Radiation Physics for Medical Physicists (eBook)

Ervin B. Podgorsak was born in Vienna, Austria and grew up in Ljubljana, Slovenia where he completed his undergraduate studies in technical physics at the University of Ljubljana in 1968. He then studied at the University of Wisconsin in Madison, Wisconsin, USA and obtained M.Sc. and Ph.D. degrees in physics. He completed his post-doctoral studies in medical physics at the University of Toronto in 1974 and moved to McGill University in Montreal, where he currently holds positions of Professor of Medical Physics and Director of the Medical Physics department.

Preface 7
Medical Physics: A Specialty and Profession 9
Current Status 9
Brief History 9
Educational Requirements 10
Accreditation of Medical Physics Educational Programs 11
Certi.cation 12
Appointments and Areas of Activities 12
Career in Medical Physics 12
Contents 13
1 Introduction to Modern Physics 23
1.1 Fundamental Physical Constants 24
1.2 Derived Physical Constants and Relationships 25
1.3 Milestones in Modern Physics and Medical Physics 26
1.4 Physical Quantities and Units 27
1.5 Classification of Forces in Nature 28
1.6 Classification of Fundamental Particles 28
1.7 Classification of Radiation 29
1.8 Types and Sources of Directly Ionizing Radiation 30
1.8.1 Electrons 30
1.8.2 Positrons 30
1.8.3 Heavy Charged Particles 30
1.8.4 Heavier Charged Particles 31
1.8.5 Pions 31
1.9 Classification of Indirectly Ionizing Photon Radiation 31
1.10 Radiation Quantities and Units 31
1.11 Dose in Water for Various Radiation Beams 32
1.11.1 Dose Distributions for Photon Beams 33
1.11.2 Dose Distributions for Neutron Beams 35
1.11.3 Dose Distributions for Electron Beams 35
1.11.4 Dose Distributions for Heavy Charged Particle Beams 36
1.12 Basic Definitions for Atomic Structure 36
1.13 Basic Definitions for Nuclear Structure 37
1.14 Nuclear Binding Energies 38
1.15 Nuclear Models 40
1.15.1 Liquid-Drop Nuclear Model 40
1.15.2 Shell Structure Nuclear Model 42
1.16 Physics of Small Dimensions and Large Velocities 42
1.17 Planck’s Energy Quantization 43
1.18 Quantization of Electromagnetic Radiation 44
1.19 Einstein’s Special Theory of Relativity 45
1.20 Important Relativistic Relationships 46
1.20.1 Relativistic Mass 47
1.20.2 Relativistic Force 47
and Relativistic Acceleration 47
1.20.3 Relativistic Kinetic Energy 49
1.20.4 Total Relativistic 50
as a Function of Momentum 50
1.20.5 Taylor Expansion for Relativistic Kinetic Energy and Momentum 51
1.20.6 Relativistic Doppler Shift 51
1.21 Particle-Wave Duality: Davisson – Germer Experiment 52
1.22 Matter Waves 53
1.22.1 Introduction to Wave Mechanics 54
1.22.2 Quantum-Mechanical Wave Equation 55
1.22.3 Time-Independent Schrödinger Equation 57
1.22.4 Measurable Quantities and Operators 58
1.23 Uncertainty Principle 59
1.24 Complementarity Principle 60
1.25 Tunneling 61
1.25.1 Alpha Decay Tunneling 62
1.25.2 Field Emission Tunneling 62
1.26 Maxwell’s Equations 62
Ernest Rutherford and Niels Bohr, Giants of Modern Physics 64
2 Rutherford–Bohr Atomic Model 65
2.1 Geiger–Marsden Experiment 66
2.1.1 Parameters of the Geiger–Marsden Experiment 66
2.1.2 Thomson’s Atomic Model 68
2.2 Rutherford Atom and Rutherford Scattering 69
2.2.1 Rutherford Model of the Atom 70
2.2.2 Kinematics of Rutherford Scattering 70
Hyperbolic Trajectory 72
Hyperbola in Polar Coordinates 74
2.2.3 Differential Cross-Section for Rutherford Scattering 74
2.2.4 Minimum and Maximum Scattering Angles 75
2.2.5 Total Rutherford Scattering Cross-Section 76
2.2.6 Mean Square Scattering Angle for Single Rutherford Scattering 78
2.2.7 Mean Square Scattering Angle for Multiple Rutherford Scattering 80
2.3 Bohr Model of the Hydrogen Atom 81
2.3.1 Radius of the Bohr Atom 82
2.3.2 Velocity of the Bohr Electron 82
2.3.3 Total Energy of the Bohr Electron 83
