2nd Year Radiation Detection and
Measurement
By
Dr. P.H. Regan, Room 31BC21, Tel. x2701
Lecture Notes 1997
recommended texts,
Radiation Detection and Measurement G.K. Knoll
and Introductory Nuclear Physics Kenneth S. Krane
Contents
1 Sources of Radiation.
1.1 Electrons. : : : : : : : : : : : : : : : : : : : : : : : :
1.1.1 , + Decay. : : : : : : : : : : : : : : : : : :
1.1.2 Internal Conversion. : : : : : : : : : : : : : :
1.1.3 Auger Electrons. : : : : : : : : : : : : : : : :
1.2 Heavy Charged Particles. : : : : : : : : : : : : : : : :
1.2.1 -Decay. : : : : : : : : : : : : : : : : : : : : :
1.2.2 Spontaneous Fission. : : : : : : : : : : : : : :
1.3 Electromagnetic Radiation. : : : : : : : : : : : : : :
1.3.1 Gamma Rays. : : : : : : : : : : : : : : : : : :
1.3.2 Natural Radioactivity : : : : : : : : : : : : :
1.3.3 Bremsstrahlung. : : : : : : : : : : : : : : : : :
1.3.4 Characteristic X-rays. : : : : : : : : : : : : :
1.4 Neutron Sources. : : : : : : : : : : : : : : : : : : : :
1.4.1 Neutrons from Spontaneous Fission. : : : : : :
1.4.2 Beta Delayed Neutron Emission. : : : : : : : :
1.4.3 -Beryllium Neutron Sources. : : : : : : : : :
1.4.4 Photo-neutron Sources. : : : : : : : : : : : : :
1.4.5 Reactions from Accelerated Charged Particles.
2 Interactions of Radiations with Matter.
2.1 Units and Denitions. : : : : : : : : : :
2.1.1 Activity. : : : : : : : : : : : : : :
2.1.2 Exposure and Absorbed Dose. : :
2.1.3 Dose Equivalent. : : : : : : : : :
2.2 Interactions of Radiation with Matter. :
2.3 Interaction of Heavy Charged Particles. :
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2
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5
8
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23
2.3.1 Ranges and Stopping Powers.
2.3.2 The Bethe Formula. : : : : :
2.3.3 Stopping Time. : : : : : : : :
2.4 Fast Electrons. : : : : : : : : : : : :
2.5 Interaction of Gamma-rays. : : : : :
2.5.1 Photoelectric Absoprtion. : :
2.5.2 Compton Scattering. : : : : :
2.5.3 Pair Production. : : : : : : :
2.5.4 Attenuation Coecients. : : :
2.6 Interactions with Neutrons. : : : : :
2.6.1 Fast Neutrons. : : : : : : : :
2.6.2 Slow Neutrons. : : : : : : : :
3 General Detector Properties.
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3.1 Pulse Mode and Current Mode. : : : : : : : : : : : : : :
3.2 Pulse Height Analysis. : : : : : : : : : : : : : : : : : : :
3.3 Energy Resolution : : : : : : : : : : : : : : : : : : : : :
3.3.1 Full Width at Half Maximum. : : : : : : : : : : :
3.3.2 Gaussian Peak Shapes. : : : : : : : : : : : : : : :
3.3.3 The Fano Factor. : : : : : : : : : : : : : : : : : :
3.4 Detection Eciency. : : : : : : : : : : : : : : : : : : : :
3.4.1 Peak to Total Ratio and Intrinsic Peak Eciency.
3.5 Detector Timing and Dead Time. : : : : : : : : : : : : :
3.5.1 Rise Time. : : : : : : : : : : : : : : : : : : : : : :
4 Types of Detector.
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4.1 Gas Filled Detectors. : : : : : : : : : : : : : : : : : : : : : : : : : : :
4.1.1 The Ionization Process in Gases. : : : : : : : : : : : : : : : :
4.1.2 W-Value. : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
4.1.3 Recombination. : : : : : : : : : : : : : : : : : : : : : : : : : :
4.1.4 Drift Velocity : : : : : : : : : : : : : : : : : : : : : : : : : : :
4.1.5 Ionization Chambers. : : : : : : : : : : : : : : : : : : : : : : :
4.1.6 Avalanche/Proportional Counters. : : : : : : : : : : : : : : : :
4.1.7 Multiwire Proportional Counters (PPAC, MWPC or PWAC).
4.1.8 Geiger-Muller Tubes. : : : : : : : : : : : : : : : : : : : : : : :
4.1.9 Gas Detector Summary. : : : : : : : : : : : : : : : : : : : : :
ii
24
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49
4.2 Scintillation Detectors. : : : : : : : : : : : : : : : : : : : : : :
4.2.1 Photomultiplier Tubes. : : : : : : : : : : : : : : : : : :
4.2.2 Types of Scintillation Detectors. : : : : : : : : : : : : :
4.2.3 Organic Scintillators. : : : : : : : : : : : : : : : : : : :
4.2.4 Plastic (organic) Scintillators. : : : : : : : : : : : : : :
4.2.5 Inorganic Scintillators. : : : : : : : : : : : : : : : : : :
4.2.6 Phosphor Sandwich (`Phoswich') Detectors. : : : : : :
4.2.7 Photodiodes. : : : : : : : : : : : : : : : : : : : : : : :
4.3 Semiconductor Detectors. : : : : : : : : : : : : : : : : : : : :
4.3.1 Band Structure in Semiconductors. : : : : : : : : : : :
4.3.2 N and P-type Semiconductors. : : : : : : : : : : : : : :
4.3.3 Semiconductor Junction Diodes and Depletion Layers.
4.3.4 Reverse Biasing. : : : : : : : : : : : : : : : : : : : : : :
4.3.5 Dead Layer. : : : : : : : : : : : : : : : : : : : : : : : :
4.3.6 Silicon Surface Barrier Detectors. : : : : : : : : : : : :
4.3.7 Lithium Drifted Silicon Detectors, Si(Li). : : : : : : : :
4.3.8 Germanium Detectors. : : : : : : : : : : : : : : : : : :
4.4 Gamma-Ray Spectroscopy with Germanium Detectors. : : : :
4.4.1 Response Function of Germanium Spectra. : : : : : : :
4.4.2 Germanium Detector Eciency. : : : : : : : : : : : : :
4.4.3 The Compton Suppressed Spectrometer (CSS). : : : :
4.5 Neutron Detectors. : : : : : : : : : : : : : : : : : : : : : : : :
4.5.1 Slow Neutrons. : : : : : : : : : : : : : : : : : : : : : :
4.5.2 Fast Neutron Detection. : : : : : : : : : : : : : : : : :
5 Problems
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5.1 Set 1 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 71
5.2 Set 2 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 73
5.3 2RD exam 1996. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 74
iii
List of Tables
1.1 Examples of -decay energies (Knoll p8). : : : : : : : : : : : : : : : : 10
1.2 K-shell X-ray energies as a function of Z (atomic number). : : : : : : 16
2.1 Quality factors for dierent radiations. : : : : : : : : : : : : : : : : : 22
2.2 Path lengths for radiations in typical materials. : : : : : : : : : : : : 23
3.1 Typical resolutions for various detectors. : : : : : : : : : : : : : : : : 38
4.1 Summary of gas detector properties. : : : : : : : : : : : : : : : : : : 49
4.2 Some commonly used scintillator materials. : : : : : : : : : : : : : : : 52
iv
List of Figures
1.1 Electron energy spectrum for beta-decay. of 152 Eu (Kibedi et al). : : :
1.2 Gamma-decay following beta-decay of the parent nucleus. : : : : : : :
1.3 Schematic of nuclear decay giving rise to gamma-rays or conversion
electrons. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
1.4 Comparison of internal conversion electon spectra and gamma-ray
spectra for 202 Po (Kibedi et al.). : : : : : : : : : : : : : : : : : : : : :
1.5 Discrete peaks from internal conversion above a continuous beta-decay
background from a 152 Eu source (Kibedi et al.). : : : : : : : : : : : :
1.6 Schematic of X-ray/Auger emission. : : : : : : : : : : : : : : : : : : :
1.7 -particle spectrum for a mixed alpha source (R. Cowin, U. of York,
1996). : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
1.8 Binding energy per nucleon as a function of mass (Krane p67). : : : :
1.9 Energy (=mass) distribution of spontaneous ssion fragments (Knoll
p11). : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
1.10 Examples of gamma-decay following beta and alpha decay. : : : : : :
1.11 Decay chain of 239 Pu giving rise to natural radioactivity : : : : : : : :
1.12 Bremsstrahlung radiation spectrum (Knoll p15). : : : : : : : : : : : :
1.13 Energy spectrum of neutrons from spontaneous ssion (Knoll p21). :
1.14 Beta-delayed neutron decay of 17 N (Krane p305). : : : : : : : : : : :
Tracks of particles from 210 Po decay (see Krane p194). : : : : : : :
CHARISSA E vs DE telescope detector. : : : : : : : : : : : : : : : :
E vs dE plot for CHARISSA detector. : : : : : : : : : : : : : : : : :
Photoelectric cross-section as a function of energy in lead (Krane p199).
Compton scatttering of a -ray o an electron. : : : : : : : : : : : : :
Gamma-ray attenuation coecients for Al and Pb as a function of
energy (Krane p203). : : : : : : : : : : : : : : : : : : : : : : : : : : :
2.7 Schematic of loss of gamma-ray intensity through a thickness dx. : : :
2.1
2.2
2.3
2.4
2.5
2.6
v
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31
3.1
3.2
3.3
3.4
Schematic of a pre-amplier circuit for pulse mode operation. : : :
Pulse shapes for charge and voltage collection in pulse mode. : : :
Schematic of a circuit used for pulse height analysis experiments.
Schematic showing the resolution (FWHM) of a peak. : : : : : : :
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4.1 Applied voltage verses pulse height for gas detectors (Krane p162,
Knoll p207). : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
4.2 Schematic of a simple ionization chamber. : : : : : : : : : : : : : : :
4.3 Schematic of a proportional counter. : : : : : : : : : : : : : : : : : :
4.4 Field lines in a PPAC. : : : : : : : : : : : : : : : : : : : : : : : : : :
4.5 Schematic of a Geiger-Muller tube. : : : : : : : : : : : : : : : : : : :
4.6 Energy levels in an organic scintillator (Knoll p217). : : : : : : : : : :
4.7 Schematic of a scintillation detector (Krane p208). : : : : : : : : : : :
4.8 Schematic of a photomultiplier (Krane p212). : : : : : : : : : : : : :
4.9 Schematic showing sum of fast and slow component in a scintillator. :
4.10 Time of ight discrimination using NE213 scintillator. : : : : : : : : :
4.11 Band structure for an inorganic insulator (Krane p210). : : : : : : : :
4.12 Use of a phoswich, dE vs E detector. : : : : : : : : : : : : : : : : : :
4.13 Depletion layer from pressing P and N-type semiconductor together
(Krane p215). : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
4.14 Surface barrier silicon detectors for alpha-spectroscopy (Knoll p377).
4.15 A germanium detector. : : : : : : : : : : : : : : : : : : : : : : : : : :
4.16 Gamma-ray interactions in a germanium crystal (Knoll p297). : : : :
4.17 Gamma-ray spectra for (a) 137 Cs and (b) 60 Co sources. : : : : : : : :
4.18 Gamma-ray spectra for (a) 152 Eu and (b) 133 Ba eciency calibration
sources. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
4.19 A Compton suppressed germanium detector : : : : : : : : : : : : : :
4.20 Time of ight discimation between gamma-rays and fast neutrons
(Mohammadi et al. 1995). : : : : : : : : : : : : : : : : : : : : : : : :
4.21 Fast/slow component pulse shape discimation between gamma-rays
and fast neutrons (Mohammadi et al. 1995). : : : : : : : : : : : : : :
1
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70
Chapter 1
Sources of Radiation.
We can categorise radiation into 2 main groups.
(1) Charged particulate radiation made up from fast electrons or heavier charged
particles (protons, s, heavy-ions).
(2) Uncharged radiation such as electro-magnetic radiation ( -rays, X-rays) and neutrons.
For this course, the radiations all come from either ATOMIC or NUCLEAR processes. Energies can range from 10eV!20 MeV, ie. radiations with energies large
enough to cause ionisation. (Note Cs has the lowest ionisation potential, 3.6 eV).
