chew boon kiat
TRANSCRIPT
Optimization and Implementation of
low-background Gamma Spectrometry using
HPGe Detector in Environmental
Radioactivity Research
Author : Boon Kiat Chew
Supervisor: Dr Taw Kuei Chan
Co-supervisor : A/P Thomas Osipowicz
A Honours Thesis submitted in
partial fulfilment of the requirements for the
Degree of Bachelor of Science with Honours
Department of Physics
Faculty of Science
National University of Singapore
Academic Year 2014/2015
Abstract
We are interested in the ability of the high-purity Germanium (HPGe) de-
tector in detecting low-level gamma energies. We first did a energy calibra-
tion for the HPGe detector using a Eu-152 sample. Using this calibration,
we found the efficiency, energy resolution, minimum detectable activity and
minimum detectable mass for the detector. We then did a back-calculation
to find the activity of another Eu-152 sample. We also took a reading of rice,
flour, milk powder and soil.
Acknowledgement
I would like to thank Dr Chan and A/P Thomas for their invaluable help for
this project, where they would often draw time out from their busy sched-
ules for project meetings. I would also like to thank them for their patient
guidance and advice, for without which this project would not have been
possible.
1
Contents
Contents 2
1 Motivation 5
1.1 Environmental Effects . . . . . . . . . . . . . . . . . . . . . . 5
1.1.1 Chernobyl Nuclear Disaster . . . . . . . . . . . . . . . 5
1.1.2 Fukushima Daiichi Nuclear Disaster . . . . . . . . . . . 9
1.2 Radionuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Nuclear Plans In Asia . . . . . . . . . . . . . . . . . . . . . . 13
2 Theory 16
2.1 Gamma radiation . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.1 Compton Effect . . . . . . . . . . . . . . . . . . . . . . 17
2.1.2 Photoelectric Effect . . . . . . . . . . . . . . . . . . . . 18
2.1.3 Pair Production . . . . . . . . . . . . . . . . . . . . . . 18
2.1.4 Processes In Detector . . . . . . . . . . . . . . . . . . . 20
2.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . 25
2
CONTENTS CONTENTS
2.3.1 Semiconductor Detectors . . . . . . . . . . . . . . . . . 25
2.3.2 High Purity Ge Detector . . . . . . . . . . . . . . . . . 29
2.3.3 Pre-amplifier . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.4 Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.5 Multichannel Analyser . . . . . . . . . . . . . . . . . . 36
3 Data Analysis 38
3.1 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Background Spectrum . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Energy Peak Efficiency . . . . . . . . . . . . . . . . . . . . . . 47
3.5 Limit Of Detection . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6 Back Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 Samples 57
4.1 Food Products . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Soil Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Conclusion 63
Appendix A Gamma Vision 65
Appendix B Tables 70
B.1 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . 70
B.2 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . 71
3
CONTENTS CONTENTS
B.3 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
B.4 Minimum Detectable Activity . . . . . . . . . . . . . . . . . . 72
Bibliography 73
4
Chapter 1
Motivation
1.1 Environmental Effects
With the usage of nuclear energy, there is a chance that radionuclides can be
accidentally released into the environment. Studies have been made to study
the effect of nuclear accidents on the environment, and more importantly, to
humans. There have been two notable nuclear accidents that had resulted in
the release of large amounts of radionuclide into the environment, Chernobyl
and Fukushima Daiichi.
1.1.1 Chernobyl Nuclear Disaster
The Chernobyl nuclear disaster in 1986 resulted in large quantities of radioac-
tive particles being released into the atmosphere. resulting in radioactive con-
tamination of the surrounding environment. Environmental contamination
5
1.1. ENVIRONMENTAL EFFECTS CHAPTER 1. MOTIVATION
can result in direct exposure of radioactivity to humans, or indirect exposure
through contaminated food. Studies have been done after the accident to
study the effect on the environment and humans.
One study by the IAEA in 2005 found that most of the radionuclide re-
leased during nuclear accidents have short half-lives.1 Smaller amounts of
the long-lived radionuclide were released. Out of the short-lived radionu-
clide, radioactive iodine is a cause for concern as it will accumulate in the
thyroid after ingestion. For radionuclide with long half-lives, Cs-134 and
Cs-137 are important contributors to radioactive contamination. Other ra-
dionuclide have deposition levels were too low to cause a problem, or have
low transfer ratio of soil-to-plant to cause real problems in agriculture.
In urban areas, open surfaces such as roads and roofs became contaminated
with radionuclide. However, the water solubility of caesium resulted in high
Cs-137 activity around houses, where the rain had transported the Cs-137
from the roofs to the ground. Additionally, cleaning process lead to the sec-
ondary contamination of sewage systems. The nuclear incident also lead to
contamination of food products. Initially, milk was the main contributor to
internal dose due to large amounts of I-131 being released. The radioiodine
deposited on plant surfaces were grazed by dairy cow. Radioiodine ingested
is absorbed in the gut and is then transferred to the animal’s thyroid and
milk within a day. During this period, the I-131 activity concentration in
6
1.1. ENVIRONMENTAL EFFECTS CHAPTER 1. MOTIVATION
milk in affected regions exceeded regional action levels by a few hundred to
a few thousand Becquerel per litre. In Russia and Ukraine this lead to sig-
nificant thyroid dosage to those who consumed milk, especially children. In
the long run, milk was contaminated with radiocaesium.
Contamination of plant products happen over two phases. Initial contami-
nation was due to the direct deposition of radionuclei onto the plants. After
direct contamination, plants uptake radionuclei through contaminated soil,
hence continuing to pose a health issue. Cs-137 and Cs-134 where especially
problematic due to its solubility in water, was well as it being used by the
plant in place of other minerals such as potassium. The highest levels of
contamination with radiocaesium was observed in mushrooms, due to their
tendency to accumulate mineral nutrients, such radiocaesium. For animals,
the radionuclides circulate in the blood after ingestion. Some accumulate in
specific organs, for instance, radioiodine accumulates in the thyroid, whereas
radiocaesium is distributed throughout the soft tissues.
