THE ABSOLUTE METHOD OF NEUTRON ACTIVATION ANALYSIS USING
TRIGA NEUTRON REACTOR, NUCLEAR AGENCY, MALAYSIA
LIEW HWI FEN
UNIVERSITI TEKNOLOGI MALAYSIA
THE ABSOLUTE METHOD OF NEUTRON ACTIVATION ANALYSIS USING
TRIGA NEUTRON REACTOR, NUCLEAR AGENCY, MALAYSIA
LIEW HWI FEN
A thesis submitted in fulfillment of the
requirements for the award of the degree of
Master of Science (Physics)
Faculty of Science
Universiti Teknologi Malaysia
JANUARY 2010
ii
To beloved my mom and dad.
iii
ACKNOWLEDGEMENT
First of all, the author would like to thanks Prof. Noorddin Ibrahim and Dr.
Abdul Khalik Bin Hj. Wood for their endless advice and encouragement during this
study. The Malaysian Nuclear Agency (MNA) is gratefully acknowledged for
providing the irradiation and counting facilities. The effective cooperation of the
staffs from Analytical Chemistry Laboratory and operator of the facilities (MNA) are
also acknowledged. Finally, I would like to thank my family and friends for their
tremendous support.
iv
ABSTRACT
Neutron activation analysis (NAA) offers excellent sensitivities that are
superior to other analytical techniques in performing identification and quantitative
elemental analysis. The technique involves the irradiation of samples and the
detection of gamma energies emitted from the isotopes formed from the process of
neutron capture. Most NAA were done by comparison method, which is found to
have high errors due to the differences in the matrix composition of sample as well as
comparator. The purpose of this study is to demonstrate an alternative technique of
activation analysis based on absolute gamma ray measurements and the direct
calculation of elemental concentrations from reaction rates equation of neutron
capture process. The efficiency of the gamma-ray spectrometer as well as the neutron
spectrum parameters, thermal and epithermal neutron flux at four characterized
irradiation position of 10, 22, 27, and 31 in the rotary rack 1-MW TRIGA reactor at
Malaysia Nuclear Agency was determined. The accuracy and precision of this
absolute NAA technique were verified by analyzing two certified reference
materials, Soil-1 and Soil-7 provided by IAEA. The experimental results for both the
materials irradiated at the four characterized irradiation positions were found to be in
good agreement with the certified values. The average Z-score for the concentration
values were below two signified that the concentration results were accepted for
most elements. In conclusion, the proposed technique can be applied for many of
future activation analyses with high accuracy without having to rely on the
availability of standard samples.
v
ABSTRAK
Analisis pengaktifan neutron (NAA) memberikan kepekaan yang tinggi
berbanding dengan teknik analisis yang lain dalam mengenalpasti elemen dan
analisis kuantitatif elemen. Teknik ini melibatkan penyinaran sampel dan penentuan
tenaga gama yang dipancarkan oleh isotop yang terbentuk daripada proses
penangkapan neutron. Kebanyakan NAA menggunakan kaedah perbandingan yang
mempunyai ralat yang tinggi disebabkan perbezaan komposisi matriks di antara
sampel dan sampel perbandingan. Tujuan kajian ini adalah melaksanakan kaedah
alternatif analisis pengaktifan neutron iaitu kaedah mutlak berdasarkan pengukuran
mutlak sinar gama dan pengiraan terus kepekatan elemen daripada persamaan kaedah
tindak balas proses penangkapan neutron. Kecekapan spektrometer sinaran gama dan
parameter spektrum
neutron, fluks terma dan epiterma diukur pada lokasi
penyinaran 10, 22, 27, dan 31 di rak berputar 1-MW TRIGA reaktor Agensi Nuklear
Malaysia. Kejituan dan ketepatan kaedah mutlak ini ditentusahkan dengan
menganalisis dua sampel piawai Soil-1 dan Soil-7 yang dibekalkan oleh IAEA.
Keputusan eksperimen terhadap kedua- dua sampel piawai pada keempat–empat
kedudukan penyinaran didapati menunujukkan persamaan yang baik dengan nilai
yang disahkan. Nilai purata Z-skor kurang daripada dua menunjukkan keputusan
analisis boleh diterimapakai untuk kebanyakan elemen secara tepat. Secara
keseluruhannya, teknik yang dicadangkan boleh digunapakai untuk analisis
pengaktifan neutron pada masa hadapan dengan ketepatan yang tinggi tanpa
bergantung kepada bahan piawai.
vii
TABLE OF CONTENTS
CHAPTER
I
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF FIGURES
xi
LIST OF TABLES
xiv
LIST OF SYMBOLS
xviii
LIST OF ABBREVIATIONS
xx
LIST OF APPENDICES
xxi
INTRODUCTION
1.0
Introduction of NAA
1
1.1
Background of Study
2
1.2
Statement of Problem
3
1.3
Purpose of Research
4
1.4
Objectives of Research
4
1.5
Significant of Research
5
1.6
Research Scope
5
viii
II
III
LITERATURE REVIEWS
2.0
Introduction
7
2.1
Neutron Sources
8
2.2
Nuclear Reaction
10
2.3
The Trend of NAA
11
2.4.1
Relative Method
12
2.4.2
Ko- Standardization Method
13
THEORY
3.1
Neutron Activation Equations
15
3.2
HOGDAHL Reaction Rate
16
3.3
Non-ideal 1/E 1+á Epithermal Neutron Flux
17
Distribution
3.4
Determination of á and f parameter
19
3.4.1 The Cadmium ratio multi
20
monitor method
3.4.2 Error Analysis of á parameter
IV
22
3.5
Epithermal and thermal neutron flux
24
3.6
Full-Energy Peak Detection Efficiency
28
METHODOLOGY
4.0
Introduction
32
4.1
TRIGA Puspati Reactor (RTP)
33
4.2
Gamma-ray Spectrometry
35
4.3
Calibration of gamma ray spectrometer
36
4.4
Determination of reactor neutron spectrum
38
parameters
4.5
Analysis of Environmental reference
materials
40
ix
V
RESULT AND DISCUSSION
5.0
Introduction
42
5.1
Calibration of Detector Efficiency
42
5.2
5.1.1
Ortec Detector Calibration
43
5.1.2
Canberra Detector Calibration
48
Result of á by the Cd ratio
5.2.1
Result of á at Irradiation
54
54
Position 10
5.2.2
Result of á at Irradiation
57
Position 22
5.2.3
Result of á at Irradiation
58
Position 27
5.2.4
Result of á at Irradiation
60
Position 31
5.3
Calculation of Thermal to Epithermal Flux
62
Ratio
5.4
Thermal and Epithermal Neutron Flux
63
Results
5.5
HOGDAHL Reaction Rate for Irradiated
65
Elements
5.6
Elemental Analysis Using NAA Absolute
70
Method
VI
CONCLUSION
6.0
Conclusion
89
6.1
Recommendation
90
x
REFERENCES
91
APPENDIX A
95
APPENDIX B
96
APPENDIX C
97
APPENDIX D
98
APPENDIX E
99
PUBLICATIONS
100
xi
LIST OF FIGURES
FIGURE NO
TITLE
2.1
Nuclear Chain Reaction
8
2.2
Gamma Spectra from a Sample of Pottery
11
3.1
A reactor neutron spectrum is contributions from
PAGE
25
a purely Maxwellian shape in the thermal energy
region, an epithermal region and negligible fast
spectrum
3.2
The spectrum observed by detector contribute by
29
interaction of gamma ray with germanium.
3.3
An example of ideal efficiency curve plotted
31
against gamma energy
4.1
TRIGA Puspati Reactor (RTP) with power of 1
33
Megawatt
4.2
Reactor rotary racks with experimental
34
irradiation facility
4.3
HPGe detector operated at liquid nitrogen
35
temperature
4.4
Set up of gamma ray spectrometer
36
xii
4.5
Canberra GC3018 detector with Genie 2000
37
Software
4.6
Ortec GEM-10185 detector with Gamma
37
Vision software
4.7
2 set of monitors irradiated with bare condition
39
and cadmium cover respectively
4.8
IAEA lake sediment sample sealed in a labeled
41
plastic and irradiated with standard polyethylene
vial
5.1
Full energy peak detection efficiency curve for
48
Ortec detector at three sample-detector distances
5.2
Full energy peak detection efficiency curve for
53
Canberra detector at three sample- detector
distances
5.3
Parameter á measurement at position 10 of
56
rotary rack TRIGA reactor
5.4
Parameter á measurement at position 22 of
58
rotary rack TRIGA reactor
5.5
Parameter á measurement at position 27 of
59
rotary rack TRIGA reactor
5.6
Parameter á measurement at position 31 of
61
rotary rack TRIGA reactor
5.7
IAEA Soil-1 elements at irradiation position of
81
10 in rotary rack
5.8
IAEA Soil-7 elements at irradiation position of
82
xiii
10 in rotary rack
5.9
IAEA Soil-1 elements at irradiation position of
83
22 in rotary rack
5.10
IAEA Soil-7 elements at irradiation position of
84
22 in rotary rack
5.11
IAEA Soil-1 elements at irradiation position of
85
27 in rotary rack
5.12
IAEA Soil-7 elements at irradiation position of
86
27 in rotary rack
5.13
IAEA Soil-1 elements at irradiation position of
87
31 in rotary rack
5.14
IAEA Soil-7 elements at irradiation position of
31 in rotary rack
88
xiv
LIST OF TABLES
TABLE NO.
TITLE
PAGE
3.1
Three main neutron groups
25
3.2
The nuclear data of gold used in calculating
28
thermal and epithermal neutron fluxes
4.1
Monitors and relevant nuclear data require
40
in the work.
5.1
Activity and Information on Radioactive
43
Gamma Sources
5.2
Standard gamma sources efficiency at the
44
distance of 10 cm from Ortec detector
5.3
Standard gamma sources efficiency at the of 6 cm
45
from Ortec detector
5.4
Standard gamma sources efficiency at the
46
distance of 2 cm from Ortec detector
5.5
Parameters P1 to P5 determined at the distance of
47
10 cm from Ortec detector
5.6
Parameters P1 to P5 determined at the distance of
6 cm from Ortec detector
47
xv
5.7
Parameters P1 to P5 determined at the distance of
47
2 cm from Ortec detector
5.8
Standard gamma sources efficiency at the
49
distance of 12 cm from Canberra detector
5.9
Standard gamma sources efficiency at the
50
distance of 8 cm from Canberra detector
5.10
Standard gamma sources efficiency at the
51
distance of 2 cm from Canberra detector
5.11
Parameters P1 to P5 determined at the distance of
52
12 cm from Canberra detector
5.12
Parameters P1 to P5 determined at the distance of
52
8 cm from Canberra detector
5.13
Parameters P1 to P5 determined at the distance of
52
2 cm from Canberra detector
5.14
Specific activities for 5 monitors irradiated bare
55
and with cadmium cover at irradiation position
10 of the rotary rack
5.15
Result of á parameter at irradiation position 10
56
calculated by iterative linear regression method
5.16
Specific activities for 5 monitors irradiated bare
57
and with cadmium cover at irradiation position
22 of the rotary rack
5.17
Result of á parameter at irradiation position 22
57
calculated by iterative linear regression method
5.18
Specific activities for 5 monitors irradiated bare
58
xvi
and with cadmium cover at irradiation position
27 of the rotary rack
5.19
Result of á parameter at irradiation position 27
59
calculated by iterative linear regression method
5.20
Specific activities for 5 monitors irradiated bare
60
and with cadmium cover at irradiation position
31 of the rotary rack
5.21
Result of á parameter at irradiation position 31
60
calculated by iterative linear regression method
5.22
The results of thermal to epithermal flux ratio of
63
corresponding irradiation positions
5.23
Activity of bare gold at irradiation positions
63
10, 22, 27, and 31 of rotary rack TRIGA reactor
5.24
Activity of gold irradiated with cadmium cover at
64
irradiation positions 10, 22, 27, and 31 of the
rotary rack TRIGA reactor
5.25
The results of thermal and epithermal neutron of
64
flux corresponding irradiation position
5.26
HOGDAHL reaction rate for elements irradiated
66
at irradiation position 10 of rotary rack
5.27
HOGDAHL reaction rate for elements irradiated
67
at irradiation position 22 of rotary rack
5.28
HOGDAHL reaction rate for elements irradiated
68
at irradiation position 27 of rotary rack
5.29
HOGDAHL reaction rate for elements irradiated
69
xvii
at irradiation position 31 of rotary rack
5.30
The criterion for Z-score
71
5.31
IAEA Soil-1 result at irradiation position 10
73
by absolute method
5.32
IAEA Soil-7 result at irradiation position 10
74
by absolute method
5.33
IAEA Soil-1 result at irradiation position 22
75
by absolute method
5.34
IAEA Soil-7 result at irradiation position 22
76
by absolute method
5.35
IAEA Soil-1 result at irradiation position 27
77
by absolute method
5.36
IAEA Soil-7 result at irradiation position 27
78
by absolute method
5.37
IAEA Soil-1 result at irradiation position 31
79
by absolute method
5.38
IAEA Soil-7 result at irradiation position 31
by absolute method
80
xviii
LIST OF SYMBOLS

