One of the goals of the analysis is the particle identification by cluster
recognition. In order to reconstruct the angle(s) of incidence I first
studied the angular resolution of our detector.
The idea is simple, looking for the mean of the shower distribution to reconstruct the point of incidence and compare it with the thrown angle in the simulation. To do so, I threw positrons uniformly all over the detector array of last summer's run and looked for the crystal which had a contribution to the total energy if the maximum was within the 'inner' crystals. Since the shower develops in a cone touching some neighboring pyramids the portion of energy contributed from a crystal was weighted by some exponent a < 1 . So the formula to reconstruct the point of incidence becomes where q is the fraction of energy Ei/Etot . Now a was to be optimized.
Therefor an angle g was defined describing the deviation of the reconstructed position from the thrown position. This angle is given by and had to be minimized by varying a. Looking for the mean of the distribution of g, a was found to be 0.71 .
This gave an angular resolution of 3.7 degrees.