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Shower Origin Reconstruction Algorithm

  In order to determine kinematically the momentum of the photons from the reaction tex2html_wrap_inline4804, it is necessary to find the location of the photons' entry into the calorimeter. In addition, it is useful to know where the resulting electromagnetic shower originates, so that the neighboring crystal detectors may be identififed, and appropiately summed or ignored (see Chapter 6).

The origin of the shower is reconstructed from the CsI and NaI crystal ADC values (data) or energy depositions (simulation) using a geometric weighting algorithm. The algorithm works by first finding the fraction of energy tex2html_wrap_inline5452 deposited in each crystal,
equation1345
where the sum in the denominator includes all CsI or NaI detectors. Next, the coordinate x is calculated according to the weighting formula
equation1350
  where tex2html_wrap_inline5360 is the coordinate of the ith crystal, dx is a correction based on the angle of incidence of the particle with the detector array, and the exponent tex2html_wrap_inline5462 is a constant which is defined by the nature of the shower development in the CsI and NaI arrays. The coordinates tex2html_wrap_inline5360 of the crystals in the NaI array are defined in a Cartesian coordinate system, while those in the CsI array spherical. The values of tex2html_wrap_inline5466 and tex2html_wrap_inline5468 are determined by optimizing the average angular resolution of each crystal array in the GEANT Monte Carlo simulation. This optimization is discussed in Sec. 5.2.



Penny Slocum
Fri Apr 2 00:36:38 EST 1999