Radiation Physics for Medical Physiscists - E.B. Podgorsak

Medical Physics: A Specialty and Profession

XI

physics profession. Currently, the most common path to a career in medical physics is academic progression, through a B.Sc. degree in one of the physical sciences but preferably in physics, to a M.Sc. degree in medical physics, and then to a Ph.D. degree in medical physics.

The minimum academic requirement for a practicing medical physicist is a M.Sc. degree in medical physics, and this level is adequate for physicists who are mainly interested in clinical and service responsibilities. However, medical physicists working in academic environments should possess a Ph.D. degree in medical physics.

Academic training alone does not make a medical physicist. In addition to academic training, practical experience with medical problems and equipment is essential, and this may be acquired through on-the-job clinical training or, preferably, through a structured two-year traineeship (also referred to as internship or residency) program in a hospital after graduation with a M.Sc. or Ph.D. degree in medical physics.

Many graduate programs are now available to an aspiring medical physicist and progression through the three educational steps (undergraduate B.Sc. degree in physics; graduate degree in medical physics; and residency in medical physics) is feasible, albeit still somewhat di cult to follow in practice because of the relatively low number of accredited academic and residency programs in medical physics. The number of these programs is growing, however. We are now in a transition period and within a decade, progression through the three steps will become mandatory for physicists entering the medical physics profession. The sooner broad-based didactic and clinical training through accredited educational programs in medical physics becomes the norm, the better it will be for the medical physics profession and for the patients the profession serves.

Accreditation of Medical Physics Educational Programs

Many universities around the world o er academic and clinical educational programs in medical physics. To achieve international recognition for its graduates a medical physics educational program should be accredited by an international accreditation body that attests to the program’s meeting rigorous academic and clinical standards in medical physics. Currently, there is only one such international body, The Commission on Accreditation of Medical Physics Educational Programs (CAMPEP) that is sponsored by the American Association of Physicists in Medicine (AAPM), American College of Medical Physics (ACMP), American College of Radiology (ACR), and the Canadian College of Physicists in Medicine (CCPM). Eleven academic medical physics programs and 10 medical physics residency programs are currently accredited by the CAMPEP.

XII	Medical Physics: A Specialty and Profession

Certification

Several national professional medical physics organizations certify the competence of medical physicists. The certification is obtained through passing a rigorous written and oral examination that can be taken by candidates who possess a M.Sc. or Ph.D. degree in medical physics and have completed an accredited residency in medical physics. Currently the residency requirement is relaxed and a minimum of two years of work experience in medical physics after graduation with a M.Sc. or Ph.D. degree in medical physics is also accepted, because of the shortage of available residency positions.

The medical physics certification attests to the candidate’s competence in the delivery of patient care in one of the subspecialties of medical physics. The requirement that its medical physics sta be certified provides a medical institution with the necessary mechanism to ensure that high standard medical physics services are given to its patients.

Appointments and Areas of Activities

Medical physicists are involved in four areas of activities: (1) clinical service and consultation; (2) research and development ; (3) teaching; and (4) administration. They are usually employed in hospitals and other medical care facilities. Frequently the hospital is associated with a medical school and the physicists are members of the academic sta . In many non-teaching hospitals, physicists hold professional appointments in one of the clinical departments and are members of the professional sta of the hospital. Larger teaching hospitals usually employ a number of medical physicists who are organized into medical physics departments that provide physics services to clinical departments.

Career in Medical Physics

A career in medical physics is very rewarding and the work of medical physicists is interesting and versatile. A characteristic of modern societies is their ever-increasing preoccupation with health. Research in cancer and heart disease is growing yearly and many new methods for diagnosis and therapy are physical in nature, requiring the special skills of medical physicists not only in research but also in the direct application to patient care. Undergraduate students with a strong background in science in general and physics in particular who decide upon a career in medical physics will find their studies of medical physics interesting and enjoyable and their employment prospects after completion of studies excellent.

