MEASURMENT OF THERMAL NEUTRON CAPTURE
CROSS SECTION FOR INDIUM ( 115In)
TEKLEMARIAM TESSEMA
A DISSERTATION SUBMITTED TO THE DEPARTMENT
OF PHYSICS AT
THE UNIVERSITY OF ADDIS ABABA IN PARTIAL
FULFILMENT OF THE
DEGREE OF MASTER OF SCIENCE IN PHYSICS.
Aug 2007
ACKNOWLEDGMENT
A number of colleagues and families devoted a great deal of their time for
encouragement and their financial resources. In this respect, I would like to thank
Ertiban Yimer, Tsedale Tessema, Sahilu Tessema and Fekadu Habte. I am also
indebted to prof. Jha for taking the photos of the experimental set up and edit in this
thesis.
Finally, I am very grateful to prof. A.K. Chaubey (advisor), who is most closely
associated with this thesis, for his all round help and kindness.
ii
ABSTRACT
In this thesis an indium foil of measured mass and area is irradiated in the Am-Be
thermal neutron source. Using a pre calibrated NaI(Tl) gamma spectrometer
the
activity of the irradiated foil of indium is counted and the data are stored. The detecting
efficiency of the spectrometer is determined experimentally. On another time an indium
foil of the same mass and area is irradiated and its activity is counted using a beta
counter whose working voltage is determined and the data obtained are stored. All the
stored data are fed to a computer installed with origin and the exponential curve and the
semi logarithmic curves are plotted. Using the plots the half life and the thermal
neutron capture cross section of indium is determined. The obtained values for the half
life and the thermal neutron capture cross section are in a good agreement with the
previously known values given in tables and references of the radio isotopes.
iii
CONTENT.
PAGE
List of Tables
v
List of graphs.
vi
List of figures.
vii
CHAPTER 1 INTRODUCTION.
1
CHAPTER 2 THEORY.
3
2.1 Neutrons.
3
2.1.1 Neutron kinds.
3
2.2.2 Major neutron sources.
6
2.1.3 Neutron interaction with nucleus.
15
2.1.4 Neutron moderation.
19
2.2 Concept of cross section.
29
2.3 Neutron Activation Analysis(NAA).
31
CHAPTER 3 EXPERIMENT.
37
3.1 Objective of the experiment.
37
3.2 Materials used in the experiment.
37
3.3 Experimental set up.
38
3.4 Irradiation of the sample.
41
3.5 Calibration of the detector NaI (Tl).
41
3.6 Counting the activity of the sample.
45
3.7 Back ground measurement.
51
CHAPTER 4. ANALYSIS AND CONCLUSION.
52
4.1 Determination of efficiency of the detectors.
52
4.2 Thermal neutron capture cross section from measurements.
56
4.3 Comparison of the measured value with known values.
59
4.4 Sources of Errors.
59
4.5 Discussion and conclusion.
60
REFERENCES
61
iv
LIST OF TABLES
page
Table1: Summary of free neutron.
6
Table2: Kinds of neutrons with their energy range.
7
Table 3: Neutron yields from two types of AM-Be neutron sources.
10
Table 4: Yield of neutrons from photo neutron sources.
11
Table 5: Threshold energies (ET) for the (p, n) reaction in a few nuclides.
12
Table 6: Average number of collisions required to reduce neutrons energy
from 2MeV to 0.025eV by elastic scattering.
28
Table 7: Energies and intensities of the energies for the two standard sources
used in the experiment for the calibration.
Table 8: Counts with the channel number for
.
137
41
Cs standard around the peak,
using NaI(Tl) scintillation counter.
Table 9: Counts with the channel number for
60
42
Co standard source
around the peaks, using NaI(Tl) scintillation detector.
Table10: Gamma energy of standard sources with the peak position.
Table 11: Net counts obtained from
116
In using gamma spectroscopy.
43
44
45
Table 12: Counts for different voltage in the G-M tube using cesium source.
47
Table 13: Counts obtained from indium sample in cadmium cover.
48
116
In using beta counter. 49
Table 15 : Branching ratios of known energies of standards.
53
Table 16: Summary of the measured values of the peak count and total count.
54
Table 17: Manufacturing information of standard sources used in the experiment.
54
Table 18: Efficiency of NaI(Tl) gamma spectroscopy used in the experiment.
55
Table 14: Net counts obtained from the bare radioactive
v
LIST OF GRAPHS
Page
Graph 1: Energy spectrum curve for
137
Cs standard radioactive source
using NaI(Tl) scintillation counter.
Graph 2: Energy spectrum for
60
42
Co around the peak region
using NaI(Tl) scintillation.
43
Graph 3: Energy calibration curve for NaI(Tl) scintillation spectrometer.
Graph 4: Exponential decay curve for
116
In as counted using
NaI(Tl) gamma spectroscopy.
Graph 5: Semi logarithmic curve for
116
44
46
In counts/sec using NaI(Tl)
gamma spectroscopy.
47
Graph 6: Plateau characteristic curve for the G-M tube used
in the experiment.
48
Graph 7: Exponential decay curve of the data obtained using
the G-M counter for
116
In sample.
50
Graph 8: Semi logarithmic curve of indium ( 116 In ) counts using
beta counter.
Graph 9: Efficiency Vs energy curve for NaI(Tl) gamma spectroscopy.
51
56
vi
LIST OF FIGUERS
page
Fig. 1: A simple diagram that shows alpha particles bombarding beryllium
create a radiation that easily passes through lead and ejects fast
protons from a material containing hydrogen .
4
Fig. 2: Schematic drawing of source mount and ionization chamber used
by Chadwick in his discovery of the neutron.
4
Fig. 3: Elastic scattering.
16
Fig. 4: In elastic scattering.
17
Fig. 5:The capture of neutrons by hydrogen.
18
Fig. 6:An incident neutron of high energy on moderator nucleus.
20
Fig. 7: Velocity vector triangle.
22
Fig. 8: A scattering angle of neutron.
24
Fig. 9:The process of neutron capture by a target nucleus
followed by the emission of gamma rays.
33
Fig. 10: The schematic diagram of Am-Be neutron source.
39
Fig. 11: The set up of NaI(Tl) spectroscopy used in the experiment
39
Fig. 12: The set up of beta counter used in the experiment.
40
vii
ADDIS ABABA UNIVERSITY
FACULTY OF SCIENCE
DEPARTMENT OF PHYSICS
The under signed hereby certify that they have read and recommended
to the Faculty of science school of graduate studies for acceptance of
a thesis entitled “Thermal neutron capture cross section for
indium( 115 In )” by Teklemariam Tessema in partial fulfillment of
the requirements for the degree of Master of science in physics.
NAME
SIGNATURE
PROF.ASHOK K.CHAUBEY
(ADVISOR)
_______
Dr. TILAHUN TESFAYE
( EXAMINER)
_______
(EXAMINER)
_______
Dr. NEGUSSIE T.
viii
DECLARATION
I hereby declare that this thesis is my original work and has not been presented for
degree in any other university. All sources of materials used for the thesis have been
duly acknowledged.
Name: Teklemariam Tessema
Signature:______________________
This thesis has been submitted for examination with my approval as University advisor.
Name: Prof. A.K. Chaubey
Signature: ___________________
ix
x
CHAPTER 1
INTRODUCTION
Neutron reactions can be divided with respect to neutron energy in to three classes;
Thermal, epithermal and fast. Thermal neutrons have approximately a Maxwellian
Energy distribution having energy of 0.025ev. Fast neutrons come directly from fission,
having energies up to 20 Mev.The epithermal are partially moderated neutrons with an
energy range between about 0.1Mev and near thermal energies.
Among heavy elements thermal and epithermal neutrons can cause
(n,α) and (n, p) reactions, as well as neutron capture, depending on the energies for the
various particles. Among heavier elements the neutron result primarily in capture (n,γ)
and fission reactions, fast neutrons being required for particle emission reaction such as
(n, 2n), (n, p), etc.
The objective of this thesis is to study the capture reaction (n,γ) using
the medium element isotope ( 115
49 In ) and measure its thermal neutron capture cross section
.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, whence it is expressed in a smaller unit of area called a barn. One barn is 10-24
cm2.
1
Indium is found in the periodic table of elements in group three , which has
two isotopes available in natural states. Out of this the most abundant (95.71%) is 115-In.
The other Isotope is 113-In about 4.29%. Its alloy is used as an effective controlling rod
in pressurized water reactors, due to its high absorption cross section for thermal
neutrons. By alloying indium with cadmium and silver a highly effective neutron
absorber can be produced. The control effectiveness of such alloys in water-moderated
reactors can approach that of cadmium (an excellent controlling material) and is the
control material commonly used in pressurized water reactors. The alloys generally
contain 80% silver, 15% indium and 5% cadmium. This can readily be fabricated and
have adequate strength at water reactor temperatures. The control material is enclosed in
a stainless steel tube to protect it from corrosion by high temperature water. Therefore,
the study of neutron interaction, particularly capture cross-section in indium is very
important.
Irradiating sample of indium by a uniform neutron beam of known flux and
measuring the induced radioactivity by counting gamma and beta radiations using precalibrated detectors, NaI (Tl) and G-M tube, thermal neutron capture cross section of the
115-Indium (115In) 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, a NaI (Tl) scintillation spectrometer, G-M counting system, and
standard calibration sources are used in nuclear laboratory of AAU.
When a natural indium foil is irradiated with neutron beam, epithermal and
thermal neutrons interact with indium to produce compound nucleus of 116-In of easily
measurable life time. While decay of Indium-116 ground state proceeds directly in to
Tin-116 (116Sn) ground state, the isomeric states of Indium-116 decay in to the excited
states of
116
Sn. Several gamma rays are emitted in their de-excitation. Hence, by
measuring the spectrum of the gamma ray and beta rays emitted, the thermal neutrons
capture cross section for Indium-115 can be found.
2
CHAPTETR 2
THEORY
2.1 Neutrons
At the time of the discovery of neutrons, there were experiments taking place to
see the transmutation of atoms of one element to those of another, those were
accomplished by bombardment with alpha particles (helium nuclei). High-speed
alpha particles were available because they are emitted spontaneously from
radium and similar heavy nuclei. Rutherford accomplished the first such
transmutation with alpha particles as projectiles in 1918, when he succeeded in
changing a few atoms of nitrogen to oxygen. The nitrogen become fluorine by
absorbing the alpha particle, then by emitting a proton changed to oxygen.
In 1930 further studies of these transmutations were being carried on at
various laboratories. They observed that certain of the lighter elements such as
lithium and beryllium, emit a very penetrating radiation when they are
bombarded by α- particles from the natural radioactive elements. The absorption
in lead of this penetrating radiation was found to be such that, if the radiation
were electromagnetic, it would correspond to γ-ray of about 10Mev [1].
In 1932 Joliot-Curies, found that these strange new penetrating radiation,
when incident up on hydrogenous material such as paraffin, possessed the
property of being able to eject very energetic protons. Moreover, the energies of
these protons are such as to make it necessary to assume that the incident
radiation, if electromagnetic in nature, must consist of γ-rays having energies of
50 MeV (if the ejected protons are assumed to be in the nature of Compton
recoils).
There was thus a most serious discrepancy between the results of Bothe
and Becker, giving γ-ray energy of 10 MeV, and those of Joliot –Curies with γray energy of 50 MeV.
J.Chadwick in 1932 also investigated these radiations and concluded that
they were neutrons. His paper on “the existence of neutron” appeared in June,
1932, proceeding of the royal society. Chadwick investigated the radiation
resulted from the bombardment of beryllium with the α- particles from polonium
(210po ) using an ionization chamber connected to an amplifier and oscillograph.
He obtained about four deflections in the oscillograph per minute, and this rate
was essentially unchanged by the interposition of 2 cm of lead. On interposing
paraffin wax, instead of 2 cm lead, the number of deflections per minute
increased markedly, rather than decrease, this was the most amazing. The
protons, it was clear, were actually being ejected from the hydrogen atoms by the
mysterious rays and propelled rapidly through the ionization chamber.
3
Alpha particles
Polonium
Beryllium
Lead
Paraffin
Fig 1: A simple diagram that shows alpha particles bombarding beryllium create a
radiation that easily passes through lead and ejects fast protons from a material
containing hydrogen [1] .
