Fundamentals of Ionizing Radiation Dosimetry

Fundamentals of Ionizing RadiationDosimetry

Pedro Andreo, David T. Burns, Alan E. Nahum,Jan Seuntjens, and Frank H. Attix

Authors

Prof. Pedro Andreo, FInstP, CPhysKarolinska University Hospital171 76 StockholmSweden

Dr. David T. Burns, FInstPBureau International desPoids et MésuresPavillon de Breteuil92312 Sèvres CedexFrance

Prof. Alan E. Nahum, FIPEMVisiting ProfessorPhysics DepartmentUniversity of LiverpoolUnited Kingdom

Prof. Jan Seuntjens, FCCPM, FAAPM,FCOMPMcGill UniversityMedical Physics UnitCancer Research ProgramResearch InstituteMcGill University Health Centre1001 Décarie BlvdMontreal QC H4A 3J1Canada

Frank H. Attix†

Cover CreditsThe cover image was kindly provided byDr Jörg Wulff.

†Deceased

All books published by Wiley-VCH arecarefully produced. Nevertheless, authors,editors, and publisher do not warrant theinformation contained in these books,including this book, to be free of errors.Readers are advised to keep in mind thatstatements, data, illustrations, proceduraldetails or other items may inadvertentlybe inaccurate.

Library of Congress Card No.: applied for

British Library Cataloguing-in-PublicationDataA catalogue record for this book is avail-able from the British Library.

Bibliographic information published bythe Deutsche NationalbibliothekThe Deutsche Nationalbibliotheklists this publication in the DeutscheNationalbibliografie; detailedbibliographic data are available on theInternet at <http://dnb.d-nb.de>.

© 2017 Wiley-VCH Verlag GmbH & Co.KGaA, Boschstr. 12, 69469 Weinheim,Germany

All rights reserved (including those oftranslation into other languages). No partof this book may be reproduced in anyform – by photoprinting, microfilm, orany other means – nor transmitted ortranslated into a machine languagewithout written permission from thepublishers. Registered names, trademarks,etc. used in this book, even when notspecifically marked as such, are not to beconsidered unprotected by law.

Print ISBN: 978-3-527-40921-1ePDF ISBN: 978-3-527-80823-6ePub ISBN: 978-3-527-80824-3Mobi ISBN: 978-3-527-80822-9

Typesetting SPi Global Private Limited,Chennai, IndiaPrinting and Binding

Printed on acid-free paper

v

Contents

Preface xixQuantities and symbols xxiiiAcronyms xxxix

1 Background and Essentials 11.1 Introduction 11.2 Types and Sources of Ionizing Radiation 11.3 Consequences of the Random Nature of Radiation 41.4 Interaction Cross Sections 61.5 Kinematic Relativistic Expressions 91.6 Atomic Relaxations 111.6.1 Radiative and Non-radiative Transitions 131.6.2 Transition Probabilities and Fluorescence and Auger Yields 161.6.3 Emission Cross Sections 221.7 Evaluation of Uncertainties 221.7.1 Accuracy and Precision –Error and Uncertainty 221.7.2 Type A Standard Uncertainty 241.7.3 Type B Standard Uncertainty 251.7.4 Combined and Expanded Uncertainty 261.7.5 Law of Propagation of Uncertainty 26

Exercises 28

2 Charged-Particle Interactions with Matter 292.1 Introduction 292.2 Types of Charged-Particle Interactions 312.2.1 Elastic Interactions 322.2.2 Inelastic ‘Soft‘ Collisions 332.2.3 Inelastic ‘Hard‘ Collisions 342.2.4 Inelastic Radiative Interactions 352.3 Elastic Scattering 362.3.1 Single Elastic Scattering (Rutherford) 362.3.2 Screening Angle 382.3.3 Overview of Other Single Elastic ScatteringTheories 412.3.4 Multiple Elastic Scattering 43

vi Contents

2.3.4.1 The Gaussian Approach: Multiple Small-Angle ScatteringTheory 44

2.3.4.2 Molière’s Theory 472.3.4.3 Goudsmit – SaundersonTheory 512.3.5 Scattering Power 542.4 Inelastic Scattering and Energy Loss 552.4.1 Single Inelastic Scattering 562.4.1.1 The GOS, the OOS, and Dielectric Response