Hence it was found that I-131 and Cs-137 in meat, milk and plant products
are the most important contributors to human internal dose. However, due to
the long half-life of Cs-137, the activity concentration in these food products
have been decreasing slowly. The decrease in activity concentration is about
3 to 7 percent per year. This means that Cs-137 will continue to contribute
to human dose for years to come.
7
1.1. ENVIRONMENTAL EFFECTS CHAPTER 1. MOTIVATION
Another study of foodstuff in Poland has found that I-131, Cs-134 and Cs-
137 were the main contributors to activity in foodstuffs.2 The contamination
with I-131 decreased quickly after June 1986. The only considerable con-
centrations observed were for Cs-134 and Cs-137. It was found that the
radiation contamination of fruits and vegetable remains the same after a
few years. However, the higher radioactivity still remains in milk and forest
mushrooms. This agrees with the finding of the previous report.
Figure 1.1: Cs-137 activity in milk. It can be seen that activity is decreasingslowly, and has not returned to pre-accident levels.
For cases of transference of radionuclei from soil to grass to animals, milk
is an ideal liquid to dissolve the radionuclei.3 This is because milk contains
fat, while also existing as an aqueous solution, Therefore, both fat-soluble
and water-soluble contaminant can be found in milk as it offers both envi-
ronments. This is important as milk is a fundamental food for infants and
children, and is consumed by all the age groups. Hence from this we can
8
1.1. ENVIRONMENTAL EFFECTS CHAPTER 1. MOTIVATION
see that there is a need to identify food that are vulnerable to radioactive
contamination, and to have a reference set of data we can refer to in any
event of a contamination. Hence preliminary data is necessary for such food
products.
1.1.2 Fukushima Daiichi Nuclear Disaster
The Fukushima Daiichi Nuclear Disaster in 2011 resulted in radionuclides in
the form of fine particles or souble gas being released into the environment.
A study on the soil about thirty kilometres north-west of the power plant
shows the radioactivity of the soil samples collected.4
9
1.1. ENVIRONMENTAL EFFECTS CHAPTER 1. MOTIVATION
Figure 1.2: A larger amount of short-lived radionuclei were released initallybut decayed rapidly, resulting in Cs-134 and Cs-137 being main contributorsof activity.
As can be seen from the graph, two months after the incident, the majority
of the residual deposits were Cs-134 and Cs-137 due to other radionuclides
having shorter half-lives. Though Cs-134 and Cs-137 initially only accounted
for 9 percent of the total activity, from 20 May 2011 on, they were contribut-
ing more than 80 percent of the activity of the residual deposits in Japan.
The accident led to the contamination of the aboveground parts of the plants,
10
1.1. ENVIRONMENTAL EFFECTS CHAPTER 1. MOTIVATION
and consequentially the plant products intended for consumption. The study
found that leafy vegetables such as spinach were the most affected by the
contamination due to the fallout directly on the leaves. Over the course of
the month of March, several vegetable samples from the surrounding districts
showed contamination exceeding sales or consumption standards. Until the
end of June, caesium activites were still detected, though they are below the
sales and consumption standard limits.
Figure 1.3: Change in iodine-131 and caesium-134 and caesium-137 contam-ination in spinach from the Fukushima prefecture
Later in the year, other plant foodstuffs showed significant levels of contam-
ination with caesium-134 and caesium-137. These products did not exist at
the time of the nuclear accident and thus was not contaminated by the fall-
out. Instead it is the transfer of caesium from the soil to the roots that is the
11
1.2. RADIONUCLEI CHAPTER 1. MOTIVATION
main cause of contamination in these products. However, the contamination
is always far lower than the initial contamination caused by direct deposi-
tion. Furthermore, due to the migration time of radionuclides in soil,this
contamination is only significant for radionuclides having a necessary long
half-life, such as Cs-134 and Cs-137.
1.2 Radionuclei
From the case studies, it can be seen that the radionuclei that post the great-
est health risk are I-131 ,Cs-134 and Cs-137. I-131 has a half life of 8.02 days,
and produce gamma radiation of 364 keV.5 Cs-137 has a half-life of 30 years
and emits gamma radiation of 662 keV. In addition, another radioisoptope of
interest is K-40, which have a half-life of 1.28E10 years and produces gamma
radiation of 1460 keV.6 K-40 can be found in most soils, building materials,
plants and animals, and is present in 0.0017 % of naturally occurring potas-
sium. The radioactivity from the K-40 in our bodies contributes to about
half of our yearly exposure to all sources of radiation. Furthermore, since Cs
and K belong to the same periodic group, they are competing elements for
transfer from soil to plant, When the transfer of ceasium from soil to plants
increase, the corresponding transfer of potassium to plants decreases. The
similar chemical behaviour of caesium and potassium makes it important to
study K-40 as well. Therefore, we aim to focus on these radionuclei and to
test the capability of our gamma detector at these energy range.
12
1.3. NUCLEAR PLANS IN ASIA CHAPTER 1. MOTIVATION
1.3 Nuclear Plans In Asia
The case studies show us that nuclear accidents overseas can have a direct
impact on us, either through direct contamination or through contaminated
food. This is increasing relevant as our neighbouring countries are making
nuclear plans in the near future.7 Countries such as Vietnam and Indonesia
are actively making preparation for nuclear energy, and have already searched
out potential sites for nulcear power plants.
Figure 1.4: Proposed Sites of Nuclear Power Plants in Vietnam
However, there are some concern raised over the location of the nuclear power
plants. Vietnam is known to be vulnerable to the impacts of climate change
13
1.3. NUCLEAR PLANS IN ASIA CHAPTER 1. MOTIVATION
such as rising sea levels and stronger typhoons. In particular, Ninh Thuan is
identified as a disaster-prone coastal province. Furthermore, Vietnam’s coast
has been subject to tsunamis in the past.