-
Epithermal shape parameter
f
-
Thermal to epithermal flux ratio
th
-
Thermal neutron flux
epi
-
Epithermal neutron flux
ti
-
Irradiation time
td
-
Decay time
tm
-
Counting time
A0
-
Activity of irradiated sample
NA
-
Avogadro’s number
è
-
Natural isotopic abundance
M
-
Atomic weight
R
-
HOGDAHL Reaction Rate
S
-
Correction factors for saturation during irradiation
D
-
Correction factors for decay between irradiation and ã
counting
C
-
Correction factors for decay during counting
m
-
Mass of the target element
Np
-
full energy peak net count
ã
-
Gamma abundance
åã(E)
-
Detector efficiency at gamma energy
N
-
Number of interacting isotopes
 (E)
-
Cross-section in cm2 at neutron energy of E in
eV
ö (E)
-
Neutron flux per unit of energy interval
xix
óo
-
Thermal neutron capture cross section at 2200 ms-1
Io
-
Resonance integral for a 1/E spectrum
Io(á)
-
Resonance integral valid for 1/E 1+á spectrum
Ecd
-
Cadmium cut-off energy
Qo(á)
-
á- corrected Qo
Qo
-
Io/óo ratio of resonance integral to (n, ã ) cross section
Er
-
Effective resonance energy
Rcd
-
Ratio of the specific count rates of the samples
irradiated without and with a cadmium cover
Abare
-
Activity of bare monitor
Acd
-
Activity of monitor covered with cadmium
Fcd
-
Ratio of the activity of a monitor with a zero cadmium
cover thickness
Zá(Asp,n)
-
Specific count rate random error
Zá(Asp,n)bare
-
Bare specific count rate random error
Zá(Asp,n)cd
-
Cadmium specific count rate random error
Zá(Fcd,n)
-
Systematic errors of Fcd
Zá(Qo,n)
-
Systematic errors of Qo
Zá(Er,n)
-
Systematic errors of Er
Zá(Ecd,n)
-
Systematic errors of Ecd
Sá,T
-
Overall uncertainty of  parameter
n
-
Number of neutron per volume
v
-
Velocity of the neutron.
Pi
-
The fitted parameters of the function
E
-
Gamma energy of the ith photopeak in MeV
t1/2
-
Half Life
Z
-
Z-score
xx
LIST OF ABBREVIATIONS
NAA
-
Neutron Activation Analysis
HPGe
-
High-purity germanium detector
FNAA
-
Fast Neutron Activation Analysis
PGNAA
-
Prompt Gamma Ray Neutron Activation Analysis
NAA
-
Neutron Activation Analysis
MNA
-
Malaysia Nuclear Agency
CRM
-
Certified Reference Materials
MNA
-
Malaysia Nuclear Agency
xxi
LIST OF APPENDICES
APPENDIX NO.
TITLE
A
Scheme of Neutron Activation Analysis absolute
PAGE
95
method in determination the concentration of
element
B
Cd ratio for multi monitor method with 5
96
monitors at irradiation position 10 of the TRIGA
reactor rotary rack
C
Cd ratio for multi monitor method with 5
97
monitors at irradiation position 22 of the TRIGA
reactor rotary rack
D
Cd ratio for multi monitor method with 5
98
monitors at irradiation position 27 of the TRIGA
reactor rotary rack
E
Cd ratio for multi monitor method with 5
monitors at irradiation position 31 of the TRIGA
reactor rotary rack
99
CHAPTER I
INTRODUCTION
1.0
Introduction
Neutron activation analysis (NAA) was first discovered in 1936 and offers
excellent sensitivities and is superior to other analytical techniques. NAA perform
both qualitative and quantitative identification for a wide variety of materials in solid,
liquid, or gaseous states. The reason for the high sensitivity is that the cross section
of neutron activation is high in the thermal region for majority of the elements.
Because of its vast range of potential applications, neutron activation analysis is
utilized extensively in field such as geological science, medicine, agriculture, soil
science, and environmental studies.
Neutron activation analysis is a physical technique based on the nuclear
method. This technique is a non-destructive form of analysis. It can be used without
damaging the materials being tested and minimizing the risk for loss and
contamination. The undisputable advantage of this analytical technique is its multielemental character which enables simultaneous determination of many elements
without chemical separation. Moreover, NAA is capable of detecting many elements
at low concentrations. Nearly 70% of elements in the Periodic Table can be analyzed
2
by NAA.
1.1
Background of Study
There is a wide distribution of neutron energy in a reactor. The neutron
spectrum consists of three principal components (thermal, epithermal and fast
neutrons) based on their kinetic energies. In most reactor, thermal neutrons
component are dominant and slow neutrons are fully moderated within the reactor
with kinetic energies < 0.5 eV. Activation with epithermal neutrons is known as
Epithermal NAA. Cadmium or boron is used as thermal neutron filter. These
neutrons have been partially moderated and consist of kinetic energies of 0.5 eV to
0.5 MeV. Activation with fast neutrons (kinetic energies > 0.5MeV) is termed of Fast
NAA (FNAA).
In principal, NAA falls into two categories depending on the time of
measurement. Prompt gamma ray neutron activation analysis (PGNAA) measures
gamma ray emitted during the irradiation while delayed gamma ray neutron
activation analysis measures gamma ray as a result of radioactive decay.
There are three standard methods of NAA: relative method, kostandardization method and absolute method. Element analysis of an unknown
sample using the relative method is usually perform by firstly irradiating known
amounts of the sample and chemical standard simultaneously followed by comparing
their gamma ray spectrum of the elements interest and counting under the same
configuration. ko-standardization method is based on irradiation of a sample with a
neutron flux monitor such as gold and the use of nuclear constant called ko - factor.
This technique eliminates the need for using multi-element standards, thus is simpler
than the relative method in terms of experiment but involves more complex formulae
3
and calculation. Absolute method is a direct analysis of the irradiated samples
without using standard reference. This technique consists of absolute gamma ray
measurement and direct calculation of weights or concentrations from nuclear
constants.
1.2
Statement of Problem
The NAA relative method has been widely used in laboratory due to its direct,
simple, and accurate elemental analysis. However, in this relative method, no
detailed knowledge of the neutron flux,  in the irradiation site or the nuclear data of
the isotope concerned is required. The concentration of elements determined is
dependent on the flux gradient in the irradiation position. Therefore, when the
samples and standard have to be irradiated at different irradiation positions, the
variation of the neutron flux at different irradiation position in the reactor might
influences in the accuracy and precision of the analytical result. Besides, the different
radial shape of sample and standard can contribute to different spatial flux
distribution.
In the case of simultaneous determination of a great number of elements in
one sample, the relative method requires preparation, counting and data processing of
a standard for each element to be determined. It is also difficult to irradiate a large
number of standards and samples together in a vial. Therefore, this will limit the
samples that can be analysis by relative method.
There are possibility of instability and not homogeneity of the standard used
in NAA relative method. In addition, differences in matrix composition between the
sample and standard can contribute to uncertainty. All these factors can make relative
NAA method becoming cumbersome, time consuming, laborious and expensive,
4
despite the fact that it is a very sensitive analytical method.
1.3
Purpose of Research
The aim of this research is to develop an absolute method of Neutron
Activation Analysis that can be used in the laboratory of Analytical Chemistry,
Malaysia Nuclear Agency (MNA). The method is based solely on the reaction rate
formulations of the neutron capture processes. This absolute method requires the
input of neutron reactor parameters that have to be precisely determined by
experiment before the elemental masses of the irradiated samples can be computed.
1.4
Objectives of Research
The objectives of the study are:
i.
To calibrate the full energy peak efficiency of the detector for the
gamma ray spectrometer used.
ii.
To characterize the reactor neutron spectrum (epithermal shape
parameter , thermal to epithermal flux ratio f, thermal and epithermal
neutron flux th, epi,) at four selected irradiation locations at rotary
rack of the TRIGA MARK II reactor.
iii.
To determine the elements concentration of certified reference
materials (CRM) in order to examine the accuracy of the developed
method.
5
1.5
Significant of Research
The expected outcome from this research is a viable approach of doing NAA
which no longer rely on the use of multi standard materials that can be subjected to
many errors. This research is hoping to overcome some of the drawbacks of
conventional NAA method (Relative method) and able to produce reliable results that
can be effectively applied for NAA analysis. Besides, a large number of elements can
be determine simultaneously without the use of reference standards which can better
enhance the NAA technique. Hopefully, this new approach can be used by many
industries in the determination of elements in sample.
1.6
Research Scope
The scopes of the work have been defined to comprise:
i.
To calibrate the efficiencies of two detectors name Ortec detector
GEM10185 detector controlled by Gamma Vision software and
Canberra GC 3018 detector at different geometry.
ii.
To measure the epithermal shape parameter,  using 5 monitors (AuAl, Zr, Zn, Co and Mo) activation method with and without cadmium
cover at rotary rack facilities of 1MW TRIGA Mark II reactor at
MNA.
iii.
To determine the thermal and epithermal neutron flux of the
irradiation site by using gold foil activation method irradiated with
and without cadmium cover.
iv.
To determine the element concentration of soil-1 and soil-7. This
6
sample is intended to be used as a standard reference material in
quality control material for the assessment of a laboratory’s analytical
work.
7
CHAPTER II
LITERATURE REVIEWS
2.0
Introduction
The application and development of NAA absolute method has been
extensively dealt with by several authors such as Kafala and Macmahon [1]. The first
systematic methodological investigation was reported by Girradi et al [2]. It was
concluded that uncertainties in the nuclear data taken from the literature may be the
major source of systematic errors especially on decay schemes and activation
cross-section. Besides that, the scatter of resonance integral without taking into
account the deviation of epithermal neutron distribution, á parameter can lead to
poor accuracy of result. The NAA absolute method utilizes the formulation of
saturated gamma ray emission rate for (n, ã) reaction in a thermal reactor through
Hogdahl convection [1] and the parameters of neutron distribution. The NAA
absolute method attracted research effort in investigation the information of neutron
flux in the irradiation position, and the nuclear data concerning the product nuclides
for determine the element concentration in samples.
The nuclear data have been studied and evaluated by experimental recently.
The situation has improved significantly ever since and presently the uncertainties of
the nuclear data in literature are acceptable to be accurate for analysis purpose [3].
8
Furthermore, the nuclear data can be determine experimentally from irradiation of a
multi-element standard if information of gamma ray peak detection efficiency
function for source detector geometry was available [4]. With the expertise coupled
with the many available resources, absolute method should rekindle a new interest in
NAA technique.
2.1
Neutron Sources
The basic essentials required to carry out neutron activation analysis are
neutron sources. The existence of neutrons were proposed by Rutherford in 1920 [5]
and finally discovered by Chadwick in 1932 [6], [7].
There are different ways to obtain neutrons and nuclear chain reaction is used
in this research. Neutrons are produced from the radioactive decay of uranium atom.
Uranium is principal element used in nuclear fission reaction because it’s high
fission probability and being a naturally occurring element. Nuclear fission was
discovered by Lise Meitner, et al 1939 [8].
Figure 2.1: Nuclear Chain Reaction
9
In a nuclear fission, uranium-235 atom absorbs a neutron. This causes
uranium-235 to become unstable and break up into two lighter nuclei (fission
fragments), emitting three neutrons and a large quantity of binding energy. There are
fewer neutrons will be captured by uranium-238 to breed plutonium-239. The
released neutrons then induced fission with nearby uranium-235, which releases
another three neutrons and more binding energy. A series of fissions is called a chain
reaction [9].
A nuclear reactor is a device to initiate nuclear chain reactions and produces a
large quantity of neutrons. Reactors are often referred to as “swimming pool” type
reactors which the uranium rods are immersed in a bath of light water. Natural
uranium contains 0.7%
235
U. Therefore, the fuel must be slightly enriched in 235U to
about 3% (low enriched uranium) for uranium to work in a nuclear reactor. Neutrons
released in fission will usually travel out of one of the fuel rods, and pass through
moderator before they encounter uranium in another fuel rod. A moderator slowed
down the fast neutrons released from the uranium so that they initiate further fission
reaction. The most common moderators are graphite (carbon), light water (H2O), and
heavy water (D2O). In nuclear reactors control rods such as boron are used to capture
the neutrons to control the rate of fission. Water as the cooling system is often used
to absorb the heat produced during nuclear fission. A nuclear chain in the reactors
could be maintained in critical condition if the nuclear chain reaction is achieved
without external neutron sources (effective multiplication factor, keff = 1).
The probability that a nuclear reaction occurring is measured in units of
“barns” where 1 barn equals 10-24 cm2. The probability of the particular reaction
occurring increases with the cross section is increased. Each element has its own
neutron cross section.
10
2.2
Nuclear Reaction
Basically, a sample containing certain rare earth elements will become highly
radioactive after an exposure to a field of neutrons by neutron capture or (n,ã)
reaction as illustrated in figure 1. The binding energy of the neutron within the
nucleus produces a compound nucleus in an excited state. Then the activated nucleus
decays according to a unique half life and emit gamma quanta with specific energies
into a more stable configuration. The quantity of radioactive nuclides is determined
by measuring the intensity of the characteristic gamma-ray lines in the spectra. Since
the energy levels of a nucleus for each isotope are different, the gamma rays emitted
from one isotope will not have the same intensity. Therefore, measurement the
specific gamma ray (with specific energy) indentifies the presence of particular
element and their relative concentrations. The decay constant is inversely
proportional to the radioactive half-life. Therefore, depending upon the half life of
the nuclides, different nuclides in the irradiated samples can be determined using
gamma ray spectroscopy.
As an example, when a stable isotope of manganese-55 is bombarded with
neutron flux, a radioactive isotope manganese-56 is produced by neutron capture
reactions. The radioactive isotope produced in this activation process will decay with
a half life of 2.58 hour through the emission of three gamma rays with energies of
846.8 keV, 1810.7 keV, and 2113.1 keV. If an unknown sample is irradiated with
neutrons and emitted gamma rays with energies 846.8 keV, 1810.7 keV, and 2113.1
keV indicating the unknown sample contained manganese. The amount of
managanese present could be calculated based on the known neutron flux and the
neutron capture cross- section of manganese-55. Figure 2.2 represents the example of
gamma spectra from a sample of pottery irradiated for 5 seconds, decayed for 25
minutes, and counted for 12 minutes with an HPGe detector.
11
Figure 2.2: Gamma Spectra from a sample of pottery [10]
2.3
The Trend of NAA
Since NAA technique depends on the availability of irradiation facility (a
nuclear reactor) to activate the samples, this method is less applied compared to other
analytical technique such as atomic absorption spectroscopy. Besides that, the NAA
technique requires manpower and time for preparation and analysis procedure.
However, this technique is classified to be an excellent sensitivity and feasible
analytical method. Throughout the year, much research has been carried out to
improve and optimize this analytical method. The ko- standardization method has
been proposed and applied to simplify the NAA method by eliminating the task of
preparing numerous standards. Basically there are two standardization methods used
in NAA, the relative and the non-relative methods.
12
2.3.1
Relative Method
Relative method has been widely applied and primarily used in the analytical
laboratory due to its simplicity. A standard which consist an accurate mass of interest
element is irradiated at the same time with the unknown sample under identical
condition [11]. The concentration of the element of interest is calculated by
compared of the measured activity between the sample and the standard.
Consider a sample of mass, W is irradiated in a neutron flux, ö. After
irradiation and allowed suitable cooling time, the irradiated sample is counted for a
time tc. The mass of element, i in the sample is mi, and then the concentration ci can
be calculated through Equation (1) [12].
C
i

m
W
i 
(N
/ t ) M
p
c i
i
    ( E ) N SDCW
i i i
i
A
(1)
where Np is the net photo peak count, Mi is the atomic mass of target nuclide, ó is the
effective cross section for (n,ã) reaction, è is the abundance, ã is the gamma yield,
å(E) is the efficiency of the detector at gamma energy E, NA is the Avogadro’s
number and S= (1-exp-ëti ) is the saturation factor, D= (exp-ëtd) is the decay factor,
and C= (1-exp-ëtc)/ëtc is the counting factor.
In comparative method, it is assumed that neutron flux, cross section,
irradiation time and other variables associated with counting are constant for sample
and standard. Therefore, by corrected the counting rate of one to the same decay time
of the other, the two counting rate are in the same proportion as the weight of the
elements. The concentration of the element in the sample, Csam is found by comparing
to the standard through the following Equation (2):
C
sam

[( P
A
[( P
) CD ]
 [ CW ]
c
sam
std
/ t ) CD ]
W
A
c
std
sam
/t
(2)
13
where (PA/tc)
std
and (PA/tc)
sam
are the counting rates for standard and sample,
respectively, csam and cstd are the concentration of element in sample and standard,
respectively, C and D are are the counting and decay factor. Equation (2) can be
rewritten as:
C
sam
 C
W std
std
W
sam
A sam
A
std
(3)
Asam and Astd are respectively the count rate of element in sample and standard, Csam
and Cstd are the concentration of the element in units of ppm for sample and
standard and Wsam and Wstd are weight of the sample and standard in units of gram.
The relative method promises the highest accuracy when the standard and
sample match well in composition, irradiation and counting conditions.
2.3.2
ko- Standardization Method
As there are some difficulties associated with the comparative method,
ko- standardization method was established to complement the comparative method.
This method is based on co-irradiation of unknown sample with a single comparator
such as gold as neutron flux monitor and the use of a composite nuclear constant
called ko-factor. The peak area for the gamma ray of element in a sample is compared
to gold. Gold has been used as single comparator due to its relatively high resonance
integral value. As opposed from relative method, this method requires good
knowledge about reactor neutron parameter and ko values [13] of the gamma ray as
well as the detector's peak efficiency. The ko is a measure of the gamma ray emission
rates and activation by thermal neutrons relative to gold. In ko-standardization
method, the concentration of the element csam in ppm was calculated using Equation
(4) [12].
14
C sam

1 A ( sp , sam )
k A
( sp , Au )
(4)
The net peak area was converted to specific count rate (Asp) as shown in following
equation:
PA / t c
A sp 
SDCw
(5)
where Asp, sam and Asp ,Au are the specific count rate of an element in sample and
Au-198 as the comparator, respectively, k is the specific count rate ratio of an
individual element in sample to the comparator and is expressed by:
k  k
( f  Q
(  )) 
o
o ( f  [ Q (  )]
o
Au )  Au
(6)
where
ko 
M Au  th
M


Au Au thAu
(7)
Qo= Io/óo, where Io is the resonance integral and óo is the thermal cross section. The
Ko factors are accurately measured compound nuclear constants and independent of
irradiation and measurement conditions. These factors have been recently compiled
and published for most analytical radionuclide.
This technique has been reported to be simpler than comparative method in
term of experiment which eliminates the need for multi-element standards. Besides
that, this method also provides precision and accuracy as same as comparative
method. However, the ko-NAA technique involves complicated formulas and
calculations. Due to the apparent complexity and substantial effort required to
implement, the ko-method still not widely used in the analytical laboratory.
CHAPTER III
THEORY
3.1
Neutron Activation Equations
The intensity of the gamma line measured by gamma ray spectroscopy is
proportional to the element activity. The activity A0 formed in a sample from an
amount m of an element which is irradiated with neutron flux is described by the
activation in Equation (8).
A
o
 m
N Aè
RSDC
M
(8)
where NA is Avogadro’s number, è is the natural isotopic abundance, M is the atomic
weight, R is the predicted saturated gamma ray emission rate, S, D, and C are the
respective correction factors for saturation during irradiation, decay between
irradiation and ã counting, and decay during counting, and m is the mass of the target
element.
In absolute method, measurement of the irradiated sample with the use of an
unknown efficiency detectors enables the determination of element mass, m from the
activity of its isotope without the used of multi-element standard [13]. The neutron
16
activation analysis is based solely on the reaction rate formulations of the neutron
capture processes. The calculation of analytical results by Equation (9) is the
absolute method [14].
m 
N pM
N a è  R  ( E ) SDC
(9)
where Np is the net photo peak count, ã is the gamma yield, and å(E) is the efficiency
of detector at gamma energy E.
In order to calculate the activities, this requires accurate knowledge of
nuclear data such as atomic weight, cross section and isotopic abundance of the
isotope concerned. All nuclear data may be taken from the literature, and the
experimental parameters are determined in the laboratory.
3.2
HOGDAHL Reaction Rate
A number of formalisms have been suggested to describe the reaction rates.
The rate at which reactions occur depends on the particle energy, the flux of the
neutrons and the nuclear reaction cross section.