Contents

1 Introduction to Modern Physics . . . . . . . . . . . . . . . . . . . . . . . . . .			1
1.1	Fundamental Physical Constants . . . . . . . . . . . . . . . . . . . . . . . .		2
1.2	Derived Physical Constants and Relationships . . . . . . . . . . . .		3
1.3	Milestones in Modern Physics and Medical Physics . . . . . . . .		4
1.4	Physical Quantities and Units . . . . . . . . . . . . . . . . . . . . . . . . . .		5
1.5	Classification of Forces in Nature . . . . . . . . . . . . . . . . . . . . . . . .		6
1.6	Classification of Fundamental Particles . . . . . . . . . . . . . . . . . . .		6
1.7	Classification of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		7
1.8	Types and Sources of Directly Ionizing Radiation . . . . . . . . .		8
	1.8.1	Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	8
	1.8.2	Positrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	8
	1.8.3	Heavy Charged Particles . . . . . . . . . . . . . . . . . . . . . . . .	8
	1.8.4	Heavier Charged Particles . . . . . . . . . . . . . . . . . . . . . . .	9
	1.8.5	Pions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	9
1.9	Classification of Indirectly Ionizing Photon Radiation . . . . . .		9
1.10	Radiation Quantities and Units . . . . . . . . . . . . . . . . . . . . . . . . .		9
1.11	Dose in Water for Various Radiation Beams . . . . . . . . . . . . . .		10
	1.11.1	Dose Distributions for Photon Beams . . . . . . . . . . . . .	11
	1.11.2	Dose Distributions for Neutron Beams . . . . . . . . . . . .	13
	1.11.3	Dose Distributions for Electron Beams . . . . . . . . . . . .	13
	1.11.4	Dose Distributions
		for Heavy Charged Particle Beams . . . . . . . . . . . . . . .	14
1.12	Basic Definitions for Atomic Structure . . . . . . . . . . . . . . . . . . .		14
1.13	Basic Definitions for Nuclear Structure . . . . . . . . . . . . . . . . . . .		15
1.14	Nuclear Binding Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		16
1.15	Nuclear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		18
	1.15.1	Liquid-Drop Nuclear Model . . . . . . . . . . . . . . . . . . . . .	18
	1.15.2	Shell Structure Nuclear Model . . . . . . . . . . . . . . . . . . .	20
1.16	Physics of Small Dimensions and Large Velocities . . . . . . . . .		20
1.17	Planck’s Energy Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . .		21
1.18	Quantization of Electromagnetic Radiation . . . . . . . . . . . . . . .		22
1.19	Einstein’s Special Theory of Relativity . . . . . . . . . . . . . . . . . . .		23
1.20	Important Relativistic Relationships . . . . . . . . . . . . . . . . . . . . .		24
	1.20.1	Relativistic Mass m . . . . . . . . . . . . . . . . . . . . . . . . . . . .	25

XIV Contents
	1.20.2
		Relativistic Force F
		and Relativistic Acceleration a . . . . . . . . . . . . . . . . . . .	25
	1.20.3 Relativistic Kinetic Energy EK . . . . . . . . . . . . . . . . . . .		27
	1.20.4	Total Relativistic E
		as a Function of Momentum p . . . . . . . . . . . . . . . . . . .	28
	1.20.5 Taylor Expansion for Relativistic Kinetic Energy
		and Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	29
	1.20.6	Relativistic Doppler Shift . . . . . . . . . . . . . . . . . . . . . . .	29
1.21	Particle-Wave Duality: Davisson–Germer Experiment . . . . . .		30
1.22	Matter Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		31
	1.22.1 Introduction to Wave Mechanics . . . . . . . . . . . . . . . . .		32
	1.22.2	Quantum-Mechanical Wave Equation . . . . . . . . . . . . .	33
	1.22.3	Time-Independent Schr¨odinger Equation . . . . . . . . . .	35
	1.22.4 Measurable Quantities and Operators . . . . . . . . . . . . .		36
1.23	Uncertainty Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		37
1.24	Complementarity Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		38
1.25	Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		39
	1.25.1	Alpha Decay Tunneling . . . . . . . . . . . . . . . . . . . . . . . . .	40
	1.25.2	Field Emission Tunneling . . . . . . . . . . . . . . . . . . . . . . .	40
1.26	Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		40

