Observation of gamma ray interactions with matter
Elizabeth Manrao
Physics and Astronomy Department, San Francisco State University,
1600 Holloway Avenue, San Francisco, Ca 94132
Abstract
I outline an experimental procedure for the observation of interactions of gamma rays with matter. There are three primary ways in which gamma rays interact with matter; the photoelectric effect, the Compton effect, and pair production. Each of these three interactions releases photons of different energies. When the pulse height distribution is taken of a given material, these different energies create specific features on the pulse height distribution graph. By understanding gamma ray interactions, one can draw connections between the pulse height distribution graphs and the radioactive decay of materials. Features are observed which confirm the existence of the anti-electron.
1 Introduction
During the process of the radioactive decay of isotopes, gamma rays are released. These rays interact with matter in a variety of ways. Each of these interactions produces photons of different energies. The probability of each of these interactions depends on the energy of the incident photon as shown in Figure 1. At low energies, the Compton effect dominates, and at high energies pair production dominates.
The Photoelectric Effect
When a gamma ray is incident on a solid, a single electron absorbs the incident photon and becomes excited to the conduction band as shown in Figures 2 and 3. This excited electron will collide with other electrons, sharing the energy. This will result in many electrons excited to the conduction band, each with roughly the same energy. Eventually, these electrons will fall back to the more stable ground state. When this occurs, each will emit a photon with energy approximately equal to the band gap. Because this process happens so quickly, all the electrons will fall back to the ground state at roughly the same time. The lag in time between transitions is not detectable by the devise used in this work. This results in the recording of an energy release proportional to that of the incident photon.
The Compton Effect
When a gamma ray collides elastically with an electron, the electron absorbs some of the energy, and the photon continues in a new direction with less energy and a longer wavelength as shown in Figures 4 and 5. The amount of energy absorbed by the electron is dependent on the scattering angle of the collision. If the photon skims the top of the electron, minimum energy will be transferred. If the photon hits the electron straight on, maximum energy will be transferred. In general, the energy transfer is related to the scattering angle. When maximum energy is transferred to the electron, the rebound photon has maximum wavelength and minimum energy. The excited electron will eventually fall back down to ground state, releasing the energy it absorbed from the collision.
The Compton scattering equation relates the change in photon wavelength, (l’-l), to the scattering angle, f, and the Compton wavelength for electrons, lc. From this equation, we can calculate the maximum scattered wavelength, lmax’, the minimum energy of the scattered photon, Eg’min, and the corresponding maximum energy of the struck electron, Ee-max, as follows:
Pair Production
A gamma ray may spontaneously change into an electron and positron pair as shown in Figure 6. When this occurs, 0.511 Mev of the incident gamma ray energy goes to creating the rest energy of each particle. The remainder of the energy is released as kinetic energy. After some time, the electron and positron will recombine releasing two photons each of energy 0.511 Mev as shown in Figure 7. Overall, three separate photons are produced, two of energy 0.511Mev, and one carrying the balance of the energy.
2 Experimental method
In this experiment, we will compare the pulse height distribution from various radioactive isotopes with the expected distribution suggested by isotope diagrams. Isotope diagrams show the decay process of a particular radioactive material. As an unstable nucleus decays to ground state, it released a photon of a specific energy at each transition. The isotope diagrams tabulate the probability of each transition, and thus the probability that a photon of a particular energy will be emitted.
When these emitted photons come in contact with a solid they will interact with the matter in one or more of the three ways described above. Each type of interaction creates a specific feature on the pulse height distribution.
The photoelectric effect creates the highest energy peak on the graph as shown in Figure 8. These peaks will be at energies corresponding to the incident photon energies released during decay. These values can be read directly from the isotope diagram. If there are two consecutive transitions that the isotope must make to reach ground state, the two photons may superimpose created a “sum peak”.
The Compton effect results in a range of energies of both the resultant photon and the electron creating a Compton shoulder as shown in Figure 9. The range of possible electron energies and the range of possible scattered photon energies overlap for a specific range of energies. We expect small peaks at the energies corresponding to the minimum scattered photon energy and maximum electron energy as shown in Figure 10. These two energies are produced when the photon hits the electron straight on. We expect a dip between the maximum electron energy and the main peak because the electron cannot possibly attain these energies during the Compton effect. The Compton shoulder can be predicted by calculating the minimum scattered photon energy and maximum electron energy as described in Section 1.
Pair production and annihilation will result in two small peaks at energies 0.511 Mev and 1.022 Mev away from the main peak as shown in Figure 11. The spacing of these peaks is due to the fact that during pair annihilation, two photons each of energy 0.511 Mev are released. In addition, there may also be a small peak at 0.511 Mev corresponding to a single pair annihilation photon.
3 Experimental setup
In this experiment, the radioactive isotope is placed in a scintillation detector as shown in Diagram 1. As a radioactive material decays, it releases gamma rays with specific energies. These rays interact with the matter encasing them in one or more of the ways described above resulting in gamma rays of various energies. These rays, in turn, react with a scintillating crystal within the detector. The crystal produces a flash of light whenever it is struck by a gamma ray. The intensity of this flash of light is proportional to the energy of the ray incident on it. The light impulse is amplified by the photomultiplier within the detector resulting in an amplified signal exciting the detector as shown in Diagram 2. The scintillation detector is powered by a high voltage source.
The signal is further amplified by an external amplifier and is then passed to a pulse height analyzer which records the count of each light intensity. This count is graphed on the computer using a PCA graphing program. The graph created is the pulse height distribution for the material. Because the light impulse is proportional to the gamma ray energy, the graph can be read as energy vs. number of counts as shown in Diagram 3. A high count means that there are more photons being released with a particular energy. During this experiment, we must keep in mind that some photons may escape the detector and will not be accounted for. However, the probabilities of each type of interaction should correspond to the peaks recorded.