Figure 1.5: Proposed Sites of Nuclear Power Plants in Indonesia
Similarly, the nuclear plans in Indonesia has draw concern both domestically
and internationally due to the frequent occurrence of natural disasters such
as earthquakes and tsunamis.
Depending on the extent of an accident, sources of food can be contami-
nated by airborne radiation and radioactive water from affected power plants.
Transboundary airborne particles may contaminate agricultural farmlands
not just in Vietnam, but other countries such as Thailand. Regional fishing
grounds can also be contaminated, especially the South China Sea. This
will impact Singapore significantly as we import a large percentage of our
food. Furthermore, other South-East Asian countries such as Philippines and
14
1.3. NUCLEAR PLANS IN ASIA CHAPTER 1. MOTIVATION
Malaysia are also making nuclear plans for the near future. Hence it can be
seen that in the near future Singapore could potentially be surrounded by
countries that have nuclear power plants. There is a need to be prepared
in the event of any nuclear accident. This is especially relevant to us as
Singapore imports a large percentage of our food. Hence we need to have
the capacity to identify food products that are vulnerable to radioactive con-
tamination. We need to be have the ability to monitor food products over a
period of time as radioactive nuclulides such as caesium have long half-lives.
As such, we need to test the capability of detectors as well as calibrate them
such that prelimary work can be done. This will be the main focus of our
project.
15
Chapter 2
Theory
2.1 Gamma radiation
The activity of a radioactive source is defined by its rate of decay and is given
by 8
A = −dNdt
= −λN
where:
A = activity
N = number of radioactive nuclei
λ = decay constant
The SI unit of activity is the Becquerel (Bq). It is defined as the activity in
which one nucleus decays per second and 1 Bq is equivalent to s−1. Measure-
ment of radiation energy is done in electron volts (eV), and is defined as the
16
2.1. GAMMA RADIATION CHAPTER 2. THEORY
kinetic energy gained by an electron by its acceleration through a potential
difference of 1 volt. It is related to the Si unit of energy, Joules (J), by
1 eV = 1.602× 10−19 J
Gamma radiation is produced by an excited nucleus when it transit from
from a higher to a lower energy level. For the case of Cs-137, the caesium
can undergoes beta decay to energetic Ba-137, which is unstable and decay
to Ba-137 by emitting a gamma ray, shown in the diagram below.
Figure 2.1: Emission of Gamma Ray from Cs-137 9
Gamma rays interact with matter through 3 main processes : Compton
scattering, photoelectric absorption and pair production.
2.1.1 Compton Effect
Compton effect occurs when a photon scatters off a nearly free atomic electron.10
This results in a less energetic photon and a scattered electron carrying the
energy lost by the photon.
17
2.1. GAMMA RADIATION CHAPTER 2. THEORY
Figure 2.2
2.1.2 Photoelectric Effect
For the photoelectric effect, an atom absorbs an incoming photon and emits
a atomic electron, known as a photoelectron. The kinetic energy of the
photoelectron is given by
Te = Eγ − EB
where
Te = kinetic energy of photoelectron
Eγ = energy of incoming photon
EB = binding energy of electron
2.1.3 Pair Production
In pair production, an incoming photon interacts with an atom to create an
electron-positron pair. The energy for this process is given by
Eγ = T+ +mc2 + T− +mc2
18
2.1. GAMMA RADIATION CHAPTER 2. THEORY
where
Eγ = energy of incoming photon
T+ = kinetic energy of positron
T− = kinetic energy of electron
m = mass of electron
Since there is a energy threshold of 2mc2 = 1.022 MeV, this means that
pair production process is only significant at higher energy levels. The figure
below shows the three gamma ray interaction processes and the energy range
in which they are dominant.
Figure 2.3
19
2.1. GAMMA RADIATION CHAPTER 2. THEORY
2.1.4 Processes In Detector
Figure 2.4: Processes during gamma ray detection. (1) Photon Comptonscatters and leave crystal before depositing all its energy. (2) Compton scat-tering followed by total energy deposition though photoelectric absorption.(3) Pair production followed by total absorption. (4) Pair production fol-lowed by 1 annihilation photon escaping. (5) Pair production followed byboth annihilation photon escaping.
The figure above shows some of the processes that can occur when a gamma
ray enters a solid detector. Firstly, the photon can Compton scatter a few
time within the detector, each time losing some energy and producing a pho-
toelectron. Eventually the photon will experience 2 events: either the photon
will wander too close to the edge of the crystal and scatters outside, or it
20
2.1. GAMMA RADIATION CHAPTER 2. THEORY
will continue to lose energy and is eventually absorbed by photoelectric ef-
fect when its energy become low enough. The photoelectrons have a short
range in the crystal, and loses energy quickly by creating electron-hole pairs.
Alternatively, the photon can result in pair production. This can lead to 3
scenarios. In the first scenario, the positron undergoes annihilation, and the
resulting annihilation photons are both absorbed. In the second scenario, one
of the annihilation photons leave the detector, and the gamma ray deposits
its full energy less 511 keV. In the last scenario, both annihilation photons
leave the detector, resulting in energy deposition of the full gamma ray en-
ergy less 1022 keV.
When a gamma ray deposits all its energy in the detector (through photoelec-
tric effect), it will result in a photopeak. However, if the photon undergoes
Compton scattering and escape before being fully absorbed, it will lead to a
range of energy which forms the Compton continuum. The maximum energy
that can be deposited from this event is when the photon back scatters at
180 degrees, corresponding to the Compton edge. When one or both of the
annihilation photon escapes from the detector, it will result in a single escape
and double escape peak respectively.
21
2.2. BACKGROUND CHAPTER 2. THEORY
Figure 2.5: Response of detector to monoenergetic gamma rays
2.2 Background
The magnitude of the background determines the minimum detectable radi-
ation level, hence it is important to keep this level as low as possible. This
is especially important for our experiment, which involves sources of low ac-
tivity.
Background radiation can be grouped into five categories11:
1. The natural radioactivity from the materials of the detector itself.
2. The natural radioactivity of equipments, supports and shielding placed in
immediate vicinity of the detector.
