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University of Groningen
In-situ element analysis from gamma-ray and neutron spectra using a pulsed-neutron
source
Maleka, Peane Peter
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CHAPTER 2
INTRODUCTION
In 1803, Dalton proposed a set of postulates to describe the atom. In his
model, all matter was made of small particles called atoms. Also atom was considered
an elementary particles i.e. it was impossible to divide it into smaller particles. All of
the results of chemical experiments during that time indicated that the atom was
indivisible. With Thomson's discovery of the electron in 1897, it had already become
clear that atoms must have structure. Electrons are negatively charged particles and
constitute about 0.05% of the hydrogen atom mass. The notion of electron mass led to
the assumptions that most of the mass of an atom must reside in its positively charged
particle. Rutherford postulated in 1911 the atomic model in which the positive charge
and most of the mass of the atom resides in a very small region, less than 10-12 cm in
diameter and a small number of electrons enough to balance the positive charge are
distributed over a sphere of atomic dimensions. This positive centre later became
known as the nucleus.
In follow-up studies, Rutherford discovered the proton in 1919. Protons are
relatively large particles that have almost the same mass as a hydrogen atom and a
positive charge equal in magnitude to that of an electron. Experiments by Rutherford
revealed that the nuclear mass of most atoms surpassed the number of protons it
possessed; this led him to postulate the neutron whose existence would only be proven
in 1932 by Chadwick. This third subatomic particle, neutron, is slightly heavier than
the proton and is electrically neutral.
In 1895 Röntgen already discovered that when cathode rays struck certain
materials a new type of radiation was emitted, which he called X-rays. Becquerel in
1896, while studying the effect of X-rays on photographic film, discovered that some
materials spontaneously decompose and give off very penetrating rays. Pierre and
Marie Curie in 1898 studied uranium and thorium and called their spontaneous decay
process radioactivity. They also discovered the radioactive elements polonium and
radium.
Gamma-rays were discovered in 1900 by Villard. While studying uranium he
discovered that the rays were not bent by a magnetic field. At that time, gamma-rays
were assumed to be particles. In 1914, Rutherford and Andrade showed that gammarays were a form of electromagnetic radiation by measuring their wavelengths using
crystal diffraction. The wavelengths are similar to those of X-rays and are very short,
in the range 10-11 to 10-14 m. The distinction between the X-ray and gamma-ray
depends on the source of the radiation, X-ray photons are emitted in transition of
electrons between atomic shells and gamma-rays are emitted by excited nuclei in their
transition to lower-lying nuclear levels.
2.1
Neutron properties
Neutrons are the uncharged constituents of the nucleus and hence are highly
penetrating (see subsection 2.3.1). Neutrons are hadrons that are composed of two

1
down and one up quark, have spin-parity ( ) and a magnetic moment. The neutron
2
(at thermal energies) wavelengths are similar to atomic spacings. Outside the nucleus,
neutrons are unstable and called free neutrons with an average lifetime of (886.7 
13
INTRODUCTION
1.9) s. Free neutrons decay (beta (-)) by emitting an electron (e-) and antineutrino
 e to become a proton (p);
 