2.3.4 Transition Frequency and Wave Number 85
2.3.5 Atomic Spectra of Hydrogen 85
2.3.6 Correction for Finite Mass of the Nucleus 86
2.3.7 Positronium 87
2.3.8 Muonic Atom 87
2.3.9 Quantum Numbers 87
2.3.10 Successes and Limitations of the Bohr Atomic Model 88
2.3.11 Correspondence Principle 88
2.4 Multi-electron Atoms 90
2.4.1 Exclusion Principle 90
2.4.2 Hartree’s Approximation for Multi-electron Atoms 92
2.4.3 Periodic Table of Elements 94
2.4.4 Ionization Potential of Atoms 96
2.5 Experimental Confirmation of the Bohr Atomic Model 96
2.5.1 Emission and Absorption Spectra of Mono-Atomic Gases 98
2.5.2 Moseley’s Experiment 99
2.5.3 Franck-Hertz Experiment 100
2.6 Schrödinger Equation for the Ground State of Hydrogen 101
Linear Accelerator Waveguide 108
3 Production of X Rays 109
3.1 X-Ray Line Spectra (Characteristic Radiation) 110
3.1.1 Characteristic Radiation 110
3.1.2 Auger Effect and Fluorescent Yield 112
3.2 Emission of Radiation by Accelerated Charged Particle ( Bremsstrahlung Production) 114
3.2.1 Velocity of Charged Particles 114
Stationary Charged Particle 115
Charged Particle Moving with a Uniform Velocity 115
Accelerated Charged Particle 116
3.2.2 Electric and Magnetic Fields Produced by Accelerated Charged Particles 116
3.2.3 Energy Density of the Radiation Emitted by Accelerated Charged Particle 117
3.2.4 Intensity of the Radiation Emitted by Accelerated Charged Particle 117
3.2.5 Power Emitted by Accelerated Charged Particle Through Electromagnetic Radiation ( Classical Larmor Relationship) 118
3.2.6 Relativistic Larmor Relationship 120
3.2.7 Relativistic Electric Field Produced by Accelerated Charged Particle 120
3.2.8 Characteristic Angle 121
3.3 Synchrotron Radiation 124
3.4 .Cerenkov Radiation 125
3.5 Practical Considerations in Production of Radiation 127
3.6 Particle Accelerators 129
3.6.1 Betatron 129
3.6.2 Cyclotron 130
3.6.3 Microtron 131
3.7 Linear Accelerator 132
3.7.1 Linac Generations 132
3.7.2 Components of Modern Linacs 133
3.7.3 Linac Treatment Head 135
3.7.4 Configuration of Modern Linacs 136
An Electron Pencil Beam Penetrating into Water 138
4 Two-Particle Collisions 139
4.1 Collisions of Two Particles: General Aspects 140
4.2 Nuclear Reactions 143
4.2.1 Conservation of Momentum in Nuclear Reactions 144
4.2.2 Conservation of Energy in Nuclear Reactions 144
4.2.3 Threshold Energy Ethr for Nuclear Reactions 145
4.3 Two-Particle Elastic Scattering: Energy Transfer 146
4.3.1 General Energy Transfer from Projectile m1 to Target m2 in Elastic Scattering 147
4.3.2 Energy Transfer in a Two-Particle Elastic Head-On Collision 148
Classical Relationships for a Head-On Collision 148
Special Cases for the Classical Energy Transfer in a Head- On Collision 149
Relativistic Relationships for a Head-On Collision 150
Special Cases for the Relativistic Energy Transfer in a Head- On Collision 151
4.4 Cross Sections for Elastic Scattering of Charged Particles 152
4.4.1 Differential Scattering Cross Section for a Single Scattering Event 153
4.4.2 Effective Characteristic Distance 153
4.4.3 Minimum and Maximum Scattering Angles 155
4.4.4 Total Cross Section for a Single Scattering Event 156
4.4.5 Mean Square Angle for a Single Scattering Event 157
4.4.6 Mean Square Angle for Multiple Scattering 157
4.5 Mass Angular Scattering Power for Electrons 159
Lichtenberg Figures 162
5 Interactions of Charged Particles with Matter 163
5.1 General Aspects of Stopping Power 164
5.2 Radiative Stopping Power 165
5.3 Collision Stopping Power for Heavy Charged Particles 166
5.3.1 Momentum Transfer from Heavy Charged Particle to Orbital Electron 167
5.3.2 Linear Collision Stopping Power 169
5.3.3 Minimum Energy Transfer and Mean Ionization- Excitation Potential 171
5.3.4 Maximum Energy Transfer 171
5.4 Mass Collision Stopping Power 172
5.5 Collision Stopping Power for Light Charged Particles 176
