MEASUREMENT OF THERMAL NEUTRON CAPTURE
CROSS SECTION IN PRASEODYMIUM
By
Mekonnen Tefera Kebede
SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN PHYSICS
AT
ADDIS ABABA UNIVERSITY
ADDIS ABABA, ETHIOPIA
May 2016
© Copyright by Mekonnen Tefera Kebede, May 2016
ADDIS ABABA UNIVERSITY
DEPARTMENT OF PHYSICS
The undersigned here by certify that they have read and recommend to the School of Graduate
Studies for acceptance a thesis entitled “Measurement of Thermal neutron capture cross section
in Pr-141” by Mekonnen Tefera Kebede in partial fulfillment of the requirements for the degree
of Master of Science in Physics.
Dated:June,2016
Advisor:
____________________________________
Prof.A.K.Chaubey
Examiner:
_____________________________________
Dr. Tilahun Tesfaye
_____________________________________
Dr. Teshome Senbeta
ii
ADDIS ABABA UNIVERSITY
Date: June, 2016
Author: Mekonnen Tefera Kebede
Title: Measurement of Thermal Neutron Capture Cross Section in Praseodymium
Department: Physics
Degree: M.Sc.
Convocation: June
Year: 2016
Permission is here with granted to Addis Ababa University to circulate and to have copied for
non-commercial purposes, at its discretion, the above title upon the request of individuals or
institutions.
_____________________________
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THE AUTHOR RESERVES OTHER PUBLICATION RIGHTS, AND NEITHER THE THESIS
NOR EXTENSIVE EXTRACTS FROM IT MAY BE PRINTED OR OTHERWISE
REPRODUCED WITHOUT THE AUTHOR’S WRITTEN PERMISSION.
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EXCERPTS REQUIRING ONLY PROPER ACKNOWLEDGEMENT IN SCHOLARLY
WRITING) AND THAT ALL SUCH USE IS CLEARLY ACKNOWLEDGED.
iii
ABSTRACT
The measurement of thermal neutron capture cross sections gives basic information about the
internal structure of atomic nuclei and their structure. Measurement of Thermal Neutron capture
cross-section of 141Pr was done at the Addis Ababa University Nuclear physics Laboratory using
the GM-counter on the decay radioactivity data taken.The thermal neutron capture cross section
measured for 141Pr using slow neutrons is ( 7.557 ). The induced activity was confirmed from the
half life of the 142Pr sample. The results are discussed and compared with previous Measurement.
The cross section was also calculated using the resonance parameter. In general there is good
agreement between the observed and calculated value of thermal neutron capture cross section.
iv
ACKNOWLEDGMENT
Above all, I would like to thank the Almighty God, for letting me accomplish this stage. I am
deeply indebted Professor A.K.Chaubey, my advisor, for his many suggestions and constant
support and friendly approach during this research. His tireless follow up and his consistent
support will be in my memory forever. My special thanks also go to my father Tefera Kebede
and my mother Tsehaneshe Teferi, my uncle Alebachew Kebede and his wife Azaleche Asefaw,
my brothers Wondwesen Abate, Leulseged Tefera and my sister Fentaye Tefera
whose
eagerness to see my success and their unreserved prayer and support were engines to my
educational endeavors.
My greatest thanks go to my collegue Abdulrzak Oumer, Mengistu Balecha, Eshetu Tilahune,
Berehanu Turi, Bogaleche Tifu, Abera Demeke, Eyoel Girma, Nardose especially Mekdes
Melkamu, Yiftusera Sigebo and Wondwesen Kebede for the financial, material and constant
moral support they provided me.
My thanks also go to Ethiopian Radiation Protection Authority for their cooperation and
financial support till the end of my study years.
It gives me great pleasure to acknowledge the Department of Physics and the School of Graduate
Studies, Addis Ababa University for all their support I got during my study.
I would like to express my indebtedness to all of my friends who helped me directly or indirectly
during my stay in the graduate class.
v
TABLE OF CONTENTS
ABSTRACT.............................................................................................................................................................. IV
ACKNOWLEDGMENT............................................................................................................................................ V
TABLE OF CONTENTS.......................................................................................................................................... VI
INTRODUCTION......................................................................................................................................................1
OBJECTIVES OF THE STUDY.........................................................................................................................................3
CHAPTER ONE.........................................................................................................................................................4
1. NEUTRON............................................................................................................................................................. 4
1.1 DISCOVERY OF NEUTRON..................................................................................................................................... 4
1.2 RADIOACTIVE DECAY OF NEUTRON..................................................................................................................... 5
1.3 CLASSIFICATION OF NEUTRON.............................................................................................................................. 6
1.4 PROPERTIES OF NEUTRON.....................................................................................................................................7
CHAPTER TWO........................................................................................................................................................8
2. NEUTRON PHYSICS............................................................................................................................................8
2.1. NEUTRON SOURCES [3]........................................................................................................................................8
2.1.1 RADIOACTIVE SOURCES.....................................................................................................................................9
2.1.2 ACCELERATOR SOURCE................................................................................................................................... 11
2.2 NEUTRON INTERACTION..................................................................................................................................... 12
2.2.1 ELASTIC SCATTERING (N, N)............................................................................................................................13
2.2.2 INELASTIC SCATTERING................................................................................................................................... 14
2.2.3 TRANSMUTATION (N, P), (N, Α)........................................................................................................................ 14
2.2.4 RADIATIVE CAPTURE (N, ......................................................................... ERROR! BOOKMARK NOT DEFINED.
2.2.5 FISSION.......................................................................................................................................................... 16
2.3 MAXWELL-BOLTZMANN DISTRIBUTION........................................................................................................... 17
2.4 SLOWING DOWN OF NEUTRONS..........................................................................................................................18
2.4.1. ELASTIC SCATTERING IN THE MODERATING REGION.....................................................................................19
2.5 NEUTRON CROSS SECTION..................................................................................................................................23
2.6 NEUTRON ACTIVATION ANALYSIS......................................................................................................................24
2.6.1 PROMPT VS. DELAYED NEUTRON ACTIVATION ANALYSIS..............................................................................26
2.6.2 INSTRUMENTAL VS. RADIOCHEMICAL NAA....................................................................................................27
2.6.3 PRINCIPLES OF NEUTRON ACTIVATION ANALYSIS (NAA)..............................................................................27
2.6.4 ADVANTAGE AND DISADVANTAGE OF NAA................................................................................................... 29
2.6.5 APPLICATION....................................................................................................................................................30
2.7 RADIATION DETECTION [29]...............................................................................................................................30
2.7.1 INTRODUCTION TO GEIGER COUNTERS (TUBE) [30]........................................................................................31
2.7.2 ADVANTAGE AND DISADVANTAGE OF THE GEIGER-COUNTER........................................................................ 32
CHAPTER THREE.................................................................................................................................................. 32
3. EXPERIMENT.....................................................................................................................................................32
3.1 INTRODUCTION....................................................................................................................................................32
3.2 EXPERIMENTAL SETUP........................................................................................................................................33
3.2.1 NEUTRON SOURCE........................................................................................................................................... 33
3.2.2 GEIGER-MULLER COUNTER............................................................................................................................. 34
3.2.3 CHARACTERISTICS OF THE GM COUNTER....................................................................................................... 35
3.2.4 RESOLVING TIME OF THE GM COUNTER......................................................................................................... 38
3.3 BACKGROUND MEASUREMENTS......................................................................................................................... 38
3.4 SAMPLING AND IRRADIATION............................................................................................................................. 38
3.4.1 PRASEODYMIUM OXIDE....................................................................................................................................39
3.5 MEASUREMENT................................................................................................................................................... 41
CHAPTER FOUR.................................................................................................................................................... 41
vi
4. DATA AND DATA ANALYSIS........................................................................................................................ 41
4.1 BETA COUNTING..................................................................................................................................................41
4.1.1 MATERIALS USED IN BETA COUNTING............................................................................................................. 41
4.1.2 BETA COUNTING PROCEDURE.......................................................................................................................... 41
4.1.3 MEASUREMENTS OF BETA PARTICLES..............................................................................................................44
GRAPH4. 2: LOGARITHMIC DECAY CURVE OF FRONT KI TARGET............................................................................. 46
GRAPH4. 4: LOGARITHMIC DECAY CURVE OF BACK I TARGET................................................................................. 48
4.2 RESULTS AND DISCUSSIONS................................................................................................................................51
4.2.1 DECAY CONSTANT DETERMINATION FOR THE FRONT AND BACK I TARGET FOR fiRST EXPERIMENT............... 51
4.2. 2 DETERMINATION OF HALF-LIFE OF SAMPLE...................................................................................................51
4.2.3 NEUTRON FLUX DETERMINATION.................................................................................................................... 51
4.2.4 NEUTRON CAPTURE CROSS-SECTION OF 141PR..............................................................................................55
4.3 SOURCES OF ERROR ESTIMATION....................................................................................................................... 57
4.3.1 ERRORS IN THE MEASUREMENT.......................................................................................................................57
CHAPTER 5.............................................................................................................................................................58
5. THEORITICAL ESTIMATES OF THERMAL NEUTRON CAPTURE CROSS SECTIONS......................... 58
5.1 COMPOUND NUCLEUS.........................................................................................................................................58
5.2 STATISTICAL ESTIMATES OF THERMAL NEUTRON CAPTURE CROSS SECTIONS.................................................59
5.3. SUMMARY AND CONCLUSION............................................................................................................................ 62
REFERENCE............................................................................................................................................................... 63
DECLARATION...........................................................................................................................................................65
vii
LIST OF TABLES
TABLE 3.1: TABLE OF VOLT VS ACTIVITY DATA OF GM-COUNTER.............................................36
TABLE 4.1: DECAY TABLE OF FRONT KI TARGET.......................................................................... 44
TABLE 4. 2: DECAY TABLE OF BACK KI TARGET...........................................................................47
TABLE 4. 3: DECAY TABLE OF PR-141...........................................................................................48
viii
LIST OF FIGURE
FIG1. 1:EXPERIMENTAL SETUP TO THE DISCOVERY OF A NEUTRON ...............................................4
FIG1. 2: THREE QUARKS OF NEUTRON............................................................................................ 7
FIG2. 1: POTENTIAL ELASTIC SCATTERING...................................................................................14
FIG2. 2: NEUTRON-PROTON REACTIONS....................................................................................... 15
FIG2. 3: RADIOACTIVE CAPTURE THE DEUTERIUM FORMED IS A STABLE NUCLIDE......................16
FIG2. 4: SCATTER IN LAB AND CENTER OF MASS SYSTEMS ..........................................................19
FIG2. 5: DIAGRAM OF VELOCITIES FOR CONVERSION FROM COM TO LAB SYSTEM.....................22
FIG2. 7: CONCEPT OF NEUTRON CROSS SECTION ..........................................................................23
FIG2. 8: THE PROCESS OF NEUTRON CAPTURE BY A TARGET NUCLEUS FOLLOWED BY THE
EMISSION OF GAMMA RAYS.....................................................................................................26
FIG3. 1: SCHEMATIC DIAGRAM OF AM-BE NEUTRON SOURCE.....................................................33
FIG. 3.2: SETUP OF GM COUNTER................................................................................................ 35
FIG3. 3: PRASEODYMIUM OXIDE SAMPLE......................................................................................40
FIG4. 1: DECAY SCHEME OF I-128................................................................................................ 43
FIG4. 2: DECAY SCHEME OF PR-142............................................................................................. 44
ix
LIST OF GRAPHS
GRAPH 3. 1: GM-COUNTER CHARACTERISTICS............................................................................. 37
GRAPH 4. 1: EXPONENTIAL DECAY CURVE OF FRONT KI TARGET................................................. 45
GRAPH 4. 2: LOGARITHMIC DECAY CURVE OF FRONT KI TARGET................................................. 46
GRAPH 4. 3: EXPONENTIAL DECAY CURVE OF BACK KI TARGET................................................... 47
GRAPH 4. 4: LOGARITHMIC DECAY CURVE OF BACK I TARGET......................................................48
GRAPH 4. 5: EXPONENTIAL DECAY CURVE OF PR-142.................................................................. 49
GRAPH 4. 6: LOGARITHMIC DECAY CURVE OF PR-142.................................................................. 50
x
61
INTRODUCTION
Behavior of neutrons passing through matter is fundamentally different from that of energetic
charged particles. Because of the absence of charge they interact hardly at all with the shell
electrons and with the coulomb field of the nucleus. The chief process is scattering and
absorption by the nucleus by virtue of the nuclear force alone. If neutron traverse an absorber,
they do not, like charged particles, lose their energy gradually, but pass through unchanged
until they are either captured or scattered away so, based on the energy of neutrons and the
different techniques (methods) used in many nuclear reactions induced by neutrons many
valuable information about a nucleus can be revealed. In the literature review the cross
section for
Pr (n,142Pr reaction has been measured by detecting 642KeV gamma ray this
141
value is equal to 7.60.3b [1]. In the present work the cross-section of
Pr (n,)
141
Pr reaction
142
in our labratory has been investigated. Neutrons together with protons are the constituents of
atomic nuclei. The neutron was discovered after more than two decades of speculation that
electrically neutral particles exist in atoms. Because the neutron is electrically neutral, it
easily interacts with nuclei and does not interact directly with electrons. Since the nucleus of
an atom is about one ten-thousandth the size of the electron cloud, the chance of neutrons
interacting with a nucleus is very small, allowing them to travel long distances through matter
[2].