n  p  e   e
(2.1)
Neutrons are mainly classified according to their energies and their
classifications are presented in table 2.1. One other group of neutron class not
specified in table 2.1 is called the slow neutron group, referring to neutrons with
energies less than 1 eV, i.e. from epithermal neutrons down to cold neutrons.
Table 2.1: Classification of neutron energies.
Energy
En < 0.025 eV
En  0.025 eV
0.025 eV < En < 1 eV
1 eV < En < 500 keV
En > 0.5 MeV
2.2
Class
Cold neutrons
Thermal neutrons
Epithermal neutrons
Intermediate region
Fast neutrons
Gamma-ray properties
A gamma-ray is a packet of electromagnetic energy emitted by the nucleus of
some unstable, radioactive atoms. Gamma-rays have no mass and no electric charge.
Gamma-rays are emitted in the form of photons, discrete bundles of energy that have
both wave and particle properties. Gamma-ray photons have the highest energy in the
electromagnetic radiation spectrum and consequently their waves have the shortest
wavelength. These photons carry the energy released in a transition between states in
a nucleus. The time characteristics of their emission represents the half-life time of the
initial nuclear state, which is commonly a fraction of a second. Often gamma-ray
emission occurs after β-decay. The time characteristics then reflect the lifetime of the
β-decaying states and this may be very long, up to years. Gamma radiation is a very
high-energy ionising radiation, implying that it has enough energy to remove tightly
bound electrons from atoms.
2.3
Interaction of radiation with matter
Various types of radiation interact with matter in several ways. A large,
massive, charged alpha particle, emitted in natural decay, does not penetrate a thin
sheet of paper and even has a limited range in air. A neutrino, at the other extreme,
has a low probability of interacting with matter and can pass through the diameter of
the Earth or the Sun without being absorbed.
14
2.3.1 Neutron interaction with matter
Since neutrons are uncharged, their interaction with electrons in matter
proceeds via the magnetic moments of the two particles rather than the Coulomb
force. The neutrons interact with the nuclei of atoms through the strong nuclear
interaction. This hadronic interaction has a very short ranged, which means that the
neutrons have to pass close to a nucleus for an interaction to occur. Because of the
small size of the nucleus in relation to the atom, neutrons have a low probability of
interaction and can therefore travel considerable distances in matter.
When a neutron interacts with an atomic nucleus, the neutron can be scattered
(deflected or slowed down) or captured (absorbed). Elastic and inelastic scattering of
the neutron means that the atomic nucleus remains unexcited (in ground state) or is
excited (into an excited state), respectively. If a neutron is absorbed by a nucleus, a
compound nucleus is formed. The compound nucleus usually is formed in an excited
state and will decay by combination of gamma-radiation, particle emission or for
heavy nuclei by fission. 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 the same, the net effect of the reaction is as
if the projectile neutron had merely "bounced off" or scattered from the nucleus.
In an elastic scattering process shown in figure 2.1 between an incident
neutron and a target nucleus, there is no net energy transferred into nuclear excitation.
Elastic scattering of neutrons by nuclei can occur in two ways. The more unusual of
the two interactions is the absorption of the neutron, forming a compound nucleus,
followed by the re-emission of a neutron in such a way that the total kinetic energy is
conserved and the nucleus returns to its ground state. This is known as resonance
elastic scattering and depends upon the initial kinetic energy of the neutron, the
atomic mass (A) and atomic number (Z) of the nucleus. Due to the formation of the
compound nucleus, it is also referred to as compound elastic scattering. The other
more usual method is the potential elastic scattering and this 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 of up
to about 1 MeV. In potential scattering, the neutron does not actually touch the
nucleus and no compound nucleus is formed. Instead, the neutron is acted on and
scattered by the short-range nuclear force when it approaches close enough to the
nucleus. The two interactions are not distinguishable experimentally.
Figure 2.1: Schematic presentation of the neutron elastic scattering process
(CANDU04).
15
INTRODUCTION
Momentum and kinetic energy of the system are conserved. The target nucleus
gains the amount of kinetic energy that the neutron loses and the scattering angles are
determined by the conservation of momentum. The maximum energy Qmax that a
neutron of mass m and kinetic energy En can transfer to a target nucleus of mass M in
a single elastic collision occurs in a head-on collision (Krane, 1988);
Qmax 
4  m  M  En
(2.2)
m  M 2