Functions 582.4.2 Multiple Inelastic Scattering: Electronic Stopping Power 612.4.3 Stopping Number 662.4.4 The I-Value (Mean Excitation Energy) 682.4.5 Shell Corrections 712.4.6 Density Effect Correction (Polarization) 732.4.7 Important Features of the Stopping Power Formula 772.4.7.1 Dependence on the Stopping Medium 792.4.7.2 Dependence on Particle Energy 812.4.7.3 Dependence on Particle Charge 812.4.7.4 Dependence on Particle Mass 822.4.7.5 Relativistic Scaling Considerations 822.4.7.6 Other Aspects 822.4.8 Electronic Stopping Power for Electrons and Positrons 842.4.9 Accuracy of Stopping-Power Calculations 862.4.10 Impact Ionization 882.4.11 The Bragg Peak 902.4.12 Restricted Electronic Stopping Power 912.4.13 Energy Loss Straggling 942.5 Radiative Energy Loss: Bremsstrahlung 952.5.1 Radiative Stopping Power 982.5.2 Radiation Yield 1012.5.3 Radiation Length 1022.6 Total Stopping Power 1032.6.1 The Bragg Additive Rule for Compounds 1032.7 Range of Charged Particles 1042.7.1 Continuous-Slowing-Down Range and Range Straggling 1052.7.2 Detour Factor 1062.8 Number and Energy Distributions of Secondary Particles 1062.8.1 Number and Energy of Knock-On Electrons 1082.8.2 Number and Energy of Bremsstrahlung Photons 1092.9 Nuclear Stopping Power and Interactions by Heavy Charged

Particles 1122.10 TheW -Value (Mean Energy to Create an Ion Pair) 1142.10.1 Calculation ofW from the Energy Balance 1152.10.2 Direct Calculation from Cross Sections 1162.10.3 Calculation from the Slowing-Down Spectrum 1172.10.4 Concluding Remarks 118

Contents vii

2.11 Addendum–Derivation of Expressions for the Elastic and InelasticScattering of Heavy Charged Particles 119

2.11.1 QuantumMechanics Formalism for Elastic Scattering 1202.11.1.1 Partial-Wave Analysis (PWA) 1232.11.2 QuantumMechanics Formalism for Inelastic Scattering (Bethe

Theory) 1262.11.2.1 Stopping Power 1312.11.3 Classical Treatment of Elastic and Inelastic Scattering 1342.11.3.1 Elastic Scattering 1352.11.3.2 Inelastic Scattering 1352.11.3.3 Stopping Power 136

Exercises 139

3 Uncharged-Particle Interactions with Matter 1433.1 Introduction 1433.2 Photon Interactions with Matter 1433.3 Photoelectric Effect 1453.3.1 Kinematics 1463.3.2 Cross Section 1473.4 Thomson Scattering 1543.5 Rayleigh Scattering (Coherent Scattering) 1573.6 Compton Scattering (Incoherent Scattering) 1613.6.1 Kinematics 1623.6.2 Cross Section 1663.6.3 Binding Effects and Doppler Broadening 1723.7 Pair Production and Triplet Production 1783.7.1 Kinematics 1793.7.2 Cross Section 1813.7.2.1 Pair Production 1813.7.2.2 Triplet Production 1873.7.2.3 Total Pair-Production Cross Section 1883.8 Positron Annihilation 1883.8.1 Kinematics 1893.8.2 Cross Section 1913.9 Photonuclear Interactions 1913.9.1 Cross Section 1923.10 Photon Interaction Coefficients 1933.10.1 Photon Attenuation Coefficient 1943.10.2 Photon Energy-Transfer Coefficient 1953.10.2.1 Photoelectric Effect 1963.10.2.2 Compton Scattering 1983.10.2.3 Pair and Triplet Production 2003.10.3 Photon Energy-Absorption Coefficient 2023.10.4 Uncertainties in Photon Interaction Data 2033.11 Neutron Interactions 2043.11.1 General Aspects 2053.11.2 Elastic Scattering 206