3. Radiation from the Earth’s surface, construction materials of the labora-
tory or other far-away structures.
4. Radioactivity of the air surrounding the detector.
22
2.2. BACKGROUND CHAPTER 2. THEORY
5. The primary and secondary components of cosmic radiation.
The radioactivity of ordinary construction materials is due to the low concen-
tration of naturally occurring elements that exist in the materials as impurity.
Significant contributors are potassium, thorium, uranium and the members
of the long decays chains of thorium and uranium. Potassium is a widespread
component in concrete and other building materials. Natural potassium con-
tains 0.0017 % of radioactive K-40, with a 11 % chance to emits a gamma
ray of 1.460 MeV when it decays. This will contribute to a noticeable peak
in the background spectrum. Thorium, uranium and radium are naturally
occurring radionuclei with long decay chains. Of the natural decay chains,
the dominant contributors to background are from the decay of Rn-222 and
Rn-220. The resultant daughter nuclei such as 214-Pb and Bi-214 will result
in gamma energy peaks in the background spectra.
23
2.2. BACKGROUND CHAPTER 2. THEORY
Figure 2.6: Natural Decay Chain of U-238 series, U-235 series and TH-232series.
Furthermore, the lead shield has an intrinsic activity for Pb-210, which is
also part of the U-238 series decay chain. Cosmic rays can also interact with
the shield and the gamma detector, leading to additional background con-
tribution. Lastly, additional background radiation can also be observed as a
result of the primary gamma ray from the source interacting with the struc-
tural and shielding materials around the detector. Compton backscattering
of the primary gamma rays, the generation of secondary annihilation photos
and characteristic X-ray production through pair production or photoelectric
absorption can lead to an increased background.
24
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
2.3 Experimental Set-up
2.3.1 Semiconductor Detectors
Some semiconducting materials such as germanium forms solid crystals where
the valence-4 atoms form four covalent bonds with neighbouring atoms.12
Since all valence electrons takes part in forming bonds, we have a filled va-
lence band and an empty conduction band. Semiconductors differs from
insulators by having a small band gap of about 1 eV. At room temperature,
a small number of electrons can be thermally excited across the band gap
into the conduction band. This will leave behind a vacancy known as a ’hole’.
To control the electrical conduction, small amount of substances known as
dopants can be added into the semiconductor material. When a valence-5
atom is introduced, four of the electrons form covalent bonds with neighbour-
ing germanium atoms. The fifth electron moves through the lattice, forming
a set of donor states just below the conduction band. This material is known
as n-type semiconductor due to the excess of negative charge carriers. When
valence-3 atoms are introduced, the excess of holes will form acceptor states
just below the valence band. This is known as a p-type semiconductor as the
primary charge carriers are positively charged holes.
25
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
Figure 2.7
When the p-type and n-type materials are brought into contact, the elec-
trons from the n-type material will be able to diffuse across the junction into
the p-type material. The electrons will then recombine with the holes in
the vicinity of the junction, thereby creating a depletion region. The diffu-
sion of electrons from the p-type region will leave behind ionized donor sites.
Conversely, the diffusion of holes from the n-type region will leave behind
negatively charged acceptor sites. The charges from these sites will create an
26
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
electric field will will eventually halt further migration, resulting in a junc-
tion diode.
When radiation enters the depletion region, it will create electron-hole pairs.
The electron will flow in one direction while the hole in another, resulting
in a electronic pulse whose amplitude is proportional to the energy of the
radiation. These detectors are often operated with a reverse bias voltage.
The reverse bias voltage increases the magnitude of the electric field in the
depletion region, thus making charge collection more efficient. The reverse
bias voltage also increases the dimension of the depletion region, thereby in-
creasing the active volume of the detector.
27
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
Figure 2.8: Depletion region in the semiconductor junction.
However, simple junction detectors are not suitable for more penetrating
radiations. Their major limitation is the maximum active volume that can
be created. For germanium of normal semiconductor purity, it is difficult
to achieve a depletion depth beyond 2 to 3mm, even when applying bias
voltage of near break down level. This depletion depth is easily penetrable
for medium energy gamma rays (The range of a 100-keV gamma ray is about
28
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
4mm in germanium). A greater thickness is therefore necessary for detectors
to be used in gamma spectroscopy. The thickness of the depletion region is
given by
d =(2εVeN
) 12
where
V = the reverse bias voltage
N = the net impurity concentration in the bulk semiconductor material
ε = the dielectric constant
e = the electronic charge
Since there is a limit to the reverse bias voltage we can use, the other method
to increase the thickness of the depletion layer is by increasing the purity of
the semiconductor.
2.3.2 High Purity Ge Detector
Current refining techniques are able to reduce the impurity levels in germa-
nium such that a depletion region of about 10mm can be obtained with a
bias voltage of less than 1000V. However, the active volume in a planar con-
figuration is still insufficient. A larger active volume is necessary for gamma
spectroscopy. Our HPGe detector is constructed with a coaxial geometry
instead to obtain a much larger active volume.
29
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
As shown in the figure below, one electrode is fabricated on the other surface
of a long germanium crystal. The core of the crystal is then removed and the
other electrode is placed on the inner cylindrical surface. Since the crystal is
long in the axial direction, a larger active volume that is suitable for gamma
spectroscopy can be obtained.
Figure 2.9: Top down view of the coaxial Ge crystal
30
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
Figure 2.10: Left: Ge crystal with the thick lines signifying the inner andouter electrodes. Middle: The germanium crystal is installed in a cylindricallead shield. Right: Actual lead shield (about 4 inches thick).1
A sample is placed in the lead shield, with the lead shield closed off during
data taking. Since the HPGe detector has a small band gap, it cannot work
at room temperature due to a large thermally-induced leakage current. the
HPGe must be cooled so that thermally-induced leakage does not affect it’s
energy resolution. This is done by placing an insulated dewar beneath the
lead shield, and the detector is placed in thermal contact with a reservoir of
liquid nitrogen.