4  m  En
for M >> m
M
(2.3)
Expressing masses in units of atomic mass numbers, the neutron has mass m =
1 and the maximum fraction of a neutron's energy that can be lost in a collision with
nuclei of atomic-mass number (M) rapidly decrease for M ≠ 1. In a collision with
hydrogen nucleus (atomic mass of 1, the same mass as the neutron), the neutron can
loose almost all of its energy according to eq. 2.2 (Knoll, 2000). From eqs. 2.2 & 2.3,
it follows that elastic scattering on a light nucleus is the most efficient way to
moderate (slow down) fast neutrons.
In an inelastic scattering process, schematically shown in figure 2.2, the
incident neutron enters the nucleus for a brief period and forms a compound nucleus.
The compound nucleus will then emit a neutron (any) and a gamma-ray photon, and
thus will be reverting back to the target nucleus. The direction of the emitted neutron
is more/less random. A distinction between the elastic and inelastic scattering is that
elastic scattering can occur at any neutron energies while the inelastic process requires
excitation of the nucleus and is most probable for fast neutrons (via threshold
reactions).
Figure 2.2: Schematic presentation of the neutron inelastic scattering process
(CANDU04).
Instead of re-emitting a neutron as in inelastic scattering, the compound
nucleus may emit an alpha particle or a proton. This process is called particleemission reaction and is illustrated for an alpha particle (4He) emission in eq. 2.4.
1
n 
10
B 
 B
11
*
16
 7 Li 
4
He
(2.4)
In a radiative capture reaction, the compound nucleus looses its excitation
energy by emitting a gamma-ray. In contrast to the inelastic scattering, the neutron is
not re-emitted, the nucleus is converted into a heavier isotope of the target-nucleus
element. An example of a radioactive capture reaction is shown in eq. 2.5. Radiative
capture can practically occur with all types of nuclei and at all neutron energies, but is
more probable with slow neutrons than with fast neutrons.
1
n 
1
H  2H  
(2.5)
Another possible reaction is fission, in which a heavy nucleus that absorbs the
neutron splits into two or more medium-heavy fragments. Table 2.2 summarises the
neutron interactions with atomic nuclei classified according to their energy. The
classifications in table 2.2 illustrate the more probable interactions with atomic nuclei
and the neutron energies are represented by three classes from table 2.1.
Table 2.2: Classification of neutron interactions with atomic nuclei (Beckurts and
Wirtz, 1964). Fission is denoted by f.
Slow neutrons
(En < 1 keV)
Intermediate energy
(1 keV < En < 500 keV)
Fast neutrons
(0.5 MeV < En < 20
MeV)
Potential (elastic) scattering
Light nuclei
(A < 25)
Resonance scattering;
Reactions (n,p), (n,), (n,2n)
Resonance scattering; Radiative capture
Intermediate
nuclei
(25 < A < 80) Potential
scattering
Inelastic scattering;
Reactions (n,p), (n,),..
(n,2n)
Inelastic scattering
Heavy nuclei
(A > 80)
Radiative capture
Reactions (n,f), (n,2n)
17
INTRODUCTION
2.4
Neutron interaction cross section
The rate of neutron interactions depends on the incoming neutron flux and the
cross section for interaction. The cross section is the probability of a neutron
interacting with the material. The cross section for a particular reaction does not only
depend on the kind of nucleus involved but also on the energy of the neutron. The
absorption of a slow neutron in most materials is much more probable than the
absorption of a fast neutron. At low energies, neutron cross sections are smooth
functions of energy while at higher energies they are dominated by resonances due to
the presence of favourable states in the compound nucleus at these energies, see for