1.1 Electrons.
Electron radiation can be caused by (or +) decay, internal conversion or Auger
processes.
1.1.1
, + Decay.
(Krane p275,281, Knoll p4)
Beta decay is caused by the interaction of the weak nuclear force, which transmutes neutrons to protons (or vice versa) with the release of electrons (or positrons)
and anti-neutrinos (or netrinos). The processes can be summaried by,
AX
Z N
! AZ 1YN +1 + + + AX
Z N
! AZ+1YN 1 + + or
2
Fermi-Kurie plot; ANU SUPER-e; Aug ‘95; 0.72-6.2 Amps
200
152Eu
sqrt(N)
150
100
50
0
0
400
800
energy [keV]
1200
Figure 1.1: Electron energy spectrum for beta-decay. of 152 Eu (Kibedi et al).
-decay often populates excited states in the daughter nucleus and may therefore
be followed by -decay.
Some nuclei decay directly to the ground state in the daughter and are known
as pure beta emitters.
Since beta decay may populate several excited states in the daughter, the observed
beta spectrum may consist of several components (with dierent end points).
3
parent nucleus
β -decay
Ex
Eγ
2
2
Ex 1
Eγ
1
0
daughter nucleus
Figure 1.2: Gamma-decay following beta-decay of the parent nucleus.
Some nuclei decay directly to the ground state in the daughter and are known
as pure beta emitters.
Since beta decay may populate several excited states in the daughter, the observed
beta spectrum may consist of several components (with dierent end points).
The Q-value is the TOTAL ENERGY RELEASED in the process which is shared
between the electron (or positron, +) and the anti-neutrino (or neutrino).
n
o
Q = M (A X ) M (AY ) c2
where the masses M are the neutral atomic masses.
(1.1.1)
Q = Te + E
(1.1.2)
ie. the energy is shared between the electron, (anti-)neutrino and the recoil
energy of the daughter nucleus. This three body reaction gives rise to a continuous
electron energy spectrum (see g 1.1).
4
1.1.2 Internal Conversion.
(Knoll p5, Krane p341).
Unlike beta decay, which produces a continuous spectrum, the nuclear process of
internal conversion produces electrons with quantised (xed) energies.
An excited nuclear state usually decays via the emission of a -ray. Occasionally
however, this type of decay is inhibited (this is particularly true for low energy
gamma-rays below about 100 keV). The excitation energy is then transferred to one
of the orbital, atomic electrons, which is emitted from the atom. The kinetic energy
of the released electron is given by
KEe = Ex Eb
(1.1.3)
where Ex is the excitation energy released by the nuclear decay and Eb is the
binding energy of the atomic electron. Internal conversion electron energies range
from a few keV upto 5 MeV.
excited nuclear state
γ− ray
or conversion
electron.
E2
E γ= E2-E1
E e= E2-E1-BE of electron
E1
lower energy state
Figure 1.3: Schematic of nuclear decay giving rise to gamma-rays or conversion
electrons.
Most conversion electrons occur from interactions with the innermost or 1s electrons, called the K-shell, but emissions from higher atomic shells such as the L and
M also occur.
The internal conversion coecient, , is dened by
= e
5
(1.1.4)
202Po
442.7
where is the probabilty of electron emission compared to gamma decay (Krane
p 343). The TOTAL decay probabilty (T ) is then given by
gammas
delayed (35 - 550 ns)
676.8
571.2
800
x102
counts
912.1
526.2
385.7
400
0
electrons
442.7
571.2
676.8
4000
2000
912.1
385.7
526.2
0
400
600
800
transition energy (K) in Po [keV]
1000
Figure 1.4: Comparison of internal conversion electon spectra and gamma-ray spectra for 202 Po (Kibedi et al.).
6
108
107
122
152Eu IC electrons and β --rays
fitted β- spectrum
106
245 344
411
444
586
615
656
counts / η SW(E)
105
104
689 779
867 964
1086
1112
1408
103
102
Q β = 386
Q β = 696
101
Q β = 1064
100
0
500
1000
electron energy [keV]
Q β = 1475
1500
Figure 1.5: Discrete peaks from internal conversion above a continuous beta-decay
background from a 152 Eu source (Kibedi et al.).
7
T = (1 + )
(1.1.5)
If is the TOTAL internal conversion coecient, we can dene the PARTIAL
coecients for emission from the dierent atomic shells
T = + e;K + e;L + e;M :::: = (1 + K + L + M :::)
where
(1.1.6)
= K + L + M ::::
(1.1.7)
For example, Thallium (Tl, Z=81), the binding energies for the various electron shells are given by B(K)=85.53 keV, B(LI )=15.35 keV, B(LII )=14.70 keV
and B(MI )=3.70 keV. For the 279.19 keV nuclear decay, the energies of the respective internal conversion electrons are Te(K)=193.66 keV, Te(LI )=263.84 keV,
Te(LII )=264.49 keV and Te(MI )=275.49 keV.
Conversion electron sources are often beta-decay sources which decay to excited
states in the daughter. Therefore, often the conversion electron energy spectrum
sits ontop of a continuous beta-decay spectrum (see g. ). Commonly used sources
include 109 Cd, 113 Sn, 133 Ba, 137 Cs, 139 Ce, 152 Eu and 207 Bi.
1.1.3 Auger Electrons.
(Knoll p6)
Auger emission is an atomic process, whereby an electron is ejected. A preceding
process leaves the atom with a vacant electron orbital. Usually, a higher lying
electron will drop into the vacant level and the energy gained (from increasing the
total binding energy) is emitted in the from of an X-ray (electro-magnetic radiation).
If the binding energy of E1 >E2 then the energy of the emitted X-ray is given by
EX ray = E2 E1
(1.1.8)
Occasionally, instead of an X-ray, the energy is transferred to an outer lying
electron, causing it to be ejected from the atom. The emitted (Auger) electron has
an energy given by
EAuger = (E2 E1 ) Eb
8
(1.1.9)
electrons
E2
X-ray
E x= E2 - E1
E
e
= (E2-E1)-BE (electron)
E1
hole/vacancy
Figure 1.6: Schematic of X-ray/Auger emission.
where Eb is the binding energy of the shell from which the Auger electron was
emitted.
Auger electron emission is favoured for low-Z (atomic number) materials where
the electron binding energies are small (10 eV). Note that the energies of Auger
electrons are typically about 3-6 orders of magnitude smaller than those observed in
beta decay or electron conversion.
1.2 Heavy Charged Particles.
Heavy charged particle type radiation usually means -decay or heavier products
from spontaneous ssion.
1.2.1
-Decay.
(Knoll p7-8, Krane p246-248)
Alpha decay is a nuclear process. Due to binding energy per nucleon eects,
heavy nuclei are unstable against the emission of a 4He nucleus, also known as an
-particle. -decay is a Coulomb repulsion eect and therefore becomes increasingly
more important for heavier nuclei. This is because although the total nuclear binding energy of a nucleus increases roughly with A the atomic mass, the (repulsive)
Coulomb force which reduces the binding energy force increases as Z 2 (where Z is
9
the number of protons (atomic number) in the nucleus).
Spontaneous -emission can be represented by
AX
Z N
!AZ 42 YN 2 + (4He)
(1.2.10)
The energy released in this process is given (as usual) by the Q-value where,
Q = fMX MY M g c2
(1.2.11)
ie. the Q-value is equal to the total mass-energy of the parent before the decay
minus the total mass energy of the decay products.
The total energy released is divided between the kinetic energies of the recoiling
-particle and the daughter nucleus (and possibly into intrinsic excitation energy of
the daughter if the decay goes to an excited nuclear state in the daughter).
The kinetic energy of the alpha-particle is given by,
Q
(1.2.12)
1 + MMY
Typically the -particle carries away about 98% of the Q-value in kinetic energy.
Typical Q-values are around 5 MeV.
Multiple decay branches can occur whereby the daughter is left in dierent excited states. The alpha particle energy spectrum may therefore have a number of
discrete peaks corresponding to decays to dierent (discrete) levels in the daughter. Note that conversely the energy dierence between these alpha spectrum peaks
allows one to know the energy dierence between excited states in the daughter
(alpha-spectroscopy).
Parent Nucleus Half Life T (MeV)
148 Gd
93 yrs
3.183
232 Th
1.4 1010 yrs 4.012
3.953
235 U
8
7.110 yrs
4.598
4.401
4.374
4.365
4.219
238 Pu
88 yrs
5.499
5.456
Table 1.1: Examples of -decay energies (Knoll p8).
KE () = T =
10
60.0
239
50.0
40.0
241
Am
5486 KeV
5157 KeV
Pu
244
5806 KeV
Counts
Cm
30.0
20.0
10.0
0.0
0.0
200.0
400.0
600.0
800.0
Energy (channels)
1000.0
Figure 1.7: -particle spectrum for a mixed alpha source (R. Cowin, U. of York,
1996).
1.2.2 Spontaneous Fission.
(Knoll p7-11, Krane p67)
All heavy nuclei (A>100) are in principle unstable against breakup into two (or
occasionally more) lighter systems. This is due to the shape of the binding energy
per nucleon curve which peaks for 56 Fe and decreases with increasing mass above
this.
Figure 1.8: Binding energy per nucleon as a function of mass (Krane p67).
The heavy nucleus breaks up into two smaller fragments (binary ssion) which
11
Figure 1.9: Energy (=mass) distribution of spontaneous ssion fragments (Knoll
p11).
have larger binding energies per nucleon ( EAB ) than the parent nucleus. The ssion fragments are often left in excited states which (usually) decay via gamma-ray
emission. A few (2-5) fast neutrons are also usually released in this process.
Due to nuclear shell eects, ssion is a predominantly asymmetric process where
the fragments are distributed about two masses (a `rabbit's ears' distribution). By
conservation of momentum, the ssion fragments are emitted in opposite directions.
1.3 Electromagnetic Radiation.
For the purposes of this course, there are two main types of em radiation, gammarays which come from nuclear decays and characteristic X-rays which come from
atomic or molecular decays. Since the nuclear binding energies are much larger than
the atomic electron binding energies, gamma-rays are typically much more energetic
than X-rays. Typical characteristic X-rays energies range from a few eV upto 100
keV while typical gamma-ray energies are between 30 keV upto 10 MeV.
1.3.1 Gamma Rays.
(Knoll p11, Krane p355)
Gamma-rays are emitted when a nucleus decays from an excited state to a quantum state of a lower energy. The energy gained is emitted in the form a photon or
-ray (see gure 1.3).
The energy of the emitted gamma-ray, E is given by
12
E = E1 E2 = h
(1.3.13)
where E1 and E2 are the excitation energies of the initial and nal nuclear states.
h is Planck's constant and is the frequency of the e-m radiation.
Most gamma-ray sources are created after beta-decay leaves the daughter in an
excited state which subsequently decays via gamma emission. Gamma-rays can also
be emitted following alpha-decay.
242
Cm
60
Co
27
beta - decay
alpha-decay
branches
1173 keV
6
4
1332 keV
2
60
28
0
Ni
238
+
+
+
+
Pu
Figure 1.10: Examples of gamma-decay following beta and alpha decay.
Annihilation Radiation.
(Knoll p13)
If a nucleus undergoes + decay, the emitted positron can combine with an atomic
electron in the surrounding material. The positron-electron pair will disappear (they
are said to annihilate each other) and be replaced by 2 photons (gamma-rays), each
with an energy of 511 keV (the rest masses of both the electron and positron). Note
that to conserve momentum, the two 511 keV gamma-rays must be emitted back to
back, ie. in opposite directions.
Gamma-Rays Following Nuclear Reactions.
(Knoll p4)
Gamma-rays can also be emitted from excited states of nuclei formed by nuclear
reactions.
1
eg. 42He + 94Be ! 12
6 C + 0n
13
The 12 C nucleus is left in an excited states which decays (very rapidly) by the
emission of a gamma-ray. This sort of reaction can occur naturally, (eg. in stars or
from natural radioactivity) or can be produced using an accelerator in the laboratory.
(The accelerator is required to give the projectile enough energy to overcome the
Coulomb repulsion between the two positively charged nuclei and get them close
enough (10 14m) for the the attractive nature of strong nuclear force to dominate,
causing the two nuclei to fuse together).
Other examples of nuclear reactions are neutron capture,
eg.