Pump
To amplifier
Polonium
Beryllium
Fig 2 : Schematic drawing of source mount and ionization chamber used by Chadwick in
his discovery of the neutron. [2]
Chadwick was unable to deduce the mass of a neutron from his results for beryllium
because the nuclear reaction, which is presumed to occur, in this case was;
9
12
1
Be + 24He
6 C + 0n
and the mass of beryllium atom was not then known. But by substituting powdered Boron
deposited on graphite plate for the Beryllium target, Chadwick obtained a more accurate
4
4
value for mass of neutron. A sheet of paraffin wax was then interposed between the target
and the ionization chamber, and the maximum range and velocity of protons were
determined, by their absorption in aluminum (Al).
By measuring the velocities with which protons were ejected from various
materials and utilizing simple collision theory, it was possible for Chadwick to determine
the mass of this new particle and show that it was close to the mass of a proton.
When a neutron collides with a nucleus at rest and imparts momentum to it, the
laws that govern the collision are the same as colliding billiard balls. One law is that in a
head on collision the velocity imparted to the object struck is inversely proportional to the
mass of the object plus that of the projectile.
Chadwick used a thin sheet containing nitrogen and found that the velocity of the
ejected nitrogen nuclei ( 714N) was only about one seventh of the velocity with which
protons ( 11p) are ejected from hydrogen. This ratio of seven gives the neutron mass, M,
readily, because of the inverse proportion:
(M+14)/(M+1) = 7, and hence M = 1.16
Showing that the mass of the neutron is about 16 percent greater than the mass of the
proton a later and more accurate measurement showed that the neutron mass is extremely
close to that of the proton, exceeding it by only about one tenth of one percent.
After demonstrating the existence of new particle and measuring its mass, the
new particle, Chadwick named it the “neutron”. A free neutron has a rest mass of
939.573Mev, while a free proton has a rest mass of 938.280Mev. It has zero charge, but a
magnetic moment of -1.9135 μN, where μN is nuclear magneton. This in itself indicates
that the neutron is not an elementary particle but a composite. Its spin is the same as the
spin of the proton (spin half).
A free neutron is a neutron that exists outside of an atomic nucleus; hence, it is
unstable decay with a half-life of below 15 minutes, while neutrons bound in the nucleus
are stable. The only possible nuclear decay mode, via the weak interaction is in to a
proton, an electron, and anti-neutrino. The proton and electron forming hydrogen atom.
0
1
n
1
1
p + e + ν
Even though it is not chemical element the free neutron is often included in tables of
nuclides. It is then considered having an atomic number zero and a mass number of one.
The following table shows summary of free neutrons [3] .
5
Name, symbol
Natural abundance
Half- life
Isotope mass
Decay products
Spin
Excess energy
Binding energy
Decay mode
Decay energy
Free neutron, 01n
Synthetic
613± 0.6 sec
1.0086649 u
proton, electron, anti- neutrino
+1/2
8071.323± 0.002 Kev
0
β emission
Eβ =0.782353Mev
Table1: Summary of free neutron.
2.1-1 NEUTRON KINDS
The neutron temperature also called the neutron energy indicates a free neutron kinetic
energy, usually given in electron volts. The term temperature is used, since hot, thermal
and cold neutrons are moderated in a medium with certain temperature. The neutron
energy distribution is then adapted to the Maxwellian distribution known for thermal
motion. Qualitatively the higher the temperature, the higher is the kinetic energy of the
free neutron. Kinetic energy, speed and wavelength are related through the deBroglie
relation.
Fast neutrons are free neutrons with a kinetic energy close to 1 MeV, hence a speed
of about 14,000 km/sec. They are named fast neutrons to distinguish them from lower
energy thermal neutrons, and they are produced in accelerators or nuclear fission. Fast
neutrons can be made in to thermal neutrons via a process called moderation. This is done
with a neutron moderator.
Thermal neutrons are free neutrons with a kinetic energy of 0.025 eV hence speed of
2200m/s or 2.2 km/sec. They are named thermal, because this kinetic energy is similar to
the average kinetic energy of molecules of a gas at a room temperature. After a number
of collisions with nuclei, neutrons arrive at this energy level provided that they are not
absorbed. Thermal neutrons have much larger effective cross section of reaction than fast
neutrons, and can therefore be absorbed more easily by any atomic nuclei that they
collide with, creating a heavier and often unstable isotope of chemical element as a result.
Most fission reactors use a neutron moderator to slow down, or thermalize the
neutrons that are emitted by nuclear fission so that they are more easily captured.
Cold neutrons are thermal neutrons that have been thermalized in a very cold
substance (moderator) such as liquid deuterium.
6
Intermediate neutrons are fission energy neutrons that are slowed down, often said to
have intermediate energy. There are no many non-elastic reactions in this energy region,
so mostly what happens is just slowing to thermal speeds before eventual capture.
Moderated and other non-thermal neutron energy distributions ranges are listed in the
table below.
Neutron kinds
1
2
2
3
4
5
6
7
8
9
10
Fast neutrons
Slow neutrons
Epithermal neutrons
Hot neutrons
Thermal neutrons
Cold neutrons
Very cold neutrons
Ultra cold neutrons
Continuum region neutron
Resonance region neutron
Low energy region neutron
Neutron energy
approximately 1 MeV
less than 1 eV
from .025 eV to 1 eV
about 2ev
about 0.025 eV
from 5x10-5 eV to 0.025 eV
from 2x10-7 to 5x10-5
less than 2x10-7 eV
from 0.01 MeV to 25 MeV
from 1 eV to 0.01 MeV
less than 1 eV
Table 2: Kinds of neutrons with their energy range. [4, 5]
2.1-2 Major neutron sources
Neutrons are found bounded inside a nucleus of an atom, almost all elements in periodic
table contains at least one neutron bounded inside their nucleus except ordinary hydrogen
atom which contains only one proton inside its nucleus. If one needs neutrons of different
energy for any purpose he should extract neutrons from the nucleus of certain element by
imparting energy to it, the minimum energy needed by a nucleus to emit one neutron is
nearly equal to the binding energy of a neutron, approximately around 7Mev. There are
three major categories of neutron sources:
1. Radioactive neutron sources
In this category we will consider sources of neutrons made up of a target material mixed
or alloyed with a naturally decaying a radioactive component, which supplies the
bombarding radiation for the release of neutrons. Radioactive sources are usually
relatively small volume. Thus they are readily portable and adaptable to particular
experimental arrangements. These sources also can be calibrated quite accurately, and the
neutron output is either practically constant or its variation with the decay of the
radioactive component can be estimated reliably.
7
There are several types of radioactive neutron sources, differentiated both by the
nature of the target material and of the radioactive nuclide producing the bombarding
radiation. These radioactive sources, which have been found useful, are discussed below.
In general it may be said that neutron sources, which depend up on radioactive
preparation for the bombarding radiation, are limited in the rate of neutron emission,
which can be conveniently achieved. Most of these sources of these sources would
become awkwardly large for a total emission of neutrons of the order of 108 neutrons in
one second. Therefore the radioactive sources, which have been used in the past, have an
order of neutron emission not greatly exceeding 107 neutrons in one second.
(I) Radioactive ( α , n ) sources.
Radioactive (α, n) sources have historical significance in connection with the
discovery of neutrons and are most useful of the radioactive sources. Hence it is better to
start the discussion with the radioactive (α, n) sources. The fact that α-particles from
radioactive substances do not have energies extending much above 5Mev automatically
limits the useful target elements for this source. Those nuclides which have threshold for
the (α, n) reaction within this region of energy at first show a slow rise in the neutron
yield as the α-particle energy increases beyond the threshold. This excitation curve raises
more rapidly as the α- particle energy approaches the maximum energy of the α-particles
from radioactive preparation.
Beryllium has the highest yield of all the elements for polonium alpha particles, the
yield for thick beryllium targets being nearly four times the yield from boron, its nearest
competitor. Beryllium also has a neutron yield more than six times that of fluorine, the only other element that gives a significant yield of neutrons is polonium. Because of the high yield of neutron from beryllium, this element has been used
almost exclusively as the target material in (α,n) radioactive neutron sources. Common
beryllium target (α, n) sources are : a) Polonium - Beryllium
b) Radium – Beryllium
c) Plutonium – Beryllium
d) Americium – Beryllium
a) Polonium – Beryllium
The Polonium – Beryllium (Po– Be) neutron source has historical interest because it was
used in the discovery of neutron. This source emits gamma rays of very low intensity that
a practical advantage possessed by few other radioactive neutron sources. On the other
hand, Po – Be neutron source has relatively rapid rate of decay. 210Po, used in this
neutron source, has a half-life of approximately 140 days. The maximum α energy from
polonium is 5.3 MeV.
8
The (α, n) reaction by which alpha particles release neutrons from beryllium can be
represented by,
9
12
1
4
+ 5.7 MeV
4 B + 2 He →
6 C + 0 n
Hence the reaction is exoergic. Therefore the distribution of neutron from the reaction of
equation (1) according to energy would be expected to range from about 6.7 MeV to
10.9MeV,depending on whether the neutron is emitted in the same direction as that of
incident alpha particle or in the opposite direction. Po – Be sources have been made in a
variety of forms. One common method of preparation has been to mix fine beryllium
powder with solution of polonium. After drying thoroughly, the mixture is composed in
to small pillet, sealed in some kind of container, but this is hazardous operation.
Another way has been made a sandwich type Po-Be source. In the design, the
polonium is deposited electrolytically on one side of platinum foil and the foil inserted in
the narrow slot between two semi-cylinders of beryllium metal.
(b) Radium-Beryllium
Prior to the development and general availability of accelerators, the Ra-Be (α, n)
sources were the most common way to generate neutrons. This has been performed using
a mixture of fine beryllium powder and radium bromide as a source of neutrons. Part of
this popularity based on the case with which large preparation of radium could be
obtained and the long half- life of radium. The half- life is about 1690 years insured that
the rate of emission of neutrons would be essentially constant with time. Ra-Be sources
have the disadvantage of emitting an intense and penetrating gamma radiation. The
gamma rays are hazard to health and also produce objectionable effects in some type of
detectors of neutrons. Preparations of mixtures of radium bromide and beryllium powder
have been made in a variety of ways. The volume can be reduced considerably by
compressing the mixture to a density of about 1.75gm/cm3. Anderson and Fled (6) state
that a compressed Ra-Be source will have a yield of neutrons given approximately by
⎡
⎤
M Be
1.7 x10 7 ⎢
neutrons/sec/gm of radium. Where MBe mass of beryllium
⎥
⎣⎢ M Be + M RaBr2 ⎦⎥
and M RaBr2 is mass of radium bromide. Commonly 10g beryllium to 1g of radium is
used. Little additional gain in neutron emission is obtained from further additions of
beryllium.
(c) Plutonium – Beryllium.
Plutonium forms an inter-metallic compound with Beryllium of the definite form with a
density of 3.7 g/cm3. The conveniently available plutonium isotope is 239Pu, which emits
5.1 MeV alpha particles. The half-life is about 23 x 104 Years. The gamma rays emitted
in the radioactive decay of 239pu are weak and of low energy. Therefore Pu-Be neutron
sources have the advantage over Ra-Be sources of long half-life and the favorable
characteristic of Po-Be sources of low intensity of gamma radiation. The neutron yield is
9
somewhat lower for Pu-Be sources than from Ra-Be sources, but it is adequate for the
purpose for which radioactive neutron sources are now used. A cylindrical neutron source
approximately 2 cm in diameter and 3 cm in height will yield about 106 neutrons per
second. It is quite likely that plutonium – beryllium may replace other types of (α, n)
radioactive neutron sources when plutonium becomes more readily available.
(D) Americium – Beryllium.
This is a radioactive neutron source used in this experiment to irradiate
In for the determinations of thermal neutron capture cross section of 115In.
sample of
241
Am has a half-life of about 470 years. Although this isotope decays by emitting alpha
particles of about 5.4 MeV, these particles are followed by gamma rays in the 40 to 60
KeV regions in the majority of the disintegrations. This gamma ray emission makes
americium appear less satisfactory than plutonium for the preparation of neutron sources.
Runnels and Boucher have described the preparation of two AmBe alloys. One of these
had a Be/Am atomic ratio of 263:1 and the other had an atomic ratio of 14:1. The
observed neutron yields are given in table below. [6]
115
Property
the firs type
a. Be/Am atomic ratio
b. Am α-activity disintegrations
Per second.
c. Yield in neutrons per second.
d. Neutrons per 106 α- particles
second type
263:1
14:1
2.97 x 109
2.13 x 105
71.7
3.24 x 109
1.57 x 105
48.5
Table 3: Neutron yields from two types of AM-Be neutron sources. [6]
II. Radioactive (γ - n) sources
There are only two nuclides, which have thresholds for the (γ -n) reaction with in the
range of energies of gamma rays emitted by radioactive nuclei in their decay process.