As a free particle, the neutron is an important and yet unique tool used for various
applications: in medicine to initiate powerful nuclear interactions whose products can directly
destroy cancer cells (neutron capture therapy for example), for research on physical and
biological materials, for imaging through easy allocation of light atoms especially hydrogen,
to investigate properties of magnetic materials (neutrons possess a magnetic moment and thus
act as small magnets), to track atomic movement (thermal neutron energies almost directly
coincide with the energies of atoms in motion), and to maintain the fission chain reaction in
nuclear reactors. Free neutrons are unstable and break up in short time by decay to a proton,
electron and antineutrino. However, free neutrons will most likely interact with the
surrounding matter and disappear through nuclear interactions long before they decay [2].
1
Among heavy elements thermal and epithermal neutrons can cause (n,α) and (n, p) reactions,
as well as neutron capture. Among heavier elements the neutron result primarily in capture
(n, ) and fission reactions, fast neutrons being required for particle emission reaction such as
(n, 2n), (n, p), etc.
The probability of a neutron interacting with nucleus for a particular reaction is dependent
upon not only the kind of nucleus involved, but also the energy of neutron. Accordingly, the
absorption of thermal neutrons in most material is much more probable than the absorption of
a fast neutron. Also, the probability of interaction will vary depending up on the type of
interaction involved.
The probability of a particular interaction occurring between a neutron and a nucleus is called
the microscopic cross section (σ) of the nucleus for the particular interaction. This cross
section will vary with the energy of the neutron. The microscopic cross section may also be
regarded as the effective area of the nucleus presented to the projectile. The larger the
effective area, the larger the probability of interaction. Because the microscopic cross section
has definition of an area, it is expressed in unit of area, or square centimeters. A square
centimeter is large compared to the effective area of a nucleus; hence it is expressed in a
smaller unit of area called a barn. One barn is [3].
Praseodymium is a soft malleable, silvery-yellow metal. It is a member of the lanthanide
group of the periodic table of elements. It reacts slowly with oxygen: when exposed to air it
forms a green oxide that does not protect it from further oxidation. It is more resistant to
corrosion in air the other rare metals, but it still needs to be stored under oil or coated with
plastic. It reacts rapidly with water. It may have oxidation numbers of +3 and +4 in its
compound. This has one isotope available in natural isotope. Out of the most abundant is
Pr (100%). A major use of the metal is in a pyrophoric alloy used in cigarettes lighter flints.
141
Praseodymium compounds have different uses: the oxide is used in carbon electrodes for arc
lighting, and it is known for its ability to give glass a nice yellow color. This glass filters out
the infrared radiation, so it is used in the goggles which protect the eyes of welders. The salts
are used to color enamel and glass. Praseodymium can be used as alloying agent with
magnesium to create high strength metals that are used in aircraft engines. Praseodymium is
one of the rare chemicals that can be found in houses in equipment such as color televisions,
fluorescent lamps, energy-saving lamps and glasses. All rare chemicals have comparable
properties. The use of praseodymium is still growing, due to the fact that it is suited to
produce catalysers and to polish glass [22].
2
Irradiating sample of praseodymium by a uniform neutron beam of known flux and
measuring the induced radioactivity by counting gamma radiations using GM-counter
thermal neutron capture cross section of the Pr-141 can be measured. To perform such an
experiment one needs, standard sources for the calibration of the detector, thermal neutron
source to have beam of thermal neutrons for the activation of the sample of the isotope and
the respective detector for the measuring of emitted radiations. In performing this experiment
Am- Be neutron source of 2ci, GM-counter and standard calibration sources are used in
nuclear laboratory of AAU. When a natural praseodymium foil is irradiated with neutron
beam, thermal neutrons interact with praseodymium to produce compound nucleus of Pr-142
of easily measurable life time. While decay of Pr-142 ground state proceeds directly in to Nd142 ground state, the isomeric states of Pr-142 decay in to the excited states of Nd-142. The
gamma rays are emitted in their de-excitation. Hence, by measuring the spectrum of the
gamma ray emitted, the thermal neutrons capture cross section for Pr-141 can be also found.
Objectives of the study
 To study the capture reaction (n,using the medium element isotope (141Pr ) and
measure its thermal neutron capture cross section using Geiger muller counter (GMCounter)
 To compare the theoretical value of thermal neutron capture cross section with the
measured value and compare with theortical value.
3
CHAPTER ONE
1. NEUTRON
1.1 Discovery of Neutron
The existence of neutron was first suggested by Rutherford in 1920. He thought that an
electron could exist in a nucleus and could combine with a proton to form a neutron.
Being electrically neutral, the neutron was very difficult to discover by methods of particle
detection which depends on the deflection of the particles in a magnetic or electric field or on
their ionization of matter [2].
Fig1. 1:Experimental setup to the discovery of a neutron [24]
In 1930 it was discovered that Beryllium [24], when bombarded by alpha particles, emitted a
very energetic stream of radiation. This stream was originally thought to be gamma
radiation.
However, further investigations into the properties of the radiation revealed
contradictory results. Like gamma rays, these rays were extremely penetrating and since they
were not deflected upon passing through a magnetic field, neutral. However, unlike gamma
rays, these rays did not discharge charged electroscopes (the photoelectric effect). Irene Curie
and her husband discovered that when a beam of this radiation hit a substance rich in protons,
for example paraffin, protons were knocked loose which could be easily detected by a Geiger
counter.
In 1932, Chadwick proposed that this particle was Rutherford's neutron [2, 24]. Using
kinematics, Chadwick was able to determine the velocity of the protons. Then through
4
Conservation of momentum techniques, he was able to determine that the mass of the neutral
radiation was almost exactly the same as that of a proton. This is Chadwick's equation:
1.1
With Chadwick's announcement, Heisenberg then proposed the proton-neutron model for the
nucleus. Rutherford was incorrect in his "proton-electron" pair - there were no "free
electrons" in the nucleus. However, once free of the nucleus, evidence was mounting that
these neutrons were unstable. By 1932, the products of beta decay had been thoroughly
examined. To account for a broad spectrum of electron energies from a typical beta emitter,
discussions were taking place in which leading physicists were considering abandoning the
concepts of conservation of momentum and conservation of energy in radioactive decays. To
bring empirical evidence back into alignment with these fundamental basic principles,
Wolfgang Pauli proposed in 1930 the existence of an invisible particle that would carry off
the missing energy and momentum. He called this particle the neutrino, or little neutral one.
1.2
It wasn't until 1955 that Cowan and Reines, working with discharging radiation from the
Savannah River Nuclear Power Plant with its abundant supply of antineutrinos released
through the decay of free neutrons, discovered concrete experimental data to support the
existence of neutrinos [24].
1.2 Radioactive Decay of Neutron
The first determination of the mass of the neutron by Chadwick and Goldhaber shows that, its
mass was greater than that of proton. Depending on this fact they suggest that free neutrons
should be unstable and they should decay into a proton, electron and antineutrino.
n→p++
1.3
From the radioactive decay of neutron there is no physical law violated .In 1948, A.H Snell
and his workers were able to detect protons and electrons coming out from a thermal neutron
5
source with an estimated half-life about 10 to 30 minute. J.M.Robinson was able to determine
accurate half-life of neutron and its beta-ray (electron) spectrum using intense thermal
neutron source [17]. The end point energy spectrum of the experiment was 784kev which
were in excellent agreement with the mass deference of 784kev between a neutron and
hydrogen atom [17].
The value of half-life of neutron was determined from the value of the density of neutron
beam and the number of neutrons decaying per unit time per volume. The accepted value of
the mean lifetime of free neutron is 10.26 ± 0.04 minute; while neutrons bound in a nucleus
apparently are stable [2].
1.3 Classification of neutron
Depending on their energy neutrons can be classified into the following parts:
Neutron energy range names[25]
Neutron energy
Energy range
0.0–0.025 eV
Cold neutrons
0.025 eV
Thermal neutrons
0.025–0.4 eV
Epithermal neutrons
0.4–0.6 eV
Cadmium neutrons
0.6–1 eV
EpiCadmium neutrons
1–10 eV
Slow neutrons
10–300 eV
Resonance neutrons
300 eV–1 MeV
Intermediate neutrons
1–20 MeV
Fast neutrons
> 20 MeV
Ultrafast neutrons
But different ranges with different names are observed in other sources. For example,
Epithermal neutrons have energies between 1 eV and 10 keV and smaller nuclear cross
sections than thermal neutrons.