R  N   ( E ).  ( E ) dE
(10)
0
where N is the number of interacting isotopes, (E) is the cross-section in cm2
at neutron energy of E in eV and ö(E) is the neutron flux per unit of energy
interval in cm-2 s-1 eV-1.
The reaction rate per target nuclei, R, of a sample irradiated by reactor
neutrons is described according to the HOGDHAL convention [4] shown in Equation
(11). The HOGDHAL convention employed for the present propose is as accurate as
17
the complex formalisms such as Westcott.
R  R th  R e   th  o   epi I o
(11)
where Rth = ( öth óo) is the reaction rate induced by pure thermal neutrons and
Re = (öe Io) is the reaction rate induced by epithermal neutrons, öth is the thermal
neutron flux and öepi is the epithermal neutron flux. It is interesting to remark that
öth is related to the sum of Maxwellian neutrons up to Ecd and of epithermal neutrons
below Ecd. The division between them being the cadmium cut-off energy, Ecd = 0.55
eV. óo is the thermal neutron capture cross section at 2200 m s-1 and Io is the
resonance integral for a 1/E spectrum.
3.3
Non-ideal 1/E 1+á Epithermal Neutron Flux Distribution
For an ideal situation, the epithermal neutron flux is accepted to be inversely
proportional to the neutron energy. This happens in a reactor with none absorbing,
infinite medium where the epithermal neutron flux is constant per unit lethargy.
Therefore, the resonance integral, Io an essential nuclear parameter in neutron
activation is defined as Equation (13). A compilation of resonance integrals Io for all
nuclides is available in the literature.
I0 


Ecd
ó(E)
E
dE
(12)
However, in actual irradiation sites, the epithermal neutron flux is deviating
from the ideal 1/E epithermal spectrum to 1/E 1+á distribution, E is the neutron energy.
In absolute activation analytical techniques, epithermal neutrons give rise to an
important fraction to the overall neutron fluxes [15]. Therefore, the effect of the non
ideality of the epithermal spectrum should not be underestimated. By consequence,
the resonance integral needs to be modified with an á-dependent term and converted
18
to equation (13) or (14) instead of Equation (12) which are valid for 1/E 1+á spectrum
[16].
Iá 


Ecd
ó(E)
dE
E 1 á
(13)
or
Iá 
Q
o(  )
I
o
(14)
Therefore, in real reactor situation the modified reaction rate [4] can be
written as Equation (14).
R  R th  R epi   th  o   epi I 
(15)
The parameter  measure the deviation of the epithermal flux distribution
from the ideal 1/E distribution and is independent of neutron energy [17]. This
indicates that the resonance integrals for practical use are a function of á. Thus, in the
activation analysis with reactor neutrons, á should be known to preserve the accuracy
of the analysis results. Qo(á) is the á- corrected Qo to take care of non ideality of the
epithermal spectrum as defined by:
Qo,(á) =
I o ( )
óo

(1eV) á  ó(E)dE

ó o 0.55 E1á
(16)
The recommended value for a cylindrical cadmium box with a uniform
thickness of 1 mm is 0.55 eV. The conversion from Qo (á =0) to Qo(á) is given by:
Qo,(á) = q
o ( )
 C

(17)
with
q o (  )  ( Q o  0 .429 )( Er )  
and
(18)
19
C


0 . 429
( 2   1 )( 0 . 55 ) 
(19)
Finally Qo(á) is obtained as[18]:
Qo, (á) =
Q
o ,i
(E
 0 . 429
r ,i
)


0 . 429
( 2   1 )( 0 . 55 )

(20)
Qo is the Io/óo ratio of resonance integral to (n, ã) cross section at a 2200 m s-1
neutron velocity [19]. Qo(á) can be easily calculated from Qo if á is known and the
effective resonance energy, Er is available. Both Er and Qo value are tabulated in
literature as nuclear constants and applicable to all practical irradiation condition.
For the conversion, the effective resonance energy, Er must be used for the
correction of resonance integrals in deviating epithermal spectrum. It is the energy of
a single resonance which gives the same resonance activation effect as the actual
resonances for the isotopes. The effective resonance energy, Er,i is defined as [16]:
( Er )   
3.4
Io( )
Io
1 eV

(21)
Determination of á and f parameter
The deviation of the epithermal flux distribution from1/E, á is as fundamental
as the correction of resonance integrals Io, i.e., the conversion of Io values to Io(á)
values for its use in actual 1/E
1+á
epithermal neutron spectrum. The term  is in
small positive or small negative value constant which is assumed to be energy
independent, its values depending on the reactor configuration and irradiation
position (moderator material, geometry, etc). The parameter á can be determined by
20
cadmium ratio multi-monitor method, cadmium covered multi monitor methods or
bare multi-monitor methods [20]. In this work, the parameter á was determined using
cadmium ratio multi-monitor method as it utilizes the ratios which improves the
estimates of the uncertainty.
3.4.1
The Cadmium ratio multi monitor method
A set of N monitors are irradiated with and without a cadmium cover
respectively and counted on a Ge detector with a known detection efficiency curve.
The minimum number of monitor is two (N=2). When a sample is irradiated within a
cadmium cover, the thermal neutrons are excluded. If all the monitors have a
ó(v)~1/v dependence of up to ~1.5 eV, á can be obtained as negative slope (-á) of the
straight line [21] by plotting graph of Equation (22):
log
( Er , i )  
1
( Fcd , i R cd ,i ) Q o , i (  )
versus log Er,i
(22)
where i denotes isotope 1,2,...,N. Rcd is the ratio of the specific count rates of the
samples irradiated without and with a cadmium cover, respectively. The equation
describing the cadmium ratio method is:
R
cd

A
bare
F R
cd
cd

(  th ó th   epi I o )
 epi I o
(23)
where Abare is the activity of bare monitor. Equation can be also written as:
R
cd
  epi I o
(24)
Fcd is the ratio of the activity of a monitor with a zero cadmium cover
thickness. The specific count rate of cadmium covered isotope maybe different from
21
the specific count rate induced by epithermal neutrons. A cadmium filter may
attenuate some of the resonance neutrons which cause a reduction in the activity of
the monitor. Therefore, Equation (22) should be divided by a correction factor for
cadmium transmission of epithermal neutron, Fcd. The transmission factor of thermal
neutrons through the cadmium, Fcd for Au was taken as 0.995 while the others were
assumed to be unity.
The left hand term of Equation (22) is a function of , and thus the iterative
procedure should be applied with a least square regression analysis to fit the
experimental data to the straight lines for every iterative step. Parameter  is initially
set equal to 0 followed by iterative procedure until no significant variation of  value
is observed. Analogously, the final - result of this iteration procedure is identical
with the solution of the Equation (25) for  [21]:
á+
 log Yi (  )
 log Er , i  

  log E , r 
  log Yi (  ) 
N
N


 log Er , i 

  log Er , i 

N


where
log Yi (á) = log
2
(Er, i) 
( Fcd,i R cd,i 1 )Q o,i()


 0
(25)
(26)
The parameter f, ratio of the thermal to epithermal neutron flux can
determined from one monitor [20]. A gold monitor is suitable for these requirements.
The experimental determination of the parameter  was performed by applying the
cadmium ratio for multi-monitor method allowing the simultaneously determination
of f.
22
By simplifying Equation (23), Rcd is obtained as:
R
cd

(  th ó
th )  1
(
I )
epi o
(27)
and
( R cd  1) 
(  th )  1 


( epi )  Qo 
(28)
as the ratio of thermal to epithermal flux is generally defined as:
f 
( th )
( epi )
(29)
and the ratio of resonance integral to thermal cross section is given as:
Qo 
Io
 th
(30)
Thus, the ratio of thermal to epithermal flux can be obtained as:
(31)
f = (Fcd Rcd-1) Qo(á)
3.4.2
Error Analysis of á parameter
The accuracy and precision of á determination in 1/E
1+á
epithermal neutron
spectrum are analysis based on the error propagation theory. The overall uncertainty
on á includes random error, systematic error and gross error [22].
The random error influenced the precision of á which can be described by the
probability. The specific count rate is determined by counting statistic and thus is
essentially random. The factor of Zá (Asp,n), Zá (Asp,n)bare, and Zá (Asp,n)cd are
consider same which equal to equation (32). For n-th monitor one obtains:
23
n


 logEr, i 

 logEr, n  i



N


f  Q

o , n(  ) 1 
Z (A sp , n)  0.434

f
á
ì
i
(32)
where
N
N


log
Er
,
i
Vi


N 

i
 i     log Er , i  i
V

 i
i
N
N











(33)
0 . 26 C   1 . 67

 1

Q o ,i (  )    1 / 2

(34)
and
Vi 
q o ,i (  )
Q o ,i (  )
log Er , i 
and
qo,i(á) = Qo,i – Cá
(35)
and
C 
2 (E o )1 / 2
( 2   1)( Ecd )   1 / 2
(36)
The systematic errors influence the fixed accuracy of á determination. The
nuclear data of monitor as well as the uncertainty on Ecd contribute significantly to
the fixed accuracy. The factor to be considered are Zá (Fcd,n), Zá (Qo,n), Zá (Er,n) and
Zá (Ecd,n). The factor can be written as following equation.

f
Z (Q o , n )   Z
.

  ( A sp ,n ) f  Q
o, n ( )

and
  E r , n )    Q
 o, n
. 

Q
o , n ( )

(37)
24

f
Z  (E , n )  Z
.
r
  ( A sp ,n ) f  Q
o ,n ( )


q
.  . o ,n ( )

Q
o ,n ( )

(38)
and
N

1
n



log
Er
,
i


n 

i Q o ,i (  )
1

   log Er , i  i

N
N
i 
  Q o ,i (  )




1 

Z  ( E cd , n )  0 .434 C  (   1 / 2).

i


 

  (39)

The experimental accuracy is considered to be determined by gross error. If
the experiment is under well controlled condition, the gross error on specific count
rate can be estimated to be about 0.5%. The common experimental errors are
canceling each other as Asp ratio is introduced in á determination. The overall
uncertainty is obtained by quadratic summation of the precision, fixed accuracy, and
experimental accuracy and is defined as:
Sá,T = (S2á,R + S2á,S + S2á,G)1/2
3.5
(40)
Epithermal and thermal neutron flux
The neutron can roughly be split into 3 groups of neutrons, each with its own
characteristics as shown in Table 3.1.The neutron spectrum at an irradiation position
represented in Figure 3.1 can be expressed as a sum of thermal equilibrium spectrum:
Maxwellian distribution, neutron energy from 0 to 1 eV; epithermal spectrum in the
slowing down region and fast neutron from 1 eV to maximal.
25
Table 3.1: Three main neutron groups
Group
Energy Range
Region
Fast
>10keV
fission
Resonance
1eV-10keV
1/E*
Thermal
0-1eV
Maxwellian
*E= neutron’s energy
Figure 3.1: A reactor neutron spectrum is contributions from a purely Maxwellian
shape in the thermal energy region, an epithermal region and negligible
fast spectrum [11]
The neutron flux is important in characterizing the activation process for
producing radionuclide with neutron activation analysis. Thus, it is crucial to
understand the neutron flux gradient distribution in the irradiation position in order to
improve the accuracy and precision in the determination elemental concentration of
various samples. A gradient of neutron flux at irradiation site of a research reactor is
significant if the samples and monitor have to be irradiated at different irradiation
position [23], [24]. The specific activity of element will be influenced by the neutron
flux during the irradiation. Neutron flux defined in Equation (40) is a term referring
26
to the number of neutrons passing through an area of target nucleus in unit time [9].
It is most commonly measured in neutrons cm-2s-1.
ö = nv
(41)
where n is the number of neutron per unit volume and v is the velocity of the neutron
cross section. When an element with a relative atomic mass, M with cross section, ó
is irradiated with neutron flux ö for a time, t, the specific activity of an element Asp
can be described by the following equation:
A sp  N A

(1  e   t )
M
(42)
The large number of resonance peaks for most nuclides makes calculation of
neutron flux slightly complicated. In order to avoid these resonances, a gold standard
is used because the reaction 197Au (n,ã) 198 Au has a single resonance at 411 keV peak
and the nuclear data of standard gold has been well investigated. The activity ratio
for a gold wire irradiated with and without cadmium covers (cadmium ratio method)
is used for measuring the thermal and epithermal neutron flux. In order to separate
the activities due to thermal and resonance neutrons, bare and cadmium-covered gold
foils are exposed under identical conditions and the activities are measured. This is
because cadmium is an effective absorber of neutrons below certain energy, Ec, but it
passes neutrons of energies above Ec. Ec is known as the “effective cadmium cut-off
energy”. Gold can absorb thermal and epithermal neutrons due to its response region
is in between 0.0015 eV to 5.8 eV. Therefore, if the cut off energy of cadmium is
0.55 eV, the difference between the activity of bare gold foil and gold foil covered
with 1 mm Cadmium if both irradiated under ideal condition lead to the activity
caused by the thermal neutron flux. Aluminum diluted with gold is usually used to
avoid self shielding effect. Besides that, aluminum with short half life (2.3 minutes)
does not affect the neutron flux.
Activity of gold irradiated under bare condition:
A bare = ö th ó th N[1-exp(-ëti)exp(-ëtd)] + ö epi ó epi N[1-exp(-ëti)exp(-ëtd)]
(43)
27
Activity of gold covered with 1 mm cadmium:
A cd = ö epi ó epi N[1-exp(-ëti)exp(-ëtd)]
(44)
where N is the total number of target nuclides in the foil, ti is the irradiation time, td is
the decay time, ó
th
is the thermal cross section equal to 98.8 barn. ó
epithermal cross section, ö
th is
the thermal neutron flux and ö
epi
epi
is the
is the epithermal
flux.
The different between equation (41) and (42) is the thermal activity as proven in
Equation (43).
Athermal = Abare − ACd
(45)
Therefore,
A thermal = ö th ó th N [1-exp (-ëti) exp (-ëtd)]
(46)
From this equation, thermal neutron flux could be determined from the
thermal activity equation (44). Subsequently, the epithermal neutron flux can be
obtained via the flux ratio (th/epi).
The specific activity of bare and cadmium covered gold are calculated using the
following equation:
A
( N / m)  
 ( E )  (1  exp( t i )) exp( t d )(1  exp( t c ))
(47)
Thermal neutron flux was determined by the equation below:
 th 
A bare  A epi
(N A / M )  o
(48)
Epithermal neutron flux was obtained from thermal to epithermal flux ratio equation
and thermal neutron flux:
ö epi