example figure 2.3. An illustration in figure 2.3 shows that in the inelastic scattering
with an 56Fe nucleus a neutron energy of at least 1 MeV is required. Both the capture
reaction and elastic scattering are probable at all neutron energies with resonance
structures clearly dominating at higher energies.
3
Neutron cross-section (barns)
10
Capture
Elastic scattering
Inelastic scattering
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-11
10
-9
10
-7
-5
10
10
-3
10
-1
10
1
10
En (MeV)
Figure 2.3: An example showing the cross section for three neutron interaction
processes as a function of energy with the nucleus, 56Fe (Data source - JEF-PC
Software, 1998).
The possibility of a particular reaction occurring between a neutron and a
nucleus can be derived from the microscopic cross section (σ). The microscopic cross
section may also be regarded as the effective area that the nucleus presents to the
neutron for a particular reaction. The larger the effective area, the greater is the
probability for the reaction. The microscopic cross section is an area and is often
expressed in units of barn, and 1 barn is equivalent to 10-28 m2.
Microscopic neutron cross-section data are determined from experimental data
as a function of energy for each nuclide and each reaction. In general, these data
cannot be interpolated over large energy intervals because of the irregular resonance
structures. Shown in figure 2.4 is an example of the total (i.e. due to elastic, inelastic,
capture, etc) microscopic cross section plots for the 56Fe and 57Fe nuclei as a function
18
of energy. The differences between two iron isotopes 56Fe and 57Fe indicate that the
data cannot be interpolated readily between nuclides; each nucleus has its own
structure. As a result, measurements, calculations and evaluations of neutron cross
sections for a particular element have to be separately worked out for each isotope,
tabulated and updated whenever new information becomes available.
3
10
Neutron cross-section (barns)
56
Fe
57
Fe
2
10
1
10
0
10
-1
10
-11
-9
10
10
-7
-5
10
10
-3
10
-1
10
1
10
En (MeV)
Figure 2.4: Total microscopic cross section for two iron isotopes, 56Fe and 57Fe (Data
source - JEF-PC Software, 1998).
Whether a neutron will interact within a certain volume of material depends
not only on the microscopic cross section of the individual nuclei but also on the
number of nuclei within that volume. Therefore, it is suitable to describe another type
of cross section known as the macroscopic cross section (Σ). The macroscopic cross
section is the probability of a given reaction occurring per unit length the neutron
travelled. The macroscopic cross section, Σ (m-1) is related to the microscopic cross
section σ (m2) by the relationship shown in eq. 2.6 and is a function of neutron energy
E.
E   N   E 
(2.6)
with N (m-3) the atom density of the material defined in eq. 2.7 below.
The atom density is the number of atoms of a given type per volume of the
material. The atom density for individual materials can be calculated using the
equation,
N
  NA
(2.7)
M
19
INTRODUCTION
where  is the density of the material in (kg m-3), NA the Avogrado number (6.022 x
1023 mol-1) and M the atomic weight in (kg mol-1).
Macroscopic cross sections have the dimension of inverse length, and are
interpreted as the probability per unit path length that a specific process/interaction
will occur. Microscopic cross sections represent an effective target area that a single
nucleus presents to a bombarding particle, while a macroscopic cross section
represents the effective target area presented by all nuclei contained in 1 m 3 of
material. The average distance travelled by a neutron before interaction, known as the
mean free path  (m), is related to the macroscopic cross section Σ (m-1), by