31
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
Figure 2.11: Insulated dewar that allows the detector to be in contact withliquid nitrogen.14
Shown below is the basic schematic of the detector set-up.
Figure 2.12: Schematic of the detector
32
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
2.3.3 Pre-amplifier
The pre-amplifier converts the charge pulse from the detector into a voltage
pulse and drives the pulse to the amplifier. Since the weak electronic signal
from the detector goes directly to the pre-amplifier, the pre-amplifier is lo-
cated as close to the detector as possible to minimise capacitance. Hence the
pre-amplifier is usually packaged as part of the HPGe system. This has the
additional advantage of keeping the input part of the pre-amplifier cool to
reduce electronic noise.
2.3.4 Amplifier
The amplifier has two main roles. The first is to amplify the signal coming
from the detector.
Amplifier Gain
In the amplifier, the amplitude of incoming signal is amplified to a certain
degree. This is measured in terms of gain, which can be defined as the ra-
tio of the input signal amplitude to the output signal amplitude. Hence a
gain of 100 will amplify the amplitude of the incoming signal by 100 times.
The amplified output signal will then be sorted into a higher channel number.
For our experiment, we are interested in the detection of gamma radiation of
I-141, Cs-137 and K-40, which have energy peaks at 0.362, 0.662 and 1.460
33
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
MeV respectively. Hence we need a gain setting that is allows us to have a
good view of energies at about 1.5 MeV while still having good resolution at
the lower energy levels.
By varying the gain, it was found that a gain setting is 100 is large, and the
1.46 MeV cannot be seen. Conversely, a gain setting of 20 is too low and not
optimal for the lower energies. A gain setting of 50 is the most suitable as
we can still see the energy peak of K-40, while still maintaining reasonable
spectrum at lower energies.
The second role is to shape the signal received from the detector. In order to
ensure that total charge collection occurs, amplifiers are necessary to ensure
a decay time for the pulse. The pulses can be quite long and tend to over-
lap with each another. Furthermore, the time spacing for nuclear decay is
random and can lead to each pulse being superimposed on different residual
tail. Such a pulse train can be seen in the figure below. Since the amplitude
of a pulse measures the charge Q deposited on the detector, the resulting
amplitude is no longer a good measurement of Q.
34
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
Figure 2.13
To avoid this, we need to shape the pulses in a way such that we obtain
a pulse train shown in (b). Is this done by the amplifier. The long tails
are removed in a way such that the maximum amplitude of the pulses is
preserved.
Shaping time
To find the best shaping time for the experiment, we took readings of a Cs-
137 source at various shaping time. The full width half maximum (FWHM)
of the energy peak at 662 keV is found using the software Gamma Vision
(refer to Appendix A for more info about Gamma Vision).
35
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
Figure 2.14: FWHM (keV) of Cs-137 energy peak at different shaping time(µs)
It can be seen that 6 shaping time (6 µs) gives us the best energy resolution,
with the highest peak and lowest FWHM. This agrees with the supplier’s
recommended setting of 6 µs for the shaping time.
2.3.5 Multichannel Analyser
The multichannel analyser (MCA) is used to convert a analog signal (a pulse
amplitude) into a digital signal. The basic function of the MCA involves
an analog to digital converter (ADC) and the memory. The memory can
be illustrated as a vertical stack of addressable location, ranging from the
first address (channel number 1) at the bottom, to the maximum address
location at the top. During operation, a pulse first passes through the ADC
and is then sorted into a memory location corresponding to its amplitude.
36
2.3. EXPERIMENTAL SET-UP CHAPTER 2. THEORY
This increases the count of that location by one. A spectrum of the count
against the channel number can then be obtained and shown on the com-
puter through a software.
37
Chapter 3
Data Analysis
For this chapter we will be doing an analysis of the results we have obtained
from the HPGe detector.
3.1 Energy Calibration
We first need to do a energy calibration for the detector. We used a Eu-152
source for the calibration, which is suitable due to its multiple peaks. Using
the HPGe detector, a spectrum for Eu-152 was obtained. The count rate
(s−1) was then plotted against the channel number.
38
3.1. ENERGY CALIBRATION CHAPTER 3. DATA ANALYSIS
Figure 3.1
The 11 major peaks were then identified form literature values.14 Using liter-
ature values for the different peaks of Eu-152, we did a calibration by plotting
the energy values against the channel number. Next we want to find out if
we have a good linear fit for our data. This is done by finding the reduced
χ2 value for our linear plot, given by the equation 15
χ2ν = χ2
ν= 1
ν
N∑i=1
[(Ei − E (Chi))
2
σ2i
]
where
χ2ν = reduced χ2
ν = degrees of freedom
yi = data from theory
σ = standard deviation of the energy peak centroid
E (Chi) = A× Ch+B, the simulated data from our linear fit
39
3.1. ENERGY CALIBRATION CHAPTER 3. DATA ANALYSIS
To find σ, we first manually fitted a best Gaussian fit to a photopeak cen-
troid µ. Next, we do a manual shift of the Gaussian fit by varying the peak
centroid position to µ′. The reduced χ2 value was found for both curves.
From literature, we know that a difference of 1 for the two reduced χ2 will
mean that the resultant ∆µ = µ′ − µ is the standard deviation of the peak
centroid, σ.
It was found that the fitting at 122 keV gave us a large χ2 value of 122. The
resultant χ2ν value is 14.2, which suggest that our data is a bad fit. However,
when removed from the linear fit, the χν2 became 0.738, a much more rea-
sonable number. However, it stills differ from the ideal χν2 value of 1. This
could be due to either the over fitting of the data, or the overestimation of σ.
Hence for our calibration, we left out the 122 keV peak, and used ten energy
peaks instead.
40
3.1. ENERGY CALIBRATION CHAPTER 3. DATA ANALYSIS
Figure 3.2: Linear fit of Energy (keV) against Channel for 10 Eu-152 energypeaks
From the line of best fit we obtain the equation E = 0.206 Ch + 0.190.
