The main sources of systematic uncertainties have been stated in in the previous section. The size of the systematic uncertainties is determined by the accurate calculation of the following:
Figure: The line-shapes of photon-induced showers in CsI as calculated by GEANT, ITS and EGS4 (top panel). The calculations of the three codes show excellent agreement, especially in the region above the threshold of . The bottom panel shows the response of the plastic veto counter to showers initiated by photons which originate in the target. Here too, the results of the three different calculations agree remarkably well.
After a careful optimization of the tracking medium parameters, a remarkable agreement was observed between the results of the three simulation codes. The profiles of the shower spreadings as calculated by GEANT, are shown in figure . The top panel of figure shows the line-shape in CsI of photon-induced showers. In the region above the threshold of , the agreement between the calculations of the three different codes is excellent. The integrated detection efficiencies above agree to , which is remarkable. Similar agreement is found for the energy leaked through the back of the calorimeter.
The response of the plastic veto counter to showers initiated by photons originating in the target is presented in the bottom panel of figure for ITS, GEANT and EGS4. This response is a combination of the processes (3) and (4) and affects the overall detection efficiency for pion beta decays. The integrated yields above minimum ionizing particle (MIP) threshold differ by of the total number of shower histories. However, raising the threshold by 0.4 MeV improves the agreement to about between ITS and GEANT results and between ITS and EGS4 calculations.
Figure: The top panel is the total shower backsplash as calculated by the three different codes. This is the total energy flow back across the front face of the CsI detector. The response of the thin plastic veto detector to this backsplash is displayed in bottom panel. A very small fraction of the backsplash consists of charged particles.
To isolate the process (3), the monoenergetic photons were thrown perpendicularly incident onto the CsI detector with their origin at the front face of the CsI detector. A fraction of the showers proceed in the direction opposite to that of the original photons and flows back across the front face of the CsI detector. This shower backsplash is shown in top panel of figure . ITS and Geant calculations of the energy flow back across the front face of the CsI detector agree to better that in an integrated yield above 1 MeV. The EGS4 result is higher by almost one percent. The plastic veto counter is the first detector encountered by the shower backsplash; the response of this counter to the backsplash is shown in the bottom panel of the same figure and is the more relevant quantity from the standpoint of corrections to the detection efficiency. A very small fraction of the backsplash consists of charged particles, i.e. less than of the histories registered above the MIP threshold. The integrated yields above the MIP threshold differ by less than of the total number of histories for GEANT and EGS4 calculations. However, the ITS result is slightly higher at large deposited energies.
In conclusion, the processes which affect the detection efficiency of pion beta
decays occur at the level of few percent probability. A remarkable agreement
has been observed in the calculations of detection efficiencies using GEANT,
ITS and EGS4. Depending on the process considered, the three different
calculations agreed at the level of few per mill of better. Since these
calculations were carried out, GEANT has been the only code used for the
simulations of the various processes affecting the design of the apparatus.
This has been due to the fact that the GEANT simulation code includes the most
comprehensive geometry package and interfaces with CERN
library routines. These systematic uncertainties will have to be
evaluated experimentally during the set-up and calibration parts and monitored
throughout the data taking process.