viii Contents

3.11.3 Inelastic Scattering 2093.11.4 Neutron Capture 2103.11.5 Nuclear Spallation 2113.11.6 Neutron-Induced Fission 211

Exercises 211

4 Field and Dosimetric Quantities, RadiationEquilibrium – Definitions and Inter-Relations 215

4.1 Introduction 2154.2 Stochastic and Non-stochastic Quantities 2154.3 Radiation Field Quantities and Units 2164.3.1 Particle Number and Radiant Energy 2164.3.2 Flux and Energy Flux 2174.3.3 Fluence and Energy Fluence 2174.3.4 Fluence Rate and Energy-Fluence Rate 2184.3.5 Planar Fluence 2184.4 Distributions of Field Quantities 2194.4.1 Energy Distributions 2194.4.2 Angular Distributions – Particle Radiance and Energy Radiance 2204.4.3 Distributions in Energy and Angle 2204.5 Quantities Describing Radiation Interactions 2204.5.1 Cross Section 2214.5.2 Interaction Coefficients for Uncharged Particles 2224.5.3 Interaction Coefficients for Charged Particles 2244.5.4 Related Quantities –G(x), , andW 2274.6 Dosimetric Quantities 2294.6.1 Quantities Related to the Transfer of Energy 2294.6.2 Quantities Related to the Deposition of Energy 2324.6.3 Summary of the Definitions of Fundamental Dosimetric

Quantities 2334.7 Relationships Between Field and Dosimetric Quantities 2334.7.1 Photons 2344.7.2 Neutrons 2364.7.3 Charged Particles 2374.8 Radiation Equilibrium (RE) 2394.9 Charged-Particle Equilibrium (CPE) 2424.9.1 CPE for Distributed Radioactive Sources 2434.9.2 CPE for External Sources of Uncharged Particles 2444.9.3 Restricted CPE for External Sources of Charged Particles

(RCPE) 2474.10 Partial Charged-Particle Equilibrium (PCPE) 2484.10.1 PCPE and Relationships between Dose, Kerma, and Electronic

Kerma 2484.11 Summary of the Inter-Relations between Fluence, Kerma, Cema, and

Dose 2524.12 Addendum–Example Calculations of (Net) Energy Transferred and

Imparted 252

Contents ix

4.12.1 Energy Transferred 2524.12.2 Energy Imparted 255

Exercises 256

5 Elementary Aspects of the Attenuation of UnchargedParticles 259

5.1 Introduction 2595.2 Exponential Attenuation 2595.2.1 Simple Exponential Attenuation 2595.2.2 Exponential Attenuation for Plural Modes of Absorption 2615.3 Narrow-Beam Attenuation 2615.4 Broad-Beam Attenuation 2635.4.1 Broad-Beam Geometries 2665.5 Spectral Effects 2705.6 The Build-up Factor 2715.7 Divergent Beams–The Inverse Square Law 2735.8 The ScalingTheorem 276

Exercises 277

6 Macroscopic Aspects of the Transport of Radiation ThroughMatter 279

6.1 Introduction 2796.2 The Radiation Transport Equation Formalism 2806.2.1 Quantities Entering into the Formalism 2816.2.2 The Transport Equation 2826.3 Introduction to Monte Carlo Derived Distributions 2866.4 Electron Beam Distributions 2876.4.1 Fluence Distributions 2876.4.2 Dose Distributions 2916.4.3 Dose Distributions at Interfaces 2956.5 Protons and Heavier Charged Particle Beam

Distributions 2966.5.1 Fluence Distributions 2966.5.2 Dose Distributions 2986.6 Photon Beam Distributions 3016.6.1 Fluence Distributions 3016.6.2 Dose Distributions 3046.6.3 Dose Distributions at Interfaces 3076.7 Neutron Beam Distributions 3096.7.1 Fluence Distributions 3096.7.2 Dose Distributions 311

Exercises 313

7 Characterization of Radiation Quality 3157.1 Introduction 3157.2 General Aspects of Radiation Spectra. Mean Energy 316

x Contents

7.3 Beam Quality Specification for Kilovoltage x-ray Beams 3187.3.1 x-ray Filtration 3197.3.2 x-ray Beam Quality Specification 3217.4 Megavoltage Photon Beam Quality Specification 3267.5 High-Energy Electron Beam Quality Specification 3317.6 Beam Quality Specification of Protons and Heavier Charged