ö th
f
(49)
28
Table 3.2 listed all the nuclear data of gold extracted from literature required in
neutron flux calculations [25].
Table 3.2: The nuclear data of gold used in calculation thermal and epithermal
neutron fluxes.
Gold
Reaction
197Au(n, ã)198Au
Gamma energy
412keV (95.5%)
(ã abundance)
Half life of Au-198
2.696 days
Thermal cross section at 25 0C
98.8×10-24 cm-2
Resonance integral
1562×10-4cm-2
90% response region in reactor spectrum
0.015eV-5.8eV (epithermal + thermal)
Atomic mass of target nuclide
196.9665 gmol-1
Isotopic abundance
100%
Avogadro number
6.023×1023 mol-1
3.6
Full-Energy Peak Detection Efficiency
The knowledge of absolute photopeak efficiency is required in order to
identify specific isotope as well as to quantify the concentration in the sample
without multi-element standards. Gamma ray spectrometer determines the number
and energy of the photons emitted by the source and provides a unique identification
of the radioisotopes. The spectrum observed by detector is contributed by several
processes. Gamma rays in the energy range up to 3 MeV interact with matter by
photoelectric effect, compton scattering and pair production. When a ã-ray enters a
germanium detector volume, the energy of gamma rays can be transferred to
electrons. Low energy gamma rays may be absorbed by photoelectric effect and
produce a single electron with energy similar to initial photon. In spectrum, this
29
events show up as full energy photopeak below 0.1 MeV. The interaction between
gamma rays and germanium ranging from about 0.1 MeV to 1 MeV is through
Compton effect. Thus, Compton events provide a peak at low energy area in the
spectrum. The photon losses energy and is scattered from its original path. The pair
production event contributes at energies greater than 1.02 MeV and creates an
electron positron pair. All three processes thus convert gamma ray energy into
electrons or positrons of various energies.
Figure 3.2: The spectrum observed by detector contributed by interaction of
gamma ray with germanium. [26]
The detector efficiency is the probability of emitted gamma ray will interact
in the sensitive volume of the detector and produce a count.
Detector
Efficiency
The numbers of selected pulses recorded per unit time
=
The number of photons emit by the source per unit time.
(50)
Full energy peak efficiency is the ratio between the numbers of counts in the
net area of the full energy peak to the number of photons of that energy emitted by a
source with specified characteristics for a specified source to detector distance.
The efficiency equation can be written as:
30
çi =
Np
tm A ã
(51)
where Np is the full energy peak net count corresponding to the gamma photons with
energy E , tm is the counting time, ã is the gamma abundance and A is the activity of
the source.
For efficiency calibration, one can use any source with known nuclide
activity and gamma emission probability. Standard gamma-ray sources that cover the
energy range of interest are used to calibrate the detector and to determine the total
full-energy peak efficiency. The detector efficiency was calibrated by establishing the
detector efficiency curve as a function of defined geometry and energy range [27].
An example of ideal efficiency curve is shown in figure 3.3.
The efficiency values of sample at intermediate energies are determined by
interpolation between the measured values. The efficiency calibration points were
fitted to a polynomial function in order to obtain the most accurate intermediate
values. The following polynomial function has been applicable for a variety of
different Ge (Li) detectors [28].
å (E) =
P1  P2 ln( E)  P3 ln( E) 2  P4 ln( E)3  P5 ln( E) 4
E
(52)
Pi represents the fitted parameters of the function to be determined. E is the gamma
energy of the ith photopeak in MeV
31
Figure 3.3:
An example of ideal efficiency curve plotted against gamma
energy [28]
CHAPTER IV
METHODOLOGY
4.0
Introduction
For absolute method of NAA, it is necessary to calibrate the neutron spectrum
in the irradiation facility, i.e., the determination of the epithermal flux spectrum
shape factor ( ) and flux ratio( f ), the thermal and epithermal flux(th, epi).
Besides that, the full-energy-peak efficiencies (åã) of the gamma ray detector to those
used in counting the unknown samples have to be determined by using sources of
known activities. The flow chart of methodology for NAA absolute method was
represented in Appendix A.
4.1
Reactor TRIGA Puspati
Reactor TRIGA Puspati (RTP) is the only nuclear research reactor in
Malaysia. RTP is a pool type nuclear research reactor where the reactor core is
immersed in an open water pool as shown in Figure 4.1. Light water in the reactor
33`
tank is used as cooling agent and radiation shield. High purity graphite is used as
reflector and uranium-235 as nuclear fuel. The reactor is built with 2.5 m thick
concrete wall to attenuate radiation emission and shield the reactor from
contamination. With a thermal power capacity of 1 Megawatt, RTP has an average
neutron flux of 1.2×10 12 cm-2s-1. The cylindrical reactor is in symmetrically
geometry and compound by the fuel elements, beryllium and graphite blocks, control
rods and irradiation channels. There are four control rods to control the fission
reaction. Cherenkov radiation is used to measure the intensity of the reaction.
RTP produces free neutrons with energies ranging up to 10 MeV using a
mixture of americium and beryllium as the neutrons source. These free neutrons
produced in the cylindrical reactor core are used in neutron activation analysis (NAA)
and other nuclear application. Various irradiation facilities were located in the core or
adjacent to the core to enable the samples to be exposed to neutrons in the reactor
core. The rotary rack housed within the graphite reflector is used for irradiate the
samples at the edge of reactor core. The rotary rack contains of 40 irradiation
position and will rotate around the reactor core which aims to expose the samples
with similar neutron flux (see Figure 4). If the rotary rack is at stationary mode, the
variation of neutron flux might be more significant. The reactor are operated and
monitored by using control computer system to manage the irradiation process for
safe operation.
Figure 4.1: Reactor TRIGA Puspati (RTP) with power of 1 Megawatt.
34`
Rotary rack
Reactor core
10
31
27
22
Figure 4.2: Reactor rotary racks with experimental irradiation facility [29]
35`
4.2
Gamma-ray Spectrometry
A typical gamma-ray spectrometer consists of a Ge detector, preamplifier,
analog to digital converter (ADC), multi-channel pulse-height analyzer (MCA) and
data readout devices. Germanium detectors produce the highest resolution in
determine the gamma rays emitted by radioactive elements located in the detector.
The detector is operated at liquid nitrogen temperature in order to minimize thermal
noise. A radiation shield surrounds the detector to reduce the background counting
from surrounding environment to produce higher detection efficiency. The detector is
equivalent to a p-n junction having a thick layer of pure germanium at the position of
the junction. Photons (gamma rays) interact with the Ge crystal to produce electronhole pairs. These ionizing particles are collected to produce a pulse and the
magnitude of the output pulse is proportional to the amount of energy deposited in
the detector. These small output signals are amplified, reshaped, and sorted according
to pulse height, using an ADC to produce a histogram. The signal then converted into
a digital format. After a number of pulses, the histogram will display peaks in the
spectrum with Gaussian distribution that corresponding to the number of photons
interact with the detector. A computer with processing software or oscilloscope
display is used to display and store the resulting spectrum.
Figure 4.3: HPGe detector operated at liquid nitrogen temperature
36`
Figure 4.4: Set up of gamma ray spectrometer
4.3
Calibration of gamma ray spectrometer
The efficiency depends on the gamma energy, the detector, and the geometry
of the measurement. High-purity germanium (HPGe) detector name Ortec GEM10185 detector with Gamma Vision software and Canberra GC3018 detector with
Genie 2000 software were calibrated in this experiment. The efficiency calibration
was performed using gamma-ray standard point sources namely Ba-133, Cs-137, Co60, Am-241, Eu-152 and Na-22 with well known gamma ray intensities. The
efficiency calibration was performed in at position 12 cm, 8 cm and 2 cm from end
cap of Canberra detector. For Ortec detector calibration, the standard sources were
counted at 10 cm, 6 cm and 2 cm geometries from the detector. For large source -todetector distances, the source activity is high enough to achieve an acceptable
accuracy. Small source-to-detector distances are required for determine low activity
level samples. Changes in the source-to-detector distance can make a large different
37`
in the count rate. However, the dead time was kept below 10% in order to reduce the
counting error. The position of the sources for each calibration needs to be as close as
to identical position to perform an accurate efficiency calibration.
Figure 4.5: Canberra GC3018 detector with Genie 2000 software
Figure 4.6: Ortec GEM-10185 detector with Gamma Vision software
38
4.4
Determination of reactor neutron spectrum parameters
The thermal to epithermal neutron flux ratio, f and the deviation of the
epithermal neutron spectrum from the 1/E shape, á is the essential parameters for the
correct application of absolute NAA analyses. Among the various experimental
methods available for determining the epithermal deviation factor, the cadmium ratio
method is known to yield the most accurate results. Therefore, thermal and
epithermal neutron fluxes, as well as á and f in rotary rack irradiation facilities were
determined by applying Cadmium ratio method. Reactor neutron spectrum
parameters (á, f and neutron flux) were determined in irradiation position 10, 22,
27,and 31 of TRIGA reactor rotary rack.
The following set of monitors were used to characterize the neutron
irradiation facility: Al-Au, purity 0.1124% Au, pure 99.9845%, diam. 0.0508 mm;
Zr , purity 99.7329%; Zn, purity 99.9872%, thickness: 0.254 mm; Co , purity
99.9133% and Mo, 99.945, diam. 0.0508 mm. These elements have cross sections
and resonance energies with Qo values ranging from low to very high and thus serve
a quality control of the irradiation facility. The weighing of the monitors were
carefully carried out using the same Electronic Micro Balance and on the same day
in order to eliminate the systematic error due to weighing of small masses. Known
amount of the monitors were cut into roughly equal pieces and rolled spirally. Two
set of this five monitors were prepared. One set was irradiated bare and another for
irradiation under a cadmium cover of 1 mm thickness. For bare irradiation, the 5
monitors were packed together in a standard polyethylene vial. All the samples were
irradiated for 1 hour at maximum thermal power of 750 kW. The rotary rack was
kept stationery throughout the irradiation process. The irradiated samples were
allowed to decay with an appropriate cooling time. After one day cooling, all the
monitors were counted at the same distance from the calibrated HPGe detector with
counting time 5 to 60 minutes in order to obtain suitable counts. The monitors
irradiated at irradiation position 27 were measured using Canberra detector at
distance of 12 cm. The others irradiation positions’ monitors were measured using
Ortec detector at distance of 10 cm. Later, the ã-ray spectrum emitted from the
39`
irradiated monitor was analyzing to calculate the Rcd, á and f parameter. The
epithermal and thermal neutron fluxes, f was determined using gold monitor with the
similar procedure.
Table 4.7 shows a list of suitable monitors and relevant nuclear data. Metallic
or alloyed foil or wire monitors were chosen covering a wide range of Er (from 5 to
6000 eV). The selection of monitors ranging from low to high Er is to obtain a
linearity of the curve, thus provided á is constant over the whole epithermal neutron
energy region in the reactor position.
Polystyrene vial
(Bare Irradiation)
1mm thickness cadmium cover
(Cadmium Covered Irradiation)
Figure 4.7: 2 set of monitors irradiated in bare condition and with cadmium cover,
respectively
40`
Table 4.1: Monitors and relevant nuclear data require in the work [30].
Monitor
Er, eV
Au-197
5.65 ± 7.1
Co-59
136 ± 5.1
Qo
Half life
E, keV
Fcd
15.71± 1.8
2.69 ± 0.10 d
411.8
0.991
1.99 ± 2.7
5.27 ± 0.02 y
1173.2
1
1332.5
Zr-94
6260 ± 4.0
4.61
64.03 ± 0.01 d
724.2
1
756.7
Zr-96
338 ± 2.1
231.00
16.74 ± 0.10 h
657.9
1
743.3
Zn-64
Zn-68
Mo-98
4.5
2560 ± 10.0
590 ± 10.0
241 ± 20.0
1.91±4.9
3.19±1.4
53.10±6.3
244.00 ± 0.08 d
13.76 ± 0.15 h
6.02 ± 0.30 h
1115.5
1
438.6
1
140.5
1
Analysis of Environmental reference materials
Overall evaluation of absolute method was performed by analyzing IAEA
lake sediment Soil-1 and Soil-7 samples in order to assess the accuracy and precision
of the method. The neutron activation of Soil-1 and Soil-7 samples were carried out
at irradiation position 10, 22, 27, and 31 of the MNA TRIGA reactor. Approximately
30 mg of each sample was weighted and irradiated in calibrated position of rotary
rack facilities. The samples thus prepared were sealed in a plastic and enclosed in
polyethylene vial to avoid contamination of the samples. The samples then were
irradiated for one hour in stationary mode. The measurement was performed in two
series. The first series of measurements were performed at large sample-detector
distance after one day cooling time for short half life nuclide. The second series were
measured at 2 cm from detector after one week cooling time for longer half life
nuclide. The counting was performed using HPGe detector as close as possible of the
calibration sources. The samples irradiated at irradiation position 22 were measured
using Canberra detector while the rest of the irradiation positions were measured
41`
using Ortec detector. For each sample, measurement time was 1 hour and the dead
time did not exceed 10%. Concentrations for various elements were calculated and
the results were compared to the certified values.
Figure 4.8: IAEA lake sediment sample sealed in a labeled plastic and
irradiated with standard polyethylene vial.
CHAPTER V
RESULT AND DISCUSSION
5.0
Introduction
This chapter will discuss the results obtained from the experiment results data
are presented in the table and graph. The discussions will be on the explanation of the
analysis method and evaluation of the findings.
5.1
Calibration of Detector Efficiency
The efficiency calibration of the two HPGe detectors available at the
Malaysia Nuclear Agency, Ortec GEM-10185 detector with Gamma Vision software
and Canberra GC3018 detector with Genie 2000 software are presented. These two
calibrated detectors will be utilized to measure the energies and intensities of gamma
rays from irradiated samples.
Prior to the use of the detector in measuring monitors and samples, the
43
detectors were first calibrated extensively using six standard point sources namely
Cs-137, Am-241, Ba-133, Eu-152, Co-60 and Na-22. The original activity and the
manufacture date of the calibration standard point sources are known, and the current
activity were calculated using the half-life of the standard point sources. The current
