1.13 Basic Definitions for Atomic Structure Mean Atomic Mass (Standard Atomic Weight) Atomic Mass Constant and the Mole...

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1 Contents 1 Introduction to Modern Physics Fundamental Physical Constants Derived Physical Constants and Relationships Milestones in Modern Physics and Medical Physics Physical Quantities and Units Rules Governing Physical Quantities and Units The SI System of Units Non-SI Units Classification of Forces in Nature Classification of Fundamental Particles Classification of Radiation Classification of Ionizing Radiation Directly and Indirectly Ionizing Radiation Low LET and High LET Radiation Use of Ionizing Radiation Classification of Directly Ionizing Radiation Electrons Positrons Heavy Charged Particles Pions Classification of Indirectly Ionizing Photon Radiation Radiation Quantities and Units Dose Distribution in Water for Various Radiation Beams Dose Distribution in Water for Photon Beams Dose Distribution in Water for Neutron Beams Dose Distribution in Water for Electron Beams Dose Distribution in Water for Heavy Charged Particle Beams Choice of Radiation Beam and Prescribed Target Dose xxiii

2 xxiv Contents 1.13 Basic Definitions for Atomic Structure Mean Atomic Mass (Standard Atomic Weight) Atomic Mass Constant and the Mole Mean Molecular Mass (Standard Molecular Weight) Basic Definitions for Nuclear Structure Nuclear Binding Energies Nuclear Models Liquid-Drop Nuclear Model Shell Structure Nuclear Model Physics of Small Dimensions and Large Velocities Planck Energy Quantization Quantization of Electromagnetic Radiation Special Theory of Relativity Important Relativistic Relations Relativistic Mass Relativistic Force and Relativistic Acceleration Relativistic Kinetic Energy Total Relativistic Energy as a Function of Momentum Taylor Expansion and Classical Approximations for Kinetic Energy and Momentum Relativistic Doppler Shift Particle Wave Duality De Broglie Equation and de Broglie Wavelength Davisson Germer Experiment Thomson Reid Experiment General Confirmation of Particle Wave Duality Matter Waves Introduction to Wave Mechanics Quantum Mechanical Wave Equation Time-Independent Schrödinger Equation Measurable Quantities and Operators Transition Rate and the Fermi Second Golden Rule Particle Scattering and Born Collision Formula Uncertainty Principle Complementarity Principle Emission of Electrons from Material Surface: Work Function Thermionic Emission Tunneling Alpha Decay Tunneling Field Emission Tunneling

3 Contents xxv 1.29 Maxwell Equations Poynting Theorem and Poynting Vector Normal Probability Distribution Standard Probability Density Function Cumulative Distribution Function Error Function Coulomb Scattering General Aspects of Coulomb Scattering Geiger Marsden Experiment Thomson Model of the Atom Rutherford Model of the Atom Rutherford Scattering Kinematics of Rutherford Scattering Distance of Closest Approach in Head-on Collision Between α-particle and Nucleus General Relationship Between Impact Parameter and Scattering Angle Hyperbolic Trajectory and Distance of Closest Approach Hyperbola in Polar Coordinates Cross Sections for Rutherford Scattering Differential Cross-Section for Rutherford Scattering: Classical Derivation Differential Cross Section for Rutherford Scattering (Quantum-Mechanical Derivation) Screening of Nuclear Potential by Orbital Electrons Minimum Scattering Angle Effect of the Finite Size of the Nucleus Maximum Scattering Angle General Relationships for Differential Cross Section in Rutherford Scattering Total Rutherford Scattering Cross Section Mean Square Scattering Angle for Single Rutherford Scattering Mean Square Scattering Angle for Multiple Rutherford Scattering Importance of the Rutherford Scattering Experiment Mott Scattering Correction for Electron Spin Correction for Recoil of the Nucleus

4 xxvi Contents Differential Cross Section for Mott Scattering of Electrons on Point-Like Atomic Nuclei Hofstadter Correction for Finite Nuclear Size and the Form Factor General Aspects of Elastic Scattering of Charged Particles Differential Scattering Cross Section for a Single Scattering Event Characteristic Scattering Distance Minimum and Maximum Scattering Angles Total Cross Section for a Single Scattering Event Mean Square Scattering Angle for Single Scattering Molière Multiple Elastic Scattering Mean Square Scattering Angle for Multiple Scattering Radiation Length Mass Scattering Power Mass Scattering Power for Electrons Fermi-Eyges Pencil Beam Model for Electrons Dose Distribution for Pencil Electron Beam Determination of Electron Beam Kinetic Energy from Measured Mass Scattering Power Rutherford Bohr Model of the Atom Bohr Model of the Hydrogen Atom Radius of the Bohr Atom Velocity of the Bohr Electron Total Energy of the Bohr Electron Transition Frequency and Wave Number Atomic Spectra of Hydrogen Correction for Finite Mass of the Nucleus Positronium, Muonium, and Muonic Atom Quantum Numbers Stern Gerlach Experiment and Electron Spin Spin Orbit Coupling Successes and Limitations of the Bohr Atomic Model Correspondence Principle Multi-electron Atom Exclusion Principle Hartree Approximation for Multi-electron Atoms Periodic Table of Elements Ionization Energy of Atoms