2 Rutherford–Bohr Atomic Model . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.1 Geiger–Marsden Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.1.1Parameters of the Geiger–Marsden Experiment . . . . 44

2.1.2 Thomson’s Atomic Model . . . . . . . . . . . . . . . . . . . . . . . 46 2.2 Rutherford Atom and Rutherford Scattering . . . . . . . . . . . . . . 47 2.2.1 Rutherford Model of the Atom . . . . . . . . . . . . . . . . . . . 48 2.2.2 Kinematics of Rutherford Scattering . . . . . . . . . . . . . . 48

2.2.3Di erential Cross-Section

	for Rutherford Scattering . . . . . . . . . . . . . . . . . . . . . . .	52
2.2.4	Minimum and Maximum Scattering Angles . . . . . . . .	53
2.2.5	Total Rutherford Scattering Cross-Section . . . . . . . . .	54

2.2.6Mean Square Scattering Angle

for Single Rutherford Scattering . . . . . . . . . . . . . . . . . . 56

2.2.7Mean Square Scattering Angle

for Multiple Rutherford Scattering . . . . . . . . . . . . . . . 58 2.3 Bohr Model of the Hydrogen Atom . . . . . . . . . . . . . . . . . . . . . . 59 2.3.1 Radius of the Bohr Atom . . . . . . . . . . . . . . . . . . . . . . . 60 2.3.2 Velocity of the Bohr Electron . . . . . . . . . . . . . . . . . . . . 60 2.3.3 Total Energy of the Bohr Electron . . . . . . . . . . . . . . . . 61 2.3.4 Transition Frequency and Wave Number . . . . . . . . . . 63 2.3.5 Atomic Spectra of Hydrogen . . . . . . . . . . . . . . . . . . . . . 63 2.3.6 Correction for Finite Mass of the Nucleus . . . . . . . . . 64 2.3.7 Positronium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.3.8 Muonic Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

	Contents	XV
2.3.9	Quantum Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	65
2.3.10	Successes and Limitations
	of the Bohr Atomic Model . . . . . . . . . . . . . . . . . . . . . . .	66
2.3.11	Correspondence Principle . . . . . . . . . . . . . . . . . . . . . . .	66
2.4 Multi-electron Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		68
2.4.1	Exclusion Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	68

2.4.2Hartree’s Approximation

for Multi-electron Atoms . . . . . . . . . . . . . . . . . . . . . . . . 70 2.4.3 Periodic Table of Elements . . . . . . . . . . . . . . . . . . . . . . 72 2.4.4 Ionization Potential of Atoms . . . . . . . . . . . . . . . . . . . . 74

2.5Experimental Confirmation of the Bohr Atomic Model . . . . . 74

2.5.1Emission and Absorption Spectra

of Mono-Atomic Gases . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.5.2 Moseley’s Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.5.3 Franck-Hertz Experiment . . . . . . . . . . . . . . . . . . . . . . . 78

2.6 Schr¨odinger Equation for the Ground State of Hydrogen . . . 79

3 Production of X Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.1 X-Ray Line Spectra (Characteristic Radiation) . . . . . . . . . . . . 88 3.1.1 Characteristic Radiation . . . . . . . . . . . . . . . . . . . . . . . . 88 3.1.2 Auger E ect and Fluorescent Yield . . . . . . . . . . . . . . . 90

3.2Emission of Radiation by Accelerated Charged Particle

(Bremsstrahlung Production) . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.2.1 Velocity of Charged Particles . . . . . . . . . . . . . . . . . . . . 92