Another way to test for the goodness of the fit is to look at the residual of
the data.16 The residual is obtained by taking the theoretical energy peaks
minus the simulated (fitted) energy peaks. If the resultant data points are
random, it suggest that our fit is a good fit.
41
3.1. ENERGY CALIBRATION CHAPTER 3. DATA ANALYSIS
Figure 3.3: Plot of residual (keV) against energy (keV)
From our data, it seems that the data points are random, and close to zero,
taking into account the error. This suggest that our data is a good fit. We
next obtain a calibrated spectrum for Eu-152 using this calibration.
Figure 3.4: Spectrum of Eu-152, Count rate (s−1) against Energy (keV)
42
3.2. BACKGROUND SPECTRUM CHAPTER 3. DATA ANALYSIS
3.2 Background Spectrum
Next, we want to test the effectiveness of the lead shield of the HPGe detector.
To do so, we first obtain a background spectrum of the empty HPGe detector
when the lead cover is closed. Using the calibration found previously, a plot
of the count rate (s−1) against energy (keV) was obtained.
Figure 3.5: Spectrum of background with closed lead shield
The major peaks are identified and many were found to be of the natural
long decay series of U-238 and Th-232.17 These are natural decay chains that
are found in the environment. As discussed previously, theoretically we had
expected that these decay series will contribute to background data. Next,
a separate reading was done with the top part of the lead shield open. The
resulting data was plotted together with the closed cover reading.
43
3.3. ENERGY RESOLUTION CHAPTER 3. DATA ANALYSIS
Figure 3.6: Plot of Open Cover vs 5 x Closed Cover
As the reading of the closed cover reading is very low, the reading is multiplied
by five to allow for easier comparison. From the plot, it can be seen that there
is a significant reduction in the background activity, especially at the lower
energy range. Hence we can conclude that the lead shield is effective, and
it reduces background data by one order. With the shielding, the resultant
background is two orders smaller than the reading for Eu-152 peaks.
3.3 Energy Resolution
We are also interested in knowing the response of the detector to radiation.
The figure shows the pulse height distribution that can be produced by the
detector. The curve labelled ’Good resolution’ shows a possible distribution
around a certain energy , while the curve labelled ’Poor resolution’ shows an
44
3.3. ENERGY RESOLUTION CHAPTER 3. DATA ANALYSIS
inferior distribution around that point.
Figure 3.7: Example of pulse height distribution (count vs energy) with goodand bad resolution.
Assuming that the same number of pulses are recorded for each case, the area
under the peaks are the same. Though both distributions are centred at te
same point, the width of the poor resolution peak is much wider. This indi-
cated that a large fluctuation was recorded from pulse to pulse even though
the same energy is deposited in the detector for each event. If the amount of
fluctuation is reduced, the corresponding distribution will be made smaller
and the peak will approach a delta function. Hence the ability of a measure-
ment to resolve fine details in the incident radiation energy will be improved
with decreasing peak width.
From our data for Eu-152, the FWHM of the different peaks are recorded
using Gamma Vision.
45
3.3. ENERGY RESOLUTION CHAPTER 3. DATA ANALYSIS
Figure 3.8: FWHM of Eu-152 energy peaks
The relative resolution was then found by taking dividing the FWHM with
their corresponding energies,
Relative Resolution (%) = FWHME× 100
where E is the peak centroid energy.
46
3.4. ENERGY PEAK EFFICIENCY CHAPTER 3. DATA ANALYSIS
Figure 3.9: Relative Resolution fitted from eleven energy peaks of Eu-152
Other detectors such as Na(Ti) detectors typically have a resolution of 13.5
% at 113 keV (Lu-177), 7.7 % at 662 keV (Cs-137), and 6.07 % at 1277
keV (Na-22).18 This suggest that our HPGe detector gives a much better
resolution. Since we are interested in identifying different energy peaks in a
sample of unknown composition, we need to be able to resolve peaks that
may be close together. Hence the HPGe detector, with its high resolving
power, is suitable for our experiment.
3.4 Energy Peak Efficiency
We are interested in knowing how much activity the HPGe will detect out
of the actual activity of a source. This is known as the efficiency of the
detector. To calculate the efficiency, we took the fraction of the net area of
47
3.4. ENERGY PEAK EFFICIENCY CHAPTER 3. DATA ANALYSIS
each photopeak of Eu-152 over the actual activity.
Efficiency = Detected ActivityActual Activity
= N/tA0×B
where
N = net area of each peak
A0 = activity of the source
B = brunching ratio for different energy peaks
t = time taken for measurement
Using our Eu-152 sample, the net area of 11 major peaks was obtained from
the programme Gamma Vision. The activity was calculated from the initial
activity, and the brunching ratio obtained from literature.
Figure 3.10: Energy Efficiency across different energy, fitted from 11 peaksof Eu-152 data. From the line of best fit, efficiency = 1.0456E(−0.692)
48
3.4. ENERGY PEAK EFFICIENCY CHAPTER 3. DATA ANALYSIS
From the line of best fit, we obtain the equation efficiency = 1.0456E(−0.692).
A value of 0.01 for efficiency will indicate that out of every 100 actual ac-
tivity emitted by the source, 1 of it will be detected by the HPGe detector.
The efficiency is expected to decrease as photons of higher energy will have a
higher chance of passing through the detector undetected. For coaxial detec-
tors, there are a variety of fits used for the extrapolation of energy efficiency
over a wide energy range. One published function that fits the efficiency over
a energy of 50-8500 keV is given by20
lnε =N∑i=1
ai
(lnE
E0
)i−1where
ε = energy efficiency
ai = the fitted perimeters
E0 = a fixed reference energy
and is shown below graphically.
49
3.4. ENERGY PEAK EFFICIENCY CHAPTER 3. DATA ANALYSIS
Figure 3.11: Published fitting of Ln Efficiency against Ln Energy for a widerange of energy
Compared to our data, our spectrum seems to show agreement with litera-
ture, between an energy range of about 100 to 1400 keV.