5 Contents xxvii 3.3 Experimental Confirmation of the Bohr Atomic Model Emission and Absorption Spectra of Monoatomic Gases Moseley Experiment Franck Hertz Experiment Schrödinger Equation for Hydrogen Atom Schrödinger Equation for Ground State of Hydrogen Sample Calculations for Ground State of Hydrogen Production of X-Rays X-Ray Line Spectra Characteristic Radiation Fluorescence Yield and Auger Effect Emission of Radiation by Accelerated Charged Particle (Bremsstrahlung Production) Stationary Charged Particle: No Emission of Radiation Charged Particle Moving with Uniform Velocity: No Emission of Radiation Accelerated Charged Particle: Emission of Radiation Intensity of Radiation Emitted by Accelerated Charged Particle Power Emitted by Accelerated Charged Particle Through Electromagnetic Radiation (Classical Larmor Expression) Relativistic Larmor Relationship Relativistic Electric Field Produced by Accelerated Charged Particle Characteristic Angle Electromagnetic Fields Produced by Charged Particles Synchrotron Radiation Čerenkov Radiation Two-Particle Collisions Collisions of Two Particles: General Aspects Nuclear Reactions Conservation of Momentum in Nuclear Reaction Conservation of Energy in Nuclear Reaction Threshold Energy for Nuclear Reactions

6 xxviii Contents 5.3 Two-Particle Elastic Scattering: Energy Transfer General Energy Transfer from Projectile to Target in Elastic Scattering Energy Transfer in a Two-Particle Elastic Head-on Collision Classical Relationships for a Head-on Collision Special Cases for Classical Energy Transfer in a Head-on Collision Relativistic Relationships for a Head-on Collision Special Cases for Relativistic Energy Transfer in Head-on Collision Maximum Energy Transfer Fraction in Head-on Collision Interactions of Charged Particles with Matter General Aspects of Energy Transfer from Charged Particle to Medium Charged Particle Interaction with Coulomb Field of the Nucleus (Radiation Collision) Hard (Close) Collision Soft (Distant) Collision General Aspects of Stopping Power Radiation (Nuclear) Stopping Power Collision (Electronic) Stopping Power for Heavy Charged Particles Momentum and Energy Transfer from Heavy Charged Particle to Orbital Electron Minimum Energy Transfer and Mean Ionization/Excitation Energy Maximum Energy Transfer Classical Derivation of Mass Collision Stopping Power Bethe Collision Stopping Power Corrections to Bethe Collision Stopping Power Equation Collision Stopping Power Equations for Heavy Charged Particles Collision Stopping Power for Light Charged Particles Total Mass Stopping Power Radiation Yield Range of Charged Particles CSDA Range Maximum Penetration Depth

7 Contents xxix Range of Heavy Charged Particles in Absorbing Medium Range of Light Charged Particles (Electrons and Positrons) in Absorbers Mean Collision Stopping Power Restricted Collision Stopping Power Bremsstrahlung Targets Thin X-Ray Targets Thick X-Ray Targets Interactions of Photons with Matter General Aspects of Photon Interactions with Absorbers Narrow Beam Geometry Characteristic Absorber Thicknesses Other Attenuation Coefficients and Cross Sections Energy Transfer Coefficient and Energy Absorption Coefficient Broad Beam Geometry Classification of Photon Interactions with Absorber Atoms Thomson Scattering Thomson Differential Electronic Cross Section per Unit Solid Angle Thomson Total Electronic Cross Section Thomson Total Atomic Cross Section Incoherent Scattering (Compton Effect) Compton Wavelength-Shift Equation Relationship Between Scattering Angle and Recoil Angle Scattered Photon Energy as Function of Incident Photon Energy and Photon Scattering Angle Energy Transfer to Compton Recoil Electron Differential Electronic Cross Section for Compton Scattering Differential Electronic Cross Section per Unit Scattering Angle Differential Electronic Cross Section per Unit Recoil Angle Differential Klein Nishina Energy Transfer Cross Section Energy Distribution of Recoil Electrons Total Electronic Klein Nishina Cross Section for Compton Scattering