They are 2H and 9Be. Hence all radioactive (γ- n) neutron sources use either deuterium
or beryllium as a target material. The cross section in these nuclei for the (γ- n) reaction
near the threshold energy is of the order of a milli-barn. The cross section (σr) varies with
the energy of the gamma rays Eγ near the threshold for both deuterium and beryllium.
The most significant feature of these values of the cross section is that they are small. A
small cross section means that a photo neutron source using 2H or 9Be as a target will
emit many times as gamma rays as neutrons. Thus undesirable effects of the gamma ray
can be expected to be prominent in these photo neutron sources.
10
In principle, radioactive photo neutron sources offer the possibility of obtaining mono
energetic neutrons. If a radioactive nucleus emits only one gamma ray with energy above
the threshold for the (γ, n) reaction in either beryllium or deuterium, the neutrons emitted
should all be of the same energy, except for a small spread in energy resulting from the
difference in direction between the gamma ray and the emitted particle (neutron). The
following table gives several photo neutron sources using different nuclides as sources of
gamma rays.
Source
T½
Eγ(MeV)
En(MeV)
Yield (neutrons/sec)
24
Na + D2O
14.8 hr
2.76
0.8
29 x 104
24
Na + Be
14.8 hr
2.76
0.2
14
56
Mn + D2O
2.6 hr
2.7
0.2
0.3
56
Mn + Be
2.6 hr
1.8,2.1,2.7
0.15, 0.3
2.9
72
Ga + D2O
2.5
0.13
6.90
72
Ga + Be
14hr
1.8 ,2.2,2.5
0.2
5.9
54 min
1.8,2.1
0.2
0.8
14 hr
116
In + Be
124
Sb + Be
60 days
1.67
0.02
19
140
La + D2O
40 hr
2.5
0.15
0.7
140
La + Be
40hr
2.5
0.6
0.20
Table 4: Yield of neutrons from photo neutron sources [6] .
2. Accelerators as a source of neutrons
It is obvious that accelerators, which can impart energies to beams of charged particles in
excess of the threshold energy for release of neutrons in a target, are adaptable as source
of neutrons. In those cases where the reaction in the target is exoergic, a particle of quite
low energy can be used in the accelerator. As the control of the energy of the charged
particles in the beams measuring the energy of the beam, it has become possible to
generate neutrons with fairly well defined energies. Also as the energy to which charged
particles can be accelerated has increased, the range of target nuclides has grown.
Many accelerators of nuclear charged particles after the opportunity to accelerate
alpha particles to energies higher than those, which can be obtained, from radioactive
11
sources. A few accelerators have been used to produce neutrons by (α, n) reaction. When
alpha particles with energies of the order of 20 MeV energy are available, the range of
possible target nuclei for the (α, n) reaction covers the whole periodic table. Where as
cross sections for these (α, n) reactions are often small, of the order of milli barns, the
high intensity of alpha –particles beams in accelerators tends to counteract these
disadvantages. After Eα threshold of ( α , n) reaction reached the cross section starts to
grow rapidly. When its threshold for the (α,2n) reaction is reached, the cross section for
this reaction follows a similar course.
The (α, n) reaction has not been found very useful as a source of neutron in
accelerators. The chief reason seems to be that that production of alpha-particle beams is
difficult and the neutron yield is low.
The (p, n) reaction as source of neutron.
The (p, n) reaction has been much more popular than the (α, n) reactions as a source of
neutrons in accelerators. The lower threshold energies and greater yield of neutrons have
contributed to this popularity. The following table gives the threshold energies of
different nuclides for the yield of neutrons.
Nuclide
3
H
7
Li
60
Ni
90
Zr
101
Ru
111
Cd
ET (MeV)
1.02
1.88
6.8
7.0
1.4
1.6
Table 5: Threshold energies (ET) for the (p, n) reaction in a few nuclides. [5]
Up to the present time the 7Li (p,n) 7Be reaction has been most widely used as a
source of neutrons with energies in the Kilovolt region. The equation for the reaction is:
7
Li +
1
H 7
Be +
1
n -1.63 MeV
For energies below 80 KeV for the neutrons, large proton currents are required on
thin targets and the neutrons must be taken at angles greater than 900 to the direction of
the proton beam. The large proton currents make it mandatory to use a rotating target to
reduce evaporation of the thin lithium target by heat developed by the beam.
12
Mono energetic neutrons
Accelerated charged particles present the probability of obtaining nearly mono energetic
neutrons over a wide range of energies. Infact, the production of mono energetic
neutrons has been one of the most valuable functions of accelerators. Special precautions
are required to continue the energies of the neutrons to a narrow band. Most important is
the use of thin targets. Thin targets avoid series losses of energy by the bombarding
particles prior their interaction with nuclei.
The 3H(p, n) 3He reaction
Tritium is frequently used to produce neutrons. One reaction in which tritium may be
used to generate neutrons is
3
H
+
1
→
H
3
He
+
1
n - 0.735 MeV
Bombardment of tritium requires that it be in a form of suitable as a target. The must
also be in a position to permit neutrons to be accepted at appropriate angles when mono
energetic neutrons of special energy are needed. .
Although targets of low atomic number in the (p, n) reaction have been more
popular in the past for the generation of neutrons, targets of higher atomic number have
called attention for the production of mono-energetic neutrons in the kilovolt region of
energies.
Accelerators, which can produce beams of protons with energies of the order of
400 MeV, may be used to generate neutrons of approximately equal energy.
The (d, n) reaction as a source for neutron
Nearly all of the (d, n) reactions whish have been used in the generation of neutrons are
strongly exoergic. Hence the reactions have no thresholds and neutrons are released at
deuteron energies approaching zero. An exception is the reaction 12C(d,n)13N
Which is endoergic with Q= -0.28 MeV and a threshold energy ET = 0.33 MeV.
Otherwise devices, which can accelerate deuterons to energy of a few kilo electron volts,
are usable as source of neutrons. Although the number of (d, n) reactions is considerable,
only a few have proved valuable as source of mono-energetic neutrons. They are the 2H
(d, n) 3He and 3H (d, n) 4He reactions. Other (d, n) reactions, such as 7Li(d, n) 8Be with a
high Q value of 15MeV,and 9Be(d, n) 10Bo, while giving high neutron yields, do not give
simple neutron spectra.
2
H (d, n) 3He reaction has been widely used in the production of mono-energetic
neutrons. One of the convenient characteristics of the 2H(d, n) 3He reaction is high yield
of neutrons at deuteron energies below 1MeV.The reaction equation is:
2
H
+
2
H
„
3
He
+
1
n + 3.3 MeV.
13
A popular method for preparing targets for use in accelerators for (d, n) reaction on
deuterons has been freeze heavy water on a refrigerated metal support. The competing
reaction, 2H (d, n) 3H always along with the (d, n) reaction when deuterons are
bombarded by deuterons.
The 3H(d, n) 4He reaction as a source of neutrons
The 3H(d, n)4He reaction is outstanding, among the (d, n) reactions which have been used
for generating mono-energetic neutrons, for its high positive value of Q. The equation of
reaction is:
3
H
+
2
H
„
4
He
+
1
n + 17.6 MeV
This reaction is characterized by an intense production of neutrons of high energy for
bombarding energies of the order of Ed = 100 KeV. In the production of neutrons by the
(d, n) reaction on tritons, may be accelerated to strike a deuterium target or, for example,
the deuterons may be accelerated in to a gas target of 3H.
Deuteron stripping reactions in the generation of neutrons.
A deuteron can be considered as combination of a neutron and a proton. The structure is
not bound firmly; it is very probable that the neutron and the proton are out side the range
of their mutual nuclear forces for a large part of a time. It is not surprising therefore, that
a deuteron traveling at high speed through a target may have proton captured in a nucleus
while the neutron continues on its way. Such a process has been repeatedly observed with
neutron retaining its proportional fraction of the original energy of the deuteron, roughly
one-half. The interaction has naturally come to be known as the stripping of the deuteron.
Although the converse interaction in which the neutron is captured, releasing
proton, also occurs, it is of interest in this discussion only as a competing reaction, which
may reduce the number of neutrons released. The neutron from deuteron stripping can be
identified by the fact that the maximum of their distribution of energy is at an energy
equal to one-half the energy of the incident deuteron.
Photo neutron sources
When bremsstrahlung from betatrons with energies exceeding 20MeV became available,
it also become possible to generate neutrons by the (γ, n) reaction ranges from around
10MeV for nuclei with high mass number up to about 19MeV for A = 12. Below
A=12,the threshold energies decrease again. The intensity of the gamma rays far exceeds
that of the neutrons. The high intensity of the gamma radiation accounts in part for the
frequent use of the (γ, n) reaction as a source of neutrons in accelerators.
Example:
9
1
Be
+ γ (1.7MeV) →
n + 24He
198
Hg
+
γ (6.8 Mev)
→
1
n +
Hg*
197
14
The excited mercury decays in to gold (19779Au) with a half- life of 2.7 days [3] .
3. Nuclear reactor as a neutron source
Nuclear fission in reactor produces neutron, which can be used for experiments. This is
the purpose of nuclear research reactors but not the study of nuclear fission itself. The
high energy with which neutrons are released in fission process also accounts for the
extensive neutron moderator, which is a basic feature of reactors. The moderator serves
to reduce the energy of the fission neutrons to thermal energies with a minimum of loss
by neutron capture or escape from the moderator. Therefore a thermal neutron reactor can
be used as a source of neutrons over a considerable range of energies. However, a
thermal neutron beam from a reactor can be used to produce fission neutrons. The fission
source is obtained by placing a target of fissile material in the thermal beam, which
converts this target in to a convenient and intense source of fission neutrons.
2.1-3. Neutron interactions with nucleus
Neutrons can cause many different types of interactions. The neutron may simply scatter
off the nucleus in two different ways, or it may actually be absorbed in to the nucleus. If a
neutron is absorbed in to the nucleus it may result in the emission of a gamma ray or a
subatomic particle, or it may cause the nucleus to fission.
This section introduces five reactions that can occur, when a neutron interacts with
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 in to the nucleus and something different emerges.
I. Scattering
A neutron scattering reaction occurs when a nucleus, after having been struck by a
neutron, emits a single neutron. Despite the fact that the initial and final neutrons do not
need to be (and often are not) the same, the net effect of the reaction is as if the projectile
neutron had merely “ bounced off” or scattered from, the nucleus. The two categories of
scattering reactions are elastic and inelastic scattering.
1. Elastic scattering (n, n)
In an elastic scattering interaction is only between a neutron and a target nucleus, there is
no energy transferred in to nuclear excitation. Momentum and kinetic energy of a system
are conserved, although there is usually some transfer of kinetic energy from the neutron
to the target nucleus. The target nucleus gains the amount of kinetic energy that the
15
neutron loss, i.e. the amount of energy lost by the projectile neutron during elastic
p2
interaction is
where ‘ p ’ and ‘M’ are momentum and mass of the target nucleus.
2M
Since the mass of the nucleus is large compared to the mass of neutron for medium and
heavy nuclei this energy transfer is small in most cases. Figure below illustrates the
process of elastic scattering of a neutron off a target nucleus [6]
Neutron
Neutron
Target nucleus
Target nucleus
Figure 3: Elastic scattering.
In the elastic scattering reaction, the conservation of momentum and kinetic energy
can be written in equation form as:
i) For the conservation of momentum
mnvni + MtVt = mnvnf + MtVtf
ii) For the conservation of kinetic energy
½mnv2ni + ½ Mt(Vti)2 =
½ mn(vnf)2 +
Where:
mn = mass of the neutron
Mt = mass of the target nucleus
vni = initial neutron velocity
vnf = final neutron velocity
Vti = initial target velocity
Vtf = final target velocity
½Mt(Vtf)2
16
Elastic scattering of neutrons by nuclei can occur in two ways. The more usual of the
two interactions is the absorption of the neutron, forming a compound nucleus, followed
by the re-emission of a neutron in such away that the total kinetic energy is conserved
and nucleus returns to its ground state. This is known as resonance elastic scattering (a
collision where a nucleus absorbs a neutron and re-emits it, conserving kinetic energy).
The second elastic collision type is termed as potential elastic scattering and can be
understood by visualizing the neutrons and nuclei to be much like billiard balls with
impenetrable surfaces. Potential scattering takes place with incident neutrons that have
energy about 1 MeV. In potential scattering, a neutron collides with a nucleus, transfers
some kinetic energy to it, and bounces off in s different direction. In such interaction
compound nucleus is not formed. Instead, the neutron is acted on and scattered by the
short-range nuclear forces when it approaches close enough to the nucleus.
