Software Algorithms

The purpose of the shower cluster reconstruction in the Preshower and the Shower detector is to:

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Define all clusters of fired blocks, which belong to the showers, registered in the detector;

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Calculate parameters of showers in the detector: energy deposition of showers, $X$ and $Y$ coordinates of the shower center;

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Set parameters and identifier of the so-called ``main'' cluster.

Cluster in the shower detector is determined as follows:

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Cluster is a group of continuous blocks;

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Cluster can occupy a maximum of 6 ($2 \times 3$) blocks in the case of Preshower and 9 ($3 \times 3$) blocks in the case of Shower;

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Central block is defined as the 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 the cluster with the ``golden track'' means that the distance between the shower cluster center and crossing point of ``golden track'' with the detector plane is less than a certain magnitude. Coincidence of the Preshower and Shower clusters means, that distance between the clusters centers is less than a certain magnitude (it is assumed that both of these points are on the same $Z$-plane).

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

1. Sort fired blocks in order of decreasing deposited energy;
2. Pick out the block with maximum energy deposition and all fired blocks in its arrangement ($2 \times 3$ blocks for Preshower, $3 \times 3$ blocks for Shower), as belonging to one cluster;
3. Remove all blocks associated with the found cluster from further consideration;
4. Repeat steps 2 and 3, until all of the fired blocks are associated with a cluster;
5. Calculate energy deposition, $X$ and $Y$ coordinates of each cluster and sort clusters by decreasing energy deposit;
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 cluster centers in order to determine the ``main'' cluster and to set its parameters and identifier.

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

$$E=\sum_{i \in M}e_i\ ,\ \ \ \ X=\sum_{i \in M}e_i \cdot x_i/E\ ,\ \ \ \ Y=\sum_{i \in M}e_i \cdot y_i/E\ ,$$

where: $i$ -- number of detector block, included in the cluster; $M$ -- set of blocks numbers, included in the cluster; $e_i$ -- energy deposition in block $i$ of detector; $x_i$, $y_i$ -- $X$ and $Y$ coordinates of center of block $i$ of detector.

The shower cluster reconstruction algorithm described above has been implemented by the ESPACE analysis subroutine tot_shower. A complete description of the program as well as information about the ESPACE routines and kumac files used to perform the analysis, photographs of the detectors and more information can be found at the URL:

http://www.jlab.org/ãrmen/sh_web_page/sh_page_init.html