8 xxx Contents Electronic Energy Transfer Cross Section for Compton Effect Mean Energy Transfer Fraction for Compton Effect Binding Energy Effects and Corrections Compton Atomic Cross Section and Mass Attenuation Coefficient Compton Mass Energy Transfer Coefficient Rayleigh Scattering Differential Atomic Cross Section for Rayleigh Scattering Form Factor for Rayleigh Scattering Scattering Angles in Rayleigh Scattering Atomic Cross Section for Rayleigh Scattering Mass Attenuation Coefficient for Rayleigh Scattering Photoelectric Effect Conservation of Energy and Momentum in Photoelectric Effect Angular Distribution of Photoelectrons Atomic Cross Section for Photoelectric Effect Mass Attenuation Coefficient for Photoelectric Effect Energy Transfer to Charged Particles in Photoelectric Effect Photoelectric Probability Fluorescence Yield Mean Fluorescence Photon Energy Mean Fluorescence Emission Energy Mean Photoelectric Energy Transfer Fraction Mass Energy Transfer Coefficient for Photoelectric Effect Pair Production Conservation of Energy, Momentum and Charge in Pair Production Threshold Energy for Nuclear Pair Production and Triplet Production Energy Distribution of Electrons and Positrons in Nuclear Pair Production and Triplet Production Angular Distribution of Charged Particles in Pair Production Nuclear Screening Atomic Cross Section for Pair Production

9 Contents xxxi Mass Attenuation Coefficient for Pair Production Energy Transfer to Charged Particles in Nuclear Pair Production and Triplet Production Mass Energy Transfer Coefficient for Pair Production Positron Annihilation Photonuclear Reactions (Photodisintegration) Cross Section for Photonuclear Reaction Threshold Energy for Photonuclear Reaction Energy Transfer and Energy Absorption in Photon Interactions with Matter Macroscopic Attenuation Coefficient Energy Transfer from Photons to Charged Particles in Absorber General Characteristics of Mean Energy Transfer Fractions Relative Weights for Individual Effects Regions of Predominance for Individual Effects Mean Weighted Energy Transfer Fractions Total Mean Energy Transfer Fraction Mass Energy Transfer Coefficient Mean Energy Transferred from Photon to Charged Particles Energy Absorption Mean Radiation Fraction Total Mean Energy Absorption Fraction Mass Energy Absorption Coefficient Mean Energy Absorbed in Absorbing Medium Coefficients of Compounds and Mixtures Effects Following Photon Interactions with Absorber Summary of Photon Interactions Photoelectric Effect Rayleigh Scattering Compton Effect Pair Production Photonuclear Reactions Sample Calculations Example Example

10 xxxii Contents 9 Interactions of Neutrons with Matter General Aspects of Neutron Interactions with Absorbers Neutron Interactions with Nuclei of the Absorber Elastic Scattering Inelastic Scattering Neutron Capture Spallation Nuclear Fission Induced by Neutron Bombardment Neutron Kerma Neutron Kerma Factor Neutron Dose Deposition in Tissue Thermal Neutron Interactions in Tissue Interactions of Intermediate and Fast Neutrons with Tissue Neutron Beams in Medicine Boron Neutron Capture Therapy (BNCT) Radiotherapy with Fast Neutron Beams Machines for Production of Clinical Fast Neutron Beams Californium-252 Neutron Source In-vivo Neutron Activation Analysis Neutron Radiography Kinetics of Radioactive Decay General Aspects of Radioactivity Decay of Radioactive Parent into a Stable Daughter Radioactive Series Decay Parent! Daughter! Granddaughter Relationships Characteristic Time General Form of Daughter Activity Equilibria in Parent Daughter Activities Daughter Longer-Lived Than Parent Equal Half-Lives of Parent and Daughter Daughter Shorter-Lived Than Parent: Transient Equilibrium Daughter Much Shorter-Lived Than Parent: Secular Equilibrium Conditions for Parent Daughter Equilibrium Bateman Equations for Radioactive Decay Chain Mixture of Two or More Independently Decaying Radionuclides in a Sample Branching Decay and Branching Fraction

