S15GammaRaySpectroscopy

Investigating Edge Effects in Gamma-ray Spectroscopy

Abstract

The goal of this project was to investigate the effect the position of a gamma ray source relative to a detector crystal has on the measured spectra produced. A Monte Carlo simulation was written to predict these changes and be compared to the experimental data. The simulation predicted no measurable change in spectra dependent on the location of the source, except for changes in distance from the detector. The experimental data confirmed this, although the poor reliability of the detector limited the strength of conclusions made.

Theory

A gamma ray is produced when a nucleus changes from a higher energy state to a lower energy state through the emission of electromagnetic radiation.

The fundamental phenomenon behind gamma ray spectroscopy is scintillation, the process by which gamma rays interact with certain materials to produce photons in the visible spectrum. The distance a gamma ray travels through a substance is related to the energy of the gamma ray and the material properties of the substance, and is given by the probability distribution:

where s is the distance traveled, n is the number of atoms per unit volume, and

is the interaction cross-section of an atom of the material, a function of the atomic number of the material and the energy of the incident gamma ray that determines the probability of an interaction.

The primary gamma source used in this project was Cs

, which produces gamma rays at an energy of 0.662 MeV. At this energy, the primary way gamma rays interact with the scintillator is via either Compton scattering or the photoelectric effect [3]. The photoelectric effect is more probable to happen at lower energies, and is when an incident gamma ray is completely absorbed by an atomic electron, which excites then de-excites and releases a visible spectrum photon. Compton scattering, more likely at higher energies, is an elastic collision between a photon and an atomic electron that results in the gamma ray being scattered in a new direction after the interaction and the electron being freed from its atom. The gamma ray deposits some fraction of its energy to the electron in this interaction, dependent upon the scattering angle:

is the mass of an electron, and is the scattering angle.

Once freed, the electron travels a short distance through the scintillator dissipating its energy to other electrons, exciting these electrons and causing a small cascade of ionization in the area surrounding the initial interaction. These electrons then de-excite and emit a number of scintillation photons in the visible spectrum. These visible spectrum photons, created from either a photoelectric or Compton interaction, move essentially freely through the crystal before interacting with a photo-diode, causing a measurable electrical signal.

Changing the position of the gamma source with respect to the crystal has two primary effects on the scintillation interactions: moving the source further away will simply reduce the number of interactions, as the source emits isotropically, but moving the source around the crystal changes where the interactions are likely to occur within the crystal. This has potentially interesting consequences. If an interaction occurs very near the edge of the scintillator crystal, some of the electrons excited in the ionization cascade can escape the system before emitting a photon, changing the measured spectrum. Exactly how this could effect the spectrum is what this experiment sought to measure.

Apparatus

The experimental setup for this project was relatively simple. The scintillator we used was a small crystal of Cesium-Iodide. An avalanche photo-diode was set against the top face of the crystal using optical gel to ensure good transmission of photons from the scintillator to the diode.

This assembly was wrapped first in Teflon tape, both as a means of securing the diode to the crystal and to provide a reflective coating to reduce loss of photons, and then in opaque electrical tape to reduce the number of photons in the scintillator from sources other than scintillation. The wrapped crystal is shown below.

The signal from the photo-diode is fed through a board with an amplifier circuit, provided by the aerospace department, to amplify the signal to within the 1-10 V range that is detectable by the Ortec EASY-MCA multi-channel analyzer we used. This MCA then digitizes the signal and sorts the voltages of the signals from each event into bins, and then the Maestro program (the proprietary software bundled with the EASY-MCA) displays the spectrum and records the data for later analysis. The amplifier board is shown below.

Simulation

Using the theory outlined above we wrote a Monte Carlo simulation in C++ to simulate the interaction of gamma rays within the scintillator. A Monte Carlo simulation is a simulation in which a single set of parameters is simulated numerous times, each time only changing the variables that are given by probability distributions. The algorithm we implemented is based heavily on that given by Arqueros and Montesinos, and is outlined below.