activities of standard gamma point sources measured on 18 August 08 are shown in
Table 5.1.
Table 5.1: Activity and Information on Radioactive Gamma Sources
*
Sources
Activity*
(kBq)
Half Life,t1/2
(s)
Elapsed time,t
(s)
Cs-137
358.1
9.52E+08
1.70E+08
Activity
(kBq)
18.08.08
316443.55
Am-241
365.0
1.37E+10
1.70E+08
361868.48
Ba-133
381.8
3.31E+08
1.70E+08
267617.70
Eu-152
366.8
4.29E+08
1.57E+08
284810.89
Co-60
367.1
1.66E+08
1.70E+08
180872.45
Na-22
331.3
8.21E+07
1.70E+08
78976.82
Original activities of Cs, Am, Ba, Co and Na were measured on 01.04.2003
Original activity of Eu was measured on 01.09.2003
5.1.1 Ortec Detector Calibration
The Ortec detector efficiency calibrations were performed at 10 cm, 6 cm and
2 cm distances from the endcap detector. Table 5.2-5.4 represented the efficiency of
the standard gamma point sources measured at the three different distances. The
standard gamma source efficiencies were then fitted into a suitable poly log function
as shown in Chapter III Equation (52). The fitted parameter P1, P2, P3, P4, and P5 were
then obtained by regression statistics using Microsoft Excel data analysis. Finally, the
efficiency equation is established from the known fitted parameter which allowed for
44
the efficiency evaluation at particular energies of interest. Besides that, the resulting
full energy peak detection efficiency was plotted against gamma ray energy in
logarithmic scale.
Table 5.2: Standard gamma sources efficiency at the distance of 10 cm from Ortec
detector
Sources
Energy
(keV)
Cs-137
Am-241
Ba-133
Eu-152
Co-60
Na-22
Net peak area Efficiency,åã
(count)
Counting
time,t (s)
661.62
Gamma
Abundance,ã
(%)
0.8462
52
11056
0.00084
59.89
0.3630
169
11689
0.00053
81.43
0.3275
429
41354
0.00114
276.75
0.0730
429
10406
0.00129
303.21
0.1862
429
24989
0.00121
356.35
0.6227
429
77747
0.00113
384.16
0.0884
429
10704
0.00109
122.32
0.2924
420
46344
0.00141
245.15
0.0762
420
11783
0.00137
344.68
0.2700
420
34847
0.00115
411.53
0.0226
420
2638
0.00103
779.21
0.1299
420
10768
0.00074
867.68
0.0418
420
3300
0.00070
964.39
0.1458
420
10560
0.00064
1086.24
0.1029
420
6656
0.00057
1408.08
0.2121
420
12440
0.00052
1173.53
0.9998
118
11568
0.00057
1332.91
0.9986
118
10500
0.00052
1274.54
0.9994
233
10529
0.00056
45
Table 5.3: Standard gamma sources efficiency at the distance of 6 cm from Ortec
detector
Sources
Energy
(keV)
Cs-137
Am-241
Ba-133
Eu-152
Co-60
Na-22
Net peak
Efficiency,åã
area (count)
Counting
time,t (s)
661.62
Gamma
Abundance,ã
(%)
0.8462
18
10676
0.00258
59.89
0.3630
41
13563
0.00255
81.43
0.3275
131
56043
0.00570
276.75
0.0730
131
10663
0.00486
303.21
0.1862
131
25660
0.00459
356.35
0.6227
131
77683
0.00415
384.16
0.0884
131
10401
0.00392
122.32
0.2924
186
74571
0.00609
245.15
0.0762
186
16386
0.00514
344.68
0.2700
186
47796
0.00423
411.53
0.0226
186
3044
0.00321
779.21
0.1299
186
12612
0.00232
867.68
0.0418
186
3720
0.00213
964.39
0.1458
186
12404
0.00203
1086.24
0.1029
186
7414
0.00172
1408.08
0.2121
186
14097
0.00159
1173.53
0.9998
60
14946
0.00168
1332.91
0.9986
60
13349
0.00150
1274.54
0.9994
98
11075
0.00160
46
Table 5.4: Standard gamma sources efficiency at the distance of 2 cm from Ortec
detector
Sources
Energy
(keV)
Cs-137
Am-241
Ba-133
Eu-152
Co-60
Na-22
Net peak
Efficiency,åã
area (count)
Counting
time,t (s)
661.62
Gamma
Abundance,ã
(%)
0.8462
10
26578
0.01736
59.89
0.3630
10
21882
0.01804
81.43
0.3275
31
77486
0.05621
276.75
0.0730
31
12182
0.03964
303.21
0.1862
31
29749
0.03795
356.35
0.6227
31
85915
0.03278
384.16
0.0884
31
12509
0.03362
122.32
0.2924
40
75514
0.05792
344.68
0.2700
40
38530
0.03200
779.21
0.1299
40
7613
0.01314
867.68
0.0418
40
1915
0.01028
964.39
0.1458
40
7821
0.01203
1086.24
0.1029
40
5123
0.01117
1408.08
0.2121
40
9633
0.01019
1173.53
0.9998
30
20142
0.00742
1332.91
0.9986
30
18488
0.00682
1274.54
0.9994
36
13994
0.00737
47
Table 5.5: Parameters P1 to P5 determined at the distance of 10 cm from Ortec
detector
Parameters
P1
P2
P3
P4
P5
10 cm
0.65615
-0.83191
0.27096
-0.03113
0.00134
Efficiency equation for sample-detector distance of 10 cm from Ortec detector:
  (E) 
0.65615  0.83191ln(E)  0.27096ln(E) 2  0.03113ln(E)3  0.00134ln(E) 4
E
Table 5.6: Parameters P1 to P5 determined at the distance of 6 cm from Ortec
detector
Parameters
P1
P2
P3
P4
P5
6 cm
-16.31913
9.44252
-2.06422
0.21685
-0.00877
Efficiency equation for sample-detector distance of 6 cm from Ortec detector:
  (E) =
16.31913  9.44252 ln(E)  2.06422 ln(E)2  0.21685ln(E)3  0.00877 ln(E) 4
E
Table 5.7: Parameters P1 to P5 determined at the distance of 2 cm from Ortec
detector
Parameters
P1
P2
P3
P4
P5
2 cm
-506.79230
349.85297
-91.31518
10.83450
-0.48875
Efficiency equation for sample-detector distance of 2 cm from Ortec detector:
  (E) =
506.792  349.853ln(E)  91.315ln(E) 2  10.834 ln(E)3  0.489ln(E) 4
E
48
Figure 5.1: Full energy peak detection efficiency curve for Ortec detector at three
sample-detector distances.
5.1.2 Canberra Detector calibration
The Canberra detector efficiency calibrations were performed at 12 cm, 8 cm
and 2 cm distances from the endcap detector. The efficiency results of standard
gamma point sources were presented in Table 5.8-5.10. The fitted parameter P1, P2, P3,
P4, and P5 were determined in order to obtain the efficiency equation for the three
sources-detector distances. The efficiency curve plotted against gamma ray energy in
logarithmic scale for 12 cm, 8 cm, and 2 cm sources-detector distances are presented
in Figure 5.2.
49
Table 5.8: Standard gamma sources efficiency at the distance of 12 cm
from Canberra detector
Sources
Energy
(keV)
Cs-137
Am-241
Ba-133
Eu-152
Co-60
Na-22
Net peak
Efficiency,åã
area (count)
Counting
time,t (s)
661.62
Gamma
Abundance,ã
(%)
0.8462
40
11200
0.001116
59.89
0.3630
101
11800
0.000899
81.43
0.3275
315
41200
0.001598
276.75
0.0730
315
10200
0.001775
303.21
0.1862
315
24100
0.001644
356.35
0.6227
315
76800
0.001567
384.16
0.0884
315
10500
0.001509
122.32
0.2924
285
42400
0.001978
245.15
0.0762
285
10900
0.001952
344.68
0.2700
285
31300
0.001581
411.53
0.0226
285
2270
0.001367
779.21
0.1299
285
9970
0.001047
867.68
0.0418
285
3080
0.001006
964.39
0.1458
285
10100
0.000945
1086.24
0.1029
285
6510
0.000863
1408.08
0.2121
285
11700
0.000752
1173.53
0.9998
90
12900
0.000850
1332.91
0.9986
90
12100
0.000798
1274.54
0.9994
165
10100
0.000789
50
Table 5.9: Standard gamma sources efficiency at the distance of 8 cm from
Canberra detector
Sources
Energy
(keV)
Cs-137
Am-241
Ba-133
Eu-152
Co-60
Na-22
Net peak
Efficiency,åã
area (count)
Counting
time,t (s)
661.62
Gamma
Abundance,ã
(%)
0.8462
16
10900
0.002916
59.89
0.3630
30
11800
0.003083
81.43
0.3275
126
52300
0.005625
276.75
0.0730
126
10600
0.005115
303.21
0.1862
126
25200
0.004767
356.35
0.6227
126
78000
0.004412
384.16
0.0884
126
10600
0.004224
122.32
0.2924
131
58200
0.006689
245.15
0.0762
131
12500
0.005516
344.68
0.2700
131
36200
0.004506
411.53
0.0226
131
2610
0.003874
779.21
0.1299
131
10600
0.002742
867.68
0.0418
131
3220
0.002591
964.39
0.1458
131
10100
0.002328
1086.24
0.1029
131
6620
0.002162
1408.08
0.2121
131
11600
0.001838
1173.53
0.9998
36
11200
0.002019
1332.91
0.9986
36
10300
0.001859
1274.54
0.9994
77
10100
0.001838
51
Table 5.10: Standard gamma sources efficiency at the distance of 2 cm from
Canberra detector
Sources
Energy
(keV)
Cs-137
Am-241
Ba-133
Eu-152
Co-60
Na-22
Net peak
Efficiency,åã
area (count)
Counting
time,t (s)
661.62
Gamma
Abundance,ã
(%)
0.8462
5
22100
0.029102
59.89
0.3630
5
24500
0.047028
81.43
0.3275
30
97600
0.087898
276.75
0.0730
30
13400
0.054141
303.21
0.1862
30
33300
0.052748
356.35
0.6227
30
100000
0.047366
384.16
0.0884
30
15200
0.050715
122.32
0.2924
30
77600
0.086495
245.15
0.0762
30
13700
0.058627
344.68
0.2700
30
40400
0.048767
411.53
0.0226
30
2710
0.039012
779.21
0.1299
30
9850
0.024713
867.68
0.0418
30
2560
0.019980
964.39
0.1458
30
8840
0.019761
1086.24
0.1029
30
6840
0.021664
1408.08
0.2121
30
9470
0.014552
1173.53
0.9998
10
16000
0.016379
1332.91
0.9986
10
14400
0.014759
1274.54
0.9994
20
13100
0.012399
Table 5.11: Parameters P1 to P5 determined at the distance of 12 cm from Canberra
detector
Parameters
P1
P2
P3
P4
P5
52
12 cm
11.36677
-9.25046
2.70733
-0.33887
0.01579
Efficiency equation at sample-detector distance of 12 cm from Canberra detector:
  (E) 
11.36677  9.25046 ln(E)  2.70733ln(E)2  0.33887 ln(E)3  0.01579 ln(E) 4
E
Table 5.12: Parameters P1 to P5 determined at the distance of 8 cm from Canberra
detector
Parameters
P1
P2
P3
P4
P5
8 cm
5.74048
-7.17705
2.58056
-0.35480
0.01752
Efficiency equation at sample-detector distance of 8 cm from Canberra detector:
  (E) 
5.74048  7.17705 ln(E)  2.58056 ln(E) 2  0.35480 ln(E)3  0.01752 ln(E) 4
E
Table 5.13: Parameters P1 to P5 determined at the distance of 2 cm from Canberra
detector
Parameters
P1
P2
P3
P4
P5
2 cm
-965.20457
691.60687
-185.59302
22.27458
-1.00076
Efficiency equation at sample-detector distance of 2 cm from Canberra detector:
  (E) 
965.205  691.607 ln(E)  185.593 ln(E) 2  22.275 ln(E) 3  1.001ln(E) 4
E
53
Figure 5.2: Full energy peak detection efficiency curve for Canberra detector at
three sample- detector distances.
The value of efficiency is dependent on the sample-detector distance and
energy. Therefore, each of the counting geometry requires an efficiency calibration.
For both detector calibrations, the energies of standard gamma point sources ranged
from 59.88 keV to 1408.08 keV. There should be no large energy gaps between the
efficiency values that would cause a large efficiency interpolation error.
The efficiencies of standard gamma point sources were used in establishing
the detector efficiency curve as a function of energy for its defined distance and
energy range. The resulting efficiency curve for Ortec and Canberra detector were
shown in Fig 5.1 and Fig 5.2. The efficiency of germanium gamma ray spectroscopy
increased when the samples are placed closer to the detector for counting the low
radioactivity samples.
54
For an ideal efficiency calibration and procedure, the efficiency curve should
be a smooth function of energy at spectral range from 59.88 keV to 1332.51 keV.
Excellent efficiency curves were established for long and short sources-detector
distances with ÷ squared per degree of freedom between 0.99. Therefore, the two
detector used in this experiment have a very good resolution and sensitivity for long
and short sources-detector distances. However, the results will be less precise at
shorter distances (2 cm) as the uncertainty increases rapidly with the dead time.
The efficiency value may be interpolated or extrapolated from measured
efficiency value but resulted some loss in accuracy. Therefore, the efficiency results
were fitted into a least squares of 4 th order polynomial where P1, P2, P3, P4 and P5
represent the fitted parameters. The efficiency equation established from standard
gamma sources then can be used to estimate the irradiated sample’s efficiency in the
absolute method of NAA.
5.2
Result of á by the Cd ratio
The parameter á was determined by cadmium ratio method using five
monitors at irradiation position 10, 22, 27, and 31 of rotary rack TRIGA reactor.
5.2.1 Result of á at Irradiation Position 10
The nuclear reactions
94
Zr (n,ã)
95
Zr,
96
197
Zr (n,ã)97Zr,
Au (n,ã)
64
198
Zn (n,ã)
Au,
65
98
Zn,
Mo (n,ã)
67
99
Zn (n,ã)
determination of the á parameter to account for the 1/E
1+á
Mo,
68
59
Co (n,ã)
60
Co,
Zn were used in
spectrum. The monitors’
55
specific activities induced bare and with cadmium covered as presented in Table 5.14
were used to find the cadmium ratio.
Table 5.14: Specific activities for 5 monitors irradiated bare and with cadmium
cover at irradiation position 10 of the rotary rack
Monitors
Energy, keV
Asp, bare
Asp, cd
Rcd
Au-198
411.97
1.0790E+09
4.9858E+08
2.16
Mo-99
140.89
1.2765E+05
8.4901E+04
1.50
Zn-65
1115.67
2.2379E+06
2.1711E+05
10.31
Zn-68
438.78
9.1595E+04
1.2292E+04
7.45
1173.42
4.2631E+08
2.4319E+07
17.53
1332.5
3.9077E+08
2.2569E+07
17.31
658.22
3.8887E+04
3.4489E+04
1.13
743.41
3.2672E+04
2.9241E+04
1.12
756.67
6.7105E+04
1.7572E+04
3.82
724.13
6.2859E+04
1.4617E+04
4.30
Co-60
Zr-97
Zr-95
Table 5.15 presents part results of the “iterative linear regression” method
extracted from a spreadsheet calculation in determination of á value. Firstly, á value
is assumed to be equal to zero in order to calculate Qá, and log (Yi) for the five
monitors. The final á value was adopted from simple linear least square regression
and iterative analysis procedure to obtain a consistent value of á parameter. Figures
5.3-5.6 show the graphical representation of log (Yi) versus log (Er) for the five
irradiation positions studied at rotary rack TRIGA reactor, from which the á values
were obtained from the slope of the straight line.
56
Table 5.15: Specific activities for 5 monitors irradiated bare and with cadmium
cover at irradiation position 10 of the rotary rack
Monitors
Log (Er)
Step1
Step 8
Log (Y1)
Q(1)
Log (Y8)
Q(8)
Au-198
0.7520
-1.2549
17.0259
-1.2547
17.2206
Mo-99
2.3820
-1.4272
68.4774
-1.4265
70.9805
Zn-65
3.408
-1.2494
2.5925
-1.2206
2.7103
Zn-68
2.7709
-1.3134
4.1775
-1.2999
4.3418
Co-60
2.1335
-1.5149
2.4266
-1.4992
2.4962
Zr-97
2.5289
-1.4392
302.9429
-1.4391
314.7561
Zr-95
3.7966
-1.1406
6.7446
-1.1275
7.1215
1 = 0.04662
8 = 0.05320
The first iteration (step1) resulted in 1 = 0.04662. The resulting  value was
used as a starting point for next iteration. The iterative procedure is carried out until
no significant variation of á value. The eighth and last iteration (step 8) lead to 8 =
0.05320. The result of the last iterative derived from the cadmium covered multi
monitor method is graphically presented in Figure 5.3.
0
-0.2 0
1
2
3
4
-0.4
Log Yi
-0.6
-0.8
-1
y = 0.05320x - 1.45898
R2 = 0.14969
-1.2
-1.4
-1.6
Log Er
Figure 5.3: Parameter á measurement at position 10 of rotary rack TRIGA reactor
57
5.2.2
Result of á at Irradiation Position 22
Table 5.16: Specific activities for 5 monitors irradiated bare and with cadmium
cover at irradiation position 22 of the rotary rack
Monitors
Energy, keV
Asp, bare
Asp, cd
Rcd
Au-198
411.97
1.1982E+09
5.3275E+08
2.25
Mo-99
140.89
1.3521E+05
9.5818E+04
1.41
Zn-65
1115.67
2.6022E+06
2.1752E+05
11.96
Zn-68
438.78
9.6212E+04
1.2055E+04
7.98
1173.42
5.0521E+08
2.8173E+07
17.93
1332.5
4.7185E+08
2.6303E+07
17.94
658.22
3.7592E+04
3.5478E+04
1.06
743.41
3.4244E+04
2.9472E+04
1.16
756.67
7.7372E+04
1.6547E+04
4.68
724.13
5.8653E+04
1.2926E+04
4.54
Co-60
Zr-97
Zr-95
Table 5.17: Result of á parameter at irradiation position 22 calculated by iterative
linear regression method
Monitors
Log (Er)
Step1
Step 8
Log (Y1)
Q(1)
Log (Y8)
Q(8)
Au-198
0.7520
-1.2857
16.4477
-1.2856
16.5637
Mo-99
2.3820
-1.3390
61.3949
-1.3386
62.7741
Zn-65
3.408
-1.3205
2.2685
-1.3028
2.3304
Zn-68
2.7709
-1.3477
3.7179
-1.3394
3.8068
Co-60
2.1335
-1.5283
2.2284
-1.5188
2.2672
Zr-97
2.5289
-1.3440
269.6668
-1.3439
276.1291
Zr-95
3.7966
-1.2133
5.7222
-1.2051
5.9161
1 = 0.02661
8 = 0.03069
58
0
-0.2 0
0.5
1
1.5
2
2.5
3
3.5
4
-0.4
Log Yi
-0.6
-0.8
y = 0.03069x - 1.41137
R2 = 0.10024
-1
-1.2
-1.4
-1.6
-1.8
Log Er
Figure 5.4: Parameter á measurement at position 22 of rotary rack TRIGA reactor
5.2.3
Result of á at Irradiation Position 27
Table 5.18: Specific activities for 5 monitors irradiated bare and with cadmium
cover at irradiation position 27 of the rotary rack
Monitors
Energy, keV
Asp, bare
Asp, cd
Rcd
Au-198
411.97
1.8876E+09
8.5707E+08
2.20