(
2. Inelastic scattering n, n '
)
In inelastic scattering, the incident neutron is absorbed by the target nucleus, forming a
compound nucleus. The compound nucleus will then emit a neutron of lower kinetic
energy, which leaves the original nucleus in an excited state, The nucleus then usually, by
one or more gamma emission, emit this excess energy to reach its ground state. Fig below
shows this process of scattering:
Neutron
Gamma emitted.
Neutron
Target nucleus
Target
Figure 4: In elastic scattering [8]
Target nucleus
17
II. Absorption reaction
Most absorption reactions result in loss of a neutron coupled with the production of a
charged particle or gamma ray when the product nucleus is radioactive, additional
radiation is emitted at some later time. Radiative capture, particles ejection, and fission
are all categorized as absorption reaction.
Radiative capture (n, γ ) reaction.
In radioactive capture the incident neutron enters the target nucleus forming a compound
nucleus. The compound nucleus then decays to its ground sate by gamma emission. An
example of radioactive capture reaction is shown below.
1
n +
238
92U
(23992U )*
The radioactive uranium decays by emission of gamma ray to its ground state.
239
*
92U
239
92U
+ γ
Another example is the capture of thermal neutron by
the equation of the reaction is shown below.
115
In to form a radioactive
116
In ,
116
*
+ 11549In
49In
The radioactive indium decays to the ground state of tin by emission of gamma rays
and beta rays.
1
0n
116
β + γ.
50Sn +
In this paper this reaction has a special focus since the thesis is to experimentally verify
this reaction and determine the probability of the thermal neutron capture reaction in
indium nucleus.
Radiative capture (n, γ ) reaction is the most common reaction in that the compound
nucleus formed may emits only a gamma photon. In other words, the product nucleus
may be an isotope of the same element as the original nucleus, its mass number increases
only by one. The simplest radioactive capture occurs when hydrogen absorbs a neutron to
produce deuterium (heavy hydrogen).
116
49In
γ
=
=
Neutron
Hydrogen
Deuterium
(Radioactive)
deuterium
(Ground state)
Figure 5: The capture of neutrons by hydrogen [8]
18
2 *
2
+ 11H
=
=
1 H
1 H+ γ
The deuterium formed is a stable nuclide. Deuterium itself can capture neutron (under
goes radiative capture reaction) to form tritium.
1
0n
Particle Ejection (Transmutation) (n, p), (n, d), (n, α ) etc.
A nucleus may absorb a neutron forming a compound nucleus, which then deenergizes by emitting a charged particle, either a proton or an alpha particle. This
produces a nucleus of different element. That is the compound nucleus has been excited
to a high enough energy level to cause it to eject a new particle while the incident neutron
remains in the nucleus. After a new particle is ejected, the remaining nucleus may or may
not exist in an excited state depending up on the mass energy balance of the reaction. An
example can be: 816O (n, p)716N reaction.
In this reaction oxygen (816O) captures a neutron and emits a proton to form nitrogen
(716N). The reaction equation is :
0
1
n +
8
16
O
7
16
N
+
1
1
P.
The product nitrogen is radioactive with a half life of 7.1 seconds. It decays back to the
ground state by emission of high energy γ rays.
III.
Fission (n, f)
One of the most important interactions that neutrons can cause is fission, in which the
nucleus that absorbs the neutron actually splits in to two similarly sized parts.
2.1-4. Neutron moderation
Whichever source is chosen to use, the energy of the neutrons is high, and hence the
neutron-capture cross section is small. It is usual to reduce neutron energy by a process
called neutron moderation.
Neutrons, unlike protons, do not lose energy by ionization, since they are not ionizing
particles. Hence their range in matter is very long. The actual distance traveled before
losing their energy or being captured is of the order of centimeters. As neutrons travel
through matter they interact with nuclei. Some of these reactions lead to a compound
nucleus formation, and subsequent emission of reaction products. However one of the
dominant reaction mechanisms is elastic scattering. In this process the neutron loses
kinetic energy, and is eventually slowed down until it is in thermal equilibrium with the
thermal kinetic energy of the particles in the medium. Any high-energy neutron can be
reduced to thermal neutron. To see which nuclei is best for the moderation process and to
see how many collisions are needed for the moderation (to reduce the energy of a given
19
neutron to thermal energy) in a given nuclei medium, lets consider neutron of mass mn
moving towards a stationary nucleus of mass mt with velocity vo.
After interaction neutron is scattered with velocity v1, in the direction making an angle θ
with initial direction and the target recoils with a speed v2, at angle φ , as shown in the
figure below.
V1
θ
vo
Neutron incident
φ
Target nucleus
Target nucleus
V2
Fig 6: An incident neutron of high energy on moderator nucleus.
To reduce complexity, let the system be converted to center of mass system. In the
center of mass system, if neutron is moving towards a target nucleus with a velocity vc,
then to keep center of mass stationary, the target nucleus should be assumed to move
towards neutron with velocity v, such that
m n v c − mt v = 0
1
This is to keep center of mass stationary before and after interaction. After interaction
neutron and target nucleus again move with some momentum so that center of mass is
not disturbed and its velocity is zero. If neutron is scattered at angle (π - φ) again
equation (1) holds true. The relative velocity of neutron with respect to nucleus mt is
stationary should be v c + v.
20
Now the problem is reduced to a center of mass system, which is equivalent to the initial
laboratory system, in which the neutron was moving and target nucleus was stationary.
vc + v = v0
2
But from Eq. (1) we see that, applying the conservation of momentum,
m n v c = mt v
3
mt v
mn
Putting Eq. (4) in to Eq. (2)
vc =
4
mt v/mn + v = vo
5
⎡
⎢ 1
v = v0 ⎢
⎢1 + mt
⎢
mn
⎣
⎤
⎥
⎥
⎥
⎥
⎦
6
But the ratio of mass of the target to the mass of neutron gives the atomic weight of
the target (A).Then putting ‘A’ in place of the ratio ‘mt /mn’ we have:
⎡ 1 ⎤
v = v0 ⎢
⎥
⎣1 + A ⎦
7
and from Eq.4
v =
vc mn
mt
8
Eq.7 and Eq.8
⎡
⎢ 1
v0 ⎢
⎢1 + mt
⎢
mn
⎣
⎤
⎥
v m
⎥ = c n
mt
⎥
⎥
⎦
9
21
mt v 0
mn
vc =
m
1 + t
mn
10
vc =
Av0
1+ A
11
This the value of vc from known quantities A and vo. From the velocity vector
triangle OAB, shown below:
Av
B
(π−φ)
vc
v1
)φ
π+Φ
O
Fig 7. Velocity vector triangle
Using cosine law; v12 = vc2 + v2 + 2 vvc cosφ
12
v12 = A2 vo2 /(1+A)2 + vo2 /(1+A)2 + (2A vo2 cosφ)/(1+A)2 13
v12 / vo2 = A2 /(1+A)2 + 1 /(1+A)2 + (2A cosφ)/(1+A)2
14
E
But v12 / vo2 = 1 , where E1 and Eo are kinetic energies of neutron after
E0
and before interaction respectively.
15
There are two critical cases;
1. If φ = 0, grazing incidence i.e. when the neutron is scattered along initial
direction of motion.
E1
E0
= v12 / vo2 =
(A+1)2/(A+1)2
= 1 ; from Eq.15 and from Eq.14
for φ=0
2. If φ = 180 , when the neutron is scattered in the backward direction.
E1/ Eo = v12 / vo2 = (A-1)2/(A+1)2 = α .
o
16
α is the fraction of energy when there is maximum energy difference between the
initial and final energy of neutron. Thus it is maximum fraction of energy loss.
22
1-
E1
E0
= 1- α is remaining fraction of energy.
17
α = (A-1)2 (A + 1)-2
= (1 -
1 2
1
) (1 + )-2
A
A
2
2
) (1- )
A
A
4 4
α = 1+ 2 A A
= (1 -
using binomial approximation for A large enough
18
i) For very large A, when it is better more than the value, which allows binomial
4
4
approximation above such that ‘ 2 ’ is negligible, α = 1 19
A
A
4
ii) When A is further larger so that ‘ ’ is very small, the maximum fractional loss is
A
given by one (α = 1), this means that the initial and the final energies of the incident
neutrons are the same there is no energy loss. Therefore, for such heavy
nucleus neutrons cannot be moderated to the thermal energy, so that very heavy
elements are not good to be used as a moderator. In other hand light elements like
hydrogen, the value A=1, does not allow the approximation that
2
2⎞
( A − 1) 2
⎛
= ⎜1 − ⎟ , since A=1 is not large compared to 1. Hence putting the
2
A⎠
( A + 1)
⎝
value A=1, in the former equation before it is approximated and calculate for the
maximum fraction of energy loss;
(A − 1 )
α=
2
( A + 1)2
=0
20
This shows that when a moderating atom is hydrogen (A=1), neutron with no energy
can be obtained for the case of maximum energy loss, this means that no neutron is
found after interaction or it means that the neutrons are captured by the moderating atom.
Therefore light elements like hydrogen capture the neutron, which are needed to perform
an experiment, this is the main disadvantage of such elements, so that they are not good
to be used as a moderating atom. However, intermediate elements like graphite (12C),
heavy water (D2O), paraffin wax, liquid sodium (22Na) are good moderators.
Average energy loss per collision
23
The average energy lost by the neutron in each collision helps to find the number of
collisions needed to bring an energetic neutron to thermal energy (= 0.025ev). It depends
on the kind of (type of) moderating atom used and the initial neutron energy before each
collision. A moderator atom having less weight thermalizes the neutron with small
number of collisions than those moderators heaving greater atomic mass. To derive the
expression of average energy loss per collision ΔE , consider a sphere of unit radius
around a center of interaction ‘O’ and consider directions φ and φ + dφ in which
neutrons are scattered after interaction (i.e. φ can take any value from 0 to π).
dφ
r dφ
φ
Fig 8: A scattering angle of neutron
Consider a surface element in the limits of scattering angle φ and φ + dφ . The
whole area is sphere (S = 4πr2), the area of a surface element
ds = 2Π sin φdφ , for r = 1.
21
Then the probability that neutron is scattered in area element ( ds ) , is (dp) which is given
by ;
dp =
sin φdφ
2 ∏ sin φdφ
ds
=
=
s
2
4∏
22
in other word dp is the probability that neutron is scattered in angle φ and φ + dφ . But
sin φdφ = − d (cos φ )
23
1
dp = − d (cos φ ) , using Eq.22 and Eq.23
2
24
But the fraction of energy loss after scattering at scattering center ‘o’ is given by:
E1
A 2 + 2 A cos φ + 1
=
E0
( A + 1) 2
25
24
E1
( A + 1) 2 = A 2 + 2 A cos φ + 1
E0
E1
( A + 1) 2 − A 2 − 1 = 2 A cos φ
E0
26
27
E1 ( A + 1) 2 ( A 2 + 1)
−
2 AE 0
2A
28
( A 2 + 1) 1 + α
From Eq.16,
=
2A
1−α
29
( A − 1) 2
( A + 1) 2
30
cos φ =
1−α = 1−
1−α
1−α =
=
( A + 1) 2 + ( A − 1) 2 A 2 + 1 + 2 A − A 2 − 1 + 2 A
=
( A + 1) 2
( A + 1) 2
31
4A
( A + 1) 2
32
( A + 1) 2
2
=
2A
1−α
33
Substituting Eq.29 and Eq.33 in Eq.28 gives;
cos φ =
cos φ =
d (cos φ ) =
E1 2
1+α
(
)−
E0 1 − α 1 − α
⎤
1 ⎡ 2 E1
− (1 + α )⎥
⎢
1 − α ⎣ E0
⎦
2d ( E1 )
, where α and E0 are constants
E 0 (1 − α )
From Eq.24 and Eq.36 solving for dp we have:
− d ( E1 )
dp =
E 0 (1 − α )
Eq.37 gives probability of scattering in a small angle φ and φ + dφ .
34
35
36
37
25
P(E) =
− dp
1
=
dE1
E 0 (1 − α )
38
This Eq.38 shows that the probability of neutron kinetic energy E0 after collision
will lie in an interval dE1 , centered around a kinetic energy E1 after collision, is
independent of this energy. From the definition of probability density, the average energy
loss ( ΔE ) of the scattered neutrons after one collision is given by:
E0
ΔE =
∫ (E
− E ) p( E )dE
0
α E0
39
E0
∫α p( E )dE
E0
Where p(E) is
From the normalization condition;
E0
∫ p( E )dE
= 1
40
αE0
Eq.40 is the total probability of energy loss of neutron.