6
1.4 Properties of Neutron
Neutrons and protons are classified as hadrons, subatomic particles that are subject to the
strong force and as baryons since they are composed of three quarks. The neutron is a
composite article made of two down quarks with charge −⅓e and one up quark with charge
+⅔ e. Since the neutron has no net electric charge, it is not affected by electric forces, but the
neutron does have a slight distribution of electric charge within it. This results in non-zero
magnetic moment (dipole moment) of the neutron. Therefore the neutron interacts also via
electromagnetic interaction, but much weaker than the proton.
The mass of the neutron is 939.565 MeV/c2, whereas the mass of the three quarks is only
about 12 MeV/c2 (only about 1% of the mass-energy of the neutron). Like the proton, most of
mass (energy) of the neutron is in the form of the strong nuclear force energy (gluons). The
quarks of the neutron are held together by gluons, the exchange particles for the strong
nuclear force. Gluons carry the color charge of the strong nuclear force [20]. Neutrons are
composed of three quarks. The color assignment of individual quarks is not important, only
that all three colors down.
Fig1. 2: Three quarks of neutron
Quarks carry fractional electric charges (+ charges. There are different types of quarks. Their
masses range from ~ 5 MeVs/c2 to 180 Gev heaviest quark (t) [2].
7
CHAPTER TWO
2. NEUTRON PHYSICS
Neutrons play an important role in many nuclear reactions. For example, neutron capture
often results in neutron activation, inducing radioactivity. Neutron capture reaction can be
used to determine the energy and spin parity assignments of the capturing states. When the (n,
γ) reaction occurs, the ground state (or a long-lived isomeric state) of is itself radioactive.
We therefore accumulate activity of (usually with out bothering to observe the decay of s
from the capture state.
2.1. Neutron Sources [3]
Neutrons are one of the most powerful probes for making the arrangement of atoms visible
and for measuring the forces between them. The potential performance of a neutron source is
basically the product of two quantities, the source strength which measures the flux of useful
neutrons produced in the source and the instrumentation factor which measures how
efficiently we can detect the scattered neutrons. The first neutron sources were research
reactors and a rapid progression in neutron source performance followed the reactor
developments in the forties, fifties, and sixties. At the end of the sixties, this technology was
fully mature and from the seventies until the late nineties, advances in the scientific utility of
the technique derived mainly from improvements in instrumentation. Neutrons can also be
produced by spallation. i.e. through bombardment of a heavy atom with intense beams of
high energy protons (∼ GeV or velocities ∼ 90 percent of the velocity of light). During the
nineties, accelerator technology advanced to a state where spallation sources reached parity in
scientific performance with the best high flux reactors and the new projects, now under
8
construction or in development, promise significantly improved neutron source performance.
Coupled with ongoing improvements in instrumentation, there are exciting prospects for new
science. These prospects will not be limited to materials science but also cover a wide variety
of subjects from earth science to particle physics, from chemistry to engineering and from
solid state physics to biology and medicine. Depending up on the mechanisms used to
produce neutrons; neutron sources are divided in to two broad categories:
1. Radioactive sources
2. Accelerator based sources
2.1.1 Radioactive Sources
1. Radioisotope (α, n) Sources
These neutron sources uses (α, n) reaction in order to produce neutron, those light nuclei like;
Li, Be, B, N, O, F, are used as a targets and radio nuclide like; Pu, Ra, Am, Cm, Th, and U
are used for sources [4].
 (α,n) Reactions
One of the most known alpha particle nuclear reaction is reaction of α-particle with light
nuclei and which results in compound nucleus and it ejects a neutron when returning to the
ground state.
 ( α,n) Targets
A number of light nuclei are good to undergoing (α, n) reaction relatively with low energy
α−particle. This reaction has higher probability in light nuclei than heavy nuclei, because the
threshold energy or coulomb barrier is smaller in light nuclei.
 (α,n) Radionuclide
Alpha emitting radionuclide are also very important components of (α, n) reaction neutron
sources. Uranium and transuranic elements are usually alpha emitters since the probability of
(α,n) reaction increases with alpha -particle energy and the number of alpha-particle depends
on half-life; those alpha -emitters having high energy and long half-life on the order of 1 up
to 2500 years are preferable.
2. Spontaneous Fission Source
9
Certain transuranic heavy nuclides undergo spontaneous fission at a rate sufficient to give a
useful neutron source. Each such fission may produce several neutrons as well as beta and
gamma rays. The most commonly used spontaneous fission neutron source is Californium252.It undergoes an alpha decay with 97 percent and half-life 2.65 year. For every 32 alpha
emissions, there is a spontaneous fission with an average 3.8 neutrons and half-life of 85.5
year. The neutron yield is 2.3 x 106 n / s microgram. Hence, a small-encapsulated source
provide significant yield. The peak of relative number of neutrons lies between 0.5 Mev and
1Mev with the higher energy neutrons being 8 Mev to 10 Mev [5].
3. Nuclear Reactors Sources
Nuclear fission which takes place within the reactors produce very large quantities of
neutrons and can be used for a Variety of purposes including power generation and
experiments. A nuclear reactor is a source of products of fission process, such as, energy,
neutron and some useful radioactive isotopes. The fission reaction which takes place in the
reactors using slow or thermal neutrons having energy 0.0253 ev and velocity about 2200 m/s
[6]. These neutrons react with natural uranium producing several prompt neutrons. The
average number of neutrons produced per fission of uranium-235 by a thermal neutron is =
2.47 ± 0.03 neutron/fission [6]. The energy of neutrons from thermal fission of 235U is
different value extending from about 0.04 Mev to about 17 Mev with a distribution maximum
average value about 0.75 Mev. In order to use these neutrons having different energy value
10
for fission process in the reactor and for experiments they have to be slow down in the reactor
by using a substance moderator. The energy released and the number of neutrons per fission
of uranium-235 is given by;
+→ () →++ 3n + Q
2.1
Where Q represent the energy released in the reaction which is about 175 Mev. Such types of
nuclear reactors may produce a large number of thermal neutron flux at about 5.5 × 106 n/m2.s
and, that of fast neutron flux at about 7.1 × 1016 n/s [6].
4 Photo-neutron Source
In some nuclei, gamma radiation from radioactive isotopes with an energy exceeding the
neutron binding energy of a nucleus can eject a neutron. The minimum energy needed by the
gamma radiation to eject a neutron from a given nuclei is called threshold energy. Beryllium
and Deuteron have threshold energy about 1.666 Mev and 2.225 Mev [7] respectively, which
has smaller threshold value. Those radioisotopes, which decay with gamma ray greater than
the threshold of these nuclei, co-located with Beryllium and Deuteron, used as neutron (α, n)
source. The reaction in photo neutron source is given by;
+→++ Q
+→++ Q
2.3
2.4
Target materials which have large threshold energy needs to have gamma-radiation of several
Mev. But these radiations are dangerous which requires larger radiation shielding.
2.1.2 Accelerator Source
Accelerator neutron sources are neutron sources /devices/ which used proton, tritium or
deuteron as a projectile to hit a target material in order to emit neutrons. These systems vary
in size and diversity, and they include large installations such as the Spallation neutron
sources. Those particle accelerators have three basic parts in general. It consists of a source to
generate positively charged ions, one or more structures to accelerate the ions in keV up to
Mev and a target material. Usually these accelerators used proton and deuteron as a projectile.
The energy and intensity of projectiles can be controlled by the system in order to get the
desired amount and energy of neutron. Those materials made from light atoms, such as,
deuterium, tritium, lithium, and sodium, are taken as a target material. These devices are
11
relatively effective in producing, approximately, mono energetic neutrons with a variety of
intensity. Due to this reason, they have many industrial applications.
Neutron Producing Reaction
No neutron source is perfectly mono energetic but certain reactions can be used to produce a
neutron energy spectrum with a reasonably small energy spread. Because, the energy of
neutrons depends on certain factors, such as, energy spread of accelerated particles, the
reaction cross-section, exited level of the residual nucleus, etc. Apart from their usage
interims of the energy of neutrons produced, these particle accelerators are very important for
experiments and industrial applications due to their size, diversity, durability and their
consistency in number of neutrons produced per second. Depending up on the energy of
particles accelerated, target nucleus and the number of neutrons produced; particle
accelerators can be divided in to two broad categories.
1 Light -Ion Accelerators
Compact light-ion accelerators with hydrogen (H), deuterium (D), or tritium (T)ion sources
may be used to produce using targets of deuterium, tritium, lithium, beryllium and other lowz metals. Typically these accelerators operate with a voltage in the range of 1Mev and above.
The number of neutrons produced is smaller as Compared to the larger ones.
2 High Energy Particle Accelerators
A spallation source is one of the most high-flux neutron sources. In the neutron spallation
source, a high energy proton beam is used in order to bombard the heavy metal (like mercury)
target to yield neutrons and sometimes used to generate heat. Spallation sources may generate
an average neutron flux at about 5 × 1010 n/ cm2.s and above [4].
2.2 Neutron Interaction
Neutrons are neutral particles, therefore they travel in straight lines, deviating from their path
only when they actually collide with a nucleus to be scattered into a new direction or
absorbed. Neither the electrons surrounding (atomic electron cloud) a nucleus nor the electric
field caused by a positively charged nucleus affect a neutron’s flight. In short, neutrons
12
collide with nuclei, not with atoms. A nuclear reactor will not operate without neutrons.
Neutrons induce the fission reaction, which produces the heat in CANDU (Canadan
Deuterium Uranium) reactors, and fission creates more neutrons. The neutrons produced also
engage in other reactions. It is important to know about these neutron interactions. This
section introduces five reactions that can occur when a neutron interacts with a nucleus. In the
first two, known as scattering reactions, a neutron emerges from the reaction. In the
remaining reactions, known as absorption reactions, the neutron is absorbed into the nucleus
and something different emerges.
2.2.1 Elastic Scattering (n, n)
Elastic scattering resembles a billiard ball collision. A neutron collides with a nucleus,
transfers some energy to it, and bounces off in a different direction. (Sometimes it absorbs the
neutron and then re-emits it, conserving kinetic energy.) The fraction of its initial energy lost
depends on whether it hits the target nucleus head-on or at an angle exactly like the cue ball
striking a ball on the billiard table.
The target nucleus gains the energy lost by the neutron, and then moves at an increased speed
[9]. Light nuclei are the most effective for slowing neutrons. A neutron colliding with a heavy
nucleus rebounds with little loss of speed and transfers very little energy rather like firing the
cue ball at a cannon ball. On the other hand, neutrons will not be scattered by the light
electron clouds surrounding the nucleus, but will travel straight on much like baseballs
through a fog.