179 Hf
74
+ 10 n ! 180 Hf ! 180 Hf + and heavy-ion fusion-evaporation reactions,
96
114 110
eg. 18
8 O + 40 Zr ! 48 Cd ! 48 Cd + 4n + 1.3.2 Natural Radioactivity
The decay of elements heavier than bismuth (Z=83) in the environment gives rise
to natural radioactivity, made up of , and decays and electron conversion.
Figure 1.11: Decay chain of 239 Pu giving rise to natural radioactivity
14
1.3.3 Bremsstrahlung.
(Knoll p14, p45 Krane p196)
Electrons emitted in beta decay travel at relativistic speeds. When these electrons
interact with matter, the electron's velocity goes through very quick changes in
both magnitude and direction, ie. acceleration (or rather deceleration) takes place.
Accelerated charged particles radiate electromagnetic energy and this radiation is
called Bremsstrahlung or `braking radiation'.
The fraction of the electron energy which is turned into bremsstrahlung increases
with electron velocity and with the atomic number (Z) of the stopping material. The
bremsstrahlung spectrum is a continuous distribution with an end point equal to the
kinetic energy of the electron.
Figure 1.12: Bremsstrahlung radiation spectrum (Knoll p15).
The lower energy photons dominate the spectrum and the average photon (or
X-ray) energy is only a small fraction of the incident electron energy.
1.3.4 Characteristic X-rays.
(Knoll p15-17)
If orbital electrons are excited to higher energy states, after a short time (10 9s)
the atomic electrons will rearrange themselves to the lowest energy conguration or
ground state. As the electrons drop from one shell to a more bound orbital, energy
is released in the form of X-rays which are characteristic of the atomic number (Z)
of the material (see gure 1.6).
If a vacancy is created in the K-shell of an atom (the most bound, or 1s orbital),
when this is lled by an electron from a higher shell, a K, X-ray will be emitted. If
15
the electron drops from the L shell to the K shell, a K X-ray will be emitted with
an energy (E (K )) given by,
E (K) = EL EK
(1.3.14)
If the lling electron originated in the M shell, then a K X-ray is emitted with
energy given by
E (K ) = EM EK
(1.3.15)
If the K-shell is lled by a free or unbound electron, the maximium photon energy
will be equal to the binding energy of the K-shell orbital.
Vacancies created in the outer shell caused by electrons dropping down and lling
the K shell are subsequently lled by electrons from even higher levels. In this way,
characteristic L, M etc X-rays are also emitted.
Since they have the largest energy and highest yield, the K-series X-rays are the
most important. The energy of the characteristic K-shell X-rays varies rapidly with
atomic number ( Z 2) as table 1.2 shows.
Element
E(K-shell)
Na (Z=10) Ga (Z=31) Ra (Z=88)
1 keV 10 keV 100 keV
Table 1.2: K-shell X-ray energies as a function of Z (atomic number).
(For a list of X-ray energies see Table of Isotopes by Lederer and Shirley vol 7.
appendix III)
X-ray sources can be formed by bombarding a target with higher energy radiation
to create excited or ionised atoms which subsequently decay via X-ray emission.
Incident radiation can include X-rays themselves, electron beams or heavy charged
particles.
Fluorescent Yield.
Auger electrons can compete with X-ray emission for decays of excited atomic states.
The uorescent yield is dened as the fraction of times that a given excited atom
emits a characteristic X-ray (rather than an Auger electron) in its de-excitation.
1.4 Neutron Sources.
(Knoll p20-21, Krane p445)
16
If nuclei are created (via ssion or beta decay) at excitation energies large than
the neutron binding energy, the nucleus may decay via neutron emission.
1.4.1 Neutrons from Spontaneous Fission.
Neutrons can be emitted in spontaneous ssion with energies ranging from about
0.1 MeV upto about 10 MeV.
Figure 1.13: Energy spectrum of neutrons from spontaneous ssion (Knoll p21).
by
Note that the energy spectrum for ssion neutrons has a continous nature, given
dN = E 12 e ET
dE
where N is the number of neutrons of energy E and T is a constant.
(1.4.16)
1.4.2 Beta Delayed Neutron Emission.
(Knoll p20, Krane p302-306)
If the daughter in beta decay is left in an excited state where the excitation is
larger than the neutron binding energy, neutrons with discrete kinetic energies can
be emitted.
17 +
16
1
eg. 17
7 N ! 8 O (+ + ) ! 8 O + 0 n
In the case of 17N, the beta decay leads to the population of states in 17 O at excitation energies of 5.950, 5.387 and 4.548 MeV respectvely. The neutron separation
for 17 O is only 4.144 MeV, therefore the neutrons will be emitted with (discrete)
kinetic energies.
17
4.1 secs
17
N
7
0
β−
5950
neutron
decay
5387
4549
0
Sn = 4144 keV
0
17
O
8
16
O
8
Figure 1.14: Beta-delayed neutron decay of 17 N (Krane p305).
1.4.3
-Beryllium
Neutron Sources.
(Knoll p21)
Neutron sources can be created by placing some light elements such as Be (Z=4),
Boron (Z=5) and carbon (Z=6) together with a heavy, decaying material (such as
Amercium). The emitted alpha particle can fuse with the lighter elements to form
a compound nucleus which emits a neutron.
Examples include
9 Be+4 He ! 12 C+ 1 n
4
2
6
0
10 B + 4 He ! 13 N + 1 n
5
2
7
0
13 C + 4 He ! 16 O + 1 n
6
2
6
0
1.4.4 Photo-neutron Sources.
In a photo-neutron source a gamma-ray is used to excite a nucleus past the neutron
separation energy. Note that for this to happen, the energy of the gamma-ray must
be larger than the total Q-value for neutron separation.
eg. 21 H + ! 11H + 10n
18
1.4.5 Reactions from Accelerated Charged Particles.
Accelerated particles can be used to induce reactions which emit neutrons.
eg. D+D = 21H + 21 H ! 32He + 1n , Q=+3.26 MeV
or D+T = 21 H + 31H ! 42He + 1n , Q=+17.6 MeV
(Note that these reactions have been proposed for generating power from nuclear
fusion).
19
Chapter 2
Interactions of Radiations with
Matter.
2.1 Units and Denitions.
When measuring radiation, it is important to know not just how much there is but
also how damaging it is. This section will deal with the various ways of quantifying
radiation.
2.1.1 Activity.
(see Knoll p2, Krane p162)
The activity, A is dened as the rate of decay. Radioactive decay is a statistical
process which is governed by the fundamental law,
A = dN
dt = N
(2.1.1)
where is the decay constant, N are the number of atoms present at time t.
Note that the activity only tells us the number of disintegrations which take place
per second. It tells us NOTHING about the type of radiation or its energy.
The SI unit of activity is the Becquerel (Bq) which is dened as one disintegration
per second.
The more commonly used unit for activity is the Curie (Ci) which is dened as
the activity in 1 gram of pure 226 Ra.
1 Curie = 3.71010 Bq
The SPECIFIC ACTIVITY is dened as the activity per unit mass.
20
2.1.2 Exposure and Absorbed Dose.
(see Knoll p59, Krane p184)
The activity of a sample does not tell us anything about (i) the energy of the
radiation or (ii) the possible biological damage from a source. The activity does
NOT take into account the nature of the radiation.
eg. Does 1 mCi of 60 Co ( + ) do as much damage as 1 mCi of 238 Pu (+ ) ?
Exposure.
The exposure measures the number of electrons `knocked o' (or the ionizing power)
du to the radiation in air. (This quantity is usually only used for gamma and x-ray
sources.)
The exposure, X , is dened as the total electric charge (Q) created by the radiation in a material (usually air) of mass M . ie
Q
X=M
(2.1.2)
The SI units for exposure are Coulombs per kilogram (C/Kg), however, the
historical unit of the Roentgen, R is often used. The Roentgen is dened as the
expsoure that results in 1 electric charge per 1cm3 of air at STP (normal pressure).
Since 1cm3 has a mass of 0.001293 grams,
10 19 C = 2.58 10 4 C/Kg
1 Roentgen = 10::6001293
Kg
Exposure Rate.
(Knoll p60, Krane p185)
The amount of ionization produced by each gamma-ray depends on its energy,
a 1 MeV gamma-ray will cause more ionization than a 100 keV gamma-ray. The
:
exposure rate X is dened by
: dX
A
(2.1.3)
X = dt = d2
where A is the activity and d is the distance of the source (usually taken at 1
metre. is the exposure rate constant for the particular source.
For example,
24 Na { ,
137 Cs - ,
= 1.369, 2.754 MeV, =1.8 Rm2/hCi
= 0.032, 0.662 MeV, =0.3 Rm2/hCi
21
Absorbed Dose.
(see Knoll p61, Krane p186)
The absorbed dose is the energy absorbed per unit mass in the absorbing material
due to radiation. The SI unit is the Gray (Gy) dened as
1 Gy = 1 Joule per kilogram = 1 J/Kg
Also used as a unit of absorbed dose is the rad dened as
1 rad = 100 ergs/gram
2.1.3 Dose Equivalent.
The dose equivalent or DE, measures the biological eect of radiation. This is important since dierent types of radiation aect biological material in dierent ways.
The SI unit for the DE is the Sievert (Sv), dened by
1 Sv = 1 Gy Q , where Q is the `QUALITY FACTOR'
Table 2.1: Quality factors for dierent radiations.
Radiation Type
Quality Factor, Q
x-rays , ,
1
low energy protons and neutrons
2{5
high energy protons and neutrons
5{10
alpha particles
20
2.2 Interactions of Radiation with Matter.
As we have seen, there are two main types of radiation, (a) charged particulate radiation such as electrons, -particles, heavy-ions, ssion fragments) and (b) uncharged
radiations including x-rays, gamma-rays and neutrons.
The charged particle like radiation will continuously interact with the electrons in the detector medium through which they pass due to the Coulomb
interaction.
22
The uncharged radiations require a sudden interaction with the particles in the
target material (eletrons and nuclei) which will cause a secondary eect (such
as the scatter of electrons) which can be detected. ( rays create secondary
electrons, neutrons produce secondary heavy charged particles).
Typical path lenths for the four main types of ionizing radiation for typical
materials are given in table 2.2.
Radiation Type
path length
x-rays , -rays
10 1m
neutrons
10 1m
fast electrons
10 3m
s, heavy charged particles 10 5m
Table 2.2: Path lengths for radiations in typical materials.
Note that neutrons, x-rays and gamma-rays may easily pass through a material
without any interaction taking place at all.
2.3 Interaction of Heavy Charged Particles.
(see Knoll p31, Krane p193.)
The dominant interaction for heavy charged particles in matter comes from the
Coulomb scattering from the orbital electrons in the stopping material. Nuclear
eects are much less important due to the relatively small size of the nucleus (NB.
volume (atom): volume (nucleus) is about 1015:1).
The maximum energy that can be transferred in a single (head on) collision can
be calculated (using conservation of energy and linear momentum) as
e
dE = 4Em
(2.3.4)
M
where E is the kinetic energy of the ion, me is the electron mass and M is the
mass of the ion. Since me << M , dE is a small fraction of the total energy and
therefore many electron collisions are needed to absorb all the energy of the ion.
At any given time, the ion is interacting with many electrons. The net eect is to
continuously decrease the energy of the ion.
The paths of heavy charged particles as they pass through materials tend to be in
straight lines (until E 0, where this is some straggling at the end). This is because
(a) the ion is not deected much in each interaction and (b) the ion is interacted on
23
continuously from all sides by many dierent electrons causing any deection to be
cancelled out.
Figure 2.1: Tracks of particles from 210 Po decay (see Krane p194).
2.3.1 Ranges and Stopping Powers.
Charged particles are characterised by a RANGE in a given absorber material. This
is the distance beyond which no charged particles will penetrate. The range R can
be dened by,
!
1
dE
R=
dX dE
T
where dE
dx =S , the linear stopping power or specic energy loss.
Zo
(2.3.5)
2.3.2 The Bethe Formula.
(see Knoll p32, Krane p194)
The BETHE FORMULA is
2
4 Q2
4
e
1
dE
(2.3.6)
S = dx = m v2 NB 4
0
o
where N is the number density of the stopper material. If Z is the atomic number
of the stopper material, v is the velocity of the ion, c is the speed of light and Q is
the average charge of the ion then,
(
2
B = Z ln 2mI0v
!