5.6 Total Mass Stopping Power 178
5.7 Bremsstrahlung (Radiation) Yield 178
5.8 Range of Charged Particles 181
5.9 Mean Stopping Power 182
5.10 Restricted Collision Stopping Power 183
5.11 Bremsstrahlung Targets 184
5.11.1 Thin X-ray Targets 186
5.11.2 Thick X-ray Targets 186
5.11.3 Practical Aspects of Megavoltage X-ray Targets 187
. Cerenkov Radiation in a Nuclear Reactor 190
6 Interactions of Neutrons with Matter 191
6.1 General Aspects of Neutron Interactions with Absorbers 192
6.2 Neutron Interactions with Nuclei of the Absorber 193
6.2.1 Elastic Scattering 193
6.2.2 Inelastic Scattering 194
6.2.3 Neutron Capture 194
6.2.4 Spallation 194
6.2.5 Fission Induced by Neutron Bombardment 195
6.3 Neutron Kerma 196
6.4 Neutron Kerma Factor 197
6.5 Neutron Dose Deposition in Tissue 198
6.5.1 Thermal Neutron Interactions in Tissue 199
Thermal Neutron Capture in Nitrogen-14 in Tissue 199
Thermal Neutron Capture in Hydrogen-1 in Tissue 200
6.5.2 Interactions of Intermediate and Fast Neutrons with Tissue 201
6.6 Neutron Beams in Medicine 202
6.6.1 Boron Neutron Capture Therapy (BNCT) 202
6.6.2 Radiotherapy with Fast Neutron Beams 204
6.6.3 Machines for Production of Clinical Fast Neutron Beams 204
Deuterium-Tritium (DT) Generator 204
Fast Neutron Beams from Cyclotrons 205
6.6.4 Californium-252 Neutron Source 206
6.7 Neutron Radiography 206
Computerized Tomography Images and Leonardo Da Vinci 208
7 Interactions of Photons with Matter 209
7.1 General Aspects of Photon Interactions with Absorbers 210
7.2 Thomson Scattering 211
7.3 Compton Scattering (Compton Effect) 215
7.3.1 Relationship Between the Scattering Angle and the Recoil Angle 218
7.3.2 Scattered Photon Energy 218
7.3.3 Energy Transfer to the Compton Recoil Electron 220
7.3.4 Differential Cross Section for Compton Scattering 221
7.3.5 Differential Energy Transfer Cross Section 225
7.3.6 Energy Distribution of Recoil Electrons 225
7.3.7 Total Electronic Klein-Nishina Cross Section 226
7.3.8 Energy Transfer Cross Section for Compton Effect 228
7.3.9 Binding Energy Effects and Corrections 229
7.3.10 Mass Attenuation Coefficient for Compton E.ect 232
7.3.11 Compton Mass Energy Transfer Coefficient 234
7.4 Rayleigh Scattering 236
7.4.1 Differential Atomic Cross Sections for Rayleigh Scattering 237
7.4.2 Form Factor F(x,Z) for Rayleigh Scattering 237
7.4.3 Scattering Angles in Rayleigh Scattering 238
7.4.4 Atomic Cross Sections for Rayleigh Scattering 240
7.4.5 Mass Attenuation Coeficient for Rayleigh Scattering 241
7.5 Photoelectric Effect 241
7.5.1 Atomic Cross Section for Photoelectric Effect 244
7.5.2 Angular Distribution of Photoelectrons 245
7.5.3 Energy Transfer to Photoelectrons in Photoelectric Effect 246
7.5.4 Mass Attenuation Coefficient for the Photoelectric Effect 247
7.5.5 Mass Energy Transfer Coefficient for the Photoelectric Effect 247
7.6 Pair Production 249
7.6.1 Conservation of Energy, Momentum and Charge for Pair Production in Free Space 249
7.6.2 Threshold Energy for Pair Production and Triplet Production 250
7.6.3 Energy Transfer to Charged Particles in Pair Production 252
7.6.4 Angular Distribution of Charged Particles 252
7.6.5 Nuclear Screening 252
7.6.6 Atomic Cross Sections for Pair Production 252
7.6.7 Mass Attenuation Coefficient for Pair Production 255
7.6.8 Mass Energy Transfer Coefficient for Pair Production 255
7.6.9 Positron Annihilation 256
7.7 Photonuclear Reactions (Photodisintegration) 257
7.8 General Aspects of Photon Interaction with Absorbers 258
7.8.1 Narrow Beam Geometry 259
7.8.2 Characteristic Absorber Thicknesses 260
7.8.3 Other Attenuation Coefficients and Cross Sections 261
7.8.4 Broad Beam Geometry 262
7.8.5 Classification of Photon Interactions 263
7.8.6 Mass Attenuation Coefficient of Compounds and Mixtures 265
7.8.7 Tabulation of Attenuation Coefficients 265