3.2.2Electric and Magnetic Fields

Produced by Accelerated Charged Particles . . . . . . . . 94

3.2.3Energy Density of the Radiation

Emitted by Accelerated Charged Particle . . . . . . . . . . 95

3.2.4Intensity of the Radiation

Emitted by Accelerated Charged Particle . . . . . . . . . . 95

3.2.5Power Emitted by Accelerated Charged Particle Through Electromagnetic Radiation

	(Classical Larmor Relationship) . . . . . . . . . . . . . . . . . .	96
3.2.6	Relativistic Larmor Relationship . . . . . . . . . . . . . . . . .	98
3.2.7	Relativistic Electric Field

Produced by Accelerated Charged Particle . . . . . . . . 98 3.2.8 Characteristic Angle θmax . . . . . . . . . . . . . . . . . . . . . . . 99 3.3 Synchrotron Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

ˇ

3.4 Cerenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.5 Practical Considerations in Production of Radiation . . . . . . . 105 3.6 Particle Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.6.1 Betatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.6.2 Cyclotron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.6.3 Microtron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

3.7 Linear Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

XVI Contents

3.7.1 Linac Generations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 3.7.2 Components of Modern Linacs . . . . . . . . . . . . . . . . . . . 111 3.7.3 Linac Treatment Head . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.7.4 Configuration of Modern Linacs . . . . . . . . . . . . . . . . . . 114

4 Two-Particle Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.1 Collisions of Two Particles: General Aspects . . . . . . . . . . . . . . 118 4.2 Nuclear Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.2.1 Conservation of Momentum in Nuclear Reactions . . . 122 4.2.2 Conservation of Energy in Nuclear Reactions . . . . . . 122 4.2.3 Threshold Energy Ethr for Nuclear Reactions . . . . . . 123

4.3 Two-Particle Elastic Scattering: Energy Transfer . . . . . . . . . . 124

4.3.1General Energy Transfer from Projectile m1

to Target m2 in Elastic Scattering . . . . . . . . . . . . . . . . 125

4.3.2Energy Transfer in a Two-Particle Elastic

Head-On Collision . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. . 126
4.4 Cross Sections for Elastic Scattering of Charged Particles	. . 130
4.4.1 Di erential Scattering Cross Section
for a Single Scattering Event . . . . . . . . . . . . . . . . . .	. . 131
4.4.2 E ective Characteristic Distance . . . . . . . . . . . . . . .	. . 131
4.4.3 Minimum and Maximum Scattering Angles . . . . . .	. . 133

4.4.4Total Cross Section for a Single Scattering Event . . . 134

4.4.5Mean Square Angle for a Single Scattering Event . . . 135

4.4.6 Mean Square Angle for Multiple Scattering . . . . . . . . 135 4.5 Mass Angular Scattering Power for Electrons . . . . . . . . . . . . . 137

5 Interactions of Charged Particles with Matter . . . . . . . . . . . . 141 5.1 General Aspects of Stopping Power . . . . . . . . . . . . . . . . . . . . . . 142 5.2 Radiative Stopping Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.3Collision Stopping Power for Heavy Charged Particles . . . . . 144

5.3.1Momentum Transfer from Heavy Charged Particle

	to Orbital Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	145
5.3.2	Linear Collision Stopping Power . . . . . . . . . . . . . . . . .	147
5.3.3	Minimum Energy Transfer

and Mean Ionization-Excitation Potential . . . . . . . . . 149 5.3.4 Maximum Energy Transfer . . . . . . . . . . . . . . . . . . . . . . 149 5.4 Mass Collision Stopping Power . . . . . . . . . . . . . . . . . . . . . . . . . . 150

5.5 Collision Stopping Power for Light Charged Particles . . . . . . 154 5.6 Total Mass Stopping Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.7 Bremsstrahlung (Radiation) Yield . . . . . . . . . . . . . . . . . . . . . . . 156 5.8 Range of Charged Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 5.9 Mean Stopping Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 5.10 Restricted Collision Stopping Power . . . . . . . . . . . . . . . . . . . . . . 161 5.11 Bremsstrahlung Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

