18Ne(α,p) simulations: downstream distance of detectors

The problem: populate a resonance in the compound system and observe outgoing protons: what distance for a downstream LEDA gives the optimal energy resolution/efficiency?
The simulation: choose a random point in the gas; calculate beam energy loss up to that point; if the energy is within +- 10 keV of 13.75 MeV (2.5 MeV c.m.?), go ahead with the reaction. (This is a crude but easy approximation to a real cross section function.) Choose a random (isotropic in the lab) direction for the outgoing protons; calculate their energy losses and angular straggling in the gas and the exit foil; calculate where they hit the plane of the LEDA; if their radial position is between 5 and 13 cm, the event is a hit. Add up the total number of hits and divide by the number of reaction events to find the efficiency of LEDA at its chosen position.
Use a gas cell pressure of 150 mbar (113 Torr); length is 8 cm; 6 μm Ni exit foil; test LEDA positions between 10 cm and 30 cm downstream from exit foil.

Here are the energies measured in each strip, for different positions. The + marks represent the average energy deposited in a strip, plotted against the average angle of the hit events (rather than the strip number). The error bars are the standard deviation of the energies in each strip.
As the detector array gets closer, the range of angles covered increases, but so does the spread in energies per strip.



Here's a more succinct way of presenting the same information. The average of all the strips' energies' standard deviations is plotted against the detector position; on the other axis is the total detector efficiency.
It's pretty much a direct trade-off between efficiency and resolution. Since there's no clear optimization, it is suggested that we put the LEDA at 20 cm, to allow adequate time-of-flight measurements.