There are two possible ways for a neutron to scatter elastically from a nucleus: Resonance or
Compound elastic scattering: the neutron is absorbed by the target nucleus to form a
compound nucleus followed by re-emission of a neutron, and Potential elastic scattering: the
neutron is scattered away from the nucleus by the short range nuclear force is schematically
depicted in Fig. 2.1 Potential scattering is the most common form of neutron elastic scattering.
13
The more unusual of the two interactions is resonance elastic scattering which is highly
dependent upon initial neutron kinetic energy.
FIG2. 1: Potential Elastic Scattering
Potential scattering in which the neutron never actually touches the nucleus and a compound
nucleus is not formed takes place with incident neutrons of energies up to about 1 MeV.
Neutrons are scattered by the short range nuclear forces as they approach the nucleus. The
cross section is expressed by the relation (potential scattering) = 4πR2 (where R is the
nuclear radius) [2].
2.2.2 Inelastic Scattering
A neutron may strike a nucleus and be temporarily absorbed, forming a compound nucleus.
This will be in an excited state. It may de-excite by emitting another neutron of lower energy,
together with a gamma photon, which takes the remaining energy. This process is called
inelastic scattering. It generally happens only when high energy neutrons interact with heavy
nuclei and has little practical importance for reactor operation [2].
2.2.3 Transmutation (n, p), (n, α)
A nucleus may absorb a neutron forming a compound nucleus, which then de-energizes by
emitting a charged particle, either a proton or an alpha particle. This produces a nucleus of a
different element. Such a reaction is called a transmutation. Transmutation is the
transformation of one element into another by a nuclear reaction. 1 Neutron-Proton Reaction
(n, p) Oxygen-16 captures a neutron and emits a proton to form nitrogen-16:
14
FIG 2. 2: Neutron-Proton reactions
The product, nitrogen-16, is radioactive with a half-life of 7.1 seconds so this example is an
activation reaction. N-16 is a beta emitter, but more important, it also emits very penetrating,
high-energy gamma rays.
2 Neutron-Alpha Reactions (n, α)
Neutrons captured by boron-10 cause the following reaction:
2.5
It can be observed that the cross section is very large at low neutron energies. For this reason,
B is used as an absorber material for unwanted low energy neutrons. As neutron energy
10
increases, the cross section decreases following 1/v dependence. The charged particles
produced in this reaction are ejected in opposite directions with relatively high energies. They
produce considerable ionization along a short range and are capable of causing considerable
damage to biological tissue. This reaction is the basic interaction upon which boron neutron
capture therapy for the treatment of brain and skin cancers was developed [2].
2.2.4 Radiative Capture (n,
This is the most common nuclear reaction. The compound nucleus formed emits only a
gamma photon. In other words, the product nucleus is an isotope of the same element as the
original nucleus. Its mass number increases by one. Examples the simplest radiative capture
occurs when hydrogen absorbs a neutron to produce deuterium (heavy Hydrogen)
15
FIG2. 3: Radioactive Capture the deuterium formed is a stable nuclide.
The deuterium formed is a stable nuclide. However, many radiative capture products are
radioactive and are beta-gamma emitters. Deuterium itself undergoes a radiative capture
reaction to form tritium; the tritium isotope is unstable and is a major radiation hazard in
CANDU reactors. Stable cobalt-59 undergoes radiative capture to form highly radioactive
Co-60:
+− → + γ
2.6
Cobalt-60 has a long half-life (5.25 years) and emits very penetrating gamma radiation when
it decays, making it a serious hazard among activated corrosion products. Normal steel
usually contains a small amount of cobalt, but the concentration in reactor grade materials is
limited to reduce the radiation hazard.Cobalt-60 is an isotope commonly used in radiation
treatment of cancer [9].
2.2.5 FISSION
A nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller
parts (lighter nuclei), often producing free neutrons and photons (in the form of gamma rays).
The following examples illustrate a convenient short hand notation for these reactions [26].
U-235 + n ===> Ba-144 + Kr-90 + 2n + about 200 MeV
2.7
U-235 + n ===> Ba-141 + Kr-92 + 3n + 170 MeV
2.8
U-235 + n ===> Zr-94 + Te-139 + 3n + 197 MeV
2.9
16
2.3 Maxwell-Boltzmann Distribution
In a medium in which neutrons are not absorbed and from which neutrons cannot escape, the
only possible interaction is scattering with the nuclei of the atoms. The scattering interactions
reduce the neutron to be stationary, which is usual approximation in analyzing energy.
However, an endless slowing down process is not possible because of the thermal motion of
the atoms. Due to that fact they cannot be assumed neutron interactions. When neutron
energy becomes comparable to the energy of thermal motion of the atoms, the neutrons come
to a thermal equilibrium. It means that the probability that a neutron will gain or lose energy
in a collision with the nuclei is equal. The average kinetic energy of thermal motion of the
atoms (according to the kinetic theory of gases) is given by:
E = 3/2kT
2.10
In a thermal equilibrium state, neutrons can gain or lose kinetic energy (/2), i.e. exchange
their kinetic energy with the nuclei of atoms in the medium. In an ideal medium without
absorption and leakage, the neutron energy distribution will be the same as that of the atoms
in thermal motion. The thermal neutrons, even at a specific temperature, do not all have the
same energy or velocity. Such spectrum is called a Maxwellan-Boltzmann distribution, or
referred as a Maxwellan distribution. Although such conditions are not satisfied in a real
reactor system, it is useful to assume that neutrons become thermalized to the extent that they
follow the Maxwellian distribution
2.11
2.12
Where:
K is the Boltzmann constant = (1.380662 x/K).
T is temperature of the medium (in Kelvin) = 273+.
n is thermal neutron population per unit volume.
m is the rest mass of the neutron = 1.675.
n (E) and n (v) = Maxwellian energy (or velocity) distribution of neutrons per unit volume
and unit energy (or velocity) interval. The first represents the fraction of neutrons having
energies (or velocities) within a unit energy interval (or velocity interval) and the second
represents the Maxwellian distribution. The most probable velocity of thermal neutrons
17
would occur at the maxwellian distribution and can obtained by setting the derivative of the
neutron density distribution with respect to the velocity equal to zero.
=0
2.13
2.14
The most probable energy can be obtained in the same way to give kT/2.The kinetic energy
of thermal neutrons with most probable velocity is
2.15
Thermal neutrons are also referred to as kT neutrons. It is interesting to note that the thermal
neutrons energy is independent of its mass. The
energy is different from the average
neutrons kinetic energy which is equal to:
= 3/2kT
2.16
At the most probable velocity the thermal neutrons kinetic energy is:
= kT = 1.38 = 252.7125
= 0.025 eV
Thermal neutrons are also designated as 0.025 eV neutrons.
The most probable for neutrons at room temperature or 20 can be calculated as:
= = 22.0716
2,200 m/sec
Thermal neutrons are also designated as 2,200 m/sec neutrons.
2.4 Slowing Down of Neutrons
Neutrons are slowed down in both elastic and inelastic scattering collisions with the nuclei of
the atoms in a medium. In each collision, the neutron transfers a portion of its kinetic energy
to the target nucleus in the form of kinetic energy if the collision is elastic or excitation
energy if the collision is inelastic. Inelastic scattering is dominant with heavy nuclei, while
elastic scattering is dominant with light nuclei. Moderator materials have low mass numbers
and remove a large amount of energy from neutrons in a single collision and are also weak
18
absorbers. The slowing down of a neutron from fission energies to roughly 1 eV is called
moderation and the slowing down below 1 eV is called the thermalization [2].
2.4.1. Elastic Scattering in the Moderating Region
Elastic scattering in the moderating region is described by assuming that the colliding
particles behave as elastic spheres, with the assumption that the target nuclei are stationary. In
considering the scattering collision processes, two frames of references (Fig. below) are used
The laboratory system (LS): scattering nucleus is at rest before the collision, and the
neutron is moving toward the nucleus; after the collision, the neutron changes its direction of
motion and velocity, and the nucleus moves from the rest position with some velocity. The
viewpoint is that of a stationary external observer [2].
The center of mass system (COM): neutron and nucleus are stationary in the collision. The
observer is located at the center of mass of neutron plus the nucleus (compound nucleus) and
travels with the velocity of the compound nucleus. The center of mass is an imaginary point
where the system is balanced [2].
FIG2. 4: Scatter in lab and center of mass systems [2]
Where: = initial neutron velocity in LS
= 0: nucleus velocity in LS
19
= compound nucleus velocity in LS
= recoil nucleus velocity in the LS
v = recoil nucleus velocity in the LS
ψ = neutron scattering angle in LS with respect to original neutron direction
= recoil nucleus velocity in the COM system
= scattered neutron velocity of in the COM system
θ = neutron scattering angle in the COM system
Laboratory system: Since the nucleus is stationary, its velocity is equal to zero and the
momentum of a compound nucleus in LS is equal to the momentum of the incoming neutron
m+M=
2.17
=
=
Giving the velocity of the compound nucleus to be,
2.18
Because the mass of the neutron is 1 and the initial velocity of the target nucleus zero. The
above relation is also obtained from a momentum balance. Center of mass system: In order to
follow the splitting of the compound nucleus it is convenient to transfer to the center of mass
system. In this system, the observer travels at the velocity and direction of the compound
nucleus after the collision. Thus, the velocity of the neutron and nucleus before the collision
must be reduced by the velocity of the compound nucleus. The velocity of the compound
nucleus itself will become zero as it will appear stationary after the collision. Thus the
velocity of incident neutron
=
2.19
The velocity of nucleus: - According to the conservation of energy law, the kinetic energy
before the collision must equal the kinetic energy of the particles after the collision. The
binding energy to form and break up the compound nucleus is the same and thus cancels out.
The only energy to be conserved is, therefore, kinetic energy. The kinetic energy before the
collision and available to the compound nucleus is the sum of kinetic energy of neutron and
nucleus:
20
T= +
2.20
Eliminating the target nucleus velocity from the above equation gives
Where: =, and =
T= +A
T+
The kinetic energy of the Ls before the collision is:
T= +A,
=0
Therefore,
T=
2.21
Therefore,
T= =T
2.22
Where T (LS)o represents kinetic energy of the incident neutron in LS. From the above
equation it can be seen that the kinetic energy before the collision in the COM system for
light nuclei is half of the incident neutron energy in LS. Thus, the difference between these
two systems is more evident for light nuclei. According to Fig.2.4 the kinetic energy in the
COM system is shared between the scattered neutron and scattered nucleus flying away in
opposite directions. Thus, the conservation energy law in COM gives
= +
2.23
The conservation of momentum equation gives
=
2.24
By combining the last two equations it follows
= +
=
=
=
=
2.25
2.26
21
Laboratory system (LS): It is useful to now convert back to the LS in order to compare the
kinetic energy of the scattered neutron with the kinetic energy of the incoming neutron.