5.11.1 Thin X-ray Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

	Contents XVII
5.11.2	Thick X-ray Targets . . . . . . . . . . . . . . . . . . . . . . . .	. . . . 164
5.11.3	Practical Aspects of Megavoltage X-ray Targets	. . . . 165

6 Interactions of Neutrons with Matter . . . . . . . . . . . . . . . . . . . . . 169

6.1General Aspects of Neutron Interactions with Absorbers . . . 170

6.2	Neutron Interactions with Nuclei of the Absorber . . . . . . . . .		171
	6.2.1	Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	171
	6.2.2	Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	172
	6.2.3	Neutron Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	172
	6.2.4	Spallation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	172
	6.2.5 Fission Induced by Neutron Bombardment . . . . . . . .		173
6.3	Neutron Kerma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		174
6.4	Neutron Kerma Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		175
6.5	Neutron Dose Deposition in Tissue . . . . . . . . . . . . . . . . . . . . . .		176
	6.5.1 Thermal Neutron Interactions in Tissue . . . . . . . . . . .		177

6.5.2Interactions of Intermediate and Fast Neutrons

with Tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 6.6 Neutron Beams in Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.6.1 Boron Neutron Capture Therapy (BNCT) . . . . . . . . . 180 6.6.2 Radiotherapy with Fast Neutron Beams . . . . . . . . . . . 182

6.6.3Machines for Production

of Clinical Fast Neutron Beams . . . . . . . . . . . . . . . . . . 182

6.6.4 Californium-252 Neutron Source . . . . . . . . . . . . . . . . . 184

6.7 Neutron Radiography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

7 Interactions of Photons with Matter . . . . . . . . . . . . . . . . . . . . . . 187

7.1General Aspects of Photon Interactions with Absorbers . . . . 188

7.2 Thomson Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

7.3 Compton Scattering (Compton E ect) . . . . . . . . . . . . . . . . . . . 193

7.3.1Relationship Between the Scattering Angle θ

and the Recoil Angle φ . . . . . . . . . . . . . . . . . . . . . . . . . 196

7.3.2Scattered Photon Energy hν

as a Function of hν and θ . . . . . . . . . . . . . . . . . . . . . . . 196

7.3.3Energy Transfer to the Compton Recoil Electron . . . 198

7.3.4Di erential Cross Section for Compton Scattering

deσcKN/dΩ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

7.3.5Di erential Energy Transfer Cross Section

(deσcKN)tr/dΩ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

7.3.6Energy Distribution of Recoil Electrons

deσcKN/dEK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

7.3.7Total Electronic Klein-Nishina Cross Section

for Compton Scattering eσcKN . . . . . . . . . . . . . . . . . . . . 204

7.3.8Energy Transfer Cross Section for Compton E ect

(eσcKN)tr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 7.3.9 Binding Energy E ects and Corrections . . . . . . . . . . . 207

XVIII Contents

7.3.10 Mass Attenuation Coe cient for Compton E ect . . . 210 7.3.11 Compton Mass Energy Transfer Coe cient . . . . . . . . 212 7.4 Rayleigh Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

7.4.1Di erential Atomic Cross Sections

for Rayleigh Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 215 7.4.2 Form Factor F (x, Z) for Rayleigh Scattering . . . . . . . 215 7.4.3 Scattering Angles in Rayleigh Scattering . . . . . . . . . . 216

7.4.4Atomic Cross Sections

for Rayleigh Scattering aσR . . . . . . . . . . . . . . . . . . . . . . 218

7.4.5Mass Attenuation Coe cient

for Rayleigh Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.5 Photoelectric E ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.5.1 Atomic Cross Section for Photoelectric E ect . . . . . . 222 7.5.2 Angular Distribution of Photoelectrons . . . . . . . . . . . 223

