Gamma ray spectroscopy is a useful tool for analysing the isotopic composition of a radioactive material. The energy of photons in gamma-ray spectroscopy are typically on the order of 10-1000keV, introducing a collection of interactions not observed in traditional optical spectroscopy. These interactions include the degree of penetration through a medium of a specific composition, lead for example, and the energetic dependency on such interactions.
Gamma-ray sources in most cases are the result of a parent nucleus decaying via alpha particle emission, resulting in an daughter nucleus which is in an excited state. The nucleus transitions to the ground state configuration and releases the energy difference as a photon. The shell model of the nucleus best explains this effect, whereby a nucleon is found in a higher shell upon decay and transitions to the lowest unoccupied vacancy. (Front Matter) Figure 1 outlines this process.
As the gamma-rays are not charged particles, they cannot be detected directly, although interactions with matter can produce measurable effects such as the Photoelectric Effect and Compton Scattering. Measuring the intensity of gamma-ray emissions from a source can be completed using the apparatus shown in Figure 2. This setup involves placing a source under a photomultiplier tube (PMT) with a scintillating crystal. Gamma-rays from the source enter the scintillator, where an interaction causes an electron to be ejected into the PMT. The electron is accelerated through several dynodes to a collector plate, with each successive dynode producing greater numbers of electrons of a specific energy. The resultant voltage/current pulse recorded at the detector is proportional to the energy of the incident gamma-ray.
The pulses are shaped through an amplifier, where the height of each peak correlates to the energy of the gamma-ray. This requires the amplifier output to be analysed in steps or small windows of energy. Use of a discriminator circuit can be used to create the range of observed energy. The step is referred to as a channel for which a given energy (pulse height) can be recorded. The range of energy ’viewed’ in a channel can be varied by changing the PMT voltage or the gain of the amplifier, defined as delta E. Therefore, sweeping over a range of channels will detect a range of gamma-ray energies from the sample. This can be accomplished using a multi-channel analyser (MCA). Single photon counting is obtained using this method, hence values are reported as numbers of counts per channel. This obtains a spectrum of energy values which must be calibrated using known values of spectrum features.
Using the above described method, the resolution of the setup depends on several factors such as the voltage of the PMT, number of channels used, amplifier gain and type of scintillator crystal used. Here within the resolution is assessed using the variables which give the greatest control: the PMT voltage and amplifier gain.
The resolution of the scintillator was assessed by varying the voltage of the PMT and adjusting the amplifier gain setting. A sodium iodide crystal was used for the scintillator whilst the MCA was set for 1024 channels and kept constant for all measurements. When assessing the resolution, the 31keV peak found from Cs137 was chosen as it’s shift was observable over a wider range of parameter combinations. The full-width half-maximum (FWHM) was recorded for each peak shift, allowing the resolution to be calculated using : FWHM(keV)/31keV
Variation of the coarse gain setting was used. The gain was varied from 1 to 200, with a constant voltage. Table 1 shows the combination of parameters used for this section.
The voltage was set as low as possible to observe distinguishable peaks for the Cs137 spectrum, with a gain of 60. The voltage was increased by 100V until the PMT’s limit of 1200V. Table 2 shows the combination of paramters used for this section.
The spectrum of available sources was recorded using the highest gain setting with a mid-range voltage (700-900V). Each sample was recorded for 120 seconds using 1024 channels. The results from this section provided a set of peaks over a range of energies that were used for attenuation measurements.
Measurement of the attenuation coefficient for a series of materials of differing density was performed over a range of gamma ray energies. The materials analysed were lead, polyethylene (PE), aluminium and steel. Lead and PE discs of differing thicknesses were used, whilst sheets of steel and aluminium were added to record to attenuation of a variety of thicknesses. This process was repeated for each source. Table 3 shows the corresponding energies and sources that were used in this study. The mass attenuation coefficient was also recorded using density values provided by NIST. Each sample was recorded for 60 seconds using the parameters specific for the source, where the resultant parameters are outlined in the results section. Samples were also subject to the Grubbs test prior to processing (at g<0.05).
Increasing the gain resulted in a linear increase of peak position. The resolution is observed to increase quadratically with gain. These relationships are outlined in Figure 2.
Voltage caused a exponential shift in peak position, whilst the resolution was recorded to increase in a linear manner with respect to PMT voltage. Figure 3 shows this trend.
The complete spectrum for each isotope can be found in Apenndix A of this report. The interpretation of each spectrum is as follows.
The attenuation coefficients of each material with respect to the gamma-ray energy is shown in Figures 4-7 for lead, steel, aluminium and polyethylene. Reference data for each material was also plotted (Kumar 1997). Some measurements did not provide reliable values as the source was either completely attenuated or not affected by the thickness of material. These cases were disregarded to maintain a result which coincided with recordings of attenuated gamma-rays from the source.
Results of the attenuation coefficients were processed by dividing the attenuation by the density of the material. This is shown in Figures 4-7.
An assumption was applied: each attenuating material was treated as if it were comprised of its majority elemental composition. This results in Lead, aluminium, steel and polyethylene being treated as pure lead, pure aluminium, iron and carbon respectively. Plots of the attenuation coefficients are shown in Figures 8 and 9.