Conversion from the COM system to the LS system is depicted in Fig 2.4 above and shows
the transfer of velocities from one system to another using the Pythagorean Theorem
= +
= +
=
2.27
FIG2. 5: Diagram of velocities for conversion from COM to Lab system
From this equation it is possible to obtain the ratio of kinetic energy of the neutron after
collision to that before the collision
= =
2.28
This equation leads to the following conclusions:
This ratio reaches its maximum when θ = 0, or a glancing collision. Therefore, in forward
scattering, neutron energy is not changed
= =1
2.29
The minimum ratio of energies is obtained for a head-on collision in which the neutron does
not change its direction, or θ = π
22
= = =
2.30
In the example of hydrogen (A = 1), the value of the defined parameter α becomes indicating
that in head-on collision with a hydrogen nucleus, the neutron energy after the collision will
be zero. In other words, a hydrogen atom can cause a neutron to lose all of its energy in a
single collision event.
2.5 Neutron Cross Section
The quantitative description of nuclear interactions requires known neutron cross section data.
A rate at which a particular neutron interaction with a given target material will occur
depends on the neutron energy and speed, as well as the nature of the target nuclei. The cross
section of a target material for any given reaction thus represents the probability of a
particular interaction and is a property of the nucleus and incident neutron energy [2]. In
order to introduce the concept of a neutron cross section, consider a parallel mono-energetic
neutron beam falling on thin target of thickness x and area A, as shown in Fig 2.7 The
intensity of the incident neutron beam is described with the number of neutrons per unit
volume, n, and their velocity, v, as
= nv
2.31
The total number of nuclei in the target of atomic density N is Total number of nuclei in
target = NAx
FIG2. 6: Concept of neutron cross section [2]
The number of neutrons that collide with the target nuclei is proportional to the neutron beam
intensity and the total number of nuclei in the target. Number of neutron collisions per second
in the whole target = N
2.32
where represents the number of neutron collisions with the single target's nuclei per unit time,
and is referred to as the effective cross sectional area, frequently called the microscopic cross
23
section. It follows = number of neutron collisions per unit time with one nucleus per unit
intensity of the incident neutron beam.
The neutron microscopic cross section thus represents a visible area and for some interactions
is closely equal to an actual area,. The accepted unit of microscopic cross sections is the barn
(b), which is equal to. All neutron cross sections are functions of neutron energy and the
nature of the target nucleus. The probability of a neutron undergoing an interaction with all
nuclei in the target as sketched in Fig. 2.7 is equal to the ratio of the reaction area to the total
area
=
2.33
The reaction area of the target (of volume Ax) is defined as the number of nuclei in the target
material, N, Ax, multiplied by the area of each nucleus,
= =N
2.34
Thus, the relation between the microscopic ( ) and macroscopic ( ) cross section is
=N
2.35
The number of nuclei in a target material made of a single element (also called the number
density), N, is obtained from
N=
2.36
Where A is the atomic mass number and Na, is Avogadro's number.
2.6 Neutron Activation Analysis
Neutron Activation Analysis (NAA) is a sensitive analytical technique useful for performing
both a quantitative and qualitative method of high efficiency for the precise determination of
a number of main-components and trace elements in different types of samples. NAA, based
on the nuclear reaction between neutrons and target nuclei, is a useful method for the
24
simultaneous determination of about 25-30 major, minor and trace elements of geological,
environmental, biological samples without or with chemical separation [10].
In NAA, samples are activated by neutrons. During irradiation the naturally occurring stable
isotopes of most elements that constitute the given are transformed into radioactive isotopes
by neutron capture. Then the activated nucleus decays according to a characteristic half-life;
some nuclide emit beta particles and gamma-quanta, too, with specific energies. As the
irradiated samples contain radionuclide of different half-lives different isotopes can be
determined at various time intervals [11].
The advantage of the method is its sensitivity and accuracy especially in respect of some
trace elements. The method is of a multi-element character, i.e. it enables the simultaneous
determination of many elements without chemical separation. In the case of instrumental
determination, (INAA), the preparation of samples involves only the preparation of
representative samples, and this reduces the danger of contamination to a minimum and
accelerates the whole analytical process. If the determination of some special elements or
groups of elements can be carried out only through chemical separation, it is possible to carry
out after irradiation [12]. The development of the method has contributed to the elaboration
of some very simple and accurate methods of standardization, which lead to a surpassingly
accurate analysis.
The sequence of events occurring during the most common type of nuclear reaction used for
NAA, namely the neutron capture or ( γ ,n ) reactions is illustrated in figure 2.8.
25
FIG2. 7: the process of neutron capture by a target nucleus followed by the emission of
gamma rays
When a neutron interacts with the target nucleus via a non- elastic collision, a compound
nucleus forms in an excited state. The excitation energy of the compound nucleus is due to
the binding energy of the neutron with nucleus. The compound nucleus will almost
instantaneously de-excite into a more stable configuration through emission of one or more
characteristic prompt gamma rays. In many cases, this new configuration yields a radioactive
nucleus which also de- excites (or delays) by emission of one or more characteristic delayed
gamma rays, but at a much slower rate according to the unique half-life of the radioactive
nucleus. Depending upon the particular radioactive species, half-life can range from fractions
of a second to several life can range from fractions of a second to several years.
2.6.1 Prompt vs. Delayed Neutron Activation Analysis
Depending up on the time of measurement, NAA can be divided in two categories.
(a) PGNAA (Prompt gamma ray neutron activation analysis): The measurements should
be taking place during irradiation. The PGNAA technique is usually performed by
using a beam of neutrons extracted through a reactor beam port.
Fluxes on samples irradiated in beams are on the order of one million times lower than on
samples inside a reactor, but detectors can be placed very close to the sample compensating
for much of the loss in sensitivity due to flux. The PGNAA technique is most applicable to
26
elements with extremely high neutron capture cross section elements which decay too rapidly
to be measured by DGNAA; elements that produce only stable isotopes after the emission of
prompt gamma ray; or elements with weak gamma ray intensities [13].
(b) DGNAA (Delayed gamma ray neutron activation analysis (sometimes called conventional
NAA)); the gamma ray measurement takes place after sample irradiation. This technique is
used for the vast majority of elements that produce radioactive nuclides. The DGNAA
technique is flexible with respect to time such that the sensitivity for a Long-lived
radionuclide that suffers from the shorter-lived radionuclide to decay [13].
2.6.2 Instrumental vs. Radiochemical NAA
With the use of automated sample handling, gamma-ray measurement with solid-state
detectors, and computerized data processing it is generally possible to simultaneously
measure more than thirty elements in most sample types without chemical processing. The
application of purely instrumental procedures is commonly called instrumental neutron
activation analysis (INAA) and is one of NAA’s most important advantages over other
analytical techniques. If chemical separations are done to samples after irradiation to remove
interferences or to concentrate the radioisotope of interest, the technique is called
radiochemical
neutron
activation
analysis
(RNAA).the
latter
can
be
performed
infrequently[14].
2.6.3 Principles of Neutron Activation Analysis (NAA)
The (n, γ) reaction is the fundamental reaction for neutron activation analysis. The probability
of a neutron interacting with a nucleus is a function of the neutron energy. This probability is
referred to as the capture cross-section, and each nuclide has its own neutron energy capture
cross-section relationship. For many nuclides, the capture cross-section is greatest for low
energy neutrons (referred to as thermal neutrons). The activity for a particular radionuclide, at
any time t
27
during an irradiation, can be calculated from the following, equation.
2.37
Where At = the activity in number of decays per unit time,
The activation cross-section,
= the neutron flux (usually given in number of neutrons),
N = the number of parent atoms,
λ = the decay constant (number of decays per unit time), and
t = the irradiation time.
Note that for any particular radioactive nuclide radioactive decay is occurring during
irradiation, hence the total activity is determined by the rate of production minus the rate of
decay. If the irradiation time is much longer than the half-life of the nuclide, saturation is
achieved. What this means is that the rate of production and decay is now in equilibrium and
further irradiation will not lead to an increase in activity. The optimum irradiation time
depends on the type of sample and the elements of interest. Because the neutron flux is not
constant, the total flux (called fluence) received by each sample must be determined using an
internal or external fluence monitor. It is sometimes useful to convert from half-life to decay
constant. This can be done using the following equation;
2.38
where is the half-life and λ is the decay constant. With some notable exceptions the half-lives
earlier in the decay chain tend to be shorter than those occurring later.
Each radioactive nuclide is also decaying during the counting interval and corrections must
be made for this decay. The standard form of the radioactivity decay correction is;
A
2.39
Where A is the activity at any time t, Ao is the initial activity, λ is the decay constant and t is
time [27].
The principle of neutron activation analysis (NAA) is applicable for elements:
 Whose pair nucleus is available (stable) and natural abundance is large.
 The next isotope produced must be radioactive with measurable half life, neither too
short nor too long.
28
 The decay scheme of radioactive nuclei produced must be well known.
One can derive expression for reaction cross section (n, γ) reaction as;
2.40
Where dn/ dt, is activity of isotope produced.
Is number of nuclei of the element to be activated given as;
2.41
Where m = mass of the element in the irradiated sample
N = Avogadro number
F = natural abundance of isotopes
A = atomic weight
is flux of thermal neutron,
is geometry dependent efficiency of gamma ray of interest,
is percentage intensity of gamma ray,
K is self absorption coefficient for gamma ray absorption in the sample and
,, are time of irradiation, after the stop of irradiation and start of counting and time for the
counting activity respectively [28].
2.6.4 Advantage and Disadvantage of NAA
1. Advantage of NAA
 High sensitivity
 Easy standardization
 Direct measurement of radioactivity
 Low cost counting equipment
2 Disadvantage of NAA
 Availability of irradiation sources
29
 Delay of answer
 Variation of detection limits from one element to another
 Safety problems
2.6.5 Application
Because of its detection sensitivity, the NAA method has found important applications in
many fields, like, medicine, biology, geochemistry, industry, art, military, archaeology,
environmental science and forensic chemistry [15].
2.7 Radiation Detection [29]
A radiation detection system is composed of a detector, signal processor electronics, and a
data output display device such as a counter or multichannel analyzer. The backbone of any
radiation detection system is the radiation detector. The physical properties and
characteristics of the detector control the features of the detection system. A radiation
detector is composed of three main components:
 A sensitive volume where the radiation interactions occur.
 Structural components that enclose the sensitive volume to maintain the proper
conditions for its optimum operation.
 A signal output display device that extracts the information from the sensitive
volume and transfers it to the signal processing device.
This section deals with the main radiation detector properties and aspects of radiation
detection. There are three main radiation detectors categories: gas-filled detectors,
scintillation detectors, semiconductor detectors. Radiation detectors and detection systems are
also classified according to their physical form (gas, liquid, and solid), according to the
nature of the detector output signal (current [ions] and light), and according to their function
(counting, pulse height spectrometry, dosimetry, imaging, and timing).