Mo-99
140.89
2.2225E+05
1.4971E+05
1.48
Zn-65
1115.67
4.0181E+06
3.5312E+05
11.38
Zn-68
438.78
1.2648E+05
1.9712E+04
6.42
1173.42
8.4384E+08
4.3163E+07
19.55
1332.5
7.7893E+08
3.9894E+07
19.52
756.67
1.1598E+05
2.5262E+04
4.59
724.13
9.1537E+04
2.1999E+04
4.61
Co-60
Zr-95
59
Table 5.19: Result of á parameter at irradiation position 27 calculated by iterative
linear regression method
Monitors
Log (Er)
Step1
Step 8
Log (Y1)
Q(1)
Log (Y8)
Q(8)
Au-198
0.7520
-1.2690
16.8488
-1.2689
17.0197
Mo-99
2.3820
-1.4104
66.2525
-1.4098
68.3993
Zn-65
3.408
-1.2967
2.4891
-1.2711
2.5888
Zn-68
2.7709
-1.2375
4.0323
-1.2255
4.1724
Co-60
2.1335
-1.5676
2.3646
-1.5536
2.4245
Zr-95
3.7966
-1.1838
6.4164
-1.1721
6.7330
1 = 0.04057
8 = 0.04641
0
-0.2 0
1
2
3
4
-0.4
Log Yi
-0.6
-0.8
-1
y = 0.04641x - 1.43474
R2 = 0.12636
-1.2
-1.4
-1.6
-1.8
Log Er
Figure 5.5: Parameter á measurement at position 27 of rotary rack TRIGA reactor
60
5.2.4 Result of á at Irradiation Position 31
Table 5.20: Specific activities for 5 monitors irradiated bare and with cadmium
cover at irradiation position 31 of the rotary rack
Monitors
Energy, keV
Asp, bare
Asp, cd
Rcd
Au-198
411.97
1.2976E+09
5.7952E+08
2.24
Mo-99
140.89
1.6559E+05
1.0974E+05
1.51
Zn-65
1115.67
2.8846E+06
2.7291E+05
10.57
Zn-68
438.78
1.1780E+05
1.6951E+04
6.95
1173.42
5.3633E+08
3.1944E+07
16.79
1332.5
4.8850E+08
2.9763E+07
16.41
658.22
4.6748E+04
4.3015E+04
1.09
743.41
3.8634E+04
3.5702E+04
1.08
756.67
8.2597E+04
2.1998E+04
3.75
724.13
6.9552E+04
1.8768E+04
3.71
Co-60
Zr-97
Zr-95
Table 5.21: Result of á parameter at irradiation position 31 calculated by iterative
linear regression method
Monitors
Log (Er)
Step1
Step 8
Log (Y1)
Q(1)
Log (Y8)
Q(8)
Au-198
0.7520
-1.2821
17.2703
-1.2820
17.4860
Mo-99
2.3820
-1.4318
71.6296
-1.4310
74.4924
Zn-65
3.408
-1.2615
2.7412
-1.2286
2.8786
Zn-68
2.7709
-1.2783
4.3845
-1.2628
4.5737
Co-60
2.1335
-1.4926
2.5141
-1.4746
2.5932
Zr-97
2.5289
-1.3090
341.2223
-1.3088
355.7705
Zr-95
3.7966
-1.1320
7.9313
-1.1185
8.4202
1 = 0.05486
8 = 0.06204
61
0
0
0.5
1
1.5
2
2.5
3
3.5
4
-0.2
-0.4
Log Yi
-0.6
-0.8
-1
y = 0.06204x - 1.45844
R2 = 0.25406
-1.2
-1.4
-1.6
Log Er
Figure 5.6: Parameter á measurement at position 31 of rotary rack TRIGA reactor
The  results at irradiation position 10, 22, 27, and 31 are -0.0532±0.0056, 0.0307 ± 0.0058, -0.0464 ± 0.0048, and -0.0620 ± 0.0056, respectively. The
coefficient correlation R2 shown in graph are poor as the  values for the four
irradiation positions are small. A larger positive  value associated with a higher
thermalization will have a better coefficient correlation. It is found that the value of
parameter  is negative inside the rotary rack of reactor. The error analysis on  of
the five monitors set irradiated at irradiation position irradiation 10, 22, 27, and 31
are reported in appendix B, C, D and E, respectively. The uncertainties of the  were
estimated by using the error propagation theory [15]. The overall uncertainties
depend on the nuclear data and experimental values.
Since the rotary rack is a cylindrical model, it might be expected that the
parameter  would be the same at all the irradiation positions. However, the  results
obtained from experiment show variation at different irradiation positions. The
parameter  depends on the reactor configuration which is related to the physical
properties of the reactor system. A higher thermalization is associated with a larger
positive  value which corresponds to softening of the epithermal spectrum relatuve
62
to 1/E spectrum. The deviations of the epithermal flux distribution from ideal 1/E
distribution increase with increasing . The values of  diverge tremendously with
high or poor thermalization.
The  result (-0.03 to -0.06) for the four irradiation positions predispose the
TRIGA reactor as an under moderated thermalization reactor type. Therefore, the
irradiation facility is operated under safe condition. It is consider suitable for reactor
physics experiments and also ideal for absolute NAA application.
Knowledge of the coefficient  in the irradiation position of rotary rack is
required for correction of the resonance integral values I() in the 1/E
1+á
epithermal
neutron flux distribution. Although this effect is often overlooked or neglected, it can
have considerable influence on the value of the resonance integrals for use in a
particular irradiation position
5.3
Calculation of thermal to epithermal flux ratio
The results of f , ratios between the thermal and epithermal neutron flux,
carried out at irradiation position 10, 22, 27, and 31 are presented in Table 5.22. The f
parameter was determined using the same experiment as in á determination but using
only gold monitor. The cadmium transmission factor, Fcd for gold is 0.991. Qo (á) is
the ratio of resonance integral to (n, ã) cross section for gold monitor including a
correction parameter á. The higher the thermalization at the irradiation site the higher
is the f value. As TRIGA rector provides a stable irradiation facility, there is a slight
variation in the f value as shown in the results providing that f is consider constant
over the irradiation position.
63
Table 5.22: The results of thermal to epithermal flux ratio of corresponding
irradiation positions
Irradiation Position
Rcd
Qo (á)
f
10
2.16
17.2206
19.71 ± 0.45
22
2.25
16.5637
27
2.20
17.0197
31
2.24
17.4860
20.35 ± 0.42
20.13 ± 0.77
21.68 ± 0.48
5.4 Thermal and epithermal neutron flux Results
The thermal and epithermal neutron fluxes at irradiation position 10, 22, 27,
and 31 were determined from the reaction rates measured from the induced activities
of the
198
Au irradiated under bare and with cadmium cover condition. The gold’s
efficiency at 411.97 keV is 0.00102 (performed using Ortec detector at 10 cm) and
0.00145 (performed using Canberra detector at 12 cm).
Table 5.23: Activity of bare gold at irradiation positions 10, 22, 27, and 31 of rotary
rack TRIGA reactor
Irradiation
position
Mass
(mg)
1.9667
Net
Area
(Count)
10092
Saturation
factor,
S
1.07E-02
Decay
factor,
D
7.79E-01
Counting
factor,
C
1.51E-03
10
Asp, bare
1.11E+12
22
1.8000
12105
1.07E-02
7.80E-01
1.78E-03
1.23E+12
27
1.8000
12300
1.07E-02
7.55E-01
1.19E-03
1.37E+12
31
2.3000
11124
1.07E-02
7.77E-01
1.19E-03
1.33E+12
64
Table 5.24: Activity of gold irradiated with cadmium cover at irradiation positions
10, 22, 27, and 31 of rotary rack TRIGA reactor
Irradiation
position
Mass
(mg)
2.0330
Net
Area
(Count)
10074
Saturation
factor,
S
1.07E-02
Decay
factor,
D
8.19E-01
Counting
factor,
C
3.01E-03
10
5.12E+11
22
1.8000
21204
2.12E-02
7.73E-01
3.57E-03
5.47E+11
27
1.9000
10900
1.07E-02
7.91E-01
2.10E-03
6.20E+11
31
2.4000
10152
1.07E-02
8.11E-01
2.23E-03
5.95E+11
A
sp, cd
Table 5.25: The results of thermal and epithermal neutron flux of corresponding
irradiation position.
Irradiation position
( rotary rack reactor)
10
22
27
31
th
10 cm-2s-1
1.9553 ± 0.0455
12
epi
10 cm-2s-1
9.9192 ± 0.4571
10
2.2412 ± 0.2054
11.0132 ± 2.4494
2.4192 ± 0.0525
11.1586 ± 0.4892
2.4475 ± 0.0991
12.1597 ± 0.9575
The burn up effect of Au, due to the fact that 198Au may capture a neutron to
form another isotope is negligible for short irradiating time and moderate neutron
fluence rates. The measured thermal and epithermal neutron flux shows that the
irradiation positions in rotary rack are well thermalized with about 95% of thermal
neutrons over epithermal neutrons. Obviously, it can be observed that the thermal
neutron flux is the dominant neutron flux in the reactor. However, the relatively low
epithermal flux would result in poorer sensitivity for some elements. They are
sometimes useful in NAA for several elements (e.g. Br, Rb, Sr, Mo,Ba, Ta and U)
that have higher relative reaction rates for epithermal neutrons than for thermal
neutrons.
The result forf thermal and epithermal neutron fluxes at irradiation positions
10, 22, 27 and 31 in Table 5.25 showed a significant variation. Therefore, monitoring
the flux variation at the rotary rack in the determination of element concentration at
65
different irradiation positions will enhance the quality of result.
5.5
HOGDAHL Reaction Rate for Irradiated Elements
The knowledge of neutron reactor parameter, thermal and epithermal neutron
fluxes at the rotary racks of the reactor are required to calculate the irradiated
sample’s reaction rate using HOGDAHL convention. The HOGDAHL convention
expresses the reaction rate for irradiated element in terms of neutron flux at
irradiation site and element nuclear data parameters.
Table 5.26 - 5.29 represent the results of saturated specific gamma ray
emission rate for sample irradiated at rotary rack position of 10, 22, 27, and 31,
respectively. All nuclear data including the thermal neutron capture cross sectio , óo
and the ratio of resonance integral to (n, ã ) cross section for a 1/E spectrum, Qo are
taken from the literature data. For the correction of an epithermal neutron spectrum
of the type 1/E
, the values of Qo which is tabulated in the literature should be
1+á
converted into Qo(á) in order to determine the resonance integral, I(á). The used of
uncorrected resonance integral, Io without a correction parameter  could lead to
errors in the determination of elemental concentration.
.
66
Table 5.26: HOGDAHL reaction rate of elements irradiated at irradiation position
10 of rotary rack.
Analyte
Qo
óo
Er
Qá
Iá
R (s-1)
As
13.6
4.50E-24
106
17.34
7.81E-23
1.65E-11
La
1.32
8.93E-24
76
1.59
1.42E-23
1.89E-11
Mn
1.05
1.33E-23
468
1.33
1.76E-23
2.78E-11
Na
0.587
5.30E-25
3380
0.71
3.76E-25
1.07E-12
Sc
0.44
2.72E-23
5130
0.48
1.31E-23
5.45E-11
Sm
14.4
2.06E-22
8.53
16.12
3.32E-21
7.32E-10
Ga
6.62
4.71E-24
154
8.56
4.03E-23
1.32E-11
K
0.97
1.46E-24
2960
1.29
1.89E-24
3.04E-12
Hf
2.68
1.30E-23
115
3.36
4.38E-23
2.98E-11
Ba
17.7
1.13E-23
69.9
22.11
2.50E-22
4.69E-11
Cr
0.49
1.59E-23
7530
0.56
8.95E-24
3.20E-11
Sb
33.9
5.90E-24
13.1
38.8
2.29E-22
3.43E-11
Ce
0.82
5.70E-25
7200
1.09
6.23E-25
1.18E-12
Th
11.53
7.37E-24
54.4
14.2
1.05E-22
2.48E-11
Fe
1.33
1.28E-24
637
1.74
2.22E-24
2.72E-12
Co
1.993
3.71E-23
136
2.50
9.27E-23
8.18E-11
Rb
15.6
4.80E-25
839
22.17
1.06E-23
1.99E-12
Yb
0.46
1.26E-22
602
0.51
6.41E-23
2.53E-10
U
103.4
2.68E-24
16.9
120.15
3.22E-22
3.72E-11
Cs
15.1
2.90E-23
16.98
4.92E-22
1.06E-10
Tb
17.9
2.34E-23
18.1
20.85
4.88E-22
9.41E-11
Ca
1.3
7.40E-25
1330000
2.31
1.71E-24
1.62E-12
9.27
67
Table 5.27: HOGDAHL reaction rate for elements irradiated at irradiation position
22 rotary rack.
Analyte
Qo
óo
Er
Qá
Iá
R (s-1)
As
13.6
4.50E-24
106
15.65
7.04E-23
1.78E-11
La
1.32
8.93E-24
76
1.47
1.31E-23
2.15E-11
Mn
1.05
1.33E-23
468
1.20
1.59E-23
3.16E-11
Na
0.587
5.30E-25
3380
0.65
3.45E-25
1.23E-12
Sc
0.44
2.72E-23
5130
0.46
1.26E-23
6.23E-11
Sm
14.4
2.06E-22
8.53
15.37
3.17E-21
8.10E-10
Ga
6.62
4.71E-24
154
7.67
3.61E-23
1.45E-11
K
0.97
1.46E-24
2960
1.14
1.66E-24
3.46E-12
Hf
2.68
1.30E-23
115
3.05
3.98E-23
3.36E-11
Ba
17.7
1.13E-23
69.9
20.12
2.27E-22
5.04E-11
Cr
0.49
1.59E-23
7530
0.53
8.41E-24
3.66E-11
Sb
33.9
5.90E-24
13.1
36.67
2.16E-22
3.71E-11
Ce
0.82
5.70E-25
7200
0.96
5.48E-25
1.34E-12
Th
11.53
7.37E-24
54.4
13.00
9.58E-23
2.71E-11
Fe
1.33
1.28E-24
637
1.55
1.98E-24
3.09E-12
Rb
15.6
4.80E-25
839
19.10
9.17E-24
2.09E-12
Yb
0.46
6.94E-23
602
0.40
2.78E-23
1.59E-10
Yb
0.46
1.26E-22
602
0.49
6.13E-23
2.89E-10
U
103.4
2.68E-24
16.9
112.75
3.02E-22
3.93E-11
Tb
17.9
2.34E-23
18.1
19.54
4.57E-22
1.03E-10
Cs
15.1
2.90E-23
9.27
16.16
4.69E-22
1.17E-10
Ca
1.3
7.40E-25
1330000
1.79
1.33E-24
1.80E-12
68
Table 5.28: HOGDAHL reaction rate for elements irradiated at irradiation position
27 rotary rack.
Analyte
Qo
óo
Er
Qá
Iá
R (s-1)
As
13.6
4.50E-24
106
16.81
7.57E-23
2.02E-11
La
1.32
8.93E-24
76
1.55
1.38E-23
2.35E-11
Mn
1.05
1.33E-23
468
1.29
1.71E-23
3.46E-11
Na
0.587
5.30E-25
3380
0.69
3.66E-25
1.34E-12
Sc
0.44
2.72E-23
5130
0.48
1.30E-23
6.81E-11
Sm
14.4
2.06E-22
8.53
15.89
3.27E-21
9.02E-10
Ga
6.62
4.71E-24
154
8.28
3.90E-23
1.63E-11
K
0.97
1.46E-24
2960
1.24
1.82E-24
3.79E-12
Hf
2.68
1.30E-23
115
3.27
4.26E-23
3.71E-11
Ba
17.7
1.13E-23
69.9
21.49
2.43E-22
5.72E-11
Cr
0.49
1.59E-23
7530
0.55
8.78E-24
4.00E-11
Sb
33.9
5.90E-24
28.2
583.78
2.39E-21
4.18E-11
Ce
0.82
5.70E-25
7200
1.05
5.99E-25
1.47E-12
Th
11.53
7.37E-24
54.4
13.82
1.02E-22
3.04E-11
Fe
1.33
1.28E-24
637
1.68
2.14E-24
3.39E-12
Co
1.99
3.71E-23
136
2.42
9.00E-23
1.02E-10
Ta
32.2
2.05E-23
10.4
35.88
7.36E-22
1.40E-10
Zn
1.91
7.60E-25
2560
2.59
1.97E-24
2.10E-12
Yb
0.46
1.26E-22
602
0.50
6.42E-23
3.16E-10
U
103.4
2.68E-24
16.9
117.87
3.16E-22
4.50E-11
Tb
17.9
2.34E-23
18.1
20.44
4.78E-22
1.15E-10
Cs
15.1
2.90E-23
9.27
16.73
4.85E-22
1.30E-10
Ca
1.3
7.40E-25
1330000
1.79
1.33E-24
2.00E-12
69
Table 5.29: HOGDAHL reaction rate for elements irradiated at irradiation position
31 rotary rack.
Analyte
Qo
óo
Er
Qá
Iá
R (s-1)
As
13.6
4.50E-24
106
18.89
8.13E-23
2.00E-11
La
1.32
8.93E-24
76
1.70
1.51E-23
2.32E-11
Mn
1.05
1.33E-23
468
1.45
1.92E-23
3.42E-11
Na
0.587
5.30E-25
3380
0.76
4.04E-25
1.33E-12
Sc
0.44
2.72E-23
5130
0.50
1.36E-23
6.73E-11
Sm
14.4
2.06E-22
8.53
16.78
3.46E-21
8.76E-10
Ga
6.62
4.71E-24
154
9.37
4.41E-23
1.61E-11
K
0.97
1.46E-24
2960
1.44
2.10E-24
3.75E-12
2.68
1.30E-23
115
3.64
4.75E-23
3.66E-11
17.7
1.13E-23
69.9
22.95
2.59E-22
5.63E-11
0.49
1.59E-23
7530
0.60
9.47E-24
3.95E-11
33.9
5.90E-24
13.1
39.74
2.34E-22
4.04E-11
1.21
9.50E-25
1540
1.70
1.62E-24
2.48E-12
11.53
7.37E-24
54.4
15.27
1.13E-22
2.99E-11
1.33
1.28E-24
637
1.91
2.45E-24
3.36E-12
1.99
3.71E-23
136
2.71
1.00E-22
1.01E-10
Hf
Ba
Cr
Sb
Ce
Th
Fe
Co
Yb
U
0.39
6.94E-23
602
0.42
2.90E-23
3.12E-10
103.4
2.68E-24
16.9
126.63
3.39E-22
4.33E-11
Tb
17.9
2.34E-23
18.1
21.99
5.15E-22
1.12E-10
Cs
15.1
2.90E-23
9.27
17.70
5.13E-22
1.26E-10
1.3
7.40E-25
1330000
2.88
2.13E-24
2.00E-11
15.6
4.80E-25
839
23.51
1.13E-23
2.42E-11
Ca
Rb
70
5.6
Elemental Analysis Using Absolute Method
The elements concentrations were determined by measuring the reaction
rates of the irradiated samples and analysis by using NAA absolute method. During
the first period after one day from the end of irradiation, elements As, La, Mn, Na,
Sm, K, Sc and Ga could be determined. The other elements are counted after one
week, measured at 2 cm from the calibrated detector. A large number of gamma ray
spectra were collected for the irradiated Soil-1 and Soil-7 samples. The quantitative
analysis were carried out for radioisotopes using the most higher energy peaks,
normally having less interference than lower energy peaks and with low statistical
errors. The nuclear properties of the elements required in absolute neutron activation
technique are taken from the compiled literature data [21].
The
elemental
concentration
results
obtained
by NAA absolute
experimental were compared to the certified values issued by International Atomic
Energy Agency as clarified in Table 5.31-5.38. The results for Soil-1 and Soil-7
obtained at irradiation positions 10, 22, 27, and 31 agree reasonably well with the
certified values which reflects the accuracy of the method. The deviation between
experimental and certified value is expressed as the ratio between experimental
values and certified values. The percentage deviation between measured
concentrations and reference values are mostly below 10% and only a few element
exceeds 20%.
The accuracy of the Soil-1 and Soil-7 in term of concentration were
statistically evaluated using z-score for comparison between experimental results and
certified values. The Z-score value is defined by:
z 
x