1

(2.8)
Macroscopic cross sections for neutron reactions with materials determine the
probability of one neutron undergoing a specific reaction per metre of travel through
that material. The number of actually occurring reactions will depend on the neutron
flux. The distance these neutrons can travel per second will be determined by their
mean velocity, v (m s-1).
A way of defining the neutron flux () is to consider it to be the total path
length covered by all neutrons in one cubic metre during one second. Mathematically,
this translate to eq. 2.9,
  nv
(2.9)
where  (m-2 s-1) is the neutron flux, n (m-3) the neutron density and v (m s-1) the
neutron velocity. The neutron density, n (m-3), is the number of free neutrons moving
through a unit volume of material.
The rate Rx (m-3 s-1) at which a particular nuclear reaction will take place is
related to the neutron f l ux, the cross section for the interaction and the atom density
of the target as,
Rx    ( N   )
(2.10)
 
(2.11)
where  (m-2 s-1) is the neutron flux, N (m-3) the atom density,  (m2) the microscopic
cross section and  (m-1) the macroscopic cross section. It should be noted that eqs.
2.10 and 2.11 hold as well for a particular energy (see also eq. 2.6) as for an
interaction over a certain energy range.
The intensity of the neutron beam will decrease exponentially when traversing
a material with thickness d by (Lewis and Miller, 1984),
I  I 0  e  tot d
(2.12)
where, tot is the total macroscopic cross section for all processes occurring in the
material:
tot  inelasticscattering elasticscattering capture....
20
(2.13)
Equations 2.12 and 2.13 hold for mono-energetic beams as well as for beams
with a particular energy distribution.
2.5
Gamma-ray interaction with matter
Because gamma-rays have no mass and no charge, they need, like neutrons, an
indirect way to transfer energy. Therefore gamma-rays, compared to charged particles
have high penetrating power. Gamma radiation interacts with matter through electrons
mainly via three processes: photoelectric effect, Compton scattering and pair
production.
2.5.1 Photoelectric effect
In the process of photoelectric absorption the incident gamma-ray photon is
completely absorbed by an electron of an atom. The photoelectron is ejected with a
kinetic energy:
Ee  E  Eb
(2.14)
with E the photon energy and Eb the binding energy of the electron in its
original shell. Usually this binding energy is small compared to the photon energy and
can be ignored.
There is no analytical expression describing the cross section for the entire
range of gamma-ray energies (E) and atomic numbers Z. The general trend for the
cross section per unit mass for the photoelectric absorption  (m2 kg-1), can be
approximated by:
   Const.  Z n  E3.5
(2.15)
with n varying between 4 to 5 over the gamma-ray energy region of interest
(Knoll, 2000; Koomans, 2000). The strong Z dependence indicates that a high-Z
material is very effective in the absorption of low-energy -ray photons.
2.5.2 Compton Scattering
In the process of Compton scattering, a -ray photon is scattered off an
electron of an atom and energy and momentum are transferred to the recoil electron
according to the conservation laws of momentum and energy. The effect is
schematically illustrated in figure 2.5. The photon loses only part of its energy to the
recoil electron.
From the conservation of energy and momentum, the energy E ' of the
outgoing photon is related to the scattering angle  at which it is emitted by:
21
INTRODUCTION
E ' 
E
E
1   2 1  cos 
m0c
(2.16)
with E the incident photon energy, m0c2 = 0.511 MeV, the rest-mass energy of an
electron. The recoil energy of the electron Ee is therefore given by:
Ee  E  E '
(2.17)
E'
E
Ee
Figure 2.5: Schematic presentation of a Compton-scattering process (Hendriks,
2003).
The angular distribution of scattered gammaNishina formula for the atomic differential scattering cross section d/d:
d   Zr02 
1