ΔE =
ΔE
⎛ E0 − E ⎞
⎟⎟dE
0 (1 − α ) ⎠
E0
E0
∫ ⎜⎜
α ⎝E
⎛
⎞
E0
∫αE ⎜⎜⎝ E0 (1 − α ) ⎟⎟⎠dE 0
E0
=
ΔE =
E0
(1 − α )
2
(1 − α )
ΔE
=
E0
2
41
E0
⎛
∫α ⎜⎜⎝ E
E0
⎞
E
⎟⎟dE
0 (1 − α ) ⎠
42
43
44
ΔE
is constant, since α is a constant. Hence we see that the
E0
same fraction of neutron energy is transferred to the moderator nucleus in each of the
collisions. If the value of α from Eq.20is substituted in Eq.43;
E 0 ⎡ ( A − 1) 2 ⎤
ΔE =
45
⎢1 −
⎥
2 ⎣ ( A + 1) 2 ⎦
Eq.44 implies that
26
Using Eq.32
ΔE
E 0 ⎡ (4 A) ⎤
⎢
⎥
2 ⎣ ( A + 1) 2 ⎦
=
⎡ 2 E0 A ⎤
= ⎢
2 ⎥
⎣ ( A + 1) ⎦
ΔE
46
47
For a neutron of kinetic energy E0 encountering nucleus of atomic weight A, the
2 E0 A
average energy loss is
. This expression shows that in order to reduce the speed
( A + 1) 2
of neutrons to the thermal speed with a fewest number of elastic collisions; target nuclei
with small A should be used. Using hydrogen, A=1, the average energy loss has its
E
largest value . A neutron with 2MeV of kinetic energy will (on the average) have
2
1MeV left after one elastic collision, and it is left with a kinetic energy of 500KeV after
the second elastic collision, and so on. To achieve a kinetic energy of only 0.025ev would
take about 27 such collisions. A neutron of energy 0.025ev is roughly in thermal
equilibrium with its surrounding medium and is considered a “thermal neutron”. From
the relation E = KT, where K is Boltzmann’s constant, and T is temperature. One can
readily found that at room temperature about T=20 c0, the value of E being 0.025ev.
If after n collisions with the moderator nucleus, the neutron energy is
assumed to be changed from E0 to En. Then n (number of collisions with the moderator
nucleus) can be derived. Let ξ is the average logarithmic energy decrement per collision.
ξ = Δ ln( E ) = ln E 0 − ln En
ξ =
E0
E0
E0
n
∫α ln( E
48
) p( E )dE
49
E0
∫ p( E )dE
αE0
ξ =
E0
E0
E0
n
∫ ln( E
α
) p( E )dE
50
Using Eq.37, Eq.38 and Eq.50;
27
ξ =
E0
E0
∫ ln( E
α
E0
ξ =
ξ =
1
n
)
1
dE
E 0 (1 − α )
(1 − α )E0
1+
ξ = 1+
E0
E0
E0
n
∫ ln( E
α
51
)dE
52
α ln α
1−α
53
( A − 1) 2 ⎛ A − 1 ⎞
ln⎜
⎟
2A
⎝ A +1⎠
54
⎛E ⎞
However, ln⎜⎜ 0 ⎟⎟ is the total logarithmic energy decrement, whence the
⎝ En ⎠
number of collisions n is;
n = the ratio of total logarithmic energy decrement to the average
.
ogarithmic energy decrement per collision
⎛E
ln⎜⎜ 0
⎝ En
⎞
⎟⎟
⎠
53
n =
⎛ A −1⎞
2
( A − 1) ln⎜
⎟
A +1⎠
⎝
1+
2A
The number of elastic collisions needed to moderate neutrons of initial energy E0 to
thermal energy En = 0.025 using a moderator of atomic weight A has a logarithmic
dependence on E0 and A. The following table gives the average number of collisions
needed by some moderators to thermalize neutron of initial energy 2MeV.
Element
Hydrogen
Deuterium
Beryllium
Carbon
Atomic weight
1
2
9
12
ξ
1
0.726
0.208
0.159
n
18
25
85
115
---------------------------------------------------------------------------------------------------------Table 6: Average number of collisions required to reduce neutrons energy from 2Mev
to 0.025ev by elastic scattering [5] .
28
Inelastic scattering is similar to elastic scattering except that the nucleus undergoes an
internal arrangement in to an excited state from which it eventually release radiation. The
total kinetic energy of the outgoing neutron and nucleus is less than the kinetic energy of
the incoming neutron. Part of the original kinetic energy is used to place the nucleus into
the excited state. It is no longer easy to write expression for the average energy loss
because it depends on the energy levels within the nucleus. But the net effect on the
neutron is again to reduce its speed and change its direction. If all the excited states of the
nucleus are too high in energy to be reached with the energy available from the incoming
neutron, inelastic collision (scattering) is impossible. In particular, the hydrogen nucleus
does not have excited states, so only elastic scattering can occur in that case. In general,
scattering moderates or reduces the energy of neutrons.
2.2 The concept of cross section
The probability of a particular event occurring between a neutron and a nucleus is
expressed through the concept of the cross section. If a large number of neutrons of the
same energy in to a thin layer of a material, some may pass through with no interaction,
others may have interaction that change their directions and energies, and still others may
fail to emerge from the sample. There is a probability for each of these events. For
example, the probability of a neutron not emerging from a sample (i.e. of being captured)
is the ratio of the number of neutrons that do not emerge to the number originally incident
on the layer. The cross section for being absorbed is the probability of neutron being
absorbed divided by the aerial atom density (the number of target atoms per unit area of
the layer). The cross section thus has the dimension of area. It must be a small fraction of
square centimeters because of the large number of atoms involved. Because this type of
cross section describes the probability of neutron interaction with a single nucleus, it is
called the microscopic cross section and is given the symbol σ .
Another approach to understanding the concept of the microscopic cross section is to
consider the probability of a single neutron attempting to pass through a thin layer of
material that has an area A, thickness ‘dx’ and contains n target nuclei per unit volume,
each of cross sectional area S. The sum of all the areas of the nuclei is SnAdx. The
probability of a single neutron hitting one of these nuclei is roughly the ratio of the total
target area SnAdx to the area of the layer A. In other words, the probability of a single
neutron having collision with a nucleus is the ratio of aggregate cross sectional area to
nASdx
the total slab area. P =
, On the atomic level, however, cross-section for neutron
A
interactions is not simply the geometrical cross sectional-area of the target. By replacing
nAσdx
S by σ , P =
,
54
A
29
σ might be thought of as an effective cross sectional – area for the interaction retains the
dimension of area that S had [12] . It may be more than the geometric area or less. When a
projectile passes through that area interaction will take place. Cross section is then
measured in terms of number of events produced by a definite number of projectiles per
nuclei, it can be also measured in terms of projectiles absorbed in the target while
producing a definite kind of event.
Let ‘ N’ is number of events produced by incident particles of flux ‘I0’, hence the
probability of interaction is the ratio of particular type of events produced to the the
number of particular type of projectiles incident per unit of area per unit of time.
N
Then P=
55
I0
Equating Eq.54 and Eq.55 we get;
nAσdx N
56
=
A
I0
N
σ=
57
I 0 ndx
This Eq.57 refers to the reaction cross section for particular type of event. If many events
like (α , n ), (n, γ ), (α ,2n ) etc. are considered each of having N1,N2,etc. Total cross section
can be calculated by the estimation of all the type of events produced .
σt =
N1 + N 2 + N 3 + − − −
I 0 ndx
58
Each type of event has its own probability and cross section. The probability of each type
of event is independent of the probability of the others, so the total probability of any
event occurring is the sum of the individual probabilities. Similarly, the sum of all the
individual cross section is the total cross section. The reaction of neutrons with nucleus
leads to the formation of compound nucleus and the reaction cross section is σ r , and the
neutrons may be scattered off the target nucleus and the cross section of scattering is σ sc .
Hence, the total cross section is given by;
σ t = σ r + σ sc
59
The number of events produced is proportional to the decrease in the flux of the
incident projectile. Let ‘I’ be the flux left after an event ‘N’ is produced in a thickness
‘ dx ’.
60
- dI = N = nσIdx
− dI
= nσdx
61
I
30
− dI
= ∫ nσdx
I
62
I = I 0 exp(− nσx )
63
∫
I = I 0 exp(− εx )
64
Where ‘ ε ’ macroscopic cross section includes all reactions absorption or scattering and
Eq.63 is attenuation of projectiles by all reactions.
The physical cross sectional area S of a heavy nucleus is about 2x10-24cm2. Interaction
cross sections for most nuclei are typically between 10-27 and 10-21cm2. To avoid the
inconvenience of working with such small numbers, a different unit of area is used, the
barn, denoted by symbol ‘b’. It is defined to be 10-24cm2, so that the physical cross
sectional area of a heavy nucleus is about 2b. Many neutron interaction cross sections
range between 0.001 and 1000b.
2.3 Neutron Activation Analysis (NAA)
Neutron activation analysis was discovered in 1936 when Hevesy and Levi found that
samples containing certain rare earth elements become highly radioactive after exposure
to a source of neutrons. From this observation, they quickly recognized the potential of
employing nuclear reaction on samples followed by measurement of the induced
radioactivity to facilitate both quantitative and qualitative identification of the element
present in the samples.
Neutron activation analysis is a highly sensitive method for the accurate determination
of elemental concentrations in materials. The NAA method is based on the detection and
measurement of gamma rays emitted from radioactive isotopes produced in the sample up
on irradiation with neutrons. Sample with unknown elemental concentrations are
irradiated with thermal neutrons in a nuclear reactor together with standard materials of
known elemental concentrations. Neutrons are absorbed in the nuclei of constituent atoms
and later these nuclei emit radiation with energy and quantity characteristic of the
particular element. This emitted radiation is a fingerprint of the element, and the amount
of radiation given off at certain energy is indicative of the amount of the element present
in the sample. A comparison between specific activities induced in the standards and
unknowns provide the basis for computation of elemental abundances in the unknown
sample. In NAA process, a nucleus absorbs a neutron. The nucleus becomes excited, and
immediately releases gamma ray and decay to a lower energy level, although it still is in
an excited state. Then after a period (dependent on the nucleus), the excited nucleus
radiates beta particle and gamma ray, and the radiations are detected by a detector.
Analysis of the spectrum of gamma ray emitted allows determination of the elemental
composition of the sample [4].
31
Basic steps of NAA
There are steps that are needed to follow during NAA. The common and basic o steps
that any experimentalist should see are;
1. The sample firs carefully weighed in to a plastic or quartz container.
2. The sample is then sealed with a high-speed friction sealer.
3. The sample, along with appropriate standards, placed near the core of the reactor
irradiated for a predominant length of time. While it in the reactor, it is exposed to
high intensity neutron field. If the neutron approaches, the nucleus of an atom it may
be absorbed. When this happens, the element will become a different isotope of the
same element. This new isotope is almost always unstable it is radioactive and
usually decays by emitting a gamma ray.
4. The sample is then pulled out of the reactor it is allowed to decay for a
predetermined length of time appropriate to the radioactive half life of the indicators
for the elements being determined.
5. The may be counted immediately, for elements with short half-lives, or counted after
delay for samples with longer half lives. The reason for the delay, for isotopes is to
allow the isotopes with short half-life to decay away, thereby preventing interference
and allowing the isotope with longer, half-lives to be more easily measured.
6. After the sample decays, it is “counted" using high purity Germanium (HPGE)
gamma ray detector, or NaI(Tl) scintillation detectors. Gamma rays are very
penetrating, so the gamma rays emitted from the center of the sample easily reach the
detector. The resulting gamma ray spectra looks something like a gas chromatograph
spectra with “peaks” at different retention time.
The position of each peak determines the energy of the gamma ray (identifying
responsible element) and the area under the peak is proportional to its concentration.
Results obtained after correcting for detector efficiency, decay time, size of sample, and
counting and irradiation times. The comparator standard approach is normally employed
with this method. A “standard” is irradiated and counted along with the sample(s). This
standard contains known amount of the elements, to be determined, standards are usually
selected to be similar to the sample(s).
The basic essential required to carry out an analysis of sample by NAA are
source of neutrons, instrumentation suitable for detecting gamma rays, and a detailed
knowledge of the reaction occurs when neutron interact with target nuclei, brief
description of the NAA method, and knowledge of gamma rays detection.