exp
2
exp
 x
cert
 
2
cert

z 
x

exp
2
exp
 x
cert
 
2
cert

where xexp and xcert are the experimental and certified value, respectively, while óexp
71
and ócert are the experimental and certified uncertainty respectively. The criterion for
evaluation Z-score is as Table 5.30. In this work, all the results are graphically
presented as the ratio between experimental to certified value with Z-score plotted as
Y-error bar as presented in Figures 5.7-5.14.
Table 5.30: The criterion for Z-score
Z≤2
The result is accepted
2<Z<3
The result is inspected and possibly
accepted
Z≥3
The result is not accepted
From Table 5.31, there were 20 elements determined in Soil-1 sample
irradiated at irradiation position 10. The ratio of experimental to certified value was
between 0.77 (Rb) to 1.21 (Hf) and Z-score maximum was 1.59 (Mn). There are 18
elements determined in Soil-7 irradiated at irradiation position 10 as revealed in
Table 5.32. The ratio of experimenal to certified value was between 0.80 (Ce) to 1.29
(Tb) and Z-score maximum was 2.27 (Na).
At irradiation position 22, there were 20 elements determined in soil-1
sample and 17 elements determined in IAEA soil-7 sample as shown in Table 5.33
and 5.34. The ratio of experimental to certified value for Soil-1 sample was between
0.71(Ce) to 1.18 (Na and Sm) and Z-score maximum1.33 (Na). Lanthanum (La)
revealed a good result where the element concentration of experimental value is the
same as the certified value. For Soil-7, the ratio of experimental to certified value
was between 0.86 (Sb) to 1.28 (Cr). All elements showed Z-score less than 1 except
for Na (1.09).
The results for Soil-1 and Soil-7 irradiated at irradiation position 27 were
listed in Table 5.35 and Table 5.36. There were 20 elements identified in Soil-1
72
sample and Soil-7 sample. The ratio of experimental to certified value for Soil-1 was
between 0.74 (Hf) to 1.14 (Cs) and Z-score maximum of 2.33 (Fe). The ratio of
experimental to certified value for Soil-7 was between 0.80 (Sc) to 1.27 (Co) with Zscore maximum of 1.39 (Na).
Table 5.37 revealed the results for 20 element determined in Soil-1
irradiated at irradiation position 31. The ratio of experimental to certified value for
Soil-1 was between 0.75 (Yb) to 1.26 (Co). It can be seen that the maximum Z-score
was 2.00 (Na). The experimental value for element concentration lanthanum (La)
was the same as the certified value. Besides that, there are 17 elements determined in
Soil-7 sample irradiated at irradiation position 31. The ratio of experimental to
certified values for Soil-7 as shown in Table 5.38 was between 0.87 (Th) to 1.30 (Sm)
with maximum Z-score of 2.87 (Na). The ratio of experimental element
concentration to certified values for iron (Fe) was unity.
Based on NAA absolute method, most of the analytical results have Z-score
within 0 < |Z|< 2 and hence the results are accepted with precision. The accuracy of
the analytical result for each element in Soil-1 and Soil-7 depends obviously on
uncertainties of the involved nuclear properties and thus varied from element to
element. However, the calculated concentrations for sodium (Na) obtained by NAA
absolute method were high compared to the certified value. Overally, the accuracy of
the absolute method adopted in the analysis of the Soil-1 and Soil-7 are as good as
that of the relative method.
73
Table 5.31: IAEA Soil-1 result at irradiation position 10 by absolute method
Elements
Certified Value
ìg/ g
1ó(%)
As
27.5
11
Irradiation Position 10
ìg/ g
1ó(%) Exp/cert |Z-score|
.
29.28
11
1.06
0.41
La
52.6
6
52.12
7
0.99
0.10
Mn
3460
5
3870.51
5
1.12
1.59
Na
1720
6
1776.29
4
1.03
0.46
Sc
17.3
6
17.06
20
0.99
0.07
Sm
9.25
6
10.16
7
1.10
1.06
Ga
24.0
22
23.94
27
1.00
0.01
K
14500
15
15049.69
6
1.04
0.24
Hf
4.2
14
5.07
25
1.21
0.61
Ba
639
8
733.54
25
1.15
0.50
Cr
104
9
117.44
14
1.13
0.74
Sb
1.31
9
1.12
17
0.86
0.83
Ce
117
15
96.29
17
0.82
0.87
Th
14
7
12.13
10
0.87
1.18
Fe
67400
3
68467.55
10
1.02
0.15
Co
19.8
8
21.14
17
1.07
0.34
Rb
113
37
86.96
33
0.77
0.52
Yb
3.42
19
3.41
32
1.00
0.01
U
4.02
8
3.30
26
0.82
0.78
Cs
7.0
13
6.36
25
0.91
0.35
74
Table 5.32: IAEA Soil-7 result obtained from absolute method at irradiation position
10
Elements
Certified Value
ìg/ g
1ó(%)
As
13.4
6
Irradiation Position 10
ìg/ g
1ó(%) Exp/cert |Z-score|
.
14.07
9
1.05
0.43
La
28
4
30.75
7
1.10
1.21
Mn
631
4
750.16
11
1.19
1.39
Na
2400
4
2727.61
4
1.14
2.27
Sc
8.3
13
7.44
6
0.90
0.76
Sm
5.1
7
5.06
10
0.99
0.07
Ga
10
20
11.59
19
1.16
0.53
K
12100
6
13427.33
7
1.11
1.14
Hf
5.1
7
4.98
28
0.98
0.09
Sb
1.7
12
1.38
14
0.81
1.12
Ce
61
11
49.06
23
0.80
0.93
Th
8.2
13
7.96
13
0.97
0.15
Fe
25700
2
24628.31
14
0.96
0.31
Yb
2.4
15
2.80
34
1.17
0.40
U
2.6
21
2.82
28
1.08
0.22
Tb
0.6
33
0.78
63
1.29
0.33
Cs
5.4
14
5.90
24
1.09
0.31
Ca
163000
5
156084.48
22
0.96
0.19
75
Table 5.33: IAEA Soil-1 result at irradiation position 22 by absolute method.
Elements
Certified Value
ìg/ g
1ó(%)
As
27.5
11
Irradiation Position 22
ìg/ g
1ó(%) Exp/cert |Z-score|
.
29.45
56
1.07
0.12
La
52.6
6
52.58
18
1.00
0.00
Mn
3460
5
3788.68
12
1.09
0.70
Na
1720
6
2037.58
11
1.18
1.33
Sc
17.3
6
16.87
37
0.98
0.07
Sm
9.25
6
10.90
15
1.18
0.94
Ga
24.0
22
24.53
19
1.02
0.08
K
14500
15
14771.53
13
1.02
0.10
Hf
4.2
14
4.11
35
0.98
0.06
Ba
639
8
474.07
30
0.74
1.07
Cr
104
9
90.32
23
0.87
0.61
Sb
1.31
9
1.13
21
0.86
0.67
Ce
117
15
82.94
25
0.71
1.29
Th
14
7
14.58
39
1.04
0.10
Fe
67400
3
60773.71
16
0.90
0.65
Rb
113
37
100.62
44
0.89
0.20
Yb
3.42
19
3.94
48
1.15
0.26
U
4.02
8
3.80
30
0.95
0.19
Tb
1.4
33
1.31
45
0.94
0.12
Cs
7.0
13
6.30
32
0.90
0.32
76
Table 5.34: IAEA Soil-7 result obtained from absolute method at irradiation position
22.
Elements
Certified Value
ìg/ g
1ó(%)
As
13.4
6
Irradiation Position 22
ìg/ g
1ó(%) Exp/cert |Z-score|
.
13.26
14
0.99
0.07
La
28
4
29.53
19
1.05
0.27
Mn
631
4
728.87
19
1.16
0.71
Na
2400
4
2727.96
10
1.14
1.09
Sc
8.3
13
8.42
31
1.01
0.04
Sm
5.1
7
5.06
14
0.99
0.05
Ga
10
20
12.24
25
1.22
0.62
K
12100
6
12951.78
13
1.07
0.47
Hf
5.1
7
4.76
33
0.93
0.21
Cr
60
21
77.10
23
1.28
0.78
Sb
1.7
12
1.45
19
0.86
0.73
Ce
61
11
55.46
27
0.91
0.34
Th
8.2
13
7.95
17
0.97
0.14
Fe
25700
2
27639.06
18
1.08
0.39
Yb
2.4
15
2.17
45
0.91
0.22
Cs
5.4
14
6.14
35
1.14
0.33
Ca
163000
5
148384.82
28
0.91
0.34
77
Table 5.35: IAEA Soil-1 result at irradiation position 27 by absolute method.
Elements
Certified Value
ìg/ g
1ó(%)
As
27.5
11
Irradiation Position 27
ìg/ g
1ó(%) Exp/cert |Z-score|
.
22.07
14
0.80
1.29
La
52.6
6
46.92
8
0.89
1.13
Mn
3460
5
3151.42
7
0.91
1.18
Na
1720
6
1893.80
6
1.10
1.17
Sc
17.3
6
17.89
32
1.03
0.10
Sm
9.25
6
9.74
16
1.05
0.30
Ga
24.0
22
25.55
16
1.06
0.24
K
14500
15
12406.12
8
0.86
0.90
Hf
4.2
14
3.1
39
0.74
0.81
Ba
639
8
481.96
39
0.75
0.81
Cr
104
9
113.62
17
1.09
0.45
Sb
1.31
9
1.05
22
0.80
1.01
Th
14
7
12.80
13
0.91
0.61
Fe
67400
3
51582.66
13
0.77
2.33
Co
19.8
8
20.77
17
1.05
0.26
Ta
1.58
37
1.72
60
1.09
0.12
Zn
223
5
235.12
33
1.05
0.16
Yb
3.42
19
3.02
38
0.88
0.30
U
4.02
8
4.13
28
1.03
0.09
Cs
7.0
13
8.01
84
1.14
0.15
78
Table 5.36: IAEA Soil-7 result at irradiation position 27 by absolute method.
Elements
Certified Value
ìg/ g
1ó(%)
As
13.4
6
Irradiation Position 27
ìg/ g
1ó(%) Exp/cert |Z-score|
.
11.29
19
0.84
0.91
La
28
4
26.92
29
0.96
0.14
Mn
631
4
645.05
11
1.02
0.19
Na
2400
4
2651.22
6
1.10
1.39
Sc
8.3
13
6.66
9
0.80
1.34
Sm
5.1
7
6.30
20
1.24
0.93
Ga
10
20
11.33
25
1.13
0.38
K
12100
6
12236.70
8
1.01
0.11
Hf
5.1
7
4.37
27
0.86
0.59
Ba
159
20
180.26
83
1.13
0.14
Sb
1.7
12
1.98
96
1.16
0.15
Ce
61
11
60.36
25
0.99
0.04
Th
8.2
13
6.62
18
0.81
0.99
Fe
25700
2
21423.40
16
0.83
1.23
Co
8.9
10
11.34
23
1.27
0.88
Yb
2.4
15
3.02
50
1.26
0.40
U
2.6
21
2.47
31
0.95
0.13
Tb
0.6
33
0.52
76
0.87
0.18
Cs
5.4
14
4.93
33
0.91
0.26
Ca
163000
5
183959.21
19
1.13
0.59
79
Table 5.37: IAEA Soil-1 result at irradiation position 31 by absolute method.
Elements
Certified Value
ìg/ g
1ó(%)
As
27.5
11
Irradiation Position 31
ìg/ g
1ó(%) Exp/cert |Z-score|
.
27.94
6
1.02
0.13
La
52.6
6
52.53
6
1.00
0.02
Mn
3460
5
3431.17
33
0.99
0.03
Na
1720
6
1970.39
4
1.15
2.00
Sc
17.3
6
16.94
11
0.98
0.17
Sm
9.25
6
6.66
23
0.72
1.60
Ga
24.0
22
26.44
11
1.10
0.41
K
14500
15
13908.46
6
0.96
0.26
Hf
4.2
14
4.57
24
1.09
0.29
Ba
639
8
614.89
39
0.96
0.10
Cr
104
9
97.23
14
0.93
0.42
Sb
1.31
9
1.06
17
0.81
1.17
Ce
117
15
106.48
39
0.91
0.24
Th
14
7
12.33
9
0.88
1.09
Fe
67400
3
59585.48
10
0.88
1.30
Co
19.8
8
24.88
13
1.26
1.46
Yb
3.42
19
2.56
35
0.75
0.77
U
4.02
8
4.11
21
1.02
0.09
Tb
1.4
33
1.53
50
1.09
0.14
Cs
7.0
13
6.11
29
0.87
0.44
80
Table 5.38: IAEA Soil-7 result obtained from absolute method at irradiation position
31
Elements
Certified Value
ìg/ g
1ó(%)
As
13.4
6
Irradiation Position 31
ìg/ g
1ó(%) Exp/cert |Z-score|
.
13.49
9
1.01
0.06
La
28
4
29.94
7
1.07
0.86
Mn
631
4
749.27
12
1.19
1.32
Na
2400
4
2813.87
4
1.17
2.87
Sc
8.3
13
7.65
27
0.92
0.28
Sm
5.1
7
6.65
8
1.30
2.51
Ga
10
20
12.01
20
1.20
0.64
K
12100
6
13099.60
6
1.08
0.91
Hf
5.1
7
4.49
33
0.88
0.40
Sb
1.7
12
1.57
13
0.92
0.45
Ce
61
11
54.44
63
0.89
0.19
Th
8.2
13
7.14
12
0.87
0.75
Fe
25700
2
25798.05
12
1.00
0.03
Rb
51
9
53.98
40
1.06
0.13
Yb
2.4
15
2.85
32
1.19
0.45
U
2.6
21
2.87
23
1.11
0.31
Ca
163000
5
156080.28
21
0.96
0.20
3
1.12
Exp/Cert (Z-Score as Y error bar)
1.10
1.21
2
1.06
0.87
1.13
1.15 0.86 0.82
0.82
1.07
1.03
1.04
0.99
1.02
0.99
1.00
0.77
1.00
0.91
1
0
As La Mn Na
Sc Sm Ga
K
Hf
Ba Cr
Sb Th Fe
Co Ta Zn
Yb U
Cs
-1
Elements
Figure 5.7: IAEA Soil-1 elements at irradiation position of 10 in rotary rack
81
4.00
Exp/Cert (Z-score as Y error bar)
1.14
3.00
1.19
1.10
1.11
0.81
1.16
0.80
2.00
0.90
1.29
1.17
1.05
1.09
0.97 0.96
0.99
1.08
0.98
0.96
1.00
0.00
-1.00
As La Mn Na
-2.00
Sc
Sm
Ga K
Hf
Sb
Ce
Th Fe Yb
U Tb
Cs
Ca
Elements
Figure5.8: IAEA Soil-7 elements at irradiation position of 10 in rotary rack
82
3.00
Exp/Cert ( Z-score as Y error bar)
1.18
1.18
0.71
2.00
0.74
1.09
0.87 0.86
1.071.00
0.98
1.02
0.98
1.02
0.90
1.04
1.15
0.89 0.95 0.94 0.90
1.00
0.00
-1.00
As La Mn Na Sc Sm
Ga K
Hf Ba
Cr Sb Ce
Th Fe
Rb Yb U Tb Cs
Elements
Figure 5.9: IAEA Soil-1elements at irradiation position of 22 in rotary rack
83
3
Exp/Cert (Z-score as Y error bar)
1.14
1.28
1.16
2
1.22
0.86
1.07
1.08
1.14
1.05
0.91
0.93
0.97
1.01 0.99
0.99
0.91
1
0
As
La
Mn
Na
Sc
Sm
Ga
K
Element
Hf
Cr
Sb
Ce
Th
Fe
Yb
Cs
Figure 5.10: IAEA Soill-7 elements at irradiation position of 22 in rotary rack
84
Exp/ Cert ( Z-Score as Y error bar)
4
0.77
3
1.10
0.80 0.89 0.91
0.86
0.80
2
1.05
0.74 0.75 1.09
0.91
1.05
1.06
1.03
1.14
1.09 1.05 0.88
1.03
1
0
-1
-2
As
La Mn Na Sc Sm
Ga K
Hf
Ba
Cr
Sb Th
Fe
Co Ta Zn Yb
U Cs
Elements
Figure 5.11: IAEA Soil-1elements at irradiation position of 27 in rotary rack
85
3
Exp/Cert (Z-Score as Y error bar)
1.10
0.80 1.24
0.83 1.27
2
0.81
0.84
1.13
1.26
0.86
1.13
1.02
1.13
1.01
0.96
1.16
0.99
0.91
0.95
0.87
1
0
-1
As
La Mn Na
Sc
Sm
Ga
K
Hf
Ba
Sb Ce Th
Fe Co Yb
U
Tb
Cs Ca
Elements
Figure 5.12: IAEA Soil-7 elements at irradiation position of 27 in rotary rack
86
4
Exp/Cert (Z-Score as Y error bar)
1.15
3
1.26
0.72
0.88
0.81
0.88
2
1.10
0.75
1.09
1.09
0.93
1.02 1.00 0.99
0.98
0.96
0.87
0.91
1.02
0.96
1
0
-1
As
La Mn Na
Sc Sm
Ga
K
Hf
Ba
Cr Sb
Ce
Th Fe
Co Yb
U
Tb Cs
-2
Elements
Figure 5.13: IAEA Soil-1 elements at irradiation position of 31 in rotary rack
87
1.30
1.17
Exp/Cert (Z-score as Y error bar)
4.00
3.00
1.19
1.08
1.07
1.20
2.00
1.19
0.87
0.92
1.11
0.96
1.06
0.88
0.92
1.01
1.00
0.89
1.00
0.00
-1.00
-2.00
As
La
Mn
Na
Sc
Sm
Ga
K
Hf
Element
Sb
Ce
Th
Fe
Rb
Yb
U Ca
Figure 5.14: IAEA Soil-7 elements at irradiation position of 31 in rotary rack
88
CHAPTER VI
CONCLUSION
6.0
Conclusion
This work determines the element concentration of Soil-1 and Soil-7 using
an absolute method. The accuracy of the elemental concentration have been
statistically evaluated using Z-score. Most of the analytical results were found to be
have Z-value within 0 to 2. The elemental analysis results obtained by absolute
method were found to yield good agreement between the calculated concentration
and the certified values.
The precision of the absolute method may be affected by the coincidence
effects for certain gamma-rays. Besides that, the calculated concentration will be
higher if a peak with energy equal to the sum of the cascade gamma-rays energies.
