Two sets of detectors are placed on either side of the beam line, facing
a 6.35mm thick copper plate, 17.5 degrees from the beam line, 3 meters
from it, as shown below. A third detector set sits in the beam line.
The beam spot is a clipped Gaussian, with sigma=5cm but clipped to radius
1.25cm. This corresponds to a distant point source with divergence
(like a bremstrahlung radiator or laser backscattering with an electron
beam, two of the main methods of producing gamma rays), which is subsequently
collimated (literally a chunk of metal with a hole).
The on-axis detectors are intended to measure the absolute flux, mostly to calibrate the count rate in the off-axis detectors. One off-axis detector, which we will call the gamma detector, is intended for detecting gamma rays from atomic Compton scattering. The other, which we will call the beta detector, is intended for detecting the recoiling electron from that reaction.
Each package consists of a sodium iodide (NaI) detector, a NE102 plastic
paddle scintillator in front of it, and an iron collimator to define the
package's acceptance. The NaI detector consists of the NaI crystal,
25.4 cm in diameter and 25.4 cm long, contained in an aluminium container
with the front face 1.6mm thick, and remaining walls 6.4mm thick.
The paddle counters are 3.2mm thick, is square and has the same width as
the external diameter of the NaI casing. The collimator is 10 cm
thick, and has the same width and height as the NE102. There is a
17.78 cm circular hole in the center. We will ignore the photomultiplier
You will need to define some new materials, "NE102" and "NaI". NE102 is composed of 1 part carbon, and 1.1 part hydrogen, and has a density of 1.032 g/cm3. NaI is obviously 1 part Na and 1 part I. It has a density of 3.67 g/cm3. Since there don't seem to be any predefined entries for them, use the GEANT GSMIXT [CONS110] command instead of the usual GMAT in ugeom.f. Be sure to use material numbers not already in use. Also, since the 3 detector packages are identical, you can use the copy features of GEANT in ugeom.f and gustep.f.
Ultimately, we want to count the number of events that have simultaneously "hit" the gamma and beta detectors, and compare that against the flux measured in the on-axis detector. A "hit" in each detector is determined if sufficient energy is deposited in it, and if the particle identification indicates the correct type. In principle, we can swap the role of the beta and gamma detectors, but for the sake of simplification, we will fix them.
Start with looking at histograms of the energy
deposition in each paddle counter and in each NaI.
The level at which to choose the energy, or discriminator, threshold of the NaIs will have to be ascertained by examining these histograms for trial runs. It should be low enough to accept as many valid events as possible, yet high enough to avoid the low energy events which are undesirable. Keep in mind that your assessment may change after introducing conditions as discussed below. Determine the efficiency by also keeping track of events with the proper energy at the entry point of the NaI. The proper energy is determined by using the Compton formula with the electron as the target (mass=0.511 MeV), incident energy 10 MeV, and scattering angle 17.5 deg.
The particle identification will be determined by the energy deposition in the plastic paddle counter. If the deposition is above a threshold, it will be considered an electron, or beta particle; below that we will assume it is a gamma. The threshold will be initially determined by trial runs, similar to the NaI threshold, and may be refined with additional conditions applied. Basically, we know from previous exercises that electrons will deposit a fairly characteristic amount of energy in a thin volume, so that will determine the upper limit of the threshold. The lower limit will depend on how many intermally converted gammas you are willing to accept or reject. Looking at the NaI spectra in conjunction with the paddle conditions, and vice versa, may clarify the thresholds. Determine the efficiency of identification by also maintaining statistical information of particle types at the entry point of the paddle counter, and then comparing against your detection statistics at the end.
Once you have determined viable thresholds, you should also try to determine raw count rate of all detectors, and the "single arm" count rate of gammas and of electrons for each detector package. The latter will give you a baseline for the final coincidence count rate, and both give us an idea of how close to the limit the electronics will be pushed(e.g. dead time problems). Then generate histograms of both NaIs when the coincidence of both arms is demanded. Of course, extract the count rate, too.
The number of events (triggers) depends on the statistical uncertainty of the quantities in question. A ratio of standard deviation:mean of 3% would be good and 1% would be very good. We assume Poisson distribution for these count rate experiments, so the latter means accumulating about 10,000 counts for the quantity in question. For example, if only 1 event in 1000 resulted in a "coincidence" between the gamma and beta NaI's, then one would have to run 1000*10,000=10,000,000 triggers. However, if there is any background subtraction, error propagation will increase the required count and thus the required triggers. As a result, some Monte Carlo simulations can run a very long time, and some effort to improve the efficiency of the code could save time in the long run.
You may very well find that the coincidence of the two arms is very inefficient. One reason could be that the copper target is so thick that it is absorbing most of the useful electrons. To verify this, change the thickness of the copper target from 6.4mm to 3.2mm and then to 1.6mm. If the count rate drops by less than a factor of 2 and 4, respectively, it is conceivable that the loss of absolute counts could be offset by better signal to noise that a coincidence provides (compared to running in single arm mode).
Another reason for poor efficiency could be that the electrons are being multiple scattered out of the optimum acceptance. To determine this, generate a 2D histogram that maps phi versus theta of particles at the same distance as the electron detector on the electron side of the beam in coincidence with gammas hitting the gamma detector. If this is a serious problem, then the electron detector probably should be moved closer to the target. Determine how close, considering any trade-offs between efficiency and background levels.
Then change energies and determine the rates of Compton events and on-axis events. Do this for 20, 10, 5, and 3 MeV. Find out if there is an energy dependence for the ratio of count rates and of the detector efficiencies. Also of interest is the possibility of modifying the configuration, particularly by using a plastic counter only on one arm, so also observe the behaviour of the paddle counters. Observe the frequency of 2 charged particles being detected instead of a gamma and a beta. Would it be possible to two paddle counters alone to track the beam flux?
By doing the Compton kinematics calculation, you will find that the angles of the off-axis detectors should have have been changed, increasing as the incident energy drops. In addition to the runs at 17.5 degrees, and do one series with the angles compensated for the energy changes. Compare the responses.
At higher energies, the cross sections fall so low that this symmetric
layout is too inefficient. To compensate, one of the arms needs to
be kept at a small angle and the other at a relatively wide angle.
Place the gamma detector at 10 degrees, and calculate what angle the electron
detector must be at for an incident energy of 50 MeV. Determine the
energy of the scattered electron. Based on what you find with the
phi versus theta 2D histogram, will the electron detector have to be moved
closer to the target? Is the energy of the electron too low?