certain magnitude. Coincidence of Preshower and Shower clusters means, that distance between the clusters centers is less than a certain magnitude, in assumption, that both of this points are considered on the same $Z$-plane.

Shower clusters reconstruction in Preshower and Shower is performed by the following steps:

1.

Sort detector fired blocks in order of its energy deposition values decreasing;

2.

Pick out the block with maximum energy deposition and all fired blocks in it's arrangement ($2\; \times 3$ blocks for Preshower, $3\; \times 3$ blocks for Shower), as belong to one cluster;

3.

Remove all of blocks, associated in cluster, from following consideration;

4.

Repeat steps 2 and 3, while all of fired blocks will be associated into any cluster;

5.

Calculate energy deposition, $X$ and $Y$ coordinates of each cluster and sort clusters on its energies decreasing order;

6.

Define coordinates of crossing point of ``golden track'' with detector plane in detector local coordinate system;

7.

Analyze geometrical position of the ``golden track'' point on the detector plane and clusters centers in order to determine the ``main'' cluster and to set it parameters and identifier.

Energy deposition $E$, $X$ and $Y$ coordinates of the shower center are calculated by the formulas:

where: $i$ -- number of detector block, included into the cluster; $M$ -- set of blocks numbers, included into the cluster; $e$_i -- energy deposition in the block $i$ of detector; $x$_i , $y$_i -- $X$ and $Y$ coordinates of center of the block $i$ of detector.

Shower clusters reconstruction algorithm described above, has been realized by program tot_shower (see sec.3.2).