2
ln 1 vc2
24
!
v2
c2
!)
(2.3.7)
where I is the average ionisation potential for the absorber, which is usually
determined experimentally. (For air, I =86 eV, for aluminium, I =163 eV).
Note that
dE 1 1 Q2
(2.3.8)
dx v2 E
Therefore, those particles with the greatest charge will have the largest specic
energy loss, ie. alpha-particles lose energy faster than protons of the same velocity.
The amount of energy deposited in a thin slice of material can be used to identify
the dierence between dierent types of charged particles (eg. protons and alphaparticles).
Since E = 12 mv2,
dE Q2 mQ2
(2.3.9)
dx v2
E
Therefore, if E , the total energy and dE the energy loss in a thickness dx are
known, particles of dierent m (or atomic masses A) and Q (related to atomic
number, Z) can be separated.
Figure 2.2: CHARISSA E vs DE telescope detector.
2.3.3 Stopping Time.
(see Knoll p38)
The stopping time is the time required for a particle to stop in an absorber.
Assuming that the average particle velocity as the ion slows down is given by < v >,
and
25
25.0
521
225
169
72
54
40
30
23
17
13
9
8
7
6
5
4
3
2
1
0
Gas Energy / MeV
127
95
Si
20.0
15.0
Mg
10.0
Ne
O
5.0
C
0.0
0.0
50.0
100.0
150.0
Silicon Energy / MeV
Figure 2.3: E vs dE plot for CHARISSA detector.
< v >= kv
(2.3.10)
where v is the initial velocity and k is a constant, then the stopping time T , is
given by
s
R mc2
T = < Rv > = kc
(2.3.11)
2E
where R is the range of the absorber.
Typical values of k are about 0.6 (since particles lose a greater fraction of their
energy at the end of the stopping range).
2.4 Fast Electrons.
(see Knoll p45-50, Krane p197)
Fast electrons interact via Coulomb scattering from atomic electrons in the absorbing material. The electron energy will be dissipated in two ways (a) collisions
26
with other electrons and (b) radiative losses such as Bremsstrahlung.
The total linear stopping power can be thus written as
dE = dE ) + dE )
(2.4.12)
dx dx col dx rad
The major dierence between electrons and heavy-ion type radiation are (a) that
electrons travel at relativistic speeds, (b) electrons are subject to large deections
from collisions and (c) for electrons, the rapid changes in direction and speed lead
to losses through bremsstrahlung.
It can be shown that
(dE=dx)rad EZ
(2.4.13)
(dE=dx)col 700
where E is the electron energy in MeV and Z is the atomic number of the stopper
material. Thus, the radiative processes are only important at high energies and/or
for high-Z materials.
Positrons behave like electrons except that at low energies they will annihilate
with electrons in the target material giving rise to two 511 keV -rays.
Note that some electrons may be backscattered 180 and leave the material.
These backscattered electrons do not deposit all of their energy in the material (or
detector) and can therefore have a considerable eect on the design of detectors for
low energy electrons.
2.5 Interaction of Gamma-rays.
There are three important interactions between electromagnetic radiation and matter. These are (a) photoelectric absorption, (b) Compton scattering and (c) pair
production.
2.5.1 Photoelectric Absoprtion.
(see Knoll p50, Krane p198)
In photoelectric absorption, the gamma-ray (or X-ray) energy is completely absorbed by an atomic electron. Since the gamma-ray energy is usually much larger
than the electron binding energy, the electron is subsequently ejected from the atom.
The most probable origin of the electron is the K-shell of the atom. The photoelectron is emitted with a energy Ee where
27
Ee = h Eb
(2.5.14)
where hv is the gamma-ray energy and Eb is the binding enegy of the electron.
Photoelectric absorption is more likely for higher Z materials (since these have
more electrons around) and low energy gamma-rays. The probability for photoelectric absorption (p) is (roughly) dependent as follows
n
p Z 3:5
(2.5.15)
E
where n=4!5 depending on the stopping material.
Note that the probabilty for photoelectric absorption `jumps' at the binding
energies of the particular electron shells. For example, the K-shell binding for lead
(Z=82) is 88 keV (see gure 2.4). Therefore if E < 88keV, there is not sucient
energy to release a K-shell electron in lead.
Figure 2.4: Photoelectric cross-section as a function of energy in lead (Krane p199).
When the photon energy is increased above the K-shell binding energy, the sudden increase in abosrption probabilty is called the K-absorption edge. (Note that
the photoelectric eect requires BOUND electrons).
2.5.2 Compton Scattering.
(see Krane p200, Knoll p53)
28
In the Compton scattering process, the gamma-ray (or x-ray) scatters from a
`free' electron (see g 2.5). The photon energy is then divided between the kinetic
energy of the scattred electron and the (reduced) photon energy. (Note that for the
outer electrons, E >> Eb, so they are good approximations to free electrons).
Schematically.
scattered gamma-ray
E’=hf’
incoming gamma-ray
E=hf
θ
11
00
00
11
00
11
00
11
φ
scattered
electron
velocity=v
Figure 2.5: Compton scatttering of a -ray o an electron.
If = vc , where v= electron velocity, c is the speed of light, E is the initial
gamma-ray energy and E0 is the energy of the Compton scattered photon, then by
conservation of linear momentum and total energy (using relativistic dynamics)
and
E = E0 cos + mc
cos
p
c
c
1 2
0=
By conservation of energy,
E0
sin
p
sin mc
c
1 2
(2.5.17)
E + mec2 = E0 + p mc 2
1 (2.5.18)
E
E 1 + me c2 (1
(2.5.19)
2
and therefore
(2.5.16)
E0 =
29
cos)
ie. the energy of the scattered photon depends on the scattering angle. Note that
for =0 (no interaction), there is no change in energy. Also, even in the extreme
case where =180, some energy is always retained by the scattered photon.
The probability for Compton scattering depends on the number of electrons in
the material and therefore increases linearly with Z .
The angular distribution of Compton scattered electrons can be estimated by the
Klein-Nishina formula. This distribution shows a favouring for scattering at forward
angles at high gamma-ray energies (>100 keV).
2.5.3 Pair Production.
(see Knoll p53, Krane p201.)
For gamma-ray energies greater than 1.022 MeV, the process of pair production is
possible. Here, the gamma-ray can spontaneously convert (due to interaction with
the Coulomb eld) to an electron-positron pair. Any excess energy between the
gamma-ray energy and the mass of the two particles (2511 keV=1.022 MeV) is
taken away in the kinetic energy of the electron and positron. This is the dominant
process for gamma-ray energies above 5 MeV. The probabilty for pair production is
approximately proportional to Z 2 .
2.5.4 Attenuation Coecients.
The total probabilty per unit length that a photon interacts with a material (and
is therefore removed from a beam) is called the linear attenuation coecient ().
This is made up of three components which account for photoelectric absorption ( ),
Compton scattering () and pair-production (). Thus
= ++
(2.5.20)
The loss in intensity (dI ) of gamma radiation in crossing a thickness of material
dx is given by
dI = I
(2.5.21)
dx
where I is the intensity. Integrating, and given that at x=0, I = I0 , we obtain,
I (x) = I0e
30
x
(2.5.22)
Figure 2.6: Gamma-ray attenuation coecients for Al and Pb as a function of energy
(Krane p203).
11111111
00000000
11111111
00000000
11111111
00000000
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
11111111
00000000
11111111
00000000
00000000
11111111
00000000
11111111
00000000
11111111
11111111
00000000
11111111
00000000
11111111
00000000
00000000
11111111
1111111111
0000000000
x
gamma-ray flux
intensity =Io
attenuated gamma-ray flux
intensity = I(x)
I(x) = Io exp -(
x) µ
Figure 2.7: Schematic of loss of gamma-ray intensity through a thickness dx.
The linear attenuation coecient, is related to the mean free path () in a
material by the following expression,
=
R1
xe x dx
R0 1 x
0 e dx
= 1
(2.5.23)
where is the average distance travelled by the photon before interaction. Note
that unlike charged particles, the gamma-ray energy does NOT DECREASE as it
traverses through the material.
The mass attenuation coecient given by where is the density of the stopping
material. Note that the attenuation coecient, does not change for dierent states
of matter ((water)=(ice)) but the mass attenuation coecient takes changes in
density into account.
The product of density times the thickness of the material is known as the mass
thickness (in units of kg/m2 or g/cm2 ). This quantity allows a useful comparison
between dierent absorbers in relation to their eectivenss in stopping the raditaion.
31
2.6 Interactions with Neutrons.
(see Knoll p57)
Since neutrons are uncharged, they can not interact with the atomic electrons in
the stopper via the Coulomb force. Neutron interactions do occur however with the
NUCLEI of the absorber material.
These interactions, by which the neutron either disappears (via a nuclear reaction) or loses energy (due to a collision) result in secondary interactions occuring,
which can be detected. Most neutron detectors actually measure these secondary
radiations as `signature' of a neutron event.
The relative probabilities of various types of neutron interactions vary enormously
with the kinetic energy of the neutron. We can divide neutron events into two types,
(a) fast neutrons (E >0.5 eV) and slow neutrons (E <0.5 eV).
2.6.1 Fast Neutrons.
(see Krane p456, Knoll p531.)
When a neutron is elastically scattered o a target nucleus of mass A, at rest,
the energy of the recoil (ER ) is given by,
ER = (1 +4AA)2 cos2En
(2.6.24)
ER )max = (1 +4AA)2 En
(2.6.25)
ER )max = (2)4 2 En = En
(2.6.26)
where is the angle of the recoil scatter in the lab frame. Therefore, the maximum
recoil energy is given by
Thus, for scattering o protons (or hydrogen nuclei with A=1)
ie. the fast neutron can lose all of its energy to the proton in just ONE collision.
The neutron energy is said to be moderated in such collisions.
Therefore, for fast neutrons, the lighter the stopping material the better. Practically this means using materials with a high hydrogen content such as plastics.
2.6.2 Slow Neutrons.
(see Krane p57)
32
Due to the small kinetic energy of slow neutrons, elastic scattering will transfer
so little energy to the absorber that this method is not suitable for use on slow
neutron detection (since the detector signal would be so small).
Elastic collisions can however serve to slow the neutrons down to low enough
(thermal) energies ( 401 eV) for neutron induced nuclear reactions to take place.
These can produce charged secondary reaction products which are energetic enough
to be measured.
For most materials the (n, ) reaction is the most useful/likely. Note that due to
the gamma-rays being realeased in such reactions, when using this method to shield
for thermal neutrons, sucient gamma-ray shielding is also required.
Other possible reactions are (n,), (n,p) and (n,ssion).
33
Chapter 3
General Detector Properties.
(Knoll p103-127.)
Ionizing radiation will give rise to free charges in a material. If an large external voltage is applied, these charges can be collected to allow measurement of the
radiation.
3.1 Pulse Mode and Current Mode.
(Knoll p105-108, Krane p220.)
There are two basic modes of operation for detectors, these are
1. Current Mode: where an AVERAGE current is measured over a period of time
(eg. in a Geiger-Muller tube).
2. Pulse Mode: Most useful detector applications need information on the amplitude (and timing) properties of each individual signal. In pulse mode, this
information is kept. (For example in a gamma-ray detector for spectroscopy).
The majority of detectors discussed in this course are operated in PULSE mode.
In pulse mode, the initial signal comes in the form of a charge pulse. This is then
converted to a voltage by the use of a pre-amplier circuit (see gure 3.1).
DETECTOR
C
R
V
Figure 3.1: Schematic of a pre-amplier circuit for pulse mode operation.
34
If we take the case where RC (the product of the resistance and capacitance)
is large (ie =RC is much larger than the charge collection time in the detector),
then during the charge collection time, the capacitor is charged. As soon as the
charge collection stops, the capacitor starts to discharge through the load resistance
(returning to zero).
The two main advantages of such a system are:
1. The time required to obtain the maximum voltage is determined by the charge
collecting time in the detector material (which sets the lower limit).
2. The amplitude of the pre-amp output signal voltage is proportional to the
charge generated in the detector (and thus the energy deposited by the radiation).
Area = Q = total charge
i(t)
time---->
V(t)
rise
time
time---->
Figure 3.2: Pulse shapes for charge and voltage collection in pulse mode.