In the NAA method sequence of events occurring during the most common type
of nuclear reaction , namely the neutron capture or (n, gamma) reaction are:
I) When neutron interacts with a 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 the nucleus.
32
II) The compound nucleus will almost instantaneously de-excite in to a more stable
configuration through emission of one or more characteristics prompt gamma rays. In
many cases, this new configuration yields a radioactive nucleus.
III) The radioactive nucleus formed also de-excites (or decays) by emission of one or
more characteristic delayed gamma rays.
IV) Depending the particular radioactive species, half-lives can range from fraction of a
second to several years
Prompt gamma ray.
Neutron
incident
Target
nucleus
Compo
und
nucleus
Radioac
tive
nucleus
Product
nucleus
delayed γ − ray
The fig 9. The process of neutron capture by a target nucleus followed by the emission of
gamma rays. [4]
In principle, therefore with respect to the time of measurement, NAA falls in to two
categories.
(i). Prompt gamma ray neutron activation analysis (PGNAA).
(ii). Delayed gamma ray neutron activation analysis (DGNAA). This later operational
mode is more common.
As mentioned above the NAA technique can be categorized according to whether
gamma rays are measured during neutron irradiation (PGNAA),. The PGNAA technique
is generally performed by using a beam of neutrons extracted through a reactor beam
port. Fluxes on samples irradiated in beams are on the order one million times lower than
33
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.
Using gamma ray measurements to determine thermal neutron
capture cross section of a sample.
The procedure generally used to calculate concentration in the unknown sample and a
comparator standard containing a known amount of the element of interest together in the
reactor. If the unknown sample and the comparator standard are both measured in the
same detector, then one needs to correct the difference in decay between the two. The
mass of the element in the unknown sample relative to the comparator standard is:
M samp exp(− λt d )samp
Asamp
65
=
Astd
M std exp(− λt d )std
Where; Asamp = activity of the sample
Astd
= Activity of the standard
M std = Mass of the standard
M samp = Mass of the sample
λ
= Decay constant for the isotope
t d = Decay time
When performing short irradiations, the irradiation, decay and counting times are
normally fixed (the same for all samples and standards) such that the time dependent
factors cancel. Thus the above equation simplifies in to:
C samp =
C std Wstd Asamp
Wsamp Astd
Using M = CW
66
Where: C sam = concentration of the element in the sample
Wsamp = Weight of the standard
Wstd = Weight of the sample
C std = Concentration of the element in the standard.
The basic idea in the method of NAA is that stable isotope (X) of an element is
converted in to an unstable isotope (Y) by capture of a neutron.
X + n ⎯
⎯→ Y + z
34
The activity of Y is proportional to the amount of X present in the sample. This
amount can be found after measurement of the activity of Y provided that the
counting efficiency is known. Alternatively a standard of the same element is
irradiated together with the sample and the unknown amount is deduced simply from
the ratio of the two activities. The most common way is to measure the gamma
radiation emitted in connection with the decay of Y. Since the emitted gamma
energies are characteristic of the nuclei Y, it is possible to identify unknown elements
present in the sample. Measurements of the activity allow determination of the mass
of the element in question.
Irradiating a sample in thermal neutron flux the reaction (capture reaction) rate
during activation is proportional to the thermal neutron flux and proportional to the
number of the target nucleuses in the sample.
R ∝ φth N x
Where:
67
R =rate of reaction during irradiation
φth = Thermal neutron flux ( m −2 s −1 )
N x = Number of target atoms in the sample.
R = σ φth N x
68
Where σ -is proportionality constant that is the microscopic thermal neutron capture
cross section or it is the probability of a thermal neutron being captured by a nucleus.
It is given in units of area (barn= 10 −28 m 2 ). The rate of change of radioactive atoms
during irradiation is the difference between the rate of production and rate of decay.
dN (t )
= (φthσ N x ) − λN (t )
dt
Where: λ is decay constant of radioactive nuclei produced.
69
t is time in (s)
Using a condition that N (0) = 0 at the start of irradiation, the solution of the differential
equation becomes:
R
N (t ) = (1 − exp(−λt ) )
70
λ
Then the activity,
35
Ay = σ φ N x (1 − exp(−λt ) )
71
Let t d be the time elapsed between the end of irradiation and the start of counting, t i is
the time elapsed during irradiation of the sample and t c be the length of counting time.
Considering correction for decay during measurement the number of counts collected in
the time t c is;
n=
σ φ Nx ε p p
γ
λ
(1 − exp(−λt ) ) (exp(−λt d )(1 − exp(−λt c )
72
Where: Pγ = the intensity of the gamma radiation considered.
ε p = the counting efficiency the detector in the photo peak.
If the sample contains a mass m of the element with molar mass M And the
abundance of the isotope X to be activated is Px
Then the number of target atoms N x is:
m N A Px
M
Where N A = Avogadros number (1.02 x1026 particles/Kmol)
Combining Eq.132 and Eq.133, gives:
Nx =
σ=
nMλ
φ ε p p N A Px m(1 − exp(−λt i ) ) (exp(−λt d )(1 − exp(−λt c )
73
74
γ
Using λ =
ln 2
T1
2
σ=
nM ln 2
T1 φ ε p p N A Px m(1 − exp(−λt i ) ) (exp(−λt d )(1 − exp(−λt c )
2
75
γ
Thus, Eq.135 gives the thermal neutron capture cross section of the element in the
sample [14], [15].
36
CHAPTER III
EXPERIMENT
3.1 Objective of the experiment
When a sample of an element irradiated with thermal neutrons it produces an induced
activity or emits gamma rays following a capture of neutrons. The gamma rays following
the 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 a separate series of study, there is a great capability of
determining the cross section of the neutron capture reaction, by detecting gamma rays
with a sensitive detecting system. In this experiment, delayed gamma rays emitted in
neutron capture reaction by 115 In will be measured. From the measurement, the thermal
neutron capture reaction σ of the
115
In ( n, γ )
116
Sn reaction will be deduced.
3.2 Materials used in the experiment.
◊ Thermal neutron source; Americium-beryllium neutron source of strength 2Ci is used.
◊ Plexiglas rod, used to place the foils of indium in the neutron source. The disturbance
of neutron flux at the center of the source due to the rod is negligible.
◊ Scintillation detector
- NaI (Tl ) detector fixed in PM tube.
-Linear amplifier
-Single channel analyzer
-Auto scaler
-Oscilloscope
◊ Indium foils
◊ Microgram (digital mass measuring system)
◊ Long-life standard radiation sources
- 60 Co
- 137 Cs
◊ Beta counter
◊ Stop watch (Digital timer)
◊ High and low DC voltage supply.
◊ Connecting cables of different length
37
3.3 Experimental set up
The figure of the measuring apparatuses are shown below. The basic principle behind
gamma spectroscopy used in the experiment is use of special materials, which glows or
“scintillates” when a radiation interacts with it. The most common type of such material
is a type of salt called sodium-iodide. The light produced from the scintillation process is
reflected through a clear window where it interacts with a device called a photo multiplier
tube.
A scintillator is a material that converts the energy lost by a radiation in to pulses of
light. The light emitted by the scintillating material can be detected by a sensitive light
detector, usually photo multiplier tube (PMT). The photo cathode of the PMT, which is
situated in the back side of the iterance window converts light photons in to photo
electrons. The photoelectrons are then accelerated by an electric field towards the
dynodes of the PMT where multiplication process takes place. The result is that each
light pulse (scintillation) produces a charged pulse on the anode of the PMT that can
subsequently be detected by other electronic equipment, analyzed or counted by a scaler
or a rate meter. The combination of a scintillator and a light detector is called scintillation
detector. The first part of the photo multiplier tube is made of another special material
called a photo cathode. The photo cathode has a unique characteristic of producing
electrons when light strikes its surface. These electrons are pulled towards a series of
plates, called dynodes through the application of a positive high voltage. When an
electron from the photo cathode hits the first dynode, several electrons are produced for
each initial electron hitting its surface. This “bunch” of electrons is then pulled towards
the next dynode, where more electrons “multiplication” occurs. The sequence continues
until the last dynode is reached, where the electron number is now millions of times
larger than it was at the beginning of the tube. At this point an anode at the end of the
tube forming an electronic pulse collects the electrons. The pulse is then detected or
displayed or counted by the system. Since the intensity of the light pulse emitted by
scintillator is proportional to the energy of the absorbed radiation, the latter can
determined by measuring the pulse height spectrum. This is called spectroscopy.
To irradiate a sample the Am-Be thermal neutron source is found in a cylindrical
container having five holes one is central hole giving non thermal neutrons, and the rest
four are situated around the face giving thermal neutrons. The Am-Be compound is at the
center of the cylinder giving high energy neutrons. The neutrons leading to the four holes
are moderated by a paraffin wax to thermal energy, hence putting a sample in to one of
these holes using a material which does not disturb the neutron flux at the center of the
hole for a pre determined period of time is called irradiation of the sample.
38
Fig 10. The schematic diagram of Am-Be neutron source.
5
3
2
4
1
6
Fig11: The set up of NaI(Tl) spectroscopy used in the experiment
1
2
3
4
5
6
= Sample holder
= NaI(Tl) crystal in aluminum case
= PM tube
= A system containing linear amplifier, SCA, auto scaler and Voltage supply
=Oscilloscope
= Stand base used to support the parts.
39
When a radiation enters in to the G-M tube (gas filed detector) it loses energy
ionizing the gases and a high voltage supplied through the center of the tube produces
intense electric field collecting the gas ions produced. The collected ions on the central
wire come out as an output for the G-M detector forming an electric pulse. The pulse is
detected by the counter giving digital information.
1
2
3
4
Fig 12: The set up of beta counter used in the experiment.
1= G-M tube.
2= Sample holder.
3= scaler.
4= Stand holding the parts.
40
3.4 Irradiation of the sample
The experiment has been performed at AAU department of physics. Foils of indium,
containing an isotope 115 In having a percentage abundant of 95.71%, were irradiated for
more than 24hrs using one of the pneumatic irradiation tubes of the Am-Be neutron
source found in an isolated room at about 500 meters from the nuclear laboratory. In
irradiation channel in the core an indium foil of known mass, in between two iodine
samples, is irradiated. While the samples in the Plexiglas rod are inserted for irradiation
in to the source of neutron, the time is recorded using a digit timer as the time of start of
irradiation. The neutron flux in the irradiation position in the given fixed geometry is
⎛ neutrons ⎞
1.0629 x 10 4 ⎜ 2
⎟.
⎝ m sec ⎠
3.5 Calibration of the detector (NaI (Tl) detector)
The next thing to do in the experiment is to energy calibrate the NaI (Tl ) detector. The
calibration is done by recording spectra of two standard gamma sources with well-known
gamma energies. The standards are available in the laboratory. The following table shows
a list of energies and energy-intensities of standard sources used in the calibration.
Source
137
60
Cs
Co
Energies
( Kev)
662
1173, 1333
intensity of the
Energies (%)
85
100, 100
Table 7 : Energies and intensities of the energies for the two standard sources used in the
experiment for the calibration.
The standards are placed close to the detector one by one and measurements of 100sec
for each of the standards is counted and stored in two tables, the following tables show
the data obtained around the peaks. The calibration spectrum for each of the standards
near the peak is plotted and stored as shown in the following graphs.The energy Vs
channel graph is plotted from the readings, which is called the calibration curve for the
detector.
41
Channel
12
13
14
15
16
17
18
19
20
21
22
23
counts(100sec)
7615
4746
3769
7856
18935
28233
22954
9552
1894
552
314
179
TABLE 8 : Counts with the channel number for
NaI(Tl) scintillation counter.
137
Cs standard around the peak, using
30000
C o u n ts /1 0 0 s e c
25000
20000
15000
10000
5000
0
10
12
14
16
18
20
22
24
C hannel
Graph 1 : Energy spectrum curve for
scintillation counter.
137
Cs standard radioactive source using NaI(Tl)
42
Channel
Counts(100sec)
25
921
26
874
27
860
28
998
29
1160
30
1419
31
1522
32
1327
33
1014
34
898
35
1068
36
881
37
648
38
367
39
215
40
70
TABLE 9 : Counts with the channel number for
using NaI(Tl) scintillation detector..
60
Co standard source around the peaks,
1600
c o u n ts /1 0 0 s e c
1400
1200
1000
800
600
400
200
0
24
26
28
30
32
34
36
38
40
42
C hannel
Graph 2 : Energy spectrum for
60
Co around the peak region using NaI(Tl) scintillation
43
Channel
Energy(Kev)
17
31
35
662
1173
1333
TABLE 10 : Gamma energy of standard sources with the peak position.