There are two approaches to studying this subject. The first approach is to study the different
detector types in terms of their characteristic properties, such as structure, theory of operation,
response to different incident radiations, and output signals. All these determine the possible
functions of the detection system.
The second approach is to know the required detection system functions, then determine the
detector types and modes of operation. Both approaches are complementary and depend on
30
the researcher’s interests and knowledge of the scientific principles of radiation detection and
the practical aspects of radioactivity analysis.
Some of the operating characteristics for radiation detection include detection efficiency,
energy resolution, background, proportionality of the signal to the energy deposited, pulse
shape, and time resolution or dead time. The functions and applications of the different
radiation detection systems are dependent on these parameters.
2.7.1 Introduction to Geiger Counters (Tube) [30]
A Geiger counter (Geiger-Muller tube) is a device used for the detection and measurement of
all types of radiation: alpha, beta and gamma radiation. Basically it consists of a pair of
electrodes surrounded by a gas. The electrodes have a high voltage across them. The gas used
is usually Helium or Argon. When radiation enters the tube it can ionize the gas. The ions
(and electrons) are attracted to the electrodes and an electric current is produced. A scaler
counts the current pulses, and one obtains a "count" whenever radiation ionizes the gas.
The apparatus consists of two parts, the tube and the (counter + power supply).
The Geiger-Mueller tube is usually cylindrical, with a wire down the center. The (counter +
power supply) have voltage controls and timer options.
When ionizing radiation such as an alpha, beta or gamma particle enters the tube, it can
ionize some of the gas molecules in the tube. From these ionized atoms, an electron is
knocked out of the atom, and the remaining atom is positively charged.
The high voltage in the tube produces an electric field inside the tube. The electrons that were
knocked out of the atom are attracted to the positive electrode, and the positively charged
ions are attracted to the negative electrode. This produces a pulse of current in the wires
connecting the electrodes, and this pulse is counted. After the pulse is counted, the charged
ions become neutralized, and the Geiger counter is ready to record another pulse. In order for
the Geiger counter tube to restore itself quickly to its original state after radiation has entered,
a gas is added to the tube.
For proper use of the Geiger counter, one must have the appropriate voltage across the
electrodes. If the voltage is too low, the electric field in the tube is too weak to cause a
current pulse.
If the voltage is too high, the tube will undergo continuous discharge, and the tube can be
damaged. Usually the manufacture recommends the correct voltage to use for the tube.
31
Larger tubes require larger voltages to produce the necessary electric fields inside the tube.
For our experiment first we will place a radioactive isotope in from of the Geiger-Mueller
tube. Then, we will slowly vary the voltage across the tube and measure the counting rate.
For low voltages, no counts are recorded. This is because the electric field is too weak for
even one pulse to be recorded. As the voltage is increased, eventually one obtains a counting
rate. The voltage at which the G-M tube just begins to count is called the starting potential.
2.7.2 Advantage and disadvantage of the Geiger-counter
Some of the advantages of using a Geiger- counter are:
1. They are relatively inexpensive
2. They are durable and easily portable
3. They can detect all types of radiation
Some of the disadvantages of using a Geiger- counter are:
1. They cannot differentiate which type of radiation is being detected.
2. They cannot be used to determine the exact energy of the detected radiation
3. They have a very low efficiency
CHAPTER THREE
3. EXPERIMENT
3.1 Introduction
When a sample of an element irradiated with thermal neutrons it produces an induced
radioactivity or emits gamma rays. Prompt and delayed gamma rays are the two types of
gammas seen in the induced reaction and beta particles also, from fig (2.8). Gamma rays and
beta particles following capture of neutron and the formation of a compound nucleus are
characteristics of that nucleus, and their identification can lead to identification of the
presence of a particular element in the sample. In this experiment, one measurement at
ground state cross section will be done by irradiating the one stable Praseodymium isotope
(Pr-141) by using GM- counter detector and Meta stable state cross section is used from
reference for the comparison of theoretical calculation and experimental result and we will
study how to identify a given sample of interest and its capture cross section in the case of
32
radioactivity resulting from bombardment with slow neutrons. ”Slow” means with energies
comparable with the Boltzmann energy kT. i.e. around 0.03 eV.
3.2 Experimental Setup
3.2.1 Neutron Source
The AAU nuclear physics department has two facilities for the off-beam experiments, which
could be performed under the supervision of the department. One is the nuclear laboratory
and the other is the 241Am-Be neutron source, which is about 500m far from the nuclear lab it
is a bunker.
FIG3. 1: Schematic diagram of Am-Be neutron source
33
The neutrons are produced in an americium-beryllium source. In this source
241
Am is mixed
into beryllium powder. The following reactions occur [16].
241
Am → 237 Np + α (2Curie, i.e.74GBq).
3.2.1
α + 9 Be → 12 C + n (5.75MeV)
3.2.2
One in 40000 of the alphas produce two neutrons so that the yield of neutrons is about 4
million per second. Neutrons ejected with this energy can cause nuclear reactions but the
cross-section is small. They can be slowed down by putting them into a medium containing
light nuclei which does not contain nuclei that absorb them. Such a medium is called a
moderator; the neutrons elastically scatter from the light nuclei, losing a portion of their
energy at each collision. After a small number of collisions their energy becomes comparable
with the thermal energy of the scattering nuclei and they are said to be thermalized. Suitable
moderator nuclei are protons, deuterons, beryllium and all the stable nuclei of carbon,
nitrogen and oxygen. All have very low cross-sections for neutron capture except the proton.
This disadvantage is partly compensated for by the proton’s small mass and by the fact that
suitable hydrogen containing chemical compounds are freely available: water, plastics, wax
etc [16]. With a source of slow neutrons we can cause nuclear reactions to occur by processes
such as
Z+ n → A+1 Z+
A
Where
3.2.3
Z is radioactive with a “reasonable” half-life and where the slow neutron capture
A+1
cross-section is reasonably large. By “reasonable” we mean that the half-life is much greater
than the time required to take the irradiated sample from the source to the counter [16].
3.2.2 Geiger-Muller Counter
A typical Geiger-Muller (GM) Counter consists of a GM tube having a thin, micaendwindow, a voltage supply for the tube, a scalar to record the number of particles detected by
the tube, and a timer which will stop the action of the scaler at the end of a preset interval. It
34
consists of a pair of electrodes surrounded by a gas. The electrodes have a high voltage across
them. The gas used is usually Helium or Argon. GM-counter having small size, in order to
prevent the back ground radiations that falls on its body. When radiation enters the tube it can
ionize the gas. The ions (and electrons) are attracted to the electrodes and an electric current
is produced. A scalar counts the current pulses, and one obtains a "count" whenever radiation
ionizes the gas. The collection of the ionization thus produced results in the formation of a
pulse of voltage at the output of the tube. The amplitude of this pulse, on the order of a volt or
so, is sufficient to operate the scaler circuit with little further amplification.
FIG. 3.2: Setup of GM Counter
However, the pulse amplitude is largely independent of the properties of the particle detected,
and, therefore, can give little information as to the nature of the particle. In spite of this fact,
the GM Counter is a versatile device in that it may be used for counting alpha particles, beta
particles, and gamma rays with, however, varying degrees of efficiency [17].
3.2.3 Characteristics of the GM Counter
GM tube has a characteristic response of counting rate versus voltage applied to the tube. A
curve representing the variation of counting rate with voltage is called a plateau curve
because of its appearance. In this region the charge produced by multiplication speared over
whole central wire this is called avalanche production. The pulse height is very high. No preamplifier and amplifier are required. This region has small slope and is called GM-region.
The counter operating here is called GM- counter or Geiger-Muller counter. The pulse height
in this region is independent of initial charge produced. This counter is used only to detect the
radiations and not identification.
Like gamma- spectrometer G.M-counter cannot tell
anything about incoming radiation (type, energy). G.M-counter cannot give energy spectrum
35
like NaI (Tl) or HpGe gamma-spectrometer. So the plateau curve should be drawn in order to
determine the optimum operating voltage. To find the plateau curve for our tube; we have to
follow the procedure outlined below.
A. Check to see that the high voltage as indicated by the meter on the instrument is at its
minimum value.
B. Insert a radioactive source (137-Cs) into one of the shelves of the counting chamber.
C. Turn on the count switch and slowly increase the high voltage until counts just begin to be
recorded by the scalar. The voltage at which counts just begin is called the ”starting voltage”
of the tube.
D. Beginning at the nearest 20 volt mark above the starting voltage, takes 50 seconds counts
every 20 volts until a voltage is reached where a rapid increase in counts is observed.
Tabulate counts versus voltage.
E. Plot the data of (D). A plateau should be observed in the curve. The optimum operating
voltage will be about the middle of the plateau. Set the high voltage to this point and record.
No.
Volt(V)
Activity(C/100sec)
1
320
0
0
2
340
3911
62.538
3
360
3996
63.214
4
380
4029
63.474
5
400
4040
63.561
6
420
4089
63.945
7
440
4097
64.008
8
460
4104
64.062
9
480
4122
64.203
10
500
4152
64.436
11
520
4159
64.490
12
540
4167
64.552
13
560
4177
64.629
Table 3. 1: Table of volt Vs Activity Data of GM-Counter
36
The slope is defined to be the percent change in count rate per100 volts change in applied
voltage in the plateau region. A slope of greater than10 percent indicates that the tube should
no longer be used for accurate work. The slope may be computed using;
S (percent per100V) =
3.2.4
Where V2 is the voltage at the high end of plateau, C2 is the count rate at this voltage; V1 is
the voltage at the low ends of the plateau and C1 the corresponding rate. The relation between
applied volt and the count rate used to determine the effective operating voltage of the
counter.
Graph3. 1: GM-Counter characteristics
37
The slope of the Plateau in graph (3.1) region of our GM-Counter is 2.9898 percent.
1. The operating voltage is at 450v.
2. Mean count (n) = 3772.538
3. Standard deviation (±) = 61.420
4. 71 percent of the counts in the Plateau region fall between n ±.
3.2.4 Resolving time of the GM Counter
There is an interval of time following the production of a pulse in the GM tube during which
no other pulse can be recorded. This interval is called the resolving time of the system. If this
time is known it can be used to make a correction to the observed count rate to yield the true
count rate. A good estimate of the resolving time can be determined by the equation;
τ=
3.2.5
Where R1 and R2 are the counts of two separate sources and Rc is the combined count of the
two sources.
The resolving time τ may be used to correct an observed count rate using the expression:
R=
3.2.6
Where r = Observed count rate
R = True count rate
3.3 Background Measurements
Extraneous radiation called background radiation is always present. Gamma rays emitted by
certain radioisotopes in the ground, in air, and from various building materials as well as
cosmic radiation from outer space can all provide counts in a detector in addition to those
from a sample being measured. This background counting rate should always be subtracted
from a sample counting rate in order to obtain the rate from the sample alone.