7.8.8 Energy Transfer Coefficient 266
7.8.9 Energy Absorption Coefficient 270
7.8.10 Effects Following Photon Interactions 272
7.9 Summary of Photon Interactions 272
Photoelectric Effect 273
Rayleigh Scattering 274
Compton Effect 274
Pair Production 275
7.10 Example 1: Interaction of 2 MeV Photons with Lead 275
Calculate 275
7.11 Example 2: Interaction of 8 MeV Photons with Copper 278
8 Radioactivity 285
8.1 Introduction 286
8.2 Decay of Radioactive Parent into a Stable Daughter 287
8.3 Radioactive Series Decay 290
8.3.1. Parent- Daughter- Granddaughter Relationship 290
8.3.2 Characteristic Time 292
8.3.3 General Form of Daughter Activity 293
8.3.4 Equilibria in Parent-Daughter Activities 298
8.3.5 Bateman Equations 302
8.3.6 Mixture of Two or More Independently Decaying Radionuclides in a Sample 302
8.4 Activation of Nuclides 303
8.4.1 Nuclear Reaction Cross Section 303
Thin Targets 304
Thick Targets 305
8.4.2 Neutron Activation 305
8.4.3 Infinite Number of Parent Nuclei: Saturation Model 306
8.4.4 Finite Number of Parent Nuclei: Depletion Model 308
8.4.5 Maximum Attainable Specific Activities in Neutron Activation 314
8.4.6 Examples of Parent Depletion: Neutron Activation of Cobalt- 59, Iridium- 191 and Molybdenum- 98 318
8.4.7 Neutron Activation of the Daughter: Depletion- Activation Model 322
8.4.8 Example of Daughter Neutron Activation: Iridium-192 324
8.4.9 Practical Aspects of Radioactivation 329
Activation with Thermal Neutrons 329
Activation with Protons or Heavier Charged Particles 330
Targets 332
8.5 Origin of Radioactive Elements (Radionuclides) 334
8.5.1 Man-Made (Artificial) Radionuclides 334
8.5.2 Naturally-Occuring Radionuclides 334
8.5.3 Radionuclides in the Environment 336
8.6 General Aspects of Radioactive Decay Processes 336
8.7 Alpha Decay 338
8.7.1 Decay Energy in á Decay 339
8.7.2 Alpha Decay of Radium-226 into Radon-222 341
8.8 Beta Decay 343
8.8.1 General Aspects of Beta Decay 343
8.8.2 Beta Particle Spectrum 344
8.8.3 Daughter Recoil in ß- and ß+ 346
8.9 Beta Minus Decay 347
8.9.1 General Aspects of Beta Minus ( ß- Deca)y 347
8.9.2 Beta Minus ( ß-) Decay Energy 348
8.9.3 Beta Minus ( ß-) Decay of Cobalt-60 into Nickel-60 348
8.9.4 Beta Minus ( ß-) Decay of Cesium-137 into Barium-137 350
8.10 Beta Plus Decay 351
8.10.1 General Aspects of the Beta Plus ( ß+) Decay 351
8.10.2 Decay Energy in ß+ Decay 351
8.10.3 Beta Plus ( ß+) Decay of Nitrogen-13 into Carbon-13 352
8.10.4 Beta Plus ( ß+) Decay of Fluorine-18 into Oxygen-18 353
8.11 Electron Capture (EC) 354
8.11.1 Decay Energy in Electron Capture 354
8.11.2 Recoil Kinetic Energy of the Daughter Nucleus in Electron Capture Decay 355
8.11.3 Electron Capture Decay of Beryllium-7 into Lithium-7 356
8.11.4 Decay of Iridium-192 357
8.12 Gamma Decay 358
8.12.1 General Aspects of Gamma Decay 358
8.12.2 Emission of Gamma Rays in Gamma Decay 359
8.12.3 Gamma Decay Energy 359
8.12.4 Resonance Absorption and the M¨ ossbauer E.ect 360
8.13 Internal Conversion 361
8.13.1 General Aspects of Internal Conversion 361
8.13.2 Internal Conversion Factor 362
8.14 Spontaneous Fission 363
8.15 Proton Emission Decay 364
8.15.1 Decay Energy in Proton Emission Decay 365
8.15.2 Example of Proton Emission Decay 366
8.15.3 Example of Two-Proton Emission Decay 367
8.16 Neutron Emission Decay 367
8.16.1 Decay Energy in Neutron Emission Decay 368
8.16.2 Example of Neutron Emission Decay 369
8.17 Chart of the Nuclides 369
8.18 General Aspects of Radioactive Decay 371
Bibliography 381
Appendix 1. Short Biographies of Scientists Whose Work Is Discussed in This Book 383
Appendix 2. Roman Letter Symbols 425
Appendix 3. Greek Letter Symbols 433
Appendix 4. Acronyms 437
Appendix 5. Electronic Databases of Interest in Nuclear and Medical Physics 439
Appendix 6. International Organizations 443
Index 445