1400
Energy(Kev)
1200
Y=A + B(X)
A=0.06156+_0.369
-4
B=0.02675+_3.89E
1000
800
600
400
200
0
0
5
10
15
20
25
30
35
40
Channel
Graph 3 : Showing the energy calibration curve for NaI(Tl) scintillation spectrometer.
Using 137 Cs source, the threshold voltage for the beta-counter is determined by
taking readings of 100sec for different voltage. The data are fed to a computer installed
with origin program and the characteristic curve for beta counter is plotted.
44
3.6 Counting the activity of the sample
Once the energy calibration is finished, the foil is removed from the neutron source. The
exact clock time when this happens is recorded, using the same digit timer which was
used to record the time of start of irradiation, in order to identify the total time of
irradiation ( t i ). The samples are taken as fast as to the detector, found on the first floor of
physics department building in the nuclear laboratory. In the moment when the sample is
ready on the detector the clock time is recorded, this serves to determine the delayed time
t d , and search of a peak position is made a peak at channel 10.7 is obtained and more
than 50 measurements of 100sec is taken from this photo peak by adjusting threshold at 9
and window at 4. The readings obtained are stored in tables and fed to a PC where
origin-program is installed the delayed time was 147 sec. Two graphs, the counts Vs
time curve and the semi logarithmic curve, are plotted and stored, as shown below.
Time
Counts
Time
Counts
(sec)
(100sec)
(sec)
(100sec)
197
409
609
809
1009
1209
1409
1609
2009
2409
2609
2809
3009
3209
3609
3809
4029
4209
4409
4609
4809
5009
5232
5409
5609
18837±137.25
17929±133.89
17339 ± 131.67
16738± 129.37
15740±125.46
15167±123.15
14589±120.78
13892± 117.86
12732±112.83
12116±110.07
11138±105.54
11040±105.07
10213±101.05
10047±100.23
9152± 95.67
8875 ±94.20
8459± 91.97
8323 ± 91.23
7440±86.26
7365±85.82
6796± 82.44
6877± 82.92
6453±80.33
6108 ± 78.15
6080± 77.97
TABLE 11: Net counts obtained from
5809
6009
6409
6609
6809
7009
7209
7609
8009
8209
8409
8609
8809
9245
9609
10009
10409
10809
11209
11609
116
5623±74.98
5497±74.14
5065±71.17
4835± 69.53
4528 ± 67.29
4324± 65.75
4292± 65.51
4012± 63.34
3494± 59.11
3365± 58.01
3240± 56.92
3307±57.5
3008 ±54.84
2709±52.04
2460±49.60
2387±48.85
1991±44.62
1942±44.07
1843± 42.93
1751±41.84
In using gamma spectroscopy.
45
20000
18000
16000
Counts/100sec
14000
y = y0 + A exp(-x/t)
y0=-69.76694±106.51887
A=19736.82793±89.51534
t=4737.04378±67.03551
12000
10000
8000
6000
4000
2000
0
0
2000
4000
6000
8000
10000
12000
Time(sec)
Graph 4 : Exponential decay graph for
spectroscopy.
116
In as counted using NaI(Tl) gamma
To find the half life of the radioactive decay it is necessary to plot the semi logarithmic
graph of the data, i. e simply plotting the ln(counts / sec) Vs time graph. The slope of the
semi logarithmic graph is the decay constant of the radio active sample. Knowing the
decay constant one can find the half life of the radioactive sample used in the experiment
ln 2
simply using T1 =
[7]
76
decaycons
tan
t
2
The half life of
116
In from graph 5 is;
ln 2
sec
2.13337 x10 − 4
= 3249.0716 sec
3249.0716
=
= 54.1512 min
60
T1 =
2
46
5.5
5.0
y=a + b(X),
a=5.2836 +- 0.0066
-4
-6
b=-2.13337E +-1.05331E
Ln(counts/sec)
4.5
4.0
3.5
3.0
2.5
0
2000
4000
6000
8000
10000
12000
Time(sec)
Graph 5: Semi logarithmic curve for
spectroscopy.
116
In counts/sec using NaI (Tl) gamma
On the next day of the count, two samples of indium one bare and the other is in
cadmium cover are irradiated again for more than 24 hrs and counted the activities using
beta-counter. Using cesium standard source the variation of out put pulses with the
voltage of the G-M tube is recorded and the G-m tube characteristic curve is plotted as a
function of input voltage. The threshold voltage for the G-M tube is determined from the
plot before the samples are taken out from the irradiating hole of the Am-Be source.
Voltage
(Volt)
400
410
420
440
460
480
500
Counts/sec
0
342.8
416.5
446.7
443.1
449.2
456.7
Voltage
(Volt)
Counts/sec
520
540
560
580
600
464.9
463. 3
463.4
462.2
464.4
TABLE 12: Counts for different voltage in the G-M tube using cesium source.
47
c o u n ts /s e c o n d
500
400
300
200
100
0
400
450
500
550
600
G - m v o lt a g e
( v o lt )
Graph 6: Plateau characteristic curve for the G-M tube used by the experiment.
Counting the activities of the bare foil using the beta counter may help for a cross
check of results obtained from NaI(Tl) detector and to see whether there is appreciable
difference between the counts obtained from the foil in cadmium cover. The same
procedure of irradiation and counting is used as NaI (Tl ) detector the delayed time was
167 sec. Small activity is obtained from the sample, which was covered by cadmium,
compared to the activity of the bare sample. This may give an error in the result. The
counts obtained are stored and the counts from bare sample are plotted as shown below.
TIME
337
537
737
937
1137
1337
(sec)
COUNTS 441±21 453±21.3 425±20.6 407±20.2 392±19.8 411±20.2
(100sec)
TABLE 13: Counts obtained from indium sample in cadmium cover.
48
Time
(sec)
Counts
(100sec)
Time
(sec)
Counts
(100sec)
217
7121 ± 84.38
10597
816 ± 28.56
417
6882 ± 82.95
10817
791 ± 28.12
637
6579 ± 81.11
11037
772 ± 22.78
857
6242 ± 79.
11257
732 ± 27.05
1077
5860 ± 76.55
11477
675 ± 25.96
1297
5687 ± 75.41
11697
676 ± 26
1517
5460 ± 73.89
11917
622 ± 24.93
1739
5209 ± 72.77
12357
594 ± 24.37
1957
4946 ± 70.3
12577
551 ± 23.47
2177
4719 ± 68.69
12797
539 ± 23.21
2397
4528 ± 67.29
13017
451 ± 21.23
2617
4301 ± 65.59
13237
445 ± 21.09
2837
4122 ± 64.20
13457
432 ± 20.78
3057
3949 ± 62.76
13677
436 ± 20.88
3497
3614 ± 60.11
13897
432 ± 20.78
3717
3351 ± 57.88
14117
376 ± 19.39
3937
3255 ± 55.94
14557
322 ± 17.94
4377
2927 ± 54
14997
281 ± 16.76
4817
2747 ± 52.41
15217
260 ± 16.12
5037
2514 ± 50.13
15657
276 ± 16.61
5257
2538 ± 50.37
5477
2314 ± 48.13
5697
2198 ± 46.88
5917
2162 ± 46.49
6137
2030 ± 45.03
6357
1952 ± 44.18
6586
2022 ± 44.96
6797
1792 ± 42.33
7017
1786 ± 42.26
7237
1684 ± 4103
7457
1691 ± 40.01
7723
1550 ± 39.37
7897
1461 ± 38.22
8117
1435 ± 37.88
8337
1371 ± 3702
8557
1288 ± 35.88
8777
1231 ± 35.08
8997
1154 ± 33.97
9277
1137 ± 33.71
TABLE 14: Net counts obtained from the bare radioactive 116 In using beta counter
49
8000
7000
Counts/100sec
6000
5000
y = y0 + A exp(-x/C)
y0 = 0±0
A = 7448.40152±18.68907
C = 4803.37221±17.32292
4000
3000
2000
1000
0
0
2000
4000
6000
8000
10000 12000 14000 16000
Time(sec)
Graph 7: Exponential decay curve of the data obtained using the G-M counter for
sample.
116
In
50
4.5
4.0
Ln(count/sec)
3.5
y=A+BX
A=4.3381±0.01138
-4
-6
B= -2.13823E ±1.49133E
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
2000
4000
6000
8000
10000 12000 14000 16000
Time(sec)
Graph 8: Semi logarithmic curve of indium ( 116 In ) counts using beta counter.
From this curve, one can see that the half-life of
116
In is
ln 2
= 3241.6867sec
slope
= 54.028 min
3.7 Background measurement
A background count of the laboratory before and after the time of the experiment is
measured many times for longer duration and the average is taken for 100 sec and
recorded, whenever the detectors are used for the detection of photons. During the
measurements of the activity of the sample using NaI (Tl) gamma spectroscopy the
average background count was 2010 counts/100sec. Moreover, for the beta count the
average background count was 59 counts/100 sec. The background counts are subtracted
from each of the counts directly obtained from the counter to get net counts that are given
in the tables 12, 14 and 15.
51
CHAPTER IV
ANALYSIS AND CONCLUSION
4.1 Determination of efficiency of the detector
The detector counting efficiency DE relates the amount of radiation emitted by a
radioactive source to the amount measured in the detector. The DE can be used to
calculate the counting rate expected in a detector when the source strength is known or to
find the source strength by measuring the counting rate in the detector. The efficiency of
the detector can be found experimentally.
Experimental determination of an efficiency of a detector [10]
As mentioned above the detector efficiency ( DE ) is the ratio of the observed or measured
counting rate (total events in a known time interval) to the counting rate (total events
emitted by the radiation source).
D
DE =
77
N
Where: D = the photons counting rate in the detector.
N = number of photons emitted by the source.
Measuring D
For low energy photons, those that are observed as a photoelectric event in the detector,
D is the net counts in the photo peak for that energy. For NaI (Tl ) detector, photoelectric
events predominate for photons of 100KeV, Compton events become appreciable and,
above 2MeV, pair production events more observed. For these higher energy cases, it is
necessary to know the fraction of photo peak or peak-to-total ratio R so that the net
counts in the photo peak P can be related to the total counts in the detector.
P
78
R=
D
To count P open the window of the single channel analyzer to a value equal to the base
width of the peak, set the threshold at a voltage equal to the voltage at the left minimum
tail (set the baseline to the voltage of the minimum point of the peak at the left) and then
count to get the value of P .
Then D is determined from the number of counts in the photo peak divided by the
peak to total ratio.
52
D =
P
R
79
D Can also be obtained by counting all pulses above the noise threshold with a sample
in position and then counting all pulses with no sample in place. D is then obtained by
subtracting the two sets of total counts. The activity of a radioactive source is usually
given in curies (abbreviated Ci). One Ci is defined to be 3.7x1010dissintigrations per
second (dps).
Finding number of photons emitted by a source (N )
Number of photons emitted by a source can be calculated from the activity A by
multiplying the branching fraction BF for that mode of decay and the branching ratio BR
for that photon energy and the counting time interval T . Some times the total branching
ratio TB, which is the product of BF and BR, are given. Some typical values are shown in
the table below.
241
57
60
60
Radioactive source
Am
CO
CO
CO
E (keV)
59.5
122
1173
1332
Total branching
Ratio (TB)
0.36
0.86
1
1
Table 15: Table of branching ratios of known energies of standards [10].
137
Cs
662
0.85
N = BF x BR x T x A = TB x T x A
80
Where A = the activity in dps.
If the source calibration is not current, the source strength A must be corrected for
the elapsed time by the equation:
⎛ t⎞
A = A0 exp⎜ − ⎟
81
⎝ τ⎠
Where: A0 = The activity when calibrated.
t = the time interval since the source strength was calibrated.
τ = Mean life in the same unit as the time interval.
82
( τ = T1 x1.4427 )
2
By similar procedure, the photo peak counts and the total counts obtained by the
NaI(Tl) scintillation counter for different gamma energies of the standard radioactive
sources are summarized in the table below. At the time of the measurement, the
background was also measured.
53
Standard
radioactive
sources
(energy)
threshold
137
137
Above the
noise
threshold
14
60
Above the
noise
threshold
27
60
Above
noise
threshold
34
Cs (662)
Cs (662)
60
Co (1173)
Co (1173)
60
Co (1332)
Co (1332)
window
Total
counts in
100 sec
Photo peak
counts
Background
counts in
100sec
Net counts
(sec)
Peak to
total ratio
∞
125460
-
19283
1061.77
0.1864
6
-
38173
1358
368.15
∞
52888
-
19172
337.16
7
-
5156
401
47.55
∞
52888
-
19172
337.16
2
-
1819
187
16.32
0.141
0.0484
Table 16 : Summary of the measured values of the peak count and total count.