7.5.3Energy Transfer to Photoelectrons

in Photoelectric E ect . . . . . . . . . . . . . . . . . . . . . . . . . . 224

7.5.4Mass Attenuation Coe cient

for the Photoelectric E ect . . . . . . . . . . . . . . . . . . . . . . 225

7.5.5Mass Energy Transfer Coe cient

for the Photoelectric E ect . . . . . . . . . . . . . . . . . . . . . . 225 7.6 Pair Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

7.6.1Conservation of Energy, Momentum and Charge

for Pair Production in Free Space . . . . . . . . . . . . . . . . 227

7.6.2Threshold Energy for Pair Production

and Triplet Production . . . . . . . . . . . . . . . . . . . . . . . . .

228

7.6.3Energy Transfer to Charged Particles

	in Pair Production . . . . . . . . . . . . . . . . . . . . . . . . . . .	. . 230
7.6.4 Angular Distribution of Charged Particles . . . . . . .		. . 230
7.6.5	Nuclear Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. . 230
7.6.6 Atomic Cross Sections for Pair Production . . . . . .		. . 230
7.6.7	Mass Attenuation Coe cient for Pair Production	. . 233

7.6.8Mass Energy Transfer Coe cient

for Pair Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 7.6.9 Positron Annihilation . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 7.7 Photonuclear Reactions (Photodisintegration) . . . . . . . . . . . . . 235

7.8General Aspects of Photon Interaction with Absorbers . . . . . 236

7.8.1 Narrow Beam Geometry . . . . . . . . . . . . . . . . . . . . . . . . 237

7.8.2 Characteristic Absorber Thicknesses . . . . . . . . . . . . . . 238

7.8.3Other Attenuation Coe cients and Cross Sections . . 239

7.8.4	Broad Beam Geometry . . . . . . . . . . . . . . . . . . . . . . . . .	240
7.8.5	Classification of Photon Interactions . . . . . . . . . . . . . .	241

7.8.6Mass Attenuation Coe cient

of Compounds and Mixtures . . . . . . . . . . . . . . . . . . . . . 243 7.8.7 Tabulation of Attenuation Coe cients . . . . . . . . . . . . 243

Contents XIX

7.8.8 Energy Transfer Coe cient . . . . . . . . . . . . . . . . . . . . . . 244 7.8.9 Energy Absorption Coe cient . . . . . . . . . . . . . . . . . . . 248 7.8.10 E ects Following Photon Interactions . . . . . . . . . . . . . 250 7.9 Summary of Photon Interactions . . . . . . . . . . . . . . . . . . . . . . . . 250

7.10 Example 1: Interaction of 2 MeV Photons with Lead . . . . . . . 253 7.11 Example 2: Interaction of 8 MeV Photons with Copper . . . . 256

8 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 8.2 Decay of Radioactive Parent into a Stable Daughter . . . . . . . 265 8.3 Radioactive Series Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

8.3.1Parent → Daughter →

Granddaughter Relationships . . . . . . . . . . . . . . . . . . . . 268

8.3.2 Characteristic Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

8.3.3 General Form of Daughter Activity . . . . . . . . . . . . . . . 271

8.3.4 Equilibria in Parent-Daughter Activities . . . . . . . . . . 276

8.3.5 Bateman Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

8.3.6Mixture of Two or More Independently Decaying

Radionuclides in a Sample . . . . . . . . . . . . . . . . . . . . . . . 280

8.4 Activation of Nuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

8.4.1 Nuclear Reaction Cross Section . . . . . . . . . . . . . . . . . . 281

8.4.2 Neutron Activation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

8.4.3Infinite Number of Parent Nuclei:

Saturation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

8.4.4Finite Number of Parent Nuclei: Depletion Model . . 286

8.4.5Maximum Attainable Specific Activities

in Neutron Activation . . . . . . . . . . . . . . . . . . . . . . . . . .