d
2  1   1  cos  2

 2 1  cos  2  
1  cos 2  

1   1  cos    

-
(2.18)
where   E /m0c2 (photon energy in units of electron rest energy), r0 is the classical
electron radius and Z the charge of the scattering nucleus (Knoll, 2000). This
distribution becomes more and more forward peaked with increasing photon energy.
The probability of Compton scattering decreases with increasing photon
energy. Compton scattering is considered to be the principal absorption mechanism
for gamma-rays in the intermediate energy range: 100 keV to 10 MeV. The cross
section for Compton scattering per unit mass  (m2 kg-1), is given by:
   Const.  E1
(2.19)
It follows from eq. 2.19, that the probability for Compton scattering is
independent of the atomic number of the material through which the gamma-ray
traverses, and only depends on its density.
2.5.3 Pair-production
In pair production, the photon is converted into an electron-positron pair in the
Coulomb field of the nucleus. Since the energy of twice the rest mass of the electron
22
(m0c2) is required to create the electron-positron pair, this process only occurs for E >
1.022 MeV. The excess energy equal to the photon energy minus 1.022 MeV (2 x
m0c2), is shared by the electron and positron as kinetic energy. When the positron has
lost its kinetic energy it will form an intermediate state with an electron (positronium)
and subsequently annihilate with an electron, producing two photons with energy E =
0.511 MeV. To conserve momentum, the two photons are emitted in opposite
directions in the centre of mass system of the electron-positron pair. Since the process
mainly occurs after the positron has slowed down also in the laboratory system, the
two photons are emitted back to back.
The cross section for pair-production per unit mass  (m2 kg-1) increases with
atomic number Z and the square of the gamma-ray energy E:
   Const.  Z  E2
(2.20)
Pair-production becomes the dominant process for photon energies E > 3
MeV.
2.6
Implications for neutron detection
Because neutrons produce no direct ionisation events, neutron detectors are
based on detecting the secondary events produced by nuclear reactions, such as (n,p),
(n,α), (n,γ) or by nuclear scattering from light charged particles which are then
detected (Lilley, 2001; Knoll, 2000; Krane, 1988). The general principle of detecting
neutrons involves a two-step process; first the neutron must interact in the detector to
form charged particles and secondly the detector must then produce an output signal
based on the energy deposited by these charged particles. Thus the key aspects to
effective neutron detection are hardware and software. Hardware refers to the kind of
neutron detector used (the most common today is the scintillation detector) and to the
electronics used in the detection set-up. Software consists of analysis tools that give
for example graphical results for analysing the number and energies of secondary
particles reaching the detector.
The most widely used methods for fast neutron detection is based on elastic
scattering of neutrons by light nuclei (Knoll, 2000). In this interaction, an incident
neutron transfers a portion of its kinetic energy to the scattering nucleus, resulting in a
recoil nucleus and a neutron, see also subsection 2.3.1 and figure 2.1. Because the
target materials are mostly light nuclei, the recoil nucleus behaves much like a proton
or alpha particle as it loses its energy in the detector medium. The most effective
target nucleus is hydrogen because its cross section for neutron elastic scattering is
relatively large and its energy dependence is accurately known. Neutrons can transfer
an appreciable amount of energy in one collision with a hydrogen nucleus or even
lose all their energy. The energy (ER) given to the recoil nucleus is uniquely
determined by the scattering angle θ (see also eq. 2.2).
ER 
4A
1  A2
cos  
2
23
En
(2.21)
INTRODUCTION
where A is the mass number of the target nucleus, En the incoming neutron
energy.
A head-on collision of the incoming neutron with the target nucleus will lead
to a recoil in the same direction (  0), thus resulting in the maximum possible recoil
energy. For such collisions, eqs. 2.2 and 2.21 show that in a single collision with a
hydrogen nucleus (A =1), a neutron can transfer all its energy whereas only a small
fraction can be transferred in collisions with heavy nuclei.
When a mono-energetic fast neutron strikes a material containing hydrogen,
the energy spectrum of the recoiling protons forms a continuum extending from zero
(for small angle scattering in eq. 2.21) to full energy for head-on collisions. Some
information about the original energy of the neutrons can be deduced by recording the
pulse-height spectrum from a hydrogen-containing detector. Thus for a hydrogenous
material bombarded with neutrons of energy En, the spectrum W(Ep) of recoil protons
in the laboratory system will have a rectangular shape (Lilley, 2001; Krane, 1988) of
the form:
W ( E p )  const
(2.22)
W (E p )  0
(2.23)
for Ep  En and
for Ep > En.
Because of non-linear light-response of the scintillator detectors, amplitude
resolution, edge effects and multiple neutron scatterings by the detector materials, the
measured spectrum deviates from the almost perfect rectangle (Krane, 1988),
illustrated also in figure 2.6.
Similarly to eq. 2.21, for momentum and energy conversation in an elastic
collision, the final energy of the neutron (Ef) after scattering is given by,
E f  En  ER
(2.24)
 A 2  1  2 A cos  
E f  En 

 A  12


(2.25)
or
where En is the incoming neutron energy, A the mass number of the target
nucleus and  the scattering angle (Krane, 1988). The average number of collisions,
nc, which is required to moderate a fast neutron with kinetic energy En to kinetic
energy Ef in hydrogen (i.e. A = 1) is equal to:
E
nc  ln  n
E
 f