From the manufacturing information of the standard radioactive sources the source
strengths can be found using Eq.81. The following table is the manufacturing information
of the standard sources used.
Name of the standard
Strength when it is
manufacture
60
1 μCi
Co
137
Cs
5μCi
Year of
Manufacture
(half life)
Dec 1993
(5.27 Yrs)
Dec 1993
(30.07 Yrs)
Mean life
7.603Yrs
43.382Yrs
Table 17: Manufacturing information of standard sources used in the experiment.
(From the source holder)
The activity of cobalt
⎛ t⎞
A = A0 exp⎜ − ⎟
⎝ τ⎠
⎛ 13.42 yrs ⎞
⎟⎟
= 1 μCi exp⎜⎜ −
⎝ 7.603 yrs ⎠
= 6333 dps
N
= A X TB using Eq.80 and table 16.
54
= 6333 x 1 disintegrations. For counting time T=1sec
The activity of cesium
⎛ t⎞
A = A0 exp⎜ − ⎟
⎝ τ⎠
⎛ 13.42Yrs ⎞
⎟⎟
= 5μCi exp⎜⎜ −
⎝ 43.382 yrs ⎠
= 135776.6 dps
N = 135776.6 x 0.85 disintegrations, using Eq.80 and table 16.
= 115410 disintegrations, for counting time T=1sec
Then the efficiency of the detector for the energies of the standards obtained as
the in the following table.
Energy of gamma in
(KeV)
662
1173
1332
Net counts in the
detector in one sec
(D)
1061.77
337.16
337.16
Number of photons
emitted
(N)
115410.1155
63333
63333
Efficiency
(D/N)
0.0092
0.005323
0.005323
Table 18: Efficiency table of NaI (Tl) gamma spectroscopy used in the experiment.
55
0.014
Efficiency
0.012
0.010
Y = y0 + A exp(-X/C)
y0 =
A =
C =
0.008
0.00467
0.03958
303.90426
±0.00032
±0.00535
± 0.0023
0.006
0.004
400
600
800
1000
1200
1400
Energy(Kev)
Graph 9 : Efficiency Vs energy curve for NaI(Tl) gamma spectroscopy
4.2 Thermal neutron capture cross section
from measurements
Using Eq.75 the experimental value of the thermal neutron capture cross- section
can be found. At the time of the counting of the irradiated indium using NaI (Tl)
detector a peak was found at channel 10.7 corresponds to energy 417 KeV using
graph.3. The intensity of the gamma ray energy is 29 [13]
In Eq.135 if the counts at t = 0, is used then no need of using the correction term for
delayed time t d , i.e. taking counts at t=0 means no time is elapsed between the stop of
irradiation and the start of counting. Since the time of irradiation is more than 24 hrs,
the correcting factor for time of irradiation gives one.
i.e. (1 − exp (−λ t i ) = 1.
Applying these conditions Eq.75 reduces to:
56
σ=
n0 M λ
φ ε p p N A Px m (1 − exp(−λt c )
, where n0 is the rate of counts at t=0.
γ
The number of counts at t=0, can be found from graph 5. The equation of the graph is
B = -2.13337x 10 −4 .
Y = A + B X , X is time in sec, A = 5.2836 ± 0.006 and
Putting X = 0,
Y = 5.2836 ± 0.006
n0 = exp (Y )
= 197.08 ± 14.04
The efficiency of the detector for energy 417 KeV is 0.0147 using the equation of
graph 9. The mass of the indium foil used was 0.116 gm.
Hence;
gm
x 2.13337 x 10 − 4 s −1
mol
σ =
parti
neut
1.0629 x 10 4 2 x 0.0147 x 29 x 95.71 x 6.02 x 10 23
x 0.116 gm x 1 − exp(−2.13337 x 10 − 2
mol
m s
197.08 ± 14.04 x 115
(
σ =
σ =
4.8199 ± 0.3797
m2
26
6.392362597 x 10
75.6384 ± 5.389 barns. This is from the gamma spectroscopy.
The value of capture cross section from the beta counts can also be found using the same
equation Eq.135. 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 ray.
To find the efficiency for the beta counter,
1
(a exp(− μ1 ∑ d ) + b exp (− μ 2 ∑ d ) + C exp(− μ 3 ∑ d ))
Efficiency =
100
−1.14
, μ 2 = 17 E 2−1.14 and μ 3 = 17 E3−1.14 are mass
Where μ1 = 17 x E1
attenuation coefficients for beta energies E1, E 2 , and E3 . of indium decay
respectively.
∑d
is the sum of the thickness of different materials between the detector
and the source. The constants a, b and C are beta energy intensities of E1, E 2 , and E3 .
respectively [11].
57
)
During the experiment, there were three thicknesses between the detector and the
source, the detector window thickness the plastic tape cover thickness and the half
thickness of the indium foil. There were no air gap between the source and the detector.
m gm
and the plastic tape thickness (d2) is equal to
The window thickness (d1) is 2.5
cm 2
1 mass
the window thickness, and the half of indium foil thickness (d3) is
. The diameter
2 area
of the indium foil used was 1.3cm, hence the half of indium sample thickness is
mass
x2
∏ D2
d3
2 x 0.116
=
3.14 x (1.3)
2
= 0.043697
gm
cm 2
gm
gm
= 0.048697 2
2
cm
cm
There are three beta energies in the decay of indium sample:
E1 = 0.87 Mev , E 2 = 0.6 Mev and E3 = 1Mev . with corresponding intensities a =28,
∑d
= d1 + d 2 + d 3 = ( 0.0025 + 0.0025 + 0.043697)
b= 21 and c = 51 [13].
μ1 = 17(0.87 )
Efficiency =
−1.14
cm 2
= 19.925
gm
, μ 2 = 17(0.6)
−1.14
cm 2
cm 2
−1.14
= 30.434
= 17
and μ 3 = 17(1)
gm
gm
1
(28 exp(− 19.925 x0.048697 ) + 21exp(− 30.434 x 0.048697 ))
100
+
1
(51 exp(− 17 x 0.048697 ))
100
= 0.061 + 0.0477 + 0.1098
Efficiency = 0.2185
σ=
n0 M λ
φ ε p p N A Px m (1 − exp(−λt c )
γ
From graph 8, the number of counts at t = 0 is:
n0 =exp(4.3381)
n0 = 76 .5619 ± 8.7499
58
gm
x 2.13823 x10 − 4 s −1
mol
σ =
par
4 neutrons
1.0629 x10
x 0.2185 x 95.71 x0.116 gm x6.02 x10 23
x 1 − exp − 2.13823 x10 − 2
2
mol
m sec
76.5619 ± 8.7499 x 115
(
(
= 67. 2424 ± 6.4635 barns
This shows that the value obtained using the beta counter is in good agreement with the
value obtained using the NaI (Tl) gamma spectroscopy with an error less than 10%.
4.3 Comparison of the measured value of thermal neutron
Capture cross section with known values
The value of the thermal neutron capture cross section for indium is given in different
references [19] , [22], [23] and [24]. In [19] the thermal neutron capture cross section is
81.3 ± 8b, in [22] it is given as 81.3 b, in [23] 65 b and in [24] 88 b. The value obtained
from the experiment seems to be in good agreement with the value given in all of the
references. Even if the values given in the references are not much nearer to the
experimental value, generally the values are close to the present value with in an error
nearly 10 percent. This is because there may be errors due to different experimental
conditions.
4.4 Sources of errors
The sources of error that may alter the experimental value are the following.
1. The thermal neutron source used in the experiment is not giving 100%thermal
neutrons, it is checked by irradiating a sample of indium covered with cadmium
,which was thick enough to totally absorb the thermal neutrons, and bare sample
(with out cadmium cover). About 8% activity is obtained in the sample which was
in cadmium cover compared to the bare indium this shows the presence of
epithermal neutrons, and hence the presence of epithermal neutrons in the thermal
neutron source will give slightly low value of cross section. May be around 8%.
2. The detectors used in the experiment are less efficient in the detection purpose in
the given geometry. There may be an error due to this small detection efficiency of
gamma rays in NaI(Tl) detector, and use of a single channel analyzer which was not
supported by a computer system.
59
))
3. An error due to large distance between neutron source and the position where
detectors are found (Nuclear laboratory). This is because many daughter nuclei
decay with out detected by the detector when the irradiated sample is taken to the
detectors. Thus short life time can not be measured.
4. An error due to personal errors in measuring mass, area and time using different
instruments.
5. An error during data analysis, long decimals are rounded off to four decimal places.
4.5 Discussion and conclusion
Since non functioning of MCA, highly pure germanium (HP(Ge)) detector could not be
used. Hence work was done using NaI(Tl) gamma ray spectrometer having poor
resolutions. Due to non availability of MCA/computer all the data were recorded
manually which took long time in analysis. The experiment is performed in a huge
effort, all the data taken are repeated at least three or more times. While working to
calibrate the NaI (Tl ) gamma spectroscopy many repeated measurements are made
because once the calibration is finished, on another day it shifts the position of the
calibration, and hence another calibration data should be taken to recalibrate the detector
and the same is repeated again and again. This took about two months. There are no
relevant and recent references in the library of AAU. Much time is lost in searching the
web pages to get an information. The experimental result , the thermal neutron capture
cross section of indium and its half life 75.6384 ± 5.389 b and 54. 1512 min using
NaI(Tl) gamma spectroscopy , and 67.2424 ± 6.4635 b and 54. 03min using beta counter,
are in good agreement with one another and with the values given in different references
with in an error around 10%. This shows that the experiment is well performed.
60
REFFERENCES
[1] .
[2].
Donald Hughes, The neutron story, Doubleday and company,Inc. garden city, New York, 1959.
S.B,Garfinkel, Radioactivity and its measurement, Van nostrand campany,inc.1986,Newyork.
[3] .
L.F. Curtiss, Introduction to neutron physics, D. van nostrand company,inc., 1985
Newyorkdon.
4 . J. Dostal and C. Elson, General principle of neutron activation analysis, Mineralogical association
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of Canada, 1998.
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[8] .
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[10] .
K.N Mukhin, Experimental nuclear physics volume I, Mir publishers, 1987, Moscow.
European commission institute for transuranium elements, Neutron interactions
with matter, 2006 Germany.
Samuel S.M. Wong, Introductory nuclear physics, New Delhi, 2002, third Ed.
U.S. Department of energy, Hand book of nuclear physics and reactor theory volume 1 of 2,
Jan 1993, Washington D.C.
G.F. Knoll, Radiation detection and measurement, John wiley, 1989.
Efficiency calculations for selected scintillators.
Web: http://www.lip.pt/~luis/so.ft/bicron.eff.pdf
11 . R.D. Evans, Atomic nucleus, Mc-Graw-Hill, New York, 1955
[ ]
[12] .
[13] .
[14] .
S.N.Ghoshal, Atomic and nuclear physics Vol II, S. chand & company. New delhi 1997.
B. S. Dzhelepov and L. K. peker, Decay schemes of radioactive nuclei, London 1981
Avinash Agarwal, M.K. Bhardwaj, I.A. Rizvi, and A.K. Chaubey,
J. phys.soci. japan, 70, 2903 (2001).
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phys. Rev. C65, 034605 (2002)
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[16] .
[17].
W.E. Weyerhof, Elements of nuclear physics, Mc-Graw-Hill, New York, 1967.
URL for table of isotopes.
Web: http://te.lbl.gov/toi,htm
18 . Journal of nuclear and radiochemical science, cross section of thermal neutron capture
cross section , 6 No 3 , 2005.
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[19] .
International atomic energy agency, Hand book on nuclear activation data, technical reports Series .
No_273, Vienna, 1987.
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[ ]
61
[21] . EXFOR data library.
[22]. Chart of the nuclides, Strasbourg, 1992, France
[23] . Karlsruher Nuklidk, etal, Chart of nuclides, 1981, japan
[24]. Standard reference data national institute of standards and technology,
CRC Hand book of Chemistry and physics, A ready reference book of chemical and physical data,
CRC press, inc. 1996, New York.
62
Appendix
Pr.A.K.Chaubey
EXPLAINING HOW TO USE THE EXPERIMENTAL APPARATUSES
DURRING EXPERIMENT.
63