Isotropic Sampling for detector geometry efficiency

_Geant4 Version: 4-11.2
_Operating System: Windows 11
_Compiler/Version: Visual Studio 17.9
_CMake Version: 3.29.2


I am pretty new to Geant4 and am hoping someone can help with a project I am trying to simulate. I have been able to construct a world volume that is a rectangular box of 6.1m L x 6.1m W x 1m H, and place my detector geometry, which is a 12.5cm W x 14.5cm L x 4.0cm H scintillator on top of a 25cm W x 38cm L x 2cm H sheet of lead, which then sits on top of a much larger 30.0cm W x 48.0cm L x 4.0cm H scintillator, such that it is centered at x, y (0, 0) and the bottom of the bottom scintillator is at the bottom of the world box, -0.5m.

I need to fire geantinos isotropically towards randomly sampled x, y positions at the planar surface of the bottom of the world box, and record how many of the geantinos go through BOTH the top and bottom scintillator. The goal is to determine the efficiency of the setup by sampling all possible directions a geantino could induce a coincidence, then take the ratio of coincidence counts to the total number of generated geantinos, and multiple that by the 6.1m x 6.1m sample area to get the efficiency.

I have tried looking online for examples that are similar to this, but I have not found much. Can someone assist me with this, or point me in the right direction a GitHub example or something similar? Thank you.

Here is my setup for the isotropic radiation field.

/gps/pos/type Surface
/gps/pos/shape Sphere
/gps/pos/centre 0 0 0  m
/gps/pos/radius xxx cm
/gps/ang/type cos
/gps/ang/surfnorm true
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