Note that the rise time (the time taken for the pre-amplied output voltage to
reach its maximum value) is determined purely by the charge collection time of the
detector. It is NOT aected by the value chosen for the components of the external
circuit. BUT the decay of the pulses is determined by the choice of values for R and
C (typical values for RC1 s).
35
ie. the leading edge is detector dependent, the trailing edge is circuit dependent.
Note that the timing resolution of such a system is as fast as the charge collection
time.
3.2 Pulse Height Analysis.
(Krane p220, Knoll p110)
The output pulses from the pre-amplier are typically too small (a few mV) to
put into an analogue to digital converter (ADC). In order to convert the individual
voltage pulses from the pre-amplier circuit into a useful spectrum, the pre-amplied
signal needs to be amplied and shaped. This has the eect of amplifying the signal
to a magnitude of a few volts (typically) and a more symmteric shape.
The (analogue) amplied voltage is then coverted into a digital number using
an ADC. By digitising the voltage, one can now place voltages into certain discrete
channels (or `bins') to form a spectrum. Usually, the output of an ADC gives a linear
output with respect to the size of the input voltage, ie. a range of 0!8V for the
amplied input voltage, will give digitised output between 0{2048 (2K), or 0{4096
(4K) or 0{8192 (8K) channels.
This digitised energy information can then be stored in a multi-channel analyser.
Schematically,
detector
pre-amp
amplifier
multichannel analyser/ADC
Figure 3.3: Schematic of a circuit used for pulse height analysis experiments.
Note that if a radiation of the same energy hits the detector on a number of
occasions (or `events') a `peak' will form in the MCA spectrum.
Note also that the MCA spectrum will contain various types of background, ie.
unwanted counts due to, for example, the radiation being scattered out of the detector before all the radiation has been absorbed. In such as case, only part of the
full signal is recorded and a counts appears in the `wrong place' in the MCA spectrum. (A good example of this is discussed in the section on Compton suppression
of germanium detectors, see later.)
36
3.3 Energy Resolution
(Knoll p115-117, Krane p224)
In many cases when measuring radiation, the aim is to accurately measure the
energy (and intensity) of the radiation. In theory, if the same energy is deposited
into a detector (from the same radioactive source for example) pulses of the same
pulse height should be measured. However, there is a spread in the measured pulse
heights due to eects such as
1. Drift of the operating characteristics.
2. Statistical noise due to the nite number of charges collected.
3. Sources of randon noise within the detector set up such as `electrical pick up'
or `microphonics' (vibrations).
The statistical noise represents the absolute minimum uctuation in the signal.
This will always be present, and is usually the limiting factor in the energy accuracy
or `resolution' of a detector.
The statistical noise arises due to the charge being deposited in the detector (Q)
not being a continuous variable, but rather, a discrete number of charge carriers.
The number will vary from event to event, even if the same amount of energy is
deposited in the detector.
3.3.1 Full Width at Half Maximum.
The resolution is usually described in terms of the width of the peak (in energy, E )
at half of its maximum value (called the full width at half maximum, or FWHM),
divided by the centroid of the energy peak, E0 .
Therefore,
Resolution(R) = FWMH
E
0
(3.3.1)
This is a dimensionless quantity and is usually referred to as a percentage. The
smaller the resolution, the better. Generally, a detector should be able to resolve
two energies if their centroids are separated by the FWHM.
Note that the value of R may change with energy, depending on the type of
radiation and the detector. Typical values for R are given in table 3.1.
37
No of
counts
(dN/dE)
Eo
Area=A
No
FWHM
No/2
Energy (E) in Channels
Figure 3.4: Schematic showing the resolution (FWHM) of a peak.
Detector type radiation Resolution (FWHM/E0 )
Ge
gamma-rays
0.2%
NaI
gamma-rays
10%
diodes
-particles
1%
Table 3.1: Typical resolutions for various detectors.
3.3.2 Gaussian Peak Shapes.
If randon uctuations are the only source of uncertainty in the resoloution, for
Gaussian response, the peak should have Gaussian shape, of a form given by the
expression,
!
2
(
E
E
)
A
0
G(E ) = p exp
(3.3.2)
22
2
where A is the area of the peak and determines the FWHM via the relationship
FWHM = 2:35
(3.3.3)
Now, if a total of N charge carriers are created (on average) for a radiation of
energy E0, then the average pulse height, E0 is given by
E0 = KN
38
(3.3.4)
where K is constant of proportionalilty and the standard deviation () in the
pulse height is given by,
p
p
= K N; FWHM = 2:35K N
The resolution limit, Rlim is then
(3.3.5)
p
Rlim = FWHM
= 2:35K N = 2p:35
(3.3.6)
E0
KN
N
Therefore, in order to have a resolution of 1%, approximately 55,000 charge
carriers are required per event (on average). The more charge carriers created the
better the resolution. (This is particularly apparent for semi-conductor detectors
with small `band gaps' as we will see later).
3.3.3 The Fano Factor.
(Knoll p116-117, Krane p224)
Measurements of the FWHM of certain detectors show that in some cases the
resolution can be 3-4 times BETTER than the statistical limit! This is due to the
fact that the processes which cause the charge production are not independent of
each other and therefore pure Poisson statistics do not apply.
The Fano factor (F ) takes these deviations into account and is dened by,
variance
Fano factor; F = Poisson observed
predicted variance (= N )
2
Since the variance is equal to , the resolution limit is now given by,
(3.3.7)
s
F
R = 2:35 N
(3.3.8)
F is considerably less than one for semi-conductors detectors and close to unity
for scintillators.
Note that the higher the energy of the radiation, the more charges are created
and the better the resolution (even though the FWHM increases), since
:35 = 2q:35
Rstat = 2N
E
K
ie for a linear gain,
39
(3.3.9)
Rstat E 21
(3.3.10)
The overall FWHM can be calculated from the various components by adding in
quadrature, ie.
(FWHM)2tot = (FWHM)2stat + (FWHM)2noise + (FWHM)2drift::::
(3.3.11)
The non-statistical part can be made up of for example, eects in the detector
crystal or the photomultiplier (see later).
3.4 Detection Eciency.
(Knoll p117-119)
The absolute eciency (abs ) is given by,
: of pulses recorded
abs = no: ofnoquanta
(3.4.12)
emitted by source
However, in order to take into account the solid angle subtended by the detector,
the intrinsic ecieny (int ) is also used, where
: of pulses recorded
int = no: of no
(3.4.13)
quanta incident on detector
For isotropic (ie. no angular dependence) sources, the absolute and intrinsic
eciencies are related by
4
(3.4.14)
int = abs ; dA2
where is the solid angle subtended by a detector of cross-sectional area A, a
distance d from the source.
3.4.1 Peak to Total Ratio and Intrinsic Peak Eciency.
Not all the radiation which interacts with the detector results in a full energy peak
signal (some may for example be Compton scattered out of the detector). The Peak
to Total ratio, r. is given by,
r = peak
total
40
(3.4.15)
The intrinsic peak eciency is given by
N
S = 4
(3.4.16)
ip
where S = the number of quanta emitted by the source, N = the number in the
peak in the detector, ip = the intrinsic peak eciency and = the solid angle of
the detector.
3.5 Detector Timing and Dead Time.
(Knoll p120.)
Detectors may be insensitive immediately after recording an event (while the
charge from the event is being collected for example) or the electronic processing
may take a signicant time (for example, an ADC can take 5s to process a
gamma-ray event).
The time for which the detector is not active is known as the dead time. If the
dead time per event is a time , and c is the recorded count rate then we can dene
the live time per second (=lt) and the true count rate (=r) by,
lt = (1 c ) and r = (1 c c )
The recorded count rate (= c) is then given by,
c = (1 +r r )
(3.5.17)
(3.5.18)
3.5.1 Rise Time.
(Knoll p 585)
The rise time is usually dened as the time interval between the pulse reaching 10% and 90% of its nal (full) amplitude. The faster the rise time, the more
accurately the arrival time of the radiation in the detector can be deduced.
41
Chapter 4
Types of Detector.
We shall discuss three main types of detector in this course (a) gas detectors, inlcuding ionization chambers, proportional counters and Geiger counters; (b) scintillation
detectors, made from both organic and inorganic materials and (c) semiconductor
detectors such as germanium and silicon detectors.
4.1 Gas Filled Detectors.
The principle behind gas lled detectors is that the radiation interacts with the gas
in a chamber causing some of the gas to become ionized. The free electrons (and
positive ions) are then swept to collection electrodes under the inuence of an applied
electric eld.
This course will deal with three main types of gas lled radiation detectors, (a)
ionization chambers, (b) proportional or avalanche counters and (c) Geiger counters.
The main dierence between these three types of detector is the size of the applied
external eld and its eect on the charge collection (see g.4.1).
4.1.1 The Ionization Process in Gases.
(Knoll p131-132)
An energetic charged particle passing through a gas will create both excited and
ionized molecules. Ions are formed either by direct interaction with the particle
(radiation) or through a secondary process where some of the energy is initially
transferred to an energetic electron, called a delta-ray.
The particle must transfer at least enough energy to cause ionization for a measurement to take place. For most gases used in radiation detectors, the binding
energy of the least bound electron is 10!20 eV.
42
PROPORTIONAL
COUNTERS
G-M REGION
PULSE
HEIGHT
ION
CHAMBERS
APPLIED VOLTAGE
Figure 4.1: Applied voltage verses pulse height for gas detectors (Krane p162, Knoll
p207).
4.1.2 W-Value.
The W-value is the average energy lost by the incident particle per ion pair formed.
This takes into account that other processes occur, such as electrons being elevated
to a higher energy state and therefore not all incident particles cause ionziation.
Empirical observations show that the W-value is almost constant for dierent
types of radiation and energy (and gas). A typical value for the W-value is between
30 and 35 eV per ion pair. (Thus for a 1 MeV radiation, entirely stopped in a gas
4
detector, about 1MeV
30eV 310 ion pairs are created).
4.1.3 Recombination.
(Knoll p153)
Collisions between positive ions and free electrons may results in recombination,
ie. the electron can be captured by the ion to re-create a neutral atom/molecule.
Alternatively, a collision can occur between a positive and negative ion. In either
case, the charge generated by the incident radiation is lost to the output pulse.
43
4.1.4 Drift Velocity
(Knoll p134, Krane p204.)
For ions in a gas, the drift velocity, v is given (approximately) by,
v = E
(4.1.1)
P
where, is the mobility, E is the electric eld strength and P is the gas pressure. Therefore, as the elctric eld increases betweeen the plates, the ion velocity is
increased (reducing the amount of recombination).
Typical values for the mobility, are 1!1.510 4 m2Atm/Vs. Thus, for a typical
eld strenth of E 104V/m and a typical gas pressure, P of 1 Atm, the transit time
for ions across a detector is 10 2s, ie. very long compared to the radiation rate (for
typical sources). Since free electrons are much lighter than ions, they have a mobility
of about 1000 times greater than for the (heavy) ions. The electron mobility also
increases with EP and is higher for certain gases.
4.1.5 Ionization Chambers.
(Knoll p154-155, Krane p204)
A simple ionization chamber consists of an enclosed volume of gas, with a highvoltage eld placed across a (positive) anode and (negative) cathode as shown in
gure 4.2.
The main problems with ionization chambers are that they (a) generate small
output pulses and thus require an external amplier, (b) they have slow drift velocities (ve 103 m/s, vion 1m/s) and (c) they have poor timing properties.
The amplitude of the output signal, Vo is given simply by,
Vo = CQ
(4.1.2)
where Q is the charge collected and C is the capicitance across the plates (ie
between the anode and cathode).
Note that the size output voltage pulse is independent of the the applied voltage.
For typical radiation rates, the charge collection time is too slow to count individual puses, BUT, it has a use in measuring the TOTAL radiation in a given time,
ie. it can be used as a RADIATION MONITOR. The average radiation intensity is
Q ). (Note that the timing properties can be signicantly
measured as a current ( time
improved by the use of a Frisch grid).
44
+HV
ANODE
e-
e-
I+
I+
CATHODE
Figure 4.2: Schematic of a simple ionization chamber.
4.1.6 Avalanche/Proportional Counters.
(See Krane p160-163, Knoll p160-163)
In order to observe individual pulses extra amplication of the pulse is helpful.
