Figure: Response of the
calorimeter to 
decay events for three
different detector thickness: 10, 12 and 14 radiation lengths. These
calculations include the effects of light collection nonuniformity and
photoelectron statistics. The calorimeter response to accidentally coincident
Michel events is also shown. The actual thickness of 
was selected as
a compromise between the cost and the energy resolution of the calorimeter.
The thickness of the calorimeter was determined after Monte Carlo simulations
of its response to pion beta events. Different thicknesses of 10, 12, and 14
radiation lengths 
) were considered during the simulations which included
the effects of photoelectron statistics and light collection nonuniformity.
The detection efficiency as a function of the thickness varied
between 
(for 
) and 
(for 
). However, the higher
thickness gave a better energy resolution (see figure 
) which
is necessary in
isolating the pion beta process from the background. Therefore, 
is a
better choice for the thickness of the calorimeter whose volume, consequently
the cost, increases with the cube of the outer radius. The actual thickness of
was selected as a compromise: the energy resolution is worse but the
cost of the calorimeter is less by 
than what it would be for 
.