3.4 Sampling and Irradiation
The chemical compounds or samples prepared for the experiment are;
Potassium iodide (KI)
Pure Praseodymium oxide powder ()
38
3.4.1 Praseodymium oxide
Praseodymium was first identified in 1885, in Vienna, by Austrian scientist Carl Auer von
Welsbach. It was discovered in ‘didymium’ a substance incorrectly said by Carl Mosander to
be a new element in 1841. The nonexistent ‘didymium’ was even given the symbol Di in
Mendeleev’s first edition of the periodic table in 1869. In 1879 French chemist Lecoq de
Boisbaudran detected and separated samarium from ‘didymium’ [22]. After samarium had
been discovered, it was noted that ‘didymium’s’ absorption spectrum gave different results
depending on which mineral it had been sourced from. BohuslavBrauner working in Prague
published a paper on atomic weight determinations in 1882 for rare earth elements and his
data for ‘didymium’ were variable. Brauner became convinced that ‘didymium’ was a
mixture of elements; he attempted to separate them, but he was not successful. In 1885 Carl
Welsbach, who had discovered ‘didymium’ 14 years earlier, realized it was actually a
mixture of two entirely new elements. He named these praseodymium and neodymium.
Welsbach reacted ‘didymium’ to form nitrate salts, which he then fractionally crystallized
from nitric acid to yield greenish-brown praseodymium and pink neodymium salts. The
fractional crystallization experiments were very time consuming, involving more than one
hundred crystallization operations, each lasting up to 48 hours. Praseodymium was named
using the Greek words ‘prasiosdidymos’ meaning ‘green twin,’ reflecting its green salts and
the close association with neodymium. Pure metallic praseodymium was first produced in
1931. Praseodymium (Pr) is a chemical element with the atomic number 59.
Praseodymium reacts with water to form praseodymium hydroxide plus hydrogen gas.
Praseodymium usually exists as a trivalent ion, Pr3+, in its compounds. Most of its salts are
pale green in color. It forms a flaky black oxide coating (Pr6O11) in air. Unlike many metal
oxide layers, this one does not protect the metal from further oxidation. The pale green
sesquioxide, Pr2O3, is not stable in air.
Praseodymium oxide or (Pr6O11) is the most widely produced compound of elemental
praseodymium. Praseodymium oxide is appearing in the form of a brown powder. It’s
available in the form of spray dried, non-spray and high purity powders. Some of the
synonyms of these oxides are hexa praseodymium undeca oxide and praseodymium (III, IV)
oxide. Typical application of praseodymium oxide is the following:

As a magnetic material

As a catalyst
39

Dried powder when mixed with the binder is useful in plasma spray guns and coating.
FIG3. 3: Praseodymium oxide sample
The disadvantage of praseodymium oxide: is an eye irritant and affects the respiratory
system when inhaled.
The samples prepared for this experiment is compounds of potassium that is two potassium
iodides of different masses and praseodymium. These samples are borrowed from India by
prof.A.K Chaubey in a powder form. Due to the volatility of pure iodine atom , the metal
iodide salt is preferred for the determination of neutron flux 99 percent of the salt has I-127
than the rest isotopes of iodine and the natural abundance of Pr-141 is 100 percent. The
samples has to be prepared suitably for irradiation in solid form by Putting them in the ring of
radius 0.5 cm and fasting both side by sticky tape, so that, we can have three samples having
the following masses.
1. Potassium iodide (sample1) = 0.6192g
2. Potassium iodide (sample2) = 0.4316g
3. Praseodymium (Pr-141) (sample3) = 0.0863g
These masses are measured by using laboratory balance where even air influence is neglected.
Samples were made ready by sandwiching the praseodymium sample in between the two KI
targets by two standards these are; two potassium iodides in order to have fixed geometry.
One with high mass standard placed in the front of the sample; the one with low mass and the
other is placed at the back of the sample. In the irradiation room, the sample is exposed to the
neutron where the low mass standard is toward the source by using Plexiglas rod, used to
place in the neutron source. The disturbance of neutron flux at the center of the source due to
the rod is negligible. These samples are irradiated for a needed time based on the half life of
gamma and beta emitted from the radioactive nucleus of interest formed when the sample get
neutron from the neutron source. In irradiation process, the sample must get a perpendicular
neutron source to have a maximum flux. If the sample is tilted by certain angle, neutron flux
40
is reduced and this thermal neutron source is the main needed material in this experiment.
Irradiation process started when the samples are inserted in the Am-Be neutron source found
in our laboratory of AAU Science faculty nuclear physics department. The duration of
irradiation was about 8 days for the first experiment and 19.12 hours for the second
experiment.
3.5 Measurement
Before the measurement of the activity of the samples detection system or detector (GMCounter and the associated electronics) has to be prepared in its best operating region and the
background radiation had to be determined, then samples can be taken by noting down the
time of irradiation stopped and taken to the detector as fast as possible in order to minimize
the delay time (). The activity of each samples measured consecutively by putting at zero
distance from the GM-Counter for 100 sec and counting time (). The two KI samples counted
for 2 hours and the long half-life Pr-142 was counted for one day. At each count the
corresponding time is recorded. Such measurements were done with samples and cross
section for 141Pr (n, γ) 142Pr reaction was calculated from.
CHAPTER FOUR
4. DATA AND DATA ANALYSIS
4.1 Beta counting
The values of capture cross section from the beta counts can also be found using the same
equation Eq. [2.40]. The only change is since the beta counter does not differentiate the
energy peaks it only gives the total counts of all the peaks. Hence no need of using the
intensity of a particular energy of beta particle.
4.1.1 Materials used in beta counting
 Beta detector
 GM-counter
 Sample holder
 Connecting wires
 Stop watch
 DC power supply
 Blocks of detector covering leads
4.1.2 Beta counting procedure
GM counter is connected to a power supply and beta detector is cascaded with it. Beta
detector is placed in a blocks of lead to minimize the back ground radiation where sample
placement is labeled under the detector. The samples are placed close to detector as much as
41
possible to minimize beta absorption. After samples removed from radiation source by noting
time, it brought to the detector as fast as possible to minimize the decay time and placed on
the sample holder and putted close to window of detector. Then count will started by noting
the time for the needed seconds which is pre sated (100sec), here data taking is manual not as
gamma detector in which every things are recorded by computer. The operating voltage of
GM-counter is also pre adjusted on 450kV and GM-counter works normally. Readings are
taken until reading with presence of sample is the same with back ground reading such that
the decay of sample is seen clearly for each sample consecutively.
Using instrumental neutron activation analysis method, the reaction of thermal neutron with
Pr-141 can be studied by taking two KI samples which are used to determine the thermal
neutron flux.
Activation of KI
Thermal neutron reaction with the KI target results in (n, γ) reaction with that of I-127
Metallic element.
n 127 I → [128I] → Xe + β− + ν + 2.119Mev (93.1 percent)
[128I] → 128Te + ν + 1.252Mev (6.9 percent)
4.1.1
4.1.2
The excited iodine [128I] de-excited to the ground level of Xe atom by emitting three types
of beta particles having the following end point energy and branching ratio [17].
β1 → 2.12Mev → 76 percent
4.1.3
β2 → 1.665Mev → 15.5 percent
4.1.4
42
β3 → 1.125Mev → 2 percent
4.1.5
FIG 4.1: Decay scheme of I-128[17]
Activation of Praseodymium
During time of irradiation from praseodymium oxide only praseodymium has been excited.
Since oxygen is light element neutron activation analysis cannot provide information.
Thermal neutron reaction with the praseodymium target results in (n, ) reaction with that of
Pr-141 the lanthanide rare earth metals.
Kev.
The excited Praseodymium [Pr- 142] de-excited to the ground level of Nd-142 atom by
emitting three main types of beta particles having the following end point energy and
branching ratio [17].
43
FIG4. 2: Decay scheme of Pr-142[17]
4.1.3 Measurements of beta particles
Back ground measurement since the environment is dynamic measurement of back ground is
not the same. So several measurements were taken and the mean value of back ground was
subtracted from the sample readings which is 17 counts/100sec.
No.
Time (sec)
Activity (Count/100sec)
1
1250
310
17.607
2
1730
258
16.062
3
2270
216
14.697
4
2690
163
12.767
5
3170
140
11.832
6
3590
107
10.344
7
4070
72
8.485
8
5030
56
7.483
9
5450
49
7
Table 4.1: Decay table of front KI target
44
graph4. 1: Exponential decay curve of front KI target
45
graph4. 2: Logarithmic decay curve of front KI target
46
Background radiation = 16/100sec
No.
Time(sec)
Activity(Count/100sec)
1
1610
232
15.232
2
3050
159
12.609
3
3470
115
10.723
4
3950
84
9.165
5
4430
60
7.746
6
4910
54
7.348
7
5330
34
5.831
8
6290
30
5.477
9
6770
23
4.796
Table4. 2: Decay table of back KI target
graph4. 3: Exponential decay curve of back KI
47
target
graph4. 4: Logarithmic decay curve of back I target
Background radiation = 17/100sec
No.
Time(sec)
Activity(Count/100sec)
1
26570
230
15.166
2
31730
225
15
3
40740
193
13.892
4
48170
167
12.923
5
85550
142
11.916
6
86870
122
11.0454
7
87110
112
10.583
Table4. 3: Decay table of Pr-141
48
Graph 4. 5: Exponential decay curve of Pr-142
49
Graph 4. 6: Logarithmic decay curve of Pr-142
50
4.2 Results and Discussions
4.2.1 Decay constant determination for the front and back I target for first experiment
From the logarithmic curve presented in graph (4.2) for the front KI target, the decay constant
of I-127 can be determined by computer software which shows the logarithmic decay curve
of iodine.
4.2.1
From the logarithmic graph for the back I target, graph (4.4), the decay constant or the halflife of I-127 can be calculated by determined by computer software, which represents the
logarithmic decay of its activity.
4.2.2
4.2. 2 Determination of Half-life of Sample
From the logarithmic curve presented in graph (4.6) for the praseodymium target, the decay
constant of Pr-142 can be determined by computer software which shows the logarithmic
decay curve of praseodymium.
4.2.3
Therefore from equation (4.2.3) this is exactly conceded with the literature value [17].
4.2.3 Neutron flux determination
The incident neutron flux used to activate the target elements may be calculated from the
equation [2.40];
Φ=
4.2.3.1
Where
= (1−
4.2.3.2
For large irradiation time reduced to;
= ()
4.2.3.3
51
The efficiency of GM-Counter, i.e, fraction of pulses registered by the counter can be
calculated by;
η=
4.2.3.4
Where d represent the sum of the thickness of beta absorbers in the counter.
d= + +
4.2.3.5
is the thickness of the tape.
is the thickness of the GM- Counter window.
is the half thickness of the sample.