One way of acheiving this is to increase the applied collection voltage. This has
the eect of accelerating the electrons to high enough energies that they create
other ion/electron pairs through inelastic collisions. This is known as a Townsend
avalanche.
The chamber is usually operated so that the number of secondary electrons is
proportional to the number of primary electron-ions pairs, thus the name propor45
tional counter. Typical proportional counters are cylindrical in shape with an anode
wire through the centre.
e- = electrons
I+ = positive ions
+HV
e-
e-
e-
I+
ANODE WIRE
I+
I+
OUTER CATHODE
Figure 4.3: Schematic of a proportional counter.
by
The electric eld, E at a distance r from around this anode (of radius a) is given
E (r) = V b (4.1.3)
rln a
where b is the inner radius of the surrounding cathode.
Thus the main avalanche occurs close to the wire where the electric eld is largest.
However, this corresponds to only a small fraction of the volume of the chamber.
Since the timing of the pulse is governed by the avalanche region, (ie that very
close to the anode wire), the drift time to the anode is very fast (for the avalance
electrons). This allows the proportional counter to run at much higher rates than
the simple ionization chamber. Rates of upto 106 events per second are acheivable.
Typical avalanches produce between 1,000 and 100,000 secondary electrons.
4.1.7 Multiwire Proportional Counters (PPAC, MWPC or
PWAC).
(Knoll p189-191).
By adding more than one anode wire, it is possible to make large area proportional counters which are position sensitive. Over much of the volume of the detector,
the electric eld is unifrom but a very high eld region is created in the vicinity of
each grid wire. The names for such detectors are Parallel Plate Avalanche Counter
46
(PPAC), Multiwire Proportional Counter (MWPC) or Proportional Wire Avalanche
Counter (PWAC).
Figure 4.4: Field lines in a PPAC.
.
4.1.8 Geiger-Muller Tubes.
(Krane p206, Knoll p199)
For even larger values of applied eld, secondary avalanches can be emitted.
These are triggered by photons emitted by ions excited in the initial interaction
with the radiation. Since these photons travel larger distances than the electrons,
the entire volume of the gas takes part in the charge amplication, which can lead
to amplication factors of upto 1010.
Note that as all the tube participates in every event (and the avalanche is `space
charge limited'), any information on the type and energy of the incident radiation
is lost. Due to the large amount of charge induced per event, a G-M tube does not
usually require amplication of the output pulse.
47
-ve HV
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
ANODE WIRE
+HV
gas tight insulator
THIN
END
WINDOW
Figure 4.5: Schematic of a Geiger-Muller tube.
Quenching.
(Krane p206.)
In a G-M tube, the electrons are collected within 10 6 secs, during which time
the positive ions do not move far from the avalance region. Therefore, a cloud
of positive ions surrounds the anode, with the eect of reducing the electric eld
intensity and eectively quenching the avalanche process. In order to stop these
positive ions releasing other electrons (and thus starting the process again, causing
multiple pulsing) a quenching gas is added.
The quenching gas is one that has a high probability of transfering an electron to
the ionized ll gas. The quenching gas is usually made up from complex molecules
such as ethanol, in contrast to the typically simple ll gas (such as argon).
The ll gas is thus neutralised and the quench gas molecule breaks up on contact
with the cathode (instead of liberating electrons).
Counting Eciencies for Dierent Radiations.
(Knoll p210-211.)
Charged Particles: The eciency depends on the thickness of the entrance
window compared to the range of the radiation (in the entrance window material). It is essentially 100 % for radiation that gets through the thin entrance
window. For alpha-particles, heavy-ions etc. the thickness of the window is of
great importance. Typical values are 1.5!3 mg/cm2.
48
Neutrons: Geiger tubes are not usually used for neutron detection. Thermal
neutron capture cross-sections are too small to be useful. Fast neutrons can
cause recoils which may lead to discharges. Usually used in the proportional
region for spectroscopic information. Also, proportional counters using BF3
gas can be used (see later).
Gamma-rays: The interaction cross-section between the gamma-rays and the
ll gas is very small but G-M tubes are used to measure gamma-rays by measuring the secondary photoelectrons produced by the gamma-ray interacting
with the material in the window of the counter. The probabilty increases with
the Z of the window material. Therefore, G-M tubes for gamma detection
would have bismuth (Z=83) windows. Even then, the absolute eciency is
only about 2%.
4.1.9 Gas Detector Summary.
Detector
Avalanche
good
Energy
Use as
type
amplication timing? information? monitor
ion chamber
none
no, 10 2s
none
yes
3
5
6
prop counter 10 !10
yes, 10 s
yes
no
10
6
G-M tube
10
yes, 10 s
none
yes
Table 4.1: Summary of gas detector properties.
4.2 Scintillation Detectors.
(Krane p207, Knoll p215-217.)
Gamma-rays have such a small interaction cross-section in gases that in order
to measure them properly, a (more dense) detector made of solid material is required. There are basically two types, (a) semiconductor detectors (see later) and
(b) scintillation detectors.
In a scintillator, the incident radiation excites the molecules in the material into
higher energy (excited) states. These excited states then decay back to their original
state via the emission of LIGHT. Usually, these excited states decay very promptly
(within a few nanoseconds) emitting light with a frequency near the VISIBLE region.
The material is then said to uoresce.
Occasionally, the excited molecular state will decay via a slower route, thereby
taking longer to decay. Light emitted by this process is known as phosphoresence
49
and delayed uorescence (see gure 4.6).
SINGLET STATES
S3
TRIPLET STATES
T3
S2
T2
S1
prompt
fluorescence
absorption
T1
delayed
fluorescence
(phosphorescence)
S0
Figure 4.6: Energy levels in an organic scintillator (Knoll p217).
In a scintillator detector (see gure 4.7), the emitted light from the crystal strikes
a photocathode, resulting in the emission of a photoelectron. These photoelectrons
are accelerated and multiplied in a photomultiplier tube, the output of which gives
the output pulse for the detector. A typical photocathode material is RbCs.
4.2.1 Photomultiplier Tubes.
(See Krane p212, Knoll p259.)
Electrons from the photocathode are accelerated towards an electrode at a positive voltage. As the electron hits this DYNODE, additional electrons are ejected
and accelerated towards a second dynode, then a third etc.
The overall multiplication factor for a single dynode is where
: of secondary electrons emitted
= no: ofnoprimary
(4.2.4)
electrons striking the dynode
is typically between 4 and 6. Therefore, for a pm tube with N dynodes (acceleration stages), the overall gain in electron yield is given by
50
photocathode
amplified electrons
photoelectrons
output
pulse
radiation
photomultiplier tube
scintillator
Figure 4.7: Schematic of a scintillation detector (Krane p208).
Figure 4.8: Schematic of a photomultiplier (Krane p212).
Gain = N
(4.2.5)
where 1, and represents the number collected by the p-m structure. Thus,
for =5 and N =10, the gain is about 107!
4.2.2 Types of Scintillation Detectors.
(Knoll p 221, 231.)
Scintillator detectors can be divided into two basic groups organic and inorganic.
Examples of the dierent types are given in table 4.2.
51
ORGANIC
INORGANIC
NE102-plastic
NaI(Tl)
NE213-liquid
CsI(Tl)
Anthracene(=C14 H10 )
CsI(Na)
Naphthalene (=C10 H8)
BGO
P (=C20 H14 N2O)
BaF2
PPO (=C15 H11 NO)
CaF2
Table 4.2: Some commonly used scintillator materials.
4.2.3 Organic Scintillators.
(Knoll p216-221, p544 Krane p209)
Fluorescence in organic scintillators comes from transitions in the electronic
structure of the molecule. Many organic scintillators have a so-called -electron
structure, where the electron orbital is not well localised in the molecular structure and does not participate in the bonding between the atoms in the molecule.
It is the excitation of this electron that is usually responsible for the scintillation
process.
As ionizing radiation passes through the molecule, kinetic energy can be transfered and the electron (and thus the entire molecule) is excited from its ground
state (known as the S00 state). The principle scintillation light or prompt uoresence
comes from the S10 !S00 decay (see gure 4.6).
If I0 is initial intensity (at time zero), the uorescence intensity, I as a funtion
of time t is given by
t
I = I0 exp ; a few ns (10 9s)
(4.2.6)
In some cases however, the decay is more complex and may be given by a two
component exponential of the form,
!
t
t
N = Aexp t + B exp t
(4.2.7)
f
s
where A and B are constants, tf is the fast component and ts is the slow component. (The two component nature is due to the prompt and delayed nature of the
light emission depending on which states it decays through).
The ratio of A : B varies from material to material but the fast component
usually always dominates. The ratio of A : B is often used in certain scintillation
detectors for distinguishing between dierent types of radiation (such as neutrons
52
and gamma-rays), this technique is called pulse shape discrimination.
total
LIGHT OUTPUT
fast component
delayed (slow) component
TIME
Figure 4.9: Schematic showing sum of fast and slow component in a scintillator.
NE213, Liquid Scinitillator:
This is an organic solution in xylene (liquid). It has a fast component with f 4
ns and a slow component of s 300 ns.
In NE213, the relative strength of the slow component increases with ionization density. Gamma-rays give rise to scattered electrons which have a relatively
low ionization density. By contrast, neutrons interacting with protons (via elastic
collisions) will cause much higher ionization densities. Thus, NE213 is useful for
detecting neutrons and discriminating them from gamma-rays.
4.2.4 Plastic (organic) Scintillators.
Various plastic scintillators (such as NE111) have very short prompt decay times (<2
ns) and are therefore very useful in providing fast timing information. In nuclear
physics experiments, if the source is well dened (such as if it is induced by a pulsed
beam) discrimination between neutrons and gamma-rays can be obtained by their
dierent times of ight (ie. the time it takes to travel from the source to the detector).
53
Figure 4.10: Time of ight discrimination using NE213 scintillator.
4.2.5 Inorganic Scintillators.
(Krane p210, Knoll p227)
In inorganic crystals, the electrons are held together in discrete energy bands, the
two highest of which are called the valence and conduction bands.
For insulating type materials such as sodium iodide (NaI), the valence band is
usually full and the conduction band empty. An incoming radiation can excite an
electron, causing it to be promoted from the valence band into the higher lying
conduction band. After some time, the electron decays back to the valence band via
the emission of a photon (light).
The dierence in energy between the top of the valence band and the bottom of
the conduction band is known as the energy gap and is typically around 4 eV for
inorganic scintillators.
To increase the probabilty of photon emission and reduce the self absorption of
the scintillated light (in the crystal itself), small amounts of impurites or activators
are added to the crystal (see gure 4.11). The activator atoms have the eect
of adding extra quantum levels between the valence band and conduction band,
eectively reducing the size of the energy gap.
54
conduction
band (empty)
recombination
excitation
electrons
emitted
photon
increasing
energy
extra states
due to activators
gives higher wavelength
emitted photons
valence
band (full)
holes
incoming
radiation
Figure 4.11: Band structure for an inorganic insulator (Krane p210).
NaI(Tl), Sodium Iodide:
Sodium iodide is one of the most commonly used inorganic scintillator (for gammaray detection). Pure NaI is NOT GOOD since the light emitted has a wavelenth
(200 nm) which is easily reabsorbed by the crystal1 By adding a few percent
of thallium (Tl, Z=81), intermediate acceptor states are created and visible light
( 400 nm) is emitted which can easily travel through the crystal. A yypical
energy resolution ( EE ) of about 5% is obtained for gamma-rays.
The prompt decay component is =230 ns, which is rather too long for good
timing measurements. Note also that NaI is hygroscopic, ie. it reacts with water
(vapour) and thus the crystals used in such detectors must be kept sealed from the
air.
BGO, Bismuth Germanate.
(Knoll p234)
BGO is an abbreviation for Bi4Ge3O12. Its main good property when measuing
gamma-rays is that due to its high density and large Z , (Z(Bi)=83), it has a very
high detection eciency.
However, the poor light output (about 10% of that of sodium iodide) means that
the energy resolution is poor. BGO is widely used in gamma-ray spectroscopy as an
anti-Compton or Compton veto shield (see later).
1E
= f = fc . Thus, the smaller the energy of the emitted light, the longer the wavelength.
55
BaF2 , Barium Fluoride.
(Knoll p236)
BaF2 has a very fast component in its light output (f 600 ps) which makes
barium uoride an ideal detector when good timing information is required.