Figure 3.12: Plot of Ln Efficiency against Ln Energy using Eu-152 energypeaks
50
3.5. LIMIT OF DETECTION CHAPTER 3. DATA ANALYSIS
3.5 Limit Of Detection
We are also interested in knowing the limit of detection for the HPGe detec-
tor. Let NT be the number of counts recorded with a sample at a point, and
NB be the number of counts recorded in the absence of a sample. The net
counts of the sample will then be 21
NS = NT −NB
NS is then compared to a minimum detectable value to determine whether
the sample contains activity at a particular point. If NS is less then this
value, then the sample does not contain activity at that point. Conversely,
if NS is larger then this value it is assumed that there is some real activity
present.
In the absence of statistical fluctuations, the minimum detectable value can
be set to zero, and any net postive count can be treated as evidence of real
activity. However statistical fluctuation is inevitable in any counting mea-
surement. Hence there will be instances where a postive NS will be observed
even in regions of no activity. We have to choose a minimum detectable value
that is high enough to minimise the likelihood of such false positives, while
keeping it low enough to avoid false negatives (missing real activity).
Since our counting time is sufficiently long, we can assumed that the total
number of counts of NT and NB follow a Gaussian distribution. From Poisson
51
3.5. LIMIT OF DETECTION CHAPTER 3. DATA ANALYSIS
statistics, the standard deviation in the number of recorded events N is then
expected to be
σN =√N
We are interested in knowing what is the minimum detectable activity of a
sample by the HPGe detector. The relation of actual activity of sample and
the activity detected by the detector is given by
A0 × ε = Adet
where
A0 = activity of sample
ε = efficiency
Adet = activity detected by the detector
To find the minimal detectable activity, we first found the gross area (using
Gamma Vision) of non-peak regions in our background spectra. Since these
are regions without peaks, they corresponds to background activity only.
This gives us the relation
Aactual background × ε = Adetected background = NB
t
where
NB =gross area of background
52
3.5. LIMIT OF DETECTION CHAPTER 3. DATA ANALYSIS
From Poisson statistics, the standard deviation of minimum detectable ac-
tivity of the sample is then given by
σAactual background=√NB
t× 1
ε
By taking 3σAactual background, we can then be 99.7 % certain that there is real
activity when the activity of the sample is larger than this value. This is
thus our minimum detectable activity.
Figure 3.13: Minimum detectable activity of a sample in the HPGe detector.
From this we are 99.7 % sure that any value above the limit of detection
correspond to actual activity. The error bars arise from the uncertainty in
the efficiency and the gross area.
Next, we are interested in finding the minimum detectable mass of a radionu-
clei for our detector. This is done by first interpolating from our best fit the
53
3.5. LIMIT OF DETECTION CHAPTER 3. DATA ANALYSIS
minimum detectable activity of different radionulei. It was found that the
minimum detectable activity Amin = (−7× 10−9)E2 + (2× 10−5)E + 0.0161 ,
where E is energy (keV). Next, we calculated the decay constant λ that was
found from the half-lives of the radionuclei.22 By using the relation,
Amin = λNmin
we can then obtain the minimal detectable number of radionuclei Nmin.
Lastly, the number of radionuclei is multiplied by the atomic mass to obtain
the minimal detectable mass (kg). We did a calculation for 4 radionuclei,
shown in the table below.
Radionuclei γ Energy (keV) Amin(s−1) Nmin Massmin (kg)
I-131 364 0.0225 2.25E+04 4.88E-21
Cs-137 662 0.0263 3.60E+07 8.18E-18
Co-60 1173 0.0299 6.88E+06 6.85E-19
1333 0.0303 6.97E+06 6.94E-19
K-40 1460 0.0304 1.73E+15 1.15E-10
From our results, this means that if there is a radionuclei mass above the
minimal detectable mass, there is a 99.7 % that it is detectable.
54
3.6. BACK CALCULATION CHAPTER 3. DATA ANALYSIS
3.6 Back Calculation
Now that we know the efficiency of the detector, we can find the activity of
an unknown radioactive source. To demonstrate this, we first took another
reading of a different Eu-152 source. The efficiency we calculated previously
was used to calculate the activity of the source. This values were compared
to the actual activity of the source.
Figure 3.14: Percentage discrepancy of actual activity from the calculatedactivity of new Eu-152 sample
It can be seen that there is a reasonable percentage discrepancy from the
actual activity of the Eu-152 sample. The relatively large percentage dis-
crepancy at about 200-400 keV range could be due to the relatively large
errors in the calculated activity.
The efficiency of the new Eu-152 was also found, and plotted against the
original efficiency.
55
3.6. BACK CALCULATION CHAPTER 3. DATA ANALYSIS
Figure 3.15: Plot of the original efficiency with the new efficiency obtainedfrom the second Eu-152 sample.
It can be seen that the two values are similar, suggesting good consistency
for our detector.
56
Chapter 4
Samples
4.1 Food Products
We next did a data collection for different food samples. We used a sample
of flour, rice and milk powder. For the different spectra, energy peaks of the
natural decay chains were identified. Compared to the background, there
is some increase in the different energy peaks, shown in the milk sample
spectrum below.
57
4.1. FOOD PRODUCTS CHAPTER 4. SAMPLES
Figure 4.1: Spectrum of milk powder ploted together with background spec-trum.
However, the most significant difference is the K-40 peak. In all the food
product, there was an increase in the K-40 peak. However, the K-40 peak is
significantly higher in milk power compared to the rest.
Figure 4.2: K-40 peak for background, flour, rice and milk powder spectrum
58
4.1. FOOD PRODUCTS CHAPTER 4. SAMPLES
This is due to the higher potassium content of milk. Since 0.0117% of potas-
sium occurs as K-40 naturally, this result is expected. The background count
is then subtracted from that of milk powder and the peaks were identified.
