In the Geant simulation code, the user is expected to provide the information regarding the geometry of the set-up and its position in the master reference frame where the tracking is performed. In the master reference frame, the user also supplies the kinematical information about the reaction under study. In addition, the user must make the necessary arrangement for the read out of the desired quantities. The information needed to run the simulation code is supplied via subroutines where the user is free to take any action.
In the case of the pion beta calorimeter, the nine different shapes were defined and positioned as displayed in figure . The pentagonal shape, being the only regular geometry, was simple to define.
Figure: The pion beta apparatus as defined and positioned in Geant for the simulations of the reactions relevant to the experiment and the design and understanding of the triggers. Shown here from the center, are the active target, the plastic veto detector and the calorimeter. The pentagons, the hexagons and the vetoes were each defined as two entities which are patched together to get the correct geometries: this process was necessary due to the difficulty in defining irregular objects in Geant. This segmentation in Geant reveals one property of the geodesic breakdown: from a pentagon center to another pentagon center, one can see portions of geodesics as explained in section 6.1
The other shapes, especially the hexagons have been defined as two trapezoids which were patched together to reproduce the original hexagons. The half hexagon D's were defined as trapezoids. The shower vetoes, due to their peculiar geometry, were also defined as two trapezoids connected together. The pentagons, although they can be single entities, were defined as two geometries patched together as shown in figure .
Once the shapes were defined, the next step in constructing the simulation code was the rotations and translations necessary for positioning each module in order to generate the calorimeter. This was a straightforward task since the rotation angles and translation vectors follow as the result of the geodesic breakdown described in section 6.2. The kinematics parameters for the pion beta process or other reactions of interest were set-up in the appropriate user subroutine and the energy deposited within each of the modules was recorded at the end of each track or whenever necessary during the tracking process via another user subroutine. The tracking medium parameters---their optimization is very important to interpret accurately the simulation results---were adjusted to reflect fine tracking step size and low tracking cut-offs for all shower particles. The light collection non-uniformity and the photoelectron statistics which have been measured during the pion beta test runs, were taken into account for more realistic simulations. A complete simulation code is described in appendix C and one simulated pion beta decay event is shown in figure .
Figure: A cut view of the calorimeter and the simulation of one pion beta decay event in Geant. The two photons from decay are the blue dashed lines emerging from the target. The photons reach the calorimeter where they initiate electromagnetic showers all of which are contained within the modules. The (the red line in the target) from pion beta decay annihilates in the target with an atomic electron. The two gamma rays resulting from the annihilation process are also shown as blue lines coming from the target. The red lines are charged particles.