11 Contents xxxiii 11 Modes of Radioactive Decay Introduction to Radioactive Decay Processes Alpha Decay Decay Energy in Alpha Decay Alpha Decay of Radium-226 into Radon Beta Decay General Aspects of Beta Decay Beta Particle Spectrum Daughter Recoil in Beta Minus and Beta Plus Decay Beta Minus Decay General Aspects of Beta Minus Decay Beta Minus Decay Energy Beta Minus Decay of Free Neutron into Proton Beta Minus Decay of Cobalt-60 Into Nickel Beta Minus Decay of Cesium-137 Into Barium Beta Plus Decay General Aspects of the Beta Plus Decay Decay Energy in Beta Plus Decay Beta Plus Decay of Nitrogen-13 into Carbon Beta Plus Decay of Fluorine-18 into Oxygen Electron Capture Decay Energy in Electron Capture Recoil Kinetic Energy of Daughter Nucleus in Electron Capture Decay Electron Capture Decay of Beryllium-7 into Lithium Decay of Iridium Gamma Decay General Aspects of Gamma Decay Emission of Gamma Rays in Gamma Decay Gamma Decay Energy Resonance Absorption and Mössbauer Effect Internal Conversion General Aspects of Internal Conversion Internal Conversion Factor Spontaneous Fission Proton Emission Decay Decay Energy in Proton Emission Decay Example of Proton Emission Decay Example of Two-Proton Emission Decay

12 xxxiv Contents Neutron Emission Decay Decay Energy in Neutron Emission Decay Example of Neutron Emission Decay Chart of the Nuclides (Segrè Chart) Summary of Radioactive Decay Modes Production of Radionuclides Origin of Radioactive Elements (Radionuclides) Naturally-Occurring Radionuclides Man-Made (Artificial) Radionuclides Radionuclides in the Environment General Aspects of Nuclear Activation Nuclear Reaction Cross Section Thin Targets Thick Target Nuclear Activation with Neutrons (Neutron Activation) Infinite Number of Parent Nuclei: Saturation Model Finite Number of Parent Nuclei: Depletion Model Maximum Attainable Specific Activities in Neutron Activation Examples of Parent Depletion: Neutron Activation of Cobalt-59, Iridium-191, and Molybdenum Neutron Activation of the Daughter: The Depletion Activation Model Example of Daughter Neutron Activation: Iridium Practical Aspects of Neutron Activation Nuclear Fission Induced by Neutron Bombardment Nuclear Chain Reaction Nuclear Fission Chain Reaction Nuclear Reactor Nuclear Power Nuclear Fusion Chain Reaction Production of Radionuclides with Radionuclide Generator Molybdenum Technetium Decay Scheme Molybdenum Technetium Radionuclide Generator Production of Molybdenum-99 Radionuclide

13 Contents xxxv Nuclear Activation with Protons and Heavier Charged Particles Nuclear Reaction Energy and Threshold Energy Targets in Charged Particle Activation Waveguide Theory Microwave Propagation in Uniform Waveguide Boundary Conditions Differential Wave Equation in Cylindrical Coordinates Electric and Magnetic Fields in Uniform Waveguide General Conditions for Particle Acceleration Dispersion Relationship Transverse Magnetic TM 01 Mode Relationship Between Radiofrequency Phase Velocity and Electron Velocity in Uniform Waveguide Relationship Between Velocity of Energy Flow and Group Velocity in Uniform Waveguide Disk-Loaded Waveguide Capture Condition Particle Accelerators in Medicine Basic Characteristics of Particle Accelerators Practical Use of X-Rays Medical Physics Industrial Use of X-Rays X-Ray Crystallography X-Ray Spectroscopy X-Ray Astronomy Practical Considerations in Production of X-Rays Traditional Sources of X-Rays: X-Ray Tubes Crookes Tube and Crookes X-Ray Tube Coolidge X-Ray Tube Carbon Nanotube Based X-Ray Tube Circular Accelerators Betatron Cyclotron Microtron Synchrotron Synchrotron Light Source Clinical Linear Accelerator Linac Generations Components of Modern Linacs Linac Treatment Head Configuration of Modern Linacs

14 xxxvi Contents Pulsed Operation of Linacs Practical Aspects of Megavoltage X-Ray Targets and Flattening Filters Fundamentals of Radiation Dosimetry Ionizing Radiation Beams Quantities Used for Describing a Radiation Beam Important Radiometric Quantities Important Photon Interaction Coefficients Important Dosimetric Quantities Concept of Charged Particle Equilibrium Kerma Versus Absorbed Dose Absorbed Dose for Photons Absorbed Dose for Neutrons Example of Kerma and Absorbed Dose Calculation Radiation Dosimetry Systems Active Versus Passive Radiation Dosimetry System Absolute Versus Relative Radiation Dosimetry System Main Characteristics of Radiation Dosimetry Systems Radiation Dosimeters Cavity Theories for Radiation Dosimetry Small Cavity and Bragg Gray Cavity Theory for Photon Beams Large Cavity in Photon Beam Intermediate Cavity and Burlin Cavity Theory Media Used for Cavity, Wall, and Phantom Basic Calibration of Radiotherapy Machine Output Dosimetry Protocols Absolute Radiation Dosimetry Calorimetric Absolute Radiation Dosimetry Introduction to Calorimetry Basic Aspects of Absorbed Dose Calorimetry Properties of Thermistors Measurement of Thermistor Resistance Resistance versus Temperature Relationship for Thermistor Practical Aspects of Calorimetric Radiation Dosimetry Calorimetric Absolute Radiation Dosimetry: Summary