Figure 4.3: Spectrum for the milk spectrum less the background
Hence it is shown the our detector is able to detect small amounts of radioac-
tivity in food samples. These data of food samples can be kept as a reference
for the future. Different food samples can be tested regularly as a means
of regulation and to check for contamination. Future work can be to take
identify and take data from food samples that are radiologically sensitive,
such as mushrooms and milk. We could also compare food from different
regions to compare the difference in the spectrum.
59
4.2. SOIL SAMPLES CHAPTER 4. SAMPLES
4.2 Soil Samples
Next, we did a reading of soil collected from MacRitchie reservoir. A spec-
trum of the soil sample is plotted with the background spectrum.
Figure 4.4: Spectrum of soil sample with spectrum of background
It can be seen that the readings for the energy peaks are much larger than
that of the background.
60
4.2. SOIL SAMPLES CHAPTER 4. SAMPLES
Figure 4.5: Spectrum of soil sample less the background
However, we expected that there will be a peak for Cs-137, due to atmo-
spheric fall-out from the use of nuclear weapons in the past. The reason
could be that the soil sample we took is only the top layer, which might be
mixed with new compost and fertilizer. A point for future study could be to
take a reading for different soil samples from different regions. The data for
the soil samples can then be kept as a reference for the future. We would
then be able to compare the data of soil to that of an uncontaminated soil
sample, either as regulatory checking or in the event of atmospheric contam-
ination.
We can further expand the samples in future works to include seawater and
tap water as well. Since Singapore is surrounded by the sea, we will be
61
4.2. SOIL SAMPLES CHAPTER 4. SAMPLES
vulnerable to any contamination of the surrounding seawater. Furthermore,
a portion of our drinking water is obtain from the reservoir, which might be
vulnerable to atmospheric contamination as well. Hence, a preliminary data
reading can be first done for seawater and tapwater.
62
Chapter 5
Conclusion
In conclusion, we did a energy calibration for the HPGe detector using a Eu-
152 source. Using this calibration, we found the energy resolution, efficiency,
minimum detectable activity and minimum detectable mass for the detector.
The high resolving power of the HPGe suggest that it is suitable for our
experiment, as it is able to differentiate the numerous energy peaks in an
sample of unknown composition. We next found the efficiency of the HPGe
detector. By knowing the efficiency, we will be able to calculate the actual
activity of an unknown sample from the activity detected in the detector. Our
efficiency also seems to agree with the trend of the efficiency from literature.
Next, we found the minimum detectable activity and minimum detectable
mass of radionuclei. The minimum detectable activity means we are 99.7
% certain that any activity detected about this level correspond to actual
activity. The minimum detectable mass for different radionuclei means that
63
CHAPTER 5. CONCLUSION
we are 99.7 % sure that we are able to detect the radionuclei if that amount
of it is present in the detector. We then did a back-calculation to find the
activity of another Eu-152 sample. The calculated activity has a reasonable
percentage discrepancy from the theoretical activity, taking into account the
error. The efficiency found from the new Eu-152 source also matches the
original one we found initially. Lastly, we took a reading of rice, flour, milk
powder and soil. Our data suggest that our detector is able to detect activity
in the different samples. For future work, reference data of activity can be
taken for food products, soil and seawater from various different regions.
64
Appendix A
Gamma Vision
For our experiment we made use of the program Gamma Vision for our
analysis. From the manual, the program does the analysis according to the
method shown below.23
65
APPENDIX A. GAMMA VISION
Figure A.1
The background on the low-channel side of the peak is the average of the first
three channels of the point of interest (see Fig). The channel number for the
background is The middle channel of the three points. The background on
the high-channel side of the peak is the average of the last three channels of
the point of interest. The channel number for this background point is also
the middle channel of the three points. These two points on each side of the
peak form the endpoints of the straight-line background.The background is
given by the equation
B =
(l+2∑i=l
Ci +h∑
i=h−2
Ci
)h−l+1
6
66
APPENDIX A. GAMMA VISION
where:
B = background
l = lowest channel in region of interest
h = highest channel in region of interest
Ci = content of that particular channel
6 = total number of channel used (3 on each side)
The gross area of the peak is the sum of the content of each channel between
the background, given by:
Ag =h∑i=l
Cl
where:
Ag = the gross area
Ci = the data value of channel i
l = the center channel of the background calculation width at the low
energy side of the spectrum
h = the center channel of the background calculation width at the high
energy side of the spectrum
67
APPENDIX A. GAMMA VISION
Figure A.2
The adjusted gross area is the sum of all the remaining channels that was
marked by the ROI but not used in the background, given by
Aog =h−3∑i=l+3
Ci
where:
Aog = adjusted gross area
l = the ROI low limit
h = the ROI high limit
Ci = the contents of channel i
The net area is the adjusted gross area minus the adjusted calculated back-
ground, given by
An = Aog − B(h−l−5)(h−l+1)
68
APPENDIX A. GAMMA VISION
and the uncertainty in net area is given by
σAn =√Aog +B
(h−l−5
6
) (h−l−5h−l+1
)where:
Aag = the adjusted gross area
B = the background area
l = the ROI low limit
h = the ROI high limit
The uncertainty in the net area is the square root of the sum of the squares
of the uncertainty in the adjusted gross area and the weighted error of the
adjusted background. The background uncertainty is weighted by the ratio
of the adjusted peak width to the number of channels used to calculate the
adjusted background.
69
Appendix B
Tables
B.1 Energy Calibration
Figure B.1: Calculated χ2 from the linear fit of theoretical energy againstchannel. Sigma was obtain from manual Gaussian fit of energy peaks.
70
B.2. ENERGY RESOLUTION APPENDIX B. TABLES
B.2 Energy Resolution
Figure B.2: FWHM values obtained from Gamma Vision.
B.3 Efficiency
Figure B.3: Table for efficiency calculation. Initial activity and uncertainty,energy peaks, branching ratio obtained from literature. Net area and uncer-tainty obtained from Gamma Vision.
71
B.4. MINIMUM DETECTABLE ACTIVITY APPENDIX B. TABLES
B.4 Minimum Detectable Activity
Figure B.4: Gross Area and uncertainty obtained from Gamma Vision.
72
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75