Particles 3357.7 Energy Spectra Determination 3397.7.1 Approaches for the Calculation of Energy Spectra 3397.7.2 Analytical Models for Inverse Determination of Spectra 3427.7.3 Experimental Methods 345

Exercises 346

8 The Monte Carlo Simulation of the Transport of RadiationThrough Matter 349

8.1 Introduction 3498.2 Basics of the Monte Carlo Method (MCM) 3508.2.1 Random Numbers 3508.2.2 Probability Distributions and Inverse Sampling 3518.2.3 Sampling by Rejection 3528.2.4 Sampling from Common Distributions 3538.2.5 Numerical Integration Using MCM 3568.2.6 Uncertainty, Timing, and Efficiency 3578.2.7 Combining Results from Several Monte Carlo Runs 3598.3 Simulation of Radiation Transport 3598.3.1 Generation of Particle Tracks 3618.3.2 Analogue Monte Carlo Simulation 3628.3.3 Condensed-History Monte Carlo Simulation 3658.3.4 Geometry 3698.3.5 Variance Reduction Techniques 3718.4 Monte Carlo Codes and Systems in the Public Domain 3798.5 Monte Carlo Applications in Radiation Dosimetry 3868.5.1 Radiation Sources and Generators 3878.5.2 Detector Simulation 3898.5.3 Calculation of Dosimetric Quantities 3918.6 Other Monte Carlo Developments 393

Exercises 394

9 Cavity Theory 3979.1 Introduction 3979.2 Cavities That Are Small Compared to Secondary Electron

Ranges 3999.2.1 The Stopping-Power Ratio Concept 4009.2.2 Evaluation of the Bragg –Gray Stopping-Power Ratio 4019.2.3 Spencer –Attix Cavity Theory 4049.2.4 When Does a Cavity Behave in a Bragg –Gray Manner? 4099.2.5 Kilovoltage x-ray Qualities 411

Contents xi

9.2.6 Electron Beams 4129.3 Stopping-Power Ratios 4139.3.1 Variation of Stopping-Power Ratios with Electron Energy 4139.3.2 Water/Air Stopping-Power Ratios in Megavoltage Beams 4159.3.2.1 Differences Between sBGw,air and sSAw,air; Depth Dependence 4159.3.2.2 Electrons –Dependence on Beam Energy and Depth 4209.3.2.3 Photons –Dependence on Beam Quality and Depth 4209.3.3 Stopping-Power Ratios for Non-gaseous Detectors in

Charged-Particle Beams 4229.4 Cavities That Are Large Compared to Electron Ranges 4239.5 General or Burlin Cavity Theory 4259.6 The FanoTheorem 4299.7 Practical Detectors: Deviations from ‘Ideal’ Cavity Theory

Conditions 4319.7.1 General Philosophy for Bragg –Gray Detectors 4329.7.2 Corrections for Non-Bragg –Gray Detectors 4349.8 Summary and Validation of Cavity Theory 4359.8.1 Key Expressions for fmed,det,Q 4359.8.2 Photons of 1 MeV in Water –Consistency of Different Cavity

Integrals 4359.8.3 Transition in Detector Behavior from Bragg –Gray toward ‘Large

Cavity’ 438Exercises 440

10 Overview of Radiation Detectors and Measurements 44310.1 Introduction 44310.2 Detector Response and Calibration Coefficient 44410.3 Absolute, Reference, and Relative Dosimetry 44510.4 General Characteristics and Desirable Properties of Detectors 44710.4.1 Reproducibility 44910.4.2 Dose Range 45010.4.2.1 Dose Sensitivity 45010.4.2.2 Background Readings and Lower Range Limit 45010.4.2.3 Upper Limit of the Dose Range 45110.4.3 Dose-Rate Range 45210.4.3.1 Integrating Dosimeters 45210.4.3.2 Dose-Rate Meters 45310.4.4 Stability 45310.4.4.1 Before Irradiation 45310.4.4.2 After Irradiation 45410.4.5 Energy Dependence 45410.4.5.1 Specification 45410.4.5.2 Air-Kerma Energy Dependence 45510.4.5.3 Absorbed-Dose Energy Dependence 45710.4.5.4 Intrinsic Energy Dependence 45810.4.5.5 Modification of the Energy Dependence 45910.5 Brief Description of Various Types of Detectors 460