292

8.4.6Examples of Parent Depletion: Neutron Activation

of Cobalt-59, Iridium-191 and Molybdenum-98 . . . . . 296

8.4.7Neutron Activation of the Daughter:

Depletion-Activation Model . . . . . . . . . . . . . . . . . . . . . 300

8.4.8Example of Daughter Neutron Activation:

		Iridium-192 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	302
	8.4.9 Practical Aspects of Radioactivation . . . . . . . . . . . . . .		307
8.5	Origin of Radioactive Elements (Radionuclides) . . . . . . . . . . .		312
	8.5.1	Man-Made (Artificial) Radionuclides . . . . . . . . . . . . . .	312
	8.5.2	Naturally-Occuring Radionuclides . . . . . . . . . . . . . . . .	312
	8.5.3 Radionuclides in the Environment . . . . . . . . . . . . . . . .		314
8.6	General Aspects of Radioactive Decay Processes . . . . . . . . . .		314
8.7	Alpha Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		316
	8.7.1 Decay Energy in α Decay . . . . . . . . . . . . . . . . . . . . . . .		317
	8.7.2 Alpha Decay of Radium-226 into Radon-222 . . . . . . .		319
8.8	Beta Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		321
	8.8.1 General Aspects of Beta Decay . . . . . . . . . . . . . . . . . .		321
	8.8.2	Beta Particle Spectrum . . . . . . . . . . . . . . . . . . . . . . . . .	322

XX Contents

8.8.3 Daughter Recoil in β− and β+ Decay . . . . . . . . . . . . . 324 8.9 Beta Minus Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

8.9.1 General Aspects of Beta Minus (β−) Decay . . . . . . . . 325 8.9.2 Beta Minus (β−) Decay Energy . . . . . . . . . . . . . . . . . . 326

8.9.3Beta Minus (β−) Decay of Cobalt-60

into Nickel-60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

8.9.4Beta Minus (β−) Decay of Cesium-137

into Barium-137 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 8.10 Beta Plus Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 8.10.1 General Aspects of the Beta Plus (β+) Decay . . . . . . 329 8.10.2 Decay Energy in β+ Decay . . . . . . . . . . . . . . . . . . . . . . 329

8.10.3 Beta Plus (β+) Decay of Nitrogen-13

into Carbon-13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 8.10.4 Beta Plus (β+) Decay of Fluorine-18

into Oxygen-18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 8.11 Electron Capture (EC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 8.11.1 Decay Energy in Electron Capture . . . . . . . . . . . . . . . 332

8.11.2 Recoil Kinetic Energy of the Daughter Nucleus

in Electron Capture Decay . . . . . . . . . . . . . . . . . . . . . . 333 8.11.3 Electron Capture Decay of Beryllium-7

into Lithium-7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 8.11.4 Decay of Iridium-192 . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 8.12 Gamma Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 8.12.1 General Aspects of Gamma (γ) Decay . . . . . . . . . . . . 336 8.12.2 Emission of Gamma Rays in Gamma Decay . . . . . . . 337 8.12.3 Gamma Decay Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 337 8.12.4 Resonance Absorption and the M¨ossbauer E ect . . . 338

8.13 Internal Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 8.13.1 General Aspects of Internal Conversion . . . . . . . . . . . 339 8.13.2 Internal Conversion Factor . . . . . . . . . . . . . . . . . . . . . . 340 8.14 Spontaneous Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

8.15 Proton Emission Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 8.15.1 Decay Energy in Proton Emission Decay . . . . . . . . . . 343 8.15.2 Example of Proton Emission Decay . . . . . . . . . . . . . . . 344 8.15.3 Example of Two-Proton Emission Decay . . . . . . . . . . 345 8.16 Neutron Emission Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 8.16.1 Decay Energy in Neutron Emission Decay . . . . . . . . . 346 8.16.2 Example of Neutron Emission Decay . . . . . . . . . . . . . . 347

8.17 Chart of the Nuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 8.18 General Aspects of Radioactive Decay . . . . . . . . . . . . . . . . . . . 349

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359