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Experimental Motivation for Scintillator Tomography

 

In order to calibrate the GEANT Monte Carlo simulation of the PIBETA detector response, it is necessary to account for the light output and position-dependent nonuniformities of each CsI crystal in the calorimeter. These quantities are entered into the simulation as a smearing factor and a spatially dependent weighting function in the crystal energy depositions. This chapter discusses the experimental techniques used to measure the light output and nonuniformities of the crystals, and the results of the measurements.

The light output, expressed in terms of number of photoelectrons per MeV deposited by minimum ionizing particles, can be measured by making use of the fact that the photoelectron statistics follow a Poisson distribution. Such a distribution is a limiting form of the binomial distribution
equation829
where p is the probability of success in a single trial, N is the number of trials, and P(r) is the probability of r successes in N trials. The Poisson distribution arises in the limiting case where tex2html_wrap_inline5152 and tex2html_wrap_inline5154, and takes the form
equation835
where tex2html_wrap_inline5084 is the mean. This distribution lends itself to the description of photoelectron statistics because of the low probability for a charged particle to interact with one scattering center, combined with the presence of a large number of scattering centers inside one CsI crystal. In a Poisson distribution, the standard deviation tex2html_wrap_inline5158 is equal to the square root of its mean. Consquently, if one represents the light output in the CsI crystal as the number of photoelectrons per MeV tex2html_wrap_inline5160 times the energy deposited by minimum ionizing particles E, then one can deduce
equation842
Using this relation, one can extract the number of photoelectrons per MeV from the slope of a graph of sigma squared plotted against energy.

The light output nonuniformities are measured through the transmission tomography of the CsI crystals, using high energy cosmic muons as the probe. By determining the light output and muon trajectory length in the crystal, one can calculate the spatial light output nonuniformity, normalized over pathlength. This can be done in both the longitudinal and transverse directions. These directions correspond to the z and x axes, respectively, which are shown in Figure 3.1.

  figure848
Figure 3.1: Geometry and coordinate system for a hexagonal CsI crystal. The Z axis represents the longitudinal direction, and the X axis represents the transverse direction.


next up previous contents
Next: Experimental Apparatus Up: Tomography of Scintillators Previous: Tomography of Scintillators

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