=
The constants a, b, c... represents the branching ratio of (76%, 15.5%, 2%) the respected beta
particles and the constant µ, the mass absorption co-efficient of the betas, can be;
µ = 17[5]
4.2.3.6
E is the endpoint energy of (2.12, 1.665, 1.125) from figure (4.1) the respected beta particles
in terms of Mev. For the front I target, the above constants become;
The mass of four layer thicknesses of the tape is 0.091g
The area of four layer thicknesses of the tape is 6.21cm2
So, the thickness of the tape is:d1
= 228 mg/
= 2.0 mg/
4.2.3.7
4.2.3.8
Thickness of the sample diameter is 1cm and radius of the sample is half of the diameter.
52
So, the radius of the sample is
Area of the sample is
= 0.5*0.6192g/ 0.785cm2 394.4mg/
4.2.3.9
d = 0.4244g/
4.2.4.0
= 17= 7.218/gm
4.2.4.1
= 17 = 9.509/gm
4.2.4.2
= 17 = 14.683/gm
4.2.4.3
Then putting these values in the equation (4.2.3.4)
We can have;
η =]
4.2.4.4
η = 0.04
4.2.4.5
The other parameter in the flux equation has the following values.
N1 =
4.2.4.6
Where m = measured mass of Iodine
N = Avogadro’s number
A = Atomic weight
f = percentage of gamma abundance
Therefore,
= = atoms
4.2.4.7
dn/dt = = 5.52 count/second
4.2.4.8
From graph (4.2) (the number of count at = 0)
σ = 6.2×
4.2.4.9
= 4.5×
4.2.5.0
The value of neutron flux incident is found to be;
=
4.2.5.1
Where the value of is one at = 0
53
Φ1 = 1.003×
4.2.5.2
The flux in the back I target can be found using the same procedure. All the rest
Parameters are the same except; d, n, η and N. the value of this parameters can be calculated
as,
d = d1 + d2 + d3
4.2.5.3
d1 = 28 mg/
4.2.5.4
d2 = 2.0 mg/
4.2.5.5
d3 = 0.5* 0.4316 g/0.785 cm2 0.2749 g/
4.2.5.6
d = 2.5 mg/ + 2.0 mg/ + 274.9 mg/
4.2.5.7
d = 0.3049 g/cm2
4.2.5.8
Putting the value of d of the second sample and µ‘s in the eq (5.3.6), we can get the Value of
η for the second sample.
η =8.415 + 0.853 + 0.023]
η = 0.093
4.2.5.9
The rest parameters can be;
dn/dt = = 5.42 count/second
4.2.6.0
from graph (4.4)
=[
4.2.6.1
= 4.5×
4.2.6.2
σ = 6.2×
4.2.6.3
Using the given values in the above, the neutron flux in the second I target becomes;
=
4.2.6.4
Where the value of becomes one at = 0
= 0.606×
4.2.6.5
The average neutron flux captured by the two iodine samples calculated as;
=
4.2.6.6
Then,
54
= 0.8045×
4.2.6.7
4.2.4 Neutron Capture Cross-Section of 141Pr
To evaluate the capture cross-section of Pr-141 by thermal neutron flux already determined,
we have to use the equation of flux, eq (4.2.3.1).
σ=
4.2.4.1
The half-life of 142Pr can be determined by finding the slope of logarithmic decay curve of Pr142.i.e,
= 1.009
4.2.4.2
=
4.2.4.3
4.2.4.4
The percentage error as compared to the earlier value is 0.2092 percent.
N=
=
4.2.4.5
4.2.4.6
= 1.68.
4.2.4.7
= 0.8045×
4.2.4.8
dn/dt = = 3.064count/second
4.2.4.9
From graph (4.6)
= 1.009×
4.2.5.0
The value of η has to be determined for the Pr-142 sample. Pr-142 decay from its ground
level to the ground level of Nd-142 by emitting three types of beta particles with different
branching ratio. When it is activated by thermal neutrons, but the following higher end point
energy beta particles has an effect in the absorption and counting.
55
→ 2.162Mev → 96.3 percent
4.2.5.1
→ 0.587Mev → 3.7 percent
4.2.5.2
→ 0.078Mev → 0.023 percent
4.2.5.3
The possible mass absorption coefficient of these beta particles can be;
= 17 = 7.059/gm
4.2.5.4
= 17 = 31.203/gm
4.2.5.5
= 17= /gm
4.2.5.6
The total thickness of the beta radiation absorbers may be calculated as;
d= + +
4.2.5.7
Where = 28 mg/ tape thickness
= 2.0 mg/ GM-window thickness
= 0.5 * 0.0863 g/0.785 cm2 0.05497g/ sample thickness
Then d = 0.08497g/cm2
The counting efficiency of the GM-Counter of these beta particles becomes;
η = [a]
4.2.5.8
Where a, b, c are the branching ratio of (96.3%, 3.7%, 0.023%) the beta particles respectively.
η =0.5998 + 2.651 + 26.468]
4.2.5.9
η = 0.3
4.2.6.0
Having the above calculated parameters we can evaluate the capture cross-section of Pr-141.
σ=
4.2.6.1
σ = 7.557×5.3.62
σ = 7.557 barn.
4.2.6.2
Therefore, the experimental value of thermal neutron capture cross section of Pr-141 is 7.557
56
0.28 barn which is less than the value presented in the literature which is 7.6[1].
Total error in experiment can be calculated as:
The total error in the experiment can be;
Error (%) =
4.2.6.3
Error (%) =
4.2.6.4
4.3 Sources of Error Estimation
In this experiment the measurement consists of counting the number of β− emitted in the
radioactive decay of KI and Pr-142 samples during a definite time interval ().There are two
types of errors expected in the experiment. These are;
4.3.1 Errors in the Measurement
The possible source of systematic and random source of errors in the measurement process
contains;
1. in the measuring time interval.
2. in the efficiency of Geiger tube and counter.
3. in the measurement of masses of samples.
4. in the measurement of the thickness of samples and sticky tape
5. Personal errors in the rounding of the calculated results.
57
CHAPTER 5
5. THEORITICAL ESTIMATES OF THERMAL NEUTRON CAPTURE CROSS
SECTIONS
5.1 Compound Nucleus
A nuclear reaction is usually described by an equation similar to a chemical reaction equation
thus the equation
a+X Y+b
5.1.1
The actual nuclear process in a nuclear reaction dose not start before the two initial particles a
and X have come near enough to one another, within the range of nuclear forces. The nuclear
process has ceased when the two products have separated by more than the range. During the
time of the interaction, a compound system is formed whose properties are decisive for the
course of the nuclear reaction. It was N. Bohr who first pointed out that it is useful to divide
the nuclear reaction in to two states [18].
I.
The formation of the compound nucleus C, and
II.
The disintegration of the compound system into the product of the reaction
So, Bohr’s two assumptions are:
1. When a projectile enters a nucleus it interacts with nucleons present inside the target
nucleus. Large number of collision may take place in which there is an exchange of energy
and momentum. There is thorough mixing of incoming particle with the nucleons present in
the nucleons
Entering particle makes now a new system such that
58
x + X where is the compound nucleus
Then,
5.1.2
Where: is energy of projectile in channel α, and is its binding energy in the nucleus b.
This mixing of projectile with other nucleons takes too much time (about ) so that compound
nucleus formed forgets its history of formation. During this time which is much larger as
compared with nuclear time. The life- time of the compound nucleus is about sec times the
nuclear time ( ) sec.
2. Due to the large time taken by compound nucleus formation, its decay is independent of
the mode of formation. The decay does not depend up on the nature of the incoming
projectile that is if the same compound nucleus is formed by different channels its decay will
be independent, the decay will depend only on the quantum mechanical parameters of the
compound nucleus that is energy of excitation, angular momentum and parity [18].
5.2 Statistical Estimates of Thermal Neutron Capture Cross Sections
At thermal energies neutron cross sections can differ by several
orders of magnitude even
for neighboring nuclei, and their exact values are unpredictable. This result from
(a) Variations of the strength functions from one nuclide to another
(b) Random fluctuations of the positions and widths of the low-lying resonances that
dominate the thermal cross section [19].
In particular, the expected value of the thermal capture cross section is expressed through the
strength functions of s resonances- for neutrons and for photons:
[20]
[20]
5.2.1
5.2.2
Here, A is the atomic weight of the target nucleus, = 0.025 eV is the thermal energy, and
=1eV. In Eq. 5.2.2 we assume the following: [19]
59
1. All reaction widths are equal to the corresponding mean values.
2. The energy spacing between the resonances of the same spin are constant.
3. The resonances are located symmetrically with respect to the zero neutron energy
point.
By using the above formula the thermal neutron capture cross section in praseodymium is
calculated as following: According to the extreme compound, or black, nucleus model the
strength function is constant for all nuclei, and for s-wave neutrons is given by
Where, = = 1 [8]
5.2.3
Where is the average S-wave reduced neutron width, is the average s-wave level
Spacing is the wave number for a 1eV neutron and k is the wave number inside the nucleus.
g=
[19]
Where, J = I ½
5.2.4
I = 5/2 spin of Pr- target
S = ½ spin of neutron
Then, substituting the values of S and I one can obtain the value of g = 7/12 or 5/12
= 0.5
Therefore = 0.5
[21]
5.2.5
And the value of was calculated [23]. From that paper one can drive for the
= 45 where
Therefore, = 0.00354
60
Using equation 5.2.2 thermal neutron capture cross sections for praseodymium is:
0.5
In this case of study, as the above calculation indicate the theoretical value of the thermal
neutron capture cross section agreed with the measured value of thermal neutron capture
cross section (with in error) which is obtained in our laboratory 7.557 barn.
61
5.3. Summary and Conclusion
Instrumental Neutron activation Analysis using Am-Be neutron source has profound effect in
identifying the type of given element of sample. Here in this work, the half-life and capture
cross section of the sample Pr-141 is determined. The relative error in this measurement was
taken as 0.566% percent. The result of this work suggests that, using Instrumental Neutron
Activation Analysis technique it is possible to perform environmental radio-analysis with an
improved counter shielding and good precision of measurement. Besides, these results show
that the measured thermal neutron captures cross section have good agreement with statistical
estimates of thermal neutron capture cross section. Neutron activation method, other than its
wide application in the qualitative and quantitative elemental analysis, it is also be used in the
determination of the neutron flux of a neutron source. This may very important to elemental
analysis of a given sample of interest in the fields of like, medicine, forensic, mining, industry
and any other applications.
62
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63
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64
Declaration
This thesis is my original work, has not been presented for a degree in any other University
and that all the sources of material used for the thesis have been dully acknowledged.
Name: Mekonnen Tefera Kebede
Signature:_______________
Place and time of submission: Addis Ababa University, June, 2016
This thesis has been submitted for examination with my approval as University advisor.
Name: Prof. A.K. Chaubey
Signature:________________
65