4.2.6 Phosphor Sandwich (`Phoswich') Detectors.
(Knoll p 326)
Sometimes, two dierent scintillators will be sandwiched together and use the
same photomultiplier tube. The scintillators are chosen so that they have dierent
decay times. Then, pulse shape discrimination can be used to distinguish between
dierent types of radiation, such as -rays, protons, electrons and -particles
One can use a thin, fast (dE ) and a thick slower (E ) sandwich to obtain particle
identication using the Bethe equation.
4.2.7 Photodiodes.
(Knoll p274-8).
Photomultiplier tubes are the most commonly used light amplier for scinitillation detectors. However, they are rather bulky objects and there have been recent
advances in the use of much more compact semiconductor photo-diodes for use with
scintillators.
There are essentially two types of photodiode, conventional and avalanche photodiodes. Both types are semiconductors with band gaps of between 1 and 2 eV.
Since the scintillation light has energies of 3 to 4 eV, this is sucient to create
electron-hole pairs (see next section) which can be collected as an output pulse.
The avalanche photodiode operates with larger values of applied voltage (to sweep
up the liberated charge) than the conventional one. This causes an eect analagous
to the gas multiplication eect in a proportional counter.
4.3 Semiconductor Detectors.
(Krane p213.)
Three types of semiconductor detector will be discussed in this course: (a) silicon
surface barrier detectors, mainly used for detecting alpha-particles or heavy ions;
(b) lithiun drifted silicon detectors called Si(Li) or `sillys' for electron and/or X-ray
detection; and (c) germanium detectors used for gamma-ray spectroscopy.
56
Fast plastic
scintillator (dE)
incoming
radiation
Calcium
Fluoride (E)
time
output
voltage
slow component
fast component
Figure 4.12: Use of a phoswich, dE vs E detector.
57
4.3.1 Band Structure in Semiconductors.
(Krane p214, Knoll p338-339.)
The main dience between semiconductor materials and insulators is the size of
the (energy) band gap between the valence and conduction bands. For insulators,
Ebg 5 eV, for semiconductors, Ebg 1 eV.
Germanium (Ge, Z=32) and silicon (Si, Z=14) are both semiconductors and
group IV elements. They form solid crystals where the four valence electrons form
four covalent bonds with the neighbouring atoms. Thus, in a perfect crystal, all the
electrons take part in the bonds. This results in a FULL VALENCE band and an
EMPTY CONDUCTION band.
The basic idea behind using semiconductor materials to detect radiation is that
through interactions with the radiation, it is possible to excite electrons from the
valence band into the conduction band (assuming that the energy of the radiation is
larger than the semiconductor band gap). This leaves a hole behind in the valence
band, thus a electron-hole pair has been created (the band structure is similar to
that in inorganic scintillators, see gure 4.11).. The liberated charge can be then
swept away by an applied voltage.
For temperatures greater than absolute zero, thermal energy is shared by the
electrons in the crystal lattice and thus it is possible to for an electron to be thermally
excited across the band gap into the conduction band. The probabilty per unit
time of thermally creating an electron-hole pair, P (T ), as a function of absolute
temperature, T , is given by a Boltzmann function,
E
g
P (T ) = CT exp 2kT
(4.3.8)
where Eg is the band gap, k is Boltzmann's constant and C is a constant which
is material dependent.
Thus for small value of a band gap (as is the case for semiconductors), there
is a large probability of thermal excitation, which in a detector would be a source
of unwanted noise. In order to reduce this thermal noise, semiconductor detectors
should be operated at low temperature (usually 77 K, liquid nitrogen temperature).
3
2
4.3.2 N and P-type Semiconductors.
(Krane p215, Knoll p344-5)
58
Small amounts of group three or ve type material can be added to the semiconductor to control its electrical properties. The introduction of these alien atoms is
known as doping.
If valence-5 atoms such as P (phospor), As (arsenic) or Sb (antimony) are added
to silicon or germanium, four of the electrons will form colvalent bonds with the
neighbouring germanium (silicon) atoms BUT the fth valence electron is free to
move around the lattice. This results in an excess of negative charge carriers, and the
material is called an N-type (N for negative) semiconductor. (These extra electons
form a set of discrete energy states just below the condution band known as donor
states).
Similarly, if type-3 atoms (such as lithium) are introduced, an excess of hole
states (in the valence band) will occur. This material is called P-type since there is
an excess of positive charge carriers (holes).
4.3.3 Semiconductor Junction Diodes and Depletion Layers.
(Knoll p350-353, Krane p215-216.)
When P and N type materials are pushed together, the excess electrons in the
N-type diuse into the P-type material and combine with the holes. This creates
what is known as a depletion layer.
The diusion of electrons from the N-type, leaves behind ionized, xed donor
sites. Similarly, the diusion of holes from the P-type leaves negatively charged,
xed acceptor sites. This space charge gives rise to an electric eld which halts any
further charge migration. The result is called a junction diode.
Figure 4.13: Depletion layer from pressing P and N-type semiconductor together
(Krane p215).
59
If radiation enters the electrically neutral depletion layer, electron-hole pairs can
be created. The electrons will ow towards the positive potential and the holes to
the negative. This charge can be collected and converted to an output voltage by
a pre-amplier. The number of electron-hole pairs created, and thus the size of he
output voltage, is proportional to the energy of the radiation.
4.3.4 Reverse Biasing.
(Krane p216, Knoll p356-7)
Most semiconductor junction diodes are operated with a large reverse bias voltage
(ie positive voltage on the P-type and negative voltage on the N-type) of between
1000 and 5000 volts. This is done for two reasons,
1. By increasing the electric eld in the depletion region layer, the charge collection becomes more ecient (since the charges are swept up faster and there is
less time for recombination eects).
2. Reverse biasing increases the size of the neutral depletion layer by forcing more
majority charge carriers across the junction. This makes the detectors more
ecient by making its active volume larger.
The thickness of the depletion layer, d, can be given by
s
V
d 2eN
(4.3.9)
where V is the reverse bias voltage, N is the net impurity in the bulk semiconductor, e is the electron charge and is the dielectric constant of the material in
Fm 1.
Some detectors are operated at suciently high reverse biases that the depletion
layer extends through virtually the entire volume of the detector, called a fully
depleted detector. Note that even in these cases there will be some leakage current.
4.3.5 Dead Layer.
If the surface of the P or N type material is outside of the depletion region, it is
insensitive to radiation. This volume is known as a dead layer.
Note that the radiation must pass through this region to interact with the `live'
depletion layer. In charged particle spectroscopy the dead layer eect presents a major diculty due to the small range of charged particles in dense matter. Therefore,
60
a portion of the energy of the radiation will be lost in the dead layer before it enters
the active region of the detectors.
4.3.6 Silicon Surface Barrier Detectors.
(Knoll p360,377 Krane p217,262)
These are formed by evapourating a layer of gold onto a crystal of N-type silicon.
This forms a large hole density at the surface of the detectors which acts like a
p-n junction. The main advantage of surface barriers is that they have a very thin
entrance window. Typical depletion layer depths are about 1mm so they are only
useful for charged particle work (since gamma-rays will not stop in this depth).
Surface barriers are often used in charged particle spectroscopy, particularly for
measuring the energies of alpha particles in alpha decay. Typical resolution is about
E
E
10keV
5MeV
Figure 4.14: Surface barrier silicon detectors for alpha-spectroscopy (Knoll p377).
4.3.7 Lithium Drifted Silicon Detectors, Si(Li).
(Krane p217, Knoll p444,452,462.)
Using junction diode detectors, depletion depths of greater than 2mm are difcult to achieve. To measure fast electrons and/or X-rays, larger active volumes
are required to stop the radiation (since the typical path lengths for electrons and
photons are much larger than for heavy charged particles).
By allowing an alkaline metal (usually lithium) to diuse through a p-type crystal
a large region of compensated or intrinsic (electrically neutral) silicon can be created
which acts as the active volume for the detector.
61
`Sillys' as they are usually called are often used to measure electrons or X-rays
(and/or low-energy gamma-rays). To improve the resolution (by reducing the thermal noise) Si(Li) detectors are usually operated at liquid nitrogen temperature.
The lower Z of silicon compared to germanium (14:32) means that the X-ray
escape peaks are lower and silicon is more transparent to higher energy photons.
Thus Si(Li) detectors are preferred to germanium for X-ray detection. Note that to
avoid absorption of the X-ray before it reaches the active Si(Li) volume, a low Z
material must be used as the window for Si(Li) X-ray detectors, usually beryllium,
Z (Be=4).
4.3.8 Germanium Detectors.
(Knoll p387-396.)
Ge has a higher Z than silicon, and therefore a higher photoelectric interaction
probabilty, coupled with a small band gap, which allows higher resolution. Germanium detectors are the main tool of high resolution gamma-ray spectroscopy.
Current technology produces hyper-pure germanium crystals which has made the
need for lithium drifting obsolete (although the detector still has to be operated at
LN2 temperature).
The detectors work by placing n-type material (for example lithium) and p-type
material (eg boron) on the edges of the crystal as electrical contacts.
Figure 4.15: A germanium detector.
62
4.4 Gamma-Ray Spectroscopy with Germanium
Detectors.
Gamma-ray spectroscopy is used to (a) identify the quantum levels in a nucleus
to probe the physics of nuclear structure and (b) identify radioactive substances by
measuring their characteristic decay gamma-rays (eg 662 keV line in 137 Cs). General
considerations for a good gamma-ray spectrometer device are that (a) it must have
excellent energy resolution, (b) a good photopeak eciency and (c) good timing
properties.
While sodium iodide has a better eciency than germanium, the excellent energy
resolution of germanium (better than 0.2 % at 1.333 MeV) makes it the detector of
choice for high resolution studies.
The main problems with germanium are
The most probable interaction for most gamma-rays is Compton scattering
and a sizeable portion of gamma-rays that enter the detector will scatter out
of the detector before the full energy has been absorbed by the detector. This
gives rise to a large Compton background.
Germanium detectors must be kept at liquid nitrogen temperature for good
resolution. This means that bulky liquid nitrogen dewars must be included in
the detector apparatus.
4.4.1 Response Function of Germanium Spectra.
(Knoll p289-293, p301.)
The typical germanium spectrum is made up from a number of dierent components. These include,
1. The Full Energy Peak. The peak corresponding to where all the incident
radiation's energy has been collected by photoelectric absorption (some fraction will have been Compton scattered before p-e absorption). In a perfect,
idealised detector, all the counts would be in this peak.
2. The Compton Background. The background of counts with energies less
than the full energy peak where some of the incident radiation has been Compton scattered out of the detector.
63
3. The Compton Edge. In a Compton scattering event, the energy
removed
h (1 cos) 2
m
c
by the electron is given by E , where E = h h 0 = h 1+ eh 2 (1 cos) .
me c
Therefore, the minimum energy removed by scattering an electron (when
=180) is given by E = 1+2EE , where me c2 = rest mass of the electron=
me c2
511 keV. This minimum amount of energy being lost in a Compton scattering,
gives rise to the Compton background being essentially cut o at an energy
E below the full energy peak. Note for E >> 511 keV, E ! me2c2 250
keV.
4. Escape Peak(s). For photon energies greater than twice the electron rest
mass energy (511 keV 2 = 1.022 MeV) there is a probabilty of pair production
where an electron-positron pair is created. The positron may then recombine
with an atomic electron in the detector and decay back to 2511 keV gammarays. One or both of these 511 keV gammas may then escape from the detector
with no further interaction. If the initial gamma-ray enegy has an energy E ,
then the escape peaks lie at energies E {511 keV and E {1.022 MeV
5. Backscatter Peak. These correspond to gamma-rays which have been scattered backwards in material surrounding the detector. The energy for back
scattered gamma-rays is approximately equaly for all incident energies at between 200 and 250 keV. The energy of the backscatter peak corresponds to
the energy of the photon after it is scattered. This is same as the dierence
between the full energy peak and the Compton edge.
6. Annihilation Peak. One observes a peak at 511 keV due to annihilation radiation from pair-production caused by the initial radiation in the surrounding
material (assuming E > 1.022 MeV). The 511 keV is then measured in the
detector.
