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
Figure 1. Energies at which interactions dominate.
quickly, all the electrons will fall back to the
[Figure taken from reference 2]
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.
Figure 2. Photoelectric effect conceptual drawing.
[Figure taken from unknown source]
Figure 3. Feynman diagram of the photoelectric effect.
[Figure taken from reference 5]
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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.
Figure 4. Compton effect conceptual drawing.
[Figure taken from reference 5]
Figure 5. Feynman diagram of the Compton effect.
[Figure taken from reference 5]
The Compton scattering equation relates the change in photon wavelength,’, to the scattering angle,
, and the Compton wavelength for electrons,c. From this equation, we can calculate the maximum
scattered wavelength,max’, the minimum energy of the scattered photon, E’min, and the corresponding
maximum energy of the struck electron, Eemax, as follows:

’ = +c(1 - cos )
c = xÅ
max’=+2c
E’min = hc/ max’
Eemax = E - E’min
Compton scattering equation.
[Equation taken from reference 5]
Compton wavelength for electrons.
Maximum wavelength.
[Equation taken from reference 5]
[Maximum ’ at cos  = -1]
Minimum scatted photon energy.
[Equation taken from reference 2]
Maximum electron energy.
[Required by conservation of energy]
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.
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Figure 6. Feynman diagram of pair production.
[Figure taken from reference 5]
2
Figure 7. Feynman diagram of pair annihilation.
[Figure taken from reference 5]
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
Figure 8. Photoelectric effect pulse height distribution.
range of possible scattered photon energies overlap
[Figure taken from reference 5]
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.
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Figure 9. Compton effect pulse height distribution.
[Figure taken from reference 5]
Figure 10. Compton effect energies.
[Figure adapted from reference 5]
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.
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Experimental setup
Figure 11. Pair production pulse height distribution.
[Figure taken from reference 5]
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.
Diagram 1. Experimental setup.
[Diagram taken from reference 6]
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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
Diagram 2. Scintillation detector internal amplifier.
energy, the graph can be read as
[Diagram taken from reference 7]
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.
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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.
Diagram 3. Pulse height distribution graph.
[Diagram taken from reference 8]
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
Main
Peak
Upper
shoulder
Lower
shoulder
Expected Energy (Mev)
1.17
1.33
2.50
0.96
1.12
2.28
0.21
0.21
0.23
Figure 12. Cobalt 60 isotope diagram.
[Figure taken from reference 1]
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Figure 13. Cobalt 60 expected distribution.
[Figure taken from reference 3]
Figure 14. Cobalt 60 experimental distribution.
[Figure taken from PCA program output]
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
Main Peak
Upper
shoulder
Lower
shoulder
Figure 15. Cesium 137 isotope diagram.
[Figure taken from reference 1]
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Expected Energy
(Mev)
Measured Energy
(Mev)
0.66
0.65
0.48
0.40
0.18
0.15
Figure 16. Cesium 137 expected distribution.
[Figure taken from reference 3]
Figure 17. Cesium 137 experimental distribution.
[Figure taken from PCA program output]
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.
Figure 18. Sodium 22 isotope diagram.
[Figure taken from reference 1]
Expected Energy
(Mev)
Measured
Energy (Mev)
Main Peak
Upper
shoulder
Lower
shoulder
1.27
1.28
Rest Energy
Kinetic
Energy
0.51
Main - Rest
Main +
Kinetic
0.76
1.52
1.45
Main + Rest
1.78
1.80
Feature
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1.06
0.21
0.50
0.25
Figure 19. Sodium 22 expected distribution.
[Figure taken from reference 3]
Figure 20. Sodium 22 experimental distribution.
[Figure taken from PCA program output]
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.
Figure 21. Cobalt 57 isotope diagram.
[Figure taken from reference 1]
Figure 22. Cobalt 57 expected distribution.
[Figure taken from reference 3]
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.
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Figure 23. Cobalt 57 experimental distribution high energies.
[Figure taken from PCA program output]
Figure 24. Cobalt 57 experimental distribution low energies.
[Figure taken from PCA program output]
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.
Figure 25. Americium 247 isotope diagram.
[Figure taken from reference 1]
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Figure 26. Americium 247 experimental distribution
for high energies.
[Figure taken from PCA program output]
Figure 27. Americium 247 experimental distribution
for low energies.
[Figure taken from PCA program output]
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.
Feature
Main Peak
Upper shoulder
Lower shoulder
Rest Energy
Kinetic Energy
Main - Rest
Expected Energy
(Mev)
2.20
1.97
0.23
0.51
1.18
1.69
Measured Energy
(Mev)
2.20
1.88
For a gamma ray of 2.2
Mev, we expect the
features, including pair
production, shown in the
table to the left.
0.52
Our experimental graph,
Figure 28, shows the
1.72
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.
Figure 28. Neutron howitzer experimental distribution.
[Figure taken from PCA program output]
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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.
The data collected is in agreement with the existence of antimatter. There were several materials for which
there existed a 0.511 Mev peak. For each of these cases, the only possible source of a photon of this energy
is pair production and annihilation.
Acknowledgement
I thank Dr. Bland, without whom this paper would not exist.
References
[1] Lederer, Hollander, and Perlman, Table of Isotopes (1968).
[2] R.A. Dunlap, Experimental Physics (Oxford, 1988).
[3] R.L. Heath, Scintillation Spectrometry: Gamma Ray Spectrum Catalogue, 2 nd Edition, Volume
2 of 2 (U.S. Atomic Energy Commission, 1964).
[4] Chart of nuclides
[5] Lab write up
[6] Website: http://www.wpi.edu/Academics/Depts/ME/Nuclear/Reactor/Labs/L-scin.html
[7] Website: http://jan.ucc.nau.edu/~wittke/Microprobe/WDS-Scintillation.html
[8] Website: http://www.amptek.com/gamma8k.html
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