Matrix effects such as self-shielding and self- absorption can contribute additional
error in the results. A significant deviation from those values could be caused by
inaccurate of nuclear data. By optimising the irradiation, decay and measuring times,
a lot of elements can be determined with higher sensitivity.
90
In conclusion, the absolute method had been implemented successfully and
provides the accuracy which may overcome several drawbacks of the relative method.
The NAA absolute method can be viable analytical tool in a stable neutron flux and
good thermalization nuclear reactor. Besides that, the absolute method is a time and
cost-effective analytical method particularly for industries or scientific research in
determining the concentration of element in samples. The expected outcome from
this research is as an innovation in the development and application of NAA.
6.1
Recommendation
Monte Carlo N-Particle (MCNP) approach could be used to stimulate the
reactor neutron parameter at different irradiation position of reactor rotary rack in
conjunction with the experimental measurements. Monte Carlo simulations had been
routinely used for particle transport calculations as they can provide valuable
additional information on the characteristics of irradiation fields. A complete of
reactor geometry with details dimension especially the reactor core configuration is
required in verification of the neutron parameter using Monte Carlo calculations.
Besides that, the elemental analysis of the NAA absolute method could be
developed into a computer software program. Therefore, the calculation and analysis
task of element concentration can be easily performed on a computer system. The
program can use the input values from experiment to calculate the neutron reactor
parameter and finally computed the concentration of element found in samples. The
basic nuclear data are stored in database and the program can be coded in Visual
Basic. The purpose of the software program is to reduce the complexity of the
elemental analysis.
91
LIST OF REFERENCES
1.
S.I. Kafala, T.D.Macmahon. Neutron Activation Analysis without
Multi-element Standards. 1993. J. Radioanal. Nucl. Chem., 169:187-199.
2.
Francesco Girardi, Giampaolo Guzzi, Jules. Pauly. Activation Analysis by
Absolute Gamma Ray Counting and Direct Calculation of Weights from
Nuclear Constants. 1964. Anal. Chem., 36:1588-1594
3.
De Corte. The Updated NAA Nuclear Data Library Derived From the Y2K
ko-database. 2003. J. Radioanal. Nucl. Chem., 257: 493-499.
4.
M. U. Rajput, M. Ahmad, and W. Ahmad. Thermal Neutron Cross Section
and Resonance Integral of the 159Tb (n, ã)160Tb Reaction. 2003. Pyhsical
Review C 68, 044608.
5.
Rutherford, E. Nuclear Constitution of Atoms. 1920. Proceedings of the
Royal Society. Series A 97:374.
6.
Chadwick, J. Possible Existence of a Neutron. 1932. Nature. 129:312
7.
Chadwick, J. The Existence of a Neutron. 1932. Proceedings of the Royal
Society, Series A 136:692
8.
L. Meitner and O.R. Frisch. Disintegration of Uranium by Neutrons: A
New Type of Nuclear Reaction. 1939. Nature, 143:239-240
9.
Husin Wagiran. Neutron dan Penjanaan Tenaga Nuklear. Universiti
92
Teknologi Malaysia: 2006
10.
Glascock, Michael D. & Hector Neff. Neutron activation analysis and
provenance research in archaeology. 2003. Measurement Science &
Technology, 14(9): 1516–1526.
11.
Glasgow D. C., Dyer F. F., Robinson L. Methods for preparing
comparative standards and field samples for neutron activation analysis of
soil. 1995. J. Radioanal. Nucl. Chem., 192: 361-370.
12.
B.J.B Nyarko, E.H.K.Akaho, Y.Serfor-Armah. Application of NAA
Standardization Methods using a Low Power Research Reactor. 2003. J.
Radioanal. Nucl. Chem., 257:361-366.
13.
J. St-Pierre and L.Zikovsky. Use of the absolute Method in Neutron
activation Analysis: Application to National Bureau of Standards Coal and
Spinach. 1982. J. Chem, 60: 2278-2280.
14.
A.Ahmad, P.W. Gray, T.D. Macmahon, M. Macwani. Neutron Activation
Analysis without Multielement Standards. 1982. J. Radioanal. Nucl. Chem,
72: 335-352.
15.
De Corte, L. Moens, A. Simonits, et.al. The Effect of the Epithermal
Neutron Flux Distribution on the Accuracy of Absolute and Comparator
Standardization Methods in (n,ã) Activation Analysis. 1982. J. Radioanal.
Chem., 72: 257-286.
16.
De Corte, L. Moens, K.Sordo-El Hammami, et.al. Modification and
Generalization of some Methods to Improve the Accuracy of áDetermination in the 1/E 1+á Epithermal Neutron Spectrum.1979. J.
Radioanal. Nucl. Chem, 52, No2: 305-316.
17.
A.De Wispelaere, Frans De Corte. Recalibration of the Irradiation
Facilities in the Thetis Reactor, with an Examination of the á versus
93
behavior in the keV Neutron Energy Range. 2003. J. Radioanal. Nucl.
Chem., 257: 519-523.
18.
C.O.Mustra, M.C.Freitas, S.M. Almeida. Neutron Flux and Associated ko
Parameters in the RPI after the Last Configuration Change. 2003. J.
Radioanal. Nucl. Chem., 257: 539-543.
19.
B. Smodis, A. Trkov, R. Jacimovic. Effects of the Neutron Spectrum on the
Neutron Activation Analysis Constants for 94 Zr and 96Zr”. 2003. J.
Radioanal. Nucl. Chem., 257: 481-487.
20.
Ho M. Dung, F. Sasajima. Determination of á and f for ko-NAA in
Irradiation Sites with High Thermalized Neutrons. 2003. J. Radioanal.
Nucl. Chem., 257: 509-512.
21.
Ho M. Dung, S. Y. Cho. A Simple Method for á Determination. 2003.
J.Radioanal. Nucl. Chem., 257: 573-575.
22.
Frans De Corte, K. Sordo-El Hammami, et.al. The Accuracy and Precision
of the Experimental á-Determination in the 1/E 1+á Epithermal Reactor
Neutron Spectrum. 1981. J. Radioanal. Nucl. Chem., 62: 209-255.
23.
Wee Boon Siong, Ho Manh Dong, Ab. Khalik Wood, et.al. Testing the
Applicability of the ko-NAA Method at the MINT’s TRIGA MARK II
Reactor. 2006. Nucl. Instruments and Methods in Physics Research A 564:
716-720.
24.
Khoo Kok Siong, Sukiman Sarmani,et.al. Assessment of Neutron Flux
Gradients in Irradiation Channels at the TRIGA Reactor by Au-Cr-Mo
Monitor Set Based on k0-INAA. 2008. Sains Malaysiana 37: 401-404.
25.
Faridah Mohammad Idris. Neutron Flux in Measurements of Reactor Triga
Puspati (RTP). Nuclear Energy Unit Ministry of Science, Technology and
the Environment: 1993
94
26.
K. Debertin and R.G. Helmer, Gamma- and X-Ray Spectrometry With
Semiconductor Detectors, (North Holland: New York, 1988). Chapter 6.
27.
American National Standards Institute. Calibration and Use of
Germanium Spectrometers for the Measurement of Gamma-Ray Emission
Rates of Radionuclides. American, ANSI N42.24.1991
28.
M. U. Rajput, T.D. Macmahon. Measurement of Thermal Neutron
Cross Section and Resonance Integrals of 74Se, 75As, 94Zr, 134Cs, 238U. 1995.
J. Radioanal Nucl. Chem, 189: 51-58.
29
R.Jacimovie, M. Maucec, A. Trkov. Verification of Monte Carlo
Calculations of the Neutron Flux in Typical Irradiation Channels of the
TRIGA Reactor. (2003). J. Radioanal Nucl. Chem, 257: 513-517.
30.
De Corte.The ko-Standardization Method- A Move to the Optimization of
NAA. Instituut voor Nucleaire Wetenschappen, Belgium: 1987
APPENDIX A
Scheme of Neutron Activation Analysis absolute method in determination the concentration of element
Experiment ( For monitors
and comparator)
Input: Net peak area;
Irradiation time;
cooling time;
counting time;
sample mass.
Isotope nuclear data:
T1/2, Qo, Er, Fcd
1
Calculation of
Asp and Qo (á)
2
Experiment measurement of:
Epithermal and thermal flux neutron
(öth ,öepi) using Au foil;
öth ,öepi
Rcd
Determination of
flux ratio, f and á
parameter
Qá
Calculation of
resonance
Integral, Iá
using formula.
Iá
Calculation of gamma ray
emission reaction rate:
R = öthó 0 +öepi Iá.
R
3
Calibratio the efficiency of the
detector, å.
Output
Calculation of concentration:
4
Experiment (For environmental
reference materials (IAEA-SL-1)
Input: Net peak area;
Irradiation time;
cooling time;
counting time;
sample mass.
m =
N
R  SDCt
95
APPENDIX B
Cd ratio for multi monitor method with 5 monitors at irradiation position 10 of the TRIGA reactor rotary rack
Parameter j
Position 10; á = -0.0532 ; f = 19.7
Uncertainty Sj
Au197
Mo99
Co60
Zn64
Zn67
Zr94
Zr97
Au197
Mo99
Co60
Zá(j)
Zn64
Zn67
Zr94
Zr97
(Asp)cd
1%
1%
1%
1%
1%
1%
1%
3.70
0.80
0.51
1.09
0.31
1.89
0.19
(Asp)bare
1%
1%
1%
1%
1%
1%
1%
3.70
0.80
0.51
1.09
0.31
1.89
0.19
Precision;
Sá, R
= 5.43%
Fcd
0.2%
-
-
-
-
-
-
3.70
0.80
0.51
1.09
0.31
1.89
0.19
Qo
1.8%
6.3%
2.7%
4.9%
1.4%
-
-
1.98
0.17
0.47
1.03
0.26
1.43
0.01
Er
7.1%
20.0% 5.1% 10.0% 10.0%
Ecd
15%
15%
15%
15%
15%
4.0%
2.1% 0.1023 0.0092 0.0194 0.0424 0.0122 0.0692 0.0006
15%
15%
0.13
0.13
0.13
0.13
0.13
Fixed Accuracy; Sá, S
0.13
0.13
= 8.22%
(Asp)cd
1.0%
1.1%
1.4%
4.7%
1.0%
14.8% 1.0%
3.70
0.80
0.51
1.09
0.31
1.89
0.19
(Asp)bare
1.1%
1.0%
1.1%
1.4%
1.1%
5.0%
3.70
0.80
0.51
1.09
0.31
1.89
0.19
1.0%
Experimental Accuracy;
Overall uncertainty;
Sá,G = 4.69%
Sá,T = 10.45 %
96
APPENDIX C
Cd ratio for multi monitor method with 5 monitors at irradiation position 22 of the TRIGA reactor rotary rack
Parameter j
Position 22; á = -0.0307 ; f = 20.4
Uncertainty Sj
Au197
Mo99
Co60
Zn64
Zn67
Zr94
Zr97
Au197
Mo99
Co60
Zá(j)
Zn64
Zn67
Zr94
Zr97
(Asp)cd
1%
1%
1%
1%
1%
1%
1%
6.35
1.26
0.88
1.90
0.54
3.18
0.28
(Asp)bare
1%
1%
1%
1%
1%
1%
1%
6.35
1.26
0.88
1.90
0.54
3.18
0.28
Precision;
Sá, R
= 7.53%
Fcd
0.2%
-
-
-
-
-
-
6.35
1.26
0.88
1.90
0.54
3.18
0.28
Qo
1.8%
6.3%
2.7%
4.9%
1.4%
-
-
3.50
0.31
0.81
1.77
0.46
2.51
0.02
Er
7.1%
20.0% 5.1% 10.0% 10.0%
Ecd
15%
15%
15%
15%
15%
4.0%
2.1% 0.1045 0.0094 0.0195 0.0422 0.0123 0.0699 0.0006
15%
15%
0.26
0.26
0.26
0.26
Fixed Accuracy; Sá, S
0.26
0.26
0.26
= 15.25%
(Asp)cd
0.7%
0.7%
1.0%
3.2%
0.7%
10.5% 0.3%
6.35
1.26
0.88
1.90
0.54
3.18
0.28
(Asp)bare
1.0%
0.9%
0.9%
1.4%
0.4%
6.4%
6.35
1.26
0.88
1.90
0.54
3.18
0.28
0.5%
Experimental Accuracy;
Overall uncertainty;
Sá,G = 8.17%
Sá,T = 18.85 %
97
APPENDIX D
Cd ratio for multi monitor method with 5 monitors at irradiation position 27 of the TRIGA reactor rotary rack
Parameter j
Position 27; á = -0.0464 ; f = 20.1
Uncertainty Sj
Au197
Mo99
Co60
Zn64
Zn67
Zr94
Zá(j)
Au197
Mo99
Co60
Zn64
Zn67
Zr94
(Asp)cd
1%
1%
1%
1%
1%
1%
2.27
0.78
0.04
1.20
0.62
1.86
(Asp)bare
1%
1%
1%
1%
1%
1%
2.27
0.78
0.04
1.20
0.62
1.86
Precision;
Sá, R
= 3.33%
Fcd
0.2%
-
-
-
-
-
2.27
0.78
0.04
1.20
0.62
1.86
Qo
1.8%
6.3%
2.7%
4.9%
1.4%
-
1.23
0.18
0.04
1.13
0.53
1.44
Er
7.1%
20.0%
5.1%
10.0%
10.0%
4.0%
0.0556
0.0081
0.0014
0.0405
0.0211
0.0604
Ecd
15%
15%
15%
15%
15%
15%
0.10
0.10
0.10
0.10
0.10
0.10
Fixed Accuracy; Sá, S
(Asp)cd
1.9%
2.0%
2.5%
6.5%
1.3%
17.7%
(Asp)bare
1.8%
1.8%
1.9%
2.1%
1.9%
6.0%
2.27
2.27
0.78
0.04
1.20
= 7.33%
0.62
0.78
0.04
1.20
0.62
Experimental Accuracy; Sá,G = 6.63%
Overall uncertainty;
Sá,T
1.86
1.86
= 10.43 %
98
APPENDIX E
Cd ratio for multi monitor method with 5 monitors at irradiation position 31 of the TRIGA reactor rotary rack
Parameter j
Position 22; á = -0.0620 ; f = 21.68
Uncertainty Sj
Au197
Mo99
Co60
Zn64
Zn67
Zr94
Zr97
Au197
Mo99
Co60
Zá(j)
Zn64
Zn67
Zr94
Zr97
(Asp)cd
1%
1%
1%
1%
1%
1%
1%
3.26
0.73
0.46
0.99
0.28
1.74
0.17
(Asp)bare
1%
1%
1%
1%
1%
1%
1%
3.26
0.73
0.46
0.99
0.28
1.74
0.17
Precision;
Sá, R
= 3.94%
Fcd
0.2%
-
-
-
-
-
-
3.26
1.26
0.46
0.99
0.28
1.74
0.17
Qo
1.8%
6.3%
2.7%
4.9%
1.4%
-
-
1.76
0.15
0.41
0.88
0.23
1.20
0.01
Er
7.1%
20.0% 5.1% 10.0% 10.0%
Ecd
15%
15%
15%
15%
15%
4.0%
2.1% 0.1062 0.0092 0.0198 0.0422 0.0122 0.0676 0.0006
15%
15%
0.10
0.10
0.10
0.10
0.10
Fixed Accuracy; Sá, S
0.10
0.10
=6.96%
(Asp)cd
1.0%
1.2%
1.3%
4.5%
0.8%
15.5% 1.0%
3.26
0.73
0.46
0.99
0.28
1.74
0.17
(Asp)bare
1.0%
1.1%
1.1%
1.2%
1.0%
4.5%
3.26
0.73
0.46
0.99
0.28
1.74
0.17
1.0%
Experimental Accuracy;
Overall uncertainty;
Sá,G = 4.20%
Sá,T
= 9.03 %
99
100
LIST OF PUBLICATIONS
1.
Presented and published paper entitled “Parameterisation of Fission Neutron
Spectra (TRIGA Reactor) for Neutron Activation without the Used of
Standard” in proceedings for Research and Development Conference
organized by Malaysian Nuclear Agency, MNA. (2008)
2.
Presented and published paper entitled “Parameterisation of Fission Neutron
Spectra (TRIGA Reactor) for Neutron Activation without the Used of
Standard” in proceedings for International Graduate Conference on
Engineering and Science 2008 (IGCES 2008) organized by UTM.