Basically, the simulation generates a gamma object, then computes how far it travels until an interaction. It then chooses what interaction takes place, Compton or photoelectric, and simulates the energy deposition accordingly. The specifics of this are all outlined comprehensively in reference [3]. The C++ source code for the code is attached. It currently compiles (compiler used for project was the C++ compiler in GCC 4.9.2) and creates two files, interactions.csv and locations.csv. interactions.csv is a list of energies, and when a histogram is made of this data (a python script SimplePlotSim.py that does this is also attached, although it would be simple enough to use MATLAB or similar) a simulated spectrum such as that shown below is created:

locations.csv is a list of the locations in Cartesian coordinates of where all of the interactions took place. It does not distinguish between the Compton events and the Photoelectric events took place. When the PlotLoc.py script is used to plot this data one finds a graph like that shown below, simulated for a situation where the source is underneath the crystal. Basic notes on running simulation: c_gamma.cpp has the ITERATIONS constant that determines how many times the Monte Carlo is run; this is currently set at 1000. 1,000,000 was used to produce the spectrum shown above. globals.cpp has a bunch of global constants in it, including fundamental constants and crystal dimensions. Check the python scripts for what libraries are required.

Results

The following spectra were produced in two back-to-back runs so as to minimize the change in background counts.

As one can see from the diagrams the real world predicts a few differences depeding on the placement of the source. However, the two trials are not in complete agreement with each other. Note especially the differences in the "side" configuration. All of our data had similar anomalies which proved that it was essentially unrepeatable. Once we figured out what was causing the problem (the jostling of the APD) we were able to minimize the effects it had on our experiment, but as one can see we weren't able to completely get rid of them.

The fact that our data is unrepeatable as well as the spectra predicted by the simulation, which can be seen below. Suggest that in fact the small movements of the peak we see are just errors from our jostling of the APD when moving the source.

As one can see the simulation makes no prediction that these slight changes in position have any noticeable effect on the spectrum produced.

Conclusions

By knowing that the finer parts of our data is unreliable, and that our simulation predicts no such change in the spectra produced allows us to come to the conclusion that the various positions cause no real difference in the spectrum produced. Therefore, we can conclude that the "edge effects" we were trying to see are essentially negligible.

This makes sense when one considers the plot above of the simulations predictions where the interactions take place inside the scintillator. As one can see from that diagram the majority of the interactions take place a few cm directly away from the source and fall off significantly as one moves farther away. In order for an interaction to deposit some of its energy outside the system it needs to be a few mm away from an edge. Only a very small percentage of interactions actually occur close enough to the edge for this to happen, which means any "edge effects" caused by the position of the source are essentially drowned out by the rest of the normal events.

If we did want to see some of these minute changes in the spectra we think in the future we should use a higher quality lab grade detector system. We ran one test with such a system to see how well it would agree with our simulation. The results can be seen below.

As one can see not only does this NaI scintillator have a higher resolution and less noise it also agrees with some of the smaller details predicted by our simulation. If we had to do this experiment again we think it would be smart to use a lab grade detector instead of a student built one.

References

[1] Crouthamel, C.E., and F.Adams. \textit{Applied Gamma-ray Spectrometry,}. 2d ed. Oxford:Pergamon, 1970. Print

[2] ''Development of the low-cost multi-channel analyzer system for γ-ray spectroscopy with a PC sound card''. Sugihara, Kenkoh and Nakamura, Satoshi N. and Chiga, Nobuyuki and Fujii, Yuu and Tamura, Hirokazu, American Journal of Physics, 81, 792-797 (2013), DOI:http://dx.doi.org/10.1119/1.481624

[3] ''A simple algorithm for the transport of gamma rays in a medium''. Arqueros, F. and Montesinos, G. D., American Journal of Physics, 71, 38-45 (2003), DOI:http://dx.doi.org/10.1119/1.1509416

[4] ''Avalanche Photodiodes''. (n.d.):n. pag. Laser Components. Web