7. X-ray Escape Peaks. A characteristic X-ray is emitted by the material in
the photoelectric process. This is usually reabsorbed, but occasionally it can
escape the detector. Thus a peak with an energy equal to the photo-peak
energy minus the X-ray energy can appear. This is only really a problem for
(a) low gamma-ray energies and (b) detectors with large surface to volume
ratios.
64
Figure 4.16: Gamma-ray interactions in a germanium crystal (Knoll p297).
4.4.2 Germanium Detector Eciency.
(See Knoll p427.)
The eciency of a germaium detector is usually given relative to that of a 3in
3in NaI(Tl) detector for the 1333 keV gamma-ray in 60 Ni (from a 60 Co -source).
Typical eciencies range from 30 % to 70 % for hyperpure germanium detectors.
The eciency repsonce varies as a function of energy and is usually empirically
deduced using a variety of standard calibration sources such as 152 Eu and 133 Ba (see
gure 4.18.)
4.4.3 The Compton Suppressed Spectrometer (CSS).
(Knoll p421.)
In order to reduce the (unwanted) Compton continuum events in a germanium
gamma-ray spectrum, the germanium detector can be surrounded by a high eciency gamma-ray scintillator (usually BGO or NaI(Tl)). This shield acts as veto
for Compton events which scatter out of the germanium detector. The peak to total
for the 1173+1333 keV lines from the 60 Co source for an unsuppressed detector is
only about 20 %. This rises to 50{60 % for a suppressed detector with almost no
loss in the number of counts in the full energy peak.
65
Figure 4.17: Gamma-ray spectra for (a) 137 Cs and (b) 60Co sources.
66
Figure 4.18: Gamma-ray spectra for (a) 152 Eu and (b) 133 Ba eciency calibration
sources.
NaI
photomultiplier
tubes
BGO
BGO
Liquid
nitrogen
‘cold finger’
Ge
NaI
incoming
gamma-ray
Figure 4.19: A Compton suppressed germanium detector
67
Coincidence Mode.
Compton suppression is even more valuable for coincidence measurements where 2
gamma-rays, in cascade, are measured from the same source in two separate detectors.
The P:T for 1 Ge 0.2, for 2 in coin P:T0.2 0.2 = 0.04
The P:T for 1 CSS 0.6, for 2 in coin P:T0.6 0.6 = 0.36
ie. the peak to total for gamma-gamma coincidences is 9 times better with
suppression shields than without.
4.5 Neutron Detectors.
4.5.1 Slow Neutrons.
(Knoll p481-485)
To detect neutrons with energies less than 0.5 eV (the so-called cadmium cut o),
a neutron induced reaction is used. The reaction emits charged particles (usually
alphas or protons) at high energies (5-10 MeV) due to the large Q-value for the
reaction.
Examples are the (a) 10 B+n!+7Li, (b) the 6Li+n!+3H or (c) the 3 He+n!3H+1 H
reactions which have Q-values of 2.79, 4.78 MeV and 0.76 MeV respectively.
The choice of reaction depends on the energy of the neutrons that are to be
measured, since the reaction cross-section varies largely with neutron energy. For
thermal neutrons ( 0:025eV, the 3 He+n reaction has the largest cross-section, but
the smallest energy signal. 3He is also rather expensive. The 6 L+n reaction has the
smallest cross-section for thermal neutrons but the highest Q-value (and thus the
largest output signal). The compromise is the 10 B+n reaction which is the most
widely used.
Detector Make-up.
(Knoll p487-494.)
10 B + n Reaction. Uses a BF3 proportional tube. Boron Triuoride (BF3)
acts as a target and the ll gas. The gas is enriched in the 10 B isotope.
68
6Li+n Lithium can be used in the form of Lithium Iodide an inorganic scintillator.
3He+n. Since 3He is a noble gas, detectors must be a gas detector. Usually
it is used as a ll gas for a proportional counter.
4.5.2 Fast Neutron Detection.
(Knoll p515,536)
For neutron energies comparable with the Q-values (a few MeV) the cross-section
for the nuclear reactions discussed in the previous section are vastly reduced and a
dierent method of detection is required.
Fast neutrons can be measured using methods which employ neutron moderation
(ie. slowing down the neutrons to energies low enough that the slow neutron reactions
outlined above can be used).
More usually plastic and liquid scintillator such as NE111 and NE213 are used.
These are proton recoil scintillators where the neutron elastically scatters o a hydrogen nucleus (proton).
Neutrons are often accompanied by a large gamma-ray ux. To distinguish between this gamma-ray radiation and neutrons two methods are usually used,
1. Time of Flight. Gamma-rays travel at the speed of light, regardless of their
energy. Relative to a standard timing pulse, all gamma-rays have the same time
response. Neutrons are (a) slower than gamma-rays and (b) have a distribution
of energies and thus velocities and thus `times of ight' to reach the detector
(see gure 4.20).
2. Pulse Shape Discrimination. Neutrons and gamma-rays give dierent
shaped pulses out of liquid scintillator (eg NE213). By plotting the relative
area of the fast component of the pulse against the total area, gamma-rays and
neutrons can be discimnated (see gure 4.21).
69
Figure 4.20: Time of ight discimation between gamma-rays and fast neutrons (Mohammadi et al. 1995).
Figure 4.21: Fast/slow component pulse shape discimation between gamma-rays and
fast neutrons (Mohammadi et al. 1995).
70
Chapter 5
Problems
5.1 Set 1
1. Do the following radiations have dicrete or continuous energy spectra (a) particles (b) electrons emited in -decay (c) characteristic x-rays (d) Bremstrahlung (e) -delayed neutrons (f) conversion electrons ? In those cases
where the spectrum is not discrete explain why and explain the relevance of
the end-point.
2. Dene the (a) activity, (b) exposure, (c) absorbed dose, (d) exposure rate and
dose equivalent of radioactive source.
3. (a) Estimate the exposure rate 3 metres from a 1 Ci source of 60 Co ( (60 Co)=13.2
Rcm2/hmCi). (b) Estimate the rate at 5 metres from the source.
4. For 10Ci of 60Co -radiation (1.33 and 1.17 MeV gamma-rays) emitted over
two days, assuming that the radiation is emitted isotropically, estimate the
absorbed dose and dose equivalent for an adult human being standing 5 metres
away. (Assume typical dimensions for adult human of 1.7 m tall by 0.5 m across
the shoulder, mass approximately 70 kg).
5. Assuming non-relativistic particles, estimate the energy deposited in a 100m
thick slice of silicon (Z=14) for protons and -particles at energies of (a)
5 MeV and (b) 10 MeV. (Assume that I 140 eV, 1AMU=1.6610 27 kg,
me=9.310 31 kg and N(Si)=5.41028m 3.)
6. (a) Write down the three main types of interactions between photons and
matter and give estimates of their dependence on the atomic number of the
71
stopping material. (b) Dene the term linear attenuation coecient in terms
of the partial attenuation coecients for these three processes.
7. (a) Write down the expression for the intensity of a photon beam I at a distance
x in a material given that for x = 0, I = I0. (b) Given that (Pb)=10.7
g/cm3 and (Al)=2.7 g/cm3 estimate the percentage of the radiation which
is absorbed for (i) 100 keV and (ii) 4 MeV. Assume that the thickness of the
aluminium is 5 cm and the thickness of the lead is 1 cm. (hint see gure 2.6
in the notes.)
8. What is the amplitude of the voltage pulse produced by collecting 106 electrons
on a capcitance of 100 pF?
72
5.2 Set 2
1. A spectrometer records two dierent -ray energies of 435 keV and 490 keV.
What is the required resolution of the system (in %) to just resolve the two
peaks?
2. A detector has a statistical resolution proportional to E 12 , together with a
noise contribution of 3.0 keV. At 1 MeV, the resolution is 5.0 keV. What
would be the resolution be at (1) 500 keV and (2) 2 MeV?
3. Given that a 1Ci source emits 1.33 MeV gamma-rays isotropically, and that
1000 counts per minute are measured in the photo-peak of a germanium detector placed 30 cm from the target, (a) what is the intrinsic peak eciency
of the detector at 1.33 MeV ? (b) Given that the peak to total at 1.33 MeV is
0.2, what is the intrinsic eciency at 1.33 MeV? (The detector dimensions are
10cm x 10cm x 10cm and 1 Ci=3.71010Bq).
4. What is the ion transit time for a 1 cm3 gas detector assuming a gas pressure
of 1Atm, an electric eld of 104V/m and an ion mobility of 110 4 m2Atm/Vs
?
5. For a chamber with plates 10 cm x 10 cm, separated by 1 cm, how large is the
voltage of the output pulse for a 1 MeV radiation, given that the W-value is
35 eV?
6. What is the depth of the depletion layer in a silicon diode junction with reverse bias voltage of 1 kV, assuming that the bulk impurity concentration is
1.51029m 3 and that the di-electric constant for silicon is 12.
7. Why are Si(Li) detectors usually preferred over germanium detectors for measuring X-rays ?
8. (a) Sketch a gamma-ray spectrum for a 1.333 MeV 60 Co source (ignoring the
1.17 MeV line) pointing out all the expected salient features. (b) How would
this plot change if the source was changed to a single 662 keV gamma-ray?
73
5.3 2RD exam 1996.
1. (a) Describe the physical processes which generate the following types of radiation. Do they give rise to discrete or continuous energy spectra? In the cases
where continuous spectra are observed, give an explanation of the maximum
energy. 9 marks
(1) alpha-particles
(2) beta-particles
(3) gamma-rays
(4) characteristic X-rays
(5) Bremsstrahlung
(6) Neutrons
(b) What would be the best materials (and why) to absorb these radiations
for radiation shielding puroposes. 3 marks
(c) Dene the quantity gamma-ray linear attenuation coecient, , in terms of
the various interaction processes for gamma-rays with matter. How do these
processes vary with the atomic number of the material ? 4 marks
(d) Write down an expression for the intensity of a narrow beam of photons
at a distance x through a material, if the intensity at x = 0 is I0. 1 mark
(e) Given that the density of aluminium is 2.7 g/cm3 and the mass attenuation
coecient for 1 MeV gamma-rays in aluminium is 0.1 cm2/g, what percentage of 1 MeV gamma-rays would be attenuated in (i) 1 cm and (ii) 5 cm of
aluminium shielding. 3 marks
2. (a) Dene the following quantities giving the SI units for each. (i) Activity (ii)
Exosure (iii) Absorbed Dose and (iv) Dose Equivalent 8 marks
(b) For a 10 Ci source of 60 Co (each disintegration gives rise to two gammarays, one of 1.33 MeV and the other of 1.17 MeV) emitting continuously over
an eight hour, estimate the absorbed dose and dose equivalent for a human
being standing (in air) 5m away from the source in this period of time. (You
may assume that the source emits the radiation isotropically and that typical
human dimensions are 1.7 m tall, 0.5 m across the shoulders with a mass of
about 60 kg. Assume that all the radiation stops in the human and that the
absorbed dose is uniform.) 8 marks
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(c) If instead of 2 gamma-rays, (i) 2 alpha particles were emitted from the
source, with the same energies as the gamma-rays in part (b), how would this
eect the absorbed dose and dose equivalent? 4 marks
3. (a) Sketch the pulse height spectrum for a Cs-137 source emitting a single
661 keV gamma-ray incident on a thin germanium detector, with the source is
surrounded by a lead housing. Label all the main features of the spectrum 4
marks.
(b) How would the pulse height spectrum in part (a) be altered if the energy
of the gamma-rays emitted by the source is 2.75 MeV instead of 661 keV ? 3
marks
(c) What limits the intrinsic energy resolution of germanium detectors for use
in gamma-ray studies? How can the resolution of a germanium detector be
optimised ? 3 marks
(d) If 2 gamma-ray peaks from the same source have energies of 861.3 keV and
865.3 keV, what is the required resolution of the germanium detector to just
resolve these two peaks? 2 marks
(e) A simple gas ionization chamber is used to measure the energy of 6 MeV
alpha-particles. If the W-value for the gas in the chamber is 30 eV per electronion pair, what would be the best expected full width half maximum for the
full energy peak if the Fano factor for this detector is 0.2. 5 marks
(f) If the anode and cathode plates in the detector discussed in part (e) have
dimensions of 10cm x 10 cm and are separated by 1cm, how large would the
output voltage pulse be for the 6 MeV alpha-particles. (You may assume that
1e = 1.610 19C and 0 = 8.8510 12 Fm 1). 3 marks
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