4 Results and discussion
Using this experimental setup, we looked at a variety of radioactive materials to determine if there was, in fact, a connection between the expected transitions and the pulse height distribution graphs.
Cobalt 60
By looking at the isotope diagram in Figure 12, we see that the majority of the time cobalt will decay to ground by two transitions. The first releases 1.17 Mev and the second releases 1.33 Mev.
We expect three main peaks due to the photoelectric effect; 1.17 Mev, 1.33 Mev, and the sum peak 2.50 Mev. By calculating the maximum electron energy absorbed from the Compton effect, we see that the Compton shoulders should be as listed in the table below. We notice that the shoulders for the two transition peaks are spaced closely together and are near to the 1.17 Mev peak. This will result in a more flattened distribution. We do not expect the shoulders to be pronounced. Also expected from the Compton effect we have the small peak corresponding to the minimum scattered photon energy. The expected distribution is shown in Figure 13.
Feature / Expected Energy (Mev)Main Peak / 1.17 / 1.33 / 2.50
Upper shoulder / 0.96 / 1.12 / 2.28
Lower shoulder / 0.21 / 0.21 / 0.23
We mainly used Cobalt 60 for calibration of our program. We set the three main peaks at the predicted 1.17 Mev, 1.33 Mev, and 2.50 Mev. Using these calibrations, we found at small peak located at 0.21 Mev. This value agrees well with the expected value listed above. The experimental graph is shown in Figure 14.
Cesium 137
The isotope diagram predicts only one likely transition for Cesium 137 to the ground state as shown in Figure 15. Therefore, the photoelectric effect will result in one main peak at 0.66 Mev. As with Cobalt 60, the incident energies are too small to for pair production to occur. The expected result is shown in Figure 16
Using the calibrations obtained form Cobalt 60 we measured the energies of these features. The results are given in the table below and in Figure 17. While agreement between expected and experimental values is generally good, the shoulder at 0.40 Mev is much too low.
Feature / Expected Energy (Mev) / Measured Energy (Mev)Main Peak / 0.66 / 0.65
Upper shoulder / 0.48 / 0.40
Lower shoulder / 0.18 / 0.15
Sodium 22
There is only one likely transition of sodium 22 to the ground state as shown in Figure 18, so we will have one main peak at 1.27 Mev. The Compton shoulder and the scattered wave peak is shown below. For pair production, two photons each of 0.511 Mev and one photon of 1.27-1.02=0.25 Mev will be released. We expect our two subsequent peaks as shown in the table and Figure 19.
Again using the Cobalt 60 calibrations, we found peaks at locations corresponding to the pair annihilation photon, the photoelectric effect, a sum peak of the main peak and the balance photon energy, and finally a sum peak of the main peak and the pair annihilation photon. See Figure 20. Again, the values do not perfectly match those calculated, but they are at approximately the correct placement.
Feature / Expected Energy (Mev) / Measured Energy (Mev)Main Peak / 1.27 / 1.28
Upper shoulder / 1.06
Lower shoulder / 0.21
Rest Energy / 0.51 / 0.50
Kinetic Energy / 0.25
Main - Rest / 0.76
Main + Kinetic / 1.52 / 1.45
Main + Rest / 1.78 / 1.80
Cobalt 57
There are three likely transition energies; 0.14 Mev, 0.12 Mev, and 0.01 Mev shown in Figure 21. Looking at the two larger peaks, we expect the shoulders to be at 0.08 Mev and 0.09 Mev. See Figure 22 for the expected distribution. The two larger peaks were predicted perfectly using the Cobalt 60 calibrations, see Figure 23.
Focusing on smaller energies, we see three peaks; 6 Kev, 14 Kev, and 30 Kev. These respectively correspond to a K shell doublet, which is outside the scope of this paper, the smallest phase transition peak, and the minimum ray energy peak from the larger transitions. See Figure 24 for experimental distribution.
Americium 247
A look at the isotope diagram reveals five possible phase transitions and thus five possible incident photon energies; 26, 33, 43, 60, 103 Kev. See Figure 25. Looking at our experimental graph we see a very distinct peak at the largest energy, See Figure 26. This is due to the 103 Kev transition. Zooming in on the smaller energies, see Figure 27, we measure two twin peaks at 26 and 33 Kev as expected for two other transition peaks. Due to the low energies of these transitions, it is difficult to decipher much more from the graphs.
Neutron Howitzer
A neutron howitzer is a Pu-Be Source. Plutonium 239 decays into uranium 235 and an alpha particle. The alpha particle then combines with beryllium to form carbon 12 and a neutron. The neutron combines with a proton to form a deuteron and a gamma ray. This gamma ray has an energy found from the binding energy of the deuteron and has a value of 2.2 Mev.
For a gamma ray of 2.2 Mev, we expect the features, including pair production, shown in the table to the left.
Our experimental graph, Figure 28, shows the expected pair production peaks, the Compton shoulder, and the main peak. We also found another set of transition peaks.
The other main peak is at 4.31 Mev with a shoulder at 4.02 Mev and subsequent peaks at 3.35 Mev and 3.83 Mev. The origin of this 4.31 Mev gamma ray is unknown.
5 Conclusion
Due to the limitations of the equipment used in this experiment, it is impossible to get exact values from the experimental graphs. We are able, however, to look at the experimentally produced graphs and determine that they do in fact qualitative match that expected given the known decay process of various radioactive materials. The experimental data is in agreement with the theoretical calculations of gamma ray interactions.
In addition, we see that there are sources of energy that are not accounted for by the three gamma ray interactions discussed in this paper. Namely, we saw graphical features due to a K shell doublet, and an unknown source in the neutron howitzer.