15 Contents xxxvii 16.2 Fricke Chemical Absolute Radiation Dosimetry Introduction to Fricke Chemical Absolute Radiation Dosimetry Radiolysis of Water Radiolytic Yield in Chemical Dosimetry Absorbed Dose in Chemical Dosimeter Background to Fricke Ferrous Sulfate Chemical Radiation Dosimetry Composition of Fricke Solution Components of Fricke Dosimeter Oxidation of Ferrous Ions to Ferric Ions Measurement of Radiation-Induced Ferric Concentration Molar Absorption Coefficient Versus Molecular Cross Section Dependence of Radiolytic Yield on Irradiation Conditions and Readout Temperature Determination of Cavity Dose in Fricke Chemical Dosimetry Determination of Dose to Water from Mean Dose to Cavity Fricke Chemical Absolute Radiation Dosimetry: Summary Ionometric Absolute Radiation Dosimetry Introduction to Cavity Ionization Chamber Ionization Chamber Dosimetry Systems Electrodes of an Ionization Chamber Configuration of Ionization Chamber-Based Dosimetry System Ion Pairs Produced in an Ionization Chamber Fate of Ions in an Ionization Chamber Ion Recombination Collection Efficiency and Saturation Curve of Ionization Chamber Charge Loss in Ionization Chamber for Continuous Beams Charge Loss in Ionization Chambers for Pulsed Radiation Beams Mean Energy to Produce an Ion Pair in Gas Dose to Ionization Chamber Cavity Gas Absolute Dosimetry with Ionization Chamber Standard Free-Air Ionization Chamber Standard Bragg Gray Cavity Ionization Chamber

16 xxxviii Contents Practical Ionization Chambers in Radiotherapy Department Absolute Dosimetry of Megavoltage X-Ray Beams and Electron Beams Standard Extrapolation Chamber Absolute Radiation Dosimetry: Summary Calorimetric Absolute Radiation Dosimetry System Fricke Chemical Absolute Radiation Dosimetry System Ionometric Absolute Radiation Dosimetry System Absoluteness of Absolute Radiation Dosimetry Systems Relative Radiation Dosimetry Relative Ionometric Radiation Dosimetry Area Survey Meter Re-Entrant Well Ionization Chamber Practical Ionization Chambers in Radiotherapy Department Liquid Ionization Chamber Relative Ionometric Dosimetry: Conclusions Luminescence Dosimetry Energy Band Structure in Solids Basic Aspects of Luminescence Dosimetry Kinetics of Thermoluminescence Thermoluminescence Dosimetry System TL Thermogram or TL Glow Curve Practical Considerations in Thermoluminescence Dosimetry Optically Stimulated Luminescence Dosimetry Optically Stimulated Luminescence (OSL) Reader Optically Stimulated Luminescence (OSL) Dosimeter TL Dosimetry and OSL Dosimetry: Summary Semiconductor Radiation Dosimetry Introduction to Semiconductor Physics Semiconductor p-n Junction Diode Radiation Dosimeter Silicon Diode Dosimeter: Practical Issues Diamond Radiation Dosimeter Semiconductor Dosimetry: Summary

17 Contents xxxix 17.4 Film Radiation Dosimetry Absorbance and Optical Density Radiographic Film Dosimetry General Characteristics of Radiographic Film Radiochromic Film Dosimetry Comparison Between Radiographic and Radiochromic Radiation Dosimetry Main Characteristics of Radiochromic Film Relative Radiation Dosimetry: Summary Appendix A Main Attributes of Nuclides Presented in This Book Appendix B Basic Characteristics of the Main Radioactive Decay Modes Appendix C Short Biographies of Scientists Whose Work is Discussed in This Book Appendix D Electronic Databases of Interest in Nuclear and Medical Physics Appendix E Nobel Prizes for Research in X-Rays Bibliography Index

APPLIED RADIATION PHYSICS

A PRIMER IN APPLIED RADIATION PHYSICS F A SMITH Queen Mary & Westfield College, London fe World Scientific m Singapore * New Jersey London Hong Kong CONTENTS CHAPTER 1 : SOURCES of RADIATION 1.1 Introduction