  1  ln  En

E

 f




(2.26)
 E 
with the parameter ln n  known as the logarithmic energy decrement, ξ.
 E f  av
For A > 1,
24
  1
 A  12 ln
2A
A 1
A 1
(2.27)
The average value of lnEf decreases after each collision by , and after n
collisions, the average value of lnEf is given by eq. 2.28;
ln E f  ln En  nc
(2.28)
Ep = En
Ep
Figure 2.6: Schematic presentation of an ideal spectrum of proton recoils induced by
mono-energetic neutrons and the modification of such a spectrum caused by detector
resolution and scintillator non-linearity (Krane, 1988:p455).
The cross section for neutron interactions in most materials is a strongly
varying function of neutron energy, hence several methods are developed for neutron
detection in various energy regions, see table 2.1 and table 2.2 for example. For slowneutron detection, neutrons are detected via nuclear conversion reactions to a charged
particle (for example (n,α), (n,p)) (Knoll 2000; Krane, 1988) and all techniques used
to detect slow neutrons are based on charged particle detection (Knoll, 2000). For
nuclear reactions that will be useful for slow neutron detection, it is important that the
cross section for the reaction is as large as possible so that efficient detectors can be
built with small dimensions. Hence most of the widely used slow-neutron detectors
contain (10B) or (6Li). The thermal neutron cross sections for the 10B(n,α)7Li and
6
Li(n,α)3H reactions are 3840 and 940 barns, respectively (Knoll, 2000). An example
given by Knoll (2000) estimates that with a 10 mm thick crystal prepared with highly
enriched 6LiI, the efficiency is almost 100% for neutrons with energies from thermal
(0.025 eV) to the cadmium absorption energy of 0.5 eV (Knoll, 2000). Thus 6Li is one
of the favourite components of a crystal because of its relatively large capture cross
section for thermal neutrons. The reaction shown in eq. 2.29 illustrates the process,
6
Li  1 n  4 He  3 H
25
(2.29)
INTRODUCTION
where the Q-value of about 4.78 MeV is shared between the alpha particle
( He) and the tritium (3H) (Knoll, 2000).
4
2.7
Implications for gamma-ray detection
Radiation detectors will in principle give rise to an output signal for each
quantum of radiation that interacts within its active volume. For the detector response,
gamma-rays must undergo one of the interaction mechanisms in the detector as
discussed in section 2.5. When a gamma-ray enters a detector medium, it transfers
part or all of its energy to an atomic electron, thus freeing the electron from its atomic
bond. This freed electron usually transfers its kinetic energy in a series of collision to
other atomic electrons in the detector medium as illustrated in figure 2.7. For a
gamma-ray detector, it must act as a conversion medium in which incident gamma
rays have a reasonable chance of interacting to yield one or more fast electrons and
also function as a conventional detector for these secondary electrons.
The top part of figure 2.7 shows a typical example of the interaction processes
that a photon will likely undergo inside the detector crystal, and the bottom part shows
an example of a typical resulting gamma-ray spectrum. As shown in figure 2.7, the
dimensions of the detector medium are also important, especially for Compton
scattering processes occurring at the edges of the detector medium. The electron range
with kinetic energy of a few MeV in typical solid detector media is a few millimetres
(Knoll, 2000). For the photoelectric absorption process, as long as it happens within
the detector medium, the information about the gamma-ray can be derived.
The bottom part of figure 2.7 shows a spectrum of the energy deposited in the
detector by incident photons. Its main feature is the full-energy peak (often called
photopeak). This peak stems from those events in which, in one or more steps, the full
photon energy was deposited in the detector. The peak position corresponds to the
energy of the original gamma-radiation, E = h. This makes the full-energy peak a
very useful feature in gamma-ray spectrometry. The continuum results mainly from
the single or multiple Compton-scattering events. In a Compton-scattering process, a
variable part of the photon energy is deposited via electrons, followed by the escape
of the scattered photon. This continuum reaches up to the Compton edge, which
corresponds to the maximum electron energy given by eq. 2.16. A succession of
multiple Compton events can result in a total deposited energy, which is higher than
the value corresponding to the Compton edge. For gamma-radiation with E > 1.022
MeV pair production can add two more peaks to the spectrum. The single escape peak
correspond to the initial pair production interactions in which only one annihilation
photon leaves the detector without interaction and the double escape peak is due to
events in which both annihilation photons escape.
2.8
Summary and conclusion
In this chapter, the interactions of neutral particles like neutrons and gammarays with matter have been described. An understanding of all these processes
discussed will be important to unfold and analyse the signal spectra obtained by the
NuPulse instrument radiation detectors. Neutrons are mainly detected via recoil
protons and charged particles produced in nuclear reactions, whereas gamma-rays are
26
detected by their interaction with electrons. The processes form the basis for the
detectors used in the NuPulse instrument design and optimisations e.g. via Monte
Carlo simulations. In the analyses and discussions of the spectra obtained with the
NuPulse instrument the processes described in this chapter will be used.
The next chapter introduces the NuPulse instrumentation, optimisations and
analysis procedures. A description of all components is mapped out including some
possible tool configuration. Chapter 3 will also introduce the reader to some of the test
facilities where the assembled tool was tested and optimised at the KVI.
Figure 2.7: Schematic example of γ-ray interaction processes in a detector medium
and the resulting spectrum for a mono-energetic source (from Knoll, 2000: p316).
27
INTRODUCTION
28