3 Production of X Rays ( p. 87)

This chapter is devoted to a study of the production of the two known types of x rays: characteristic radiation and bremsstrahlung. Both types of x rays are important in medical physics, since both are used extensively in diagnostic imaging and in external beam radiotherapy. Characteristic x-rays are produced by electronic transitions in atoms triggered by vacancies in inner electronic shells of the absorber atom.

Bremsstrahlung, on the other hand, is produced by Coulomb interactions between an energetic light charged particle and the nucleus of the absorber atom. Vacancies in electronic shells of atoms can be produced by various means such as Coulomb interactions, photon interactions, nuclear decay, positron annihilation and Auger effect, however, x-rays used in medicine are produced only through Coulomb interactions of energetic electrons with orbital electrons and nuclei of an x-ray target.

This chapter provides a discussion of theoretical and practical aspects of x-ray production, briefy introduces Cerenkov radiation and synchrotron radiation, both of some interest in nuclear and medical physics, and concludes with a brief discussion of various accelerators of interest in medicine.

3.1 X-Ray Line Spectra (Characteristic Radiation)
A vacancy in an atomic shell plays an important role in physics and chemistry. De.ned as an electron missing from the normal complement of electrons in a given atomic shell, a vacancy can be produced by eight different effects or interactions ranging from various photon-atom interactions through charge particle-atom interactions to nuclear effects.

Depending on the nature and energy of the interaction, the vacancy may occur in the outer shell or in one of the inner shells of the atom. The list of the 8 effects for production of shell vacancy in an atom is as follows:

1. Photoelectric effect (see Sect. 7.5)
2. Compton scattering (see Sect. 7.3)
3. Triplet production (see Sect. 7.6.1)
4. Charged particle Coulomb interaction with an atom (see Sect. 5.3.1)
5. Internal conversion (see Sect. 8.9.3)
6. Electron capture (see Sect. 8.8.4)
7. Positron annihilation (see Sect. 7.6.7)
8. Auger effect (see Sect. 3.1.2)

An atom with a vacancy in its inner shell is in a highly excited state and returns to its ground state through a series of electronic transitions. Electrons from higher atomic shells will fill the shell vacancies and the energy difference in binding energies between the initial and final shell or sub-shell will be emitted from the atom in one of two ways:

1. Radiatively in the form of characteristic (fluorescent) radiation.

2. Non-radiatively in the form of Auger electrons, Coster-Kronig electrons or super Coster-Kronig electrons.

3.1.1 Characteristic Radiation

Radiative transitions result in emission of photons that are called characteristic radiation, since the wavelength ? and energy h? of the emitted photon are characteristic of the atom in which the photon originated.