xii Contents

10.6 Addendum–The Role of the Density Effect and I-Values in theMedium-to-Water Stopping-Power Ratio 467Exercises 471

11 Primary Radiation Standards 47311.1 Introduction 47311.2 Free-Air Ionization Chambers 47411.2.1 Parallel-Plate Design and Operating Principle 47411.2.2 Correction Factors for Free-Air Chambers 47711.2.2.1 Ion Recombination, Polarity, and Field Distortion 47711.2.2.2 Photon Scatter and Fluorescence 47711.2.2.3 Electron Loss 47711.2.2.4 Diaphragm Corrections 47811.2.3 Alternative Free-Air Chamber Designs 47811.2.3.1 Cylindrical Chamber 47811.2.3.2 Wide-Angle Free-Air Chamber 48011.3 Primary Cavity Ionization Chambers 48111.3.1 Operating Principle 48111.3.2 Correction Factors for Cavity Chambers 48311.3.3 A Cavity Standard for Absorbed Dose 48311.4 Absorbed-Dose Calorimeters 48411.4.1 Overview 48411.4.2 Graphite Calorimeters 48511.4.3 Water Calorimeters 48711.5 Fricke Chemical Dosimeter 48811.6 International Framework for Traceability in Radiation

Dosimetry 49011.6.1 The BIPM and Traceability to the SI 49011.6.2 The CIPMMRA and the KCDB 49011.7 Addendum–Experimental Derivation of Fundamental Dosimetric

Quantities 49111.7.1 Derivation ofWair/e 49211.7.2 Derivation of G(Fe3+) 492

Exercises 493

12 Ionization Chambers 49712.1 Introduction 49712.2 Types of Ionization Chamber 49812.2.1 Cavity Chambers 49812.2.1.1 Wall Thickness 49912.2.1.2 Wall Materials and Insulators 50012.2.2 Parallel-Plate Chambers 50112.2.3 Transmission Monitor Chambers 50312.3 Measurement of Ionization Current 50412.3.1 General Considerations 50412.3.1.1 Electrometers 50512.3.1.2 General Precautions 505

Contents xiii

12.3.2 Charge Measurement 50612.3.2.1 Measurement Principle 50612.3.2.2 Capacitors 50712.3.3 Current Measurement and Electrometer Calibration 50812.3.4 Correction for Influence Quantities 50812.3.4.1 Air Temperature 50912.3.4.2 Air Pressure 51012.3.4.3 Air Humidity 51012.3.4.4 Polarity Effect 51212.4 Ion Recombination 51312.4.1 The Saturation Curve 51412.4.2 Initial Recombination and Diffusion 51512.4.2.1 Two-Voltage Method 51612.4.3 General (or Volume) Recombination 51712.4.3.1 Pulsed Radiation 51812.4.3.2 Continuous Radiation 52012.4.4 Niatel Method to Separate Initial and General Recombination 52212.4.5 Free-Electron Collection 52312.5 Addendum–Air Humidity in Dosimetry 52412.5.1 Density of Humid Air 52412.5.2 Influence of Humidity on Dosimetric Quantities 527

Exercises 531

13 Chemical Dosimeters 53313.1 Introduction 53313.2 Radiation Chemistry in Water 53313.2.1 Early Events 53313.2.2 Chemical Stage 53513.2.3 G(x)-Values and Primary Product Concentrations 53513.3 Chemical Heat Defect 53813.4 Ferrous Sulfate Dosimeters 53913.4.1 Determination of the Fe3+ (Ferric Ion) Concentration 54113.4.2 Temperature-Dependent Aspects of Fricke Dosimetry 54313.4.3 Composition of the Solution 54313.4.4 Irradiation Vials 54413.4.5 Energy Dependence of the Fricke Dosimeter 54413.4.5.1 Absorbed Dose to Water from Absorbed Dose to Fricke 54513.4.5.2 Energy Dependence of G(Fe3+) 54613.5 Alanine Dosimetry 54713.5.1 Signal Readout and Dose to Alanine 55213.5.2 Temperature Effects, Humidity Effect, and Linearity 55413.5.3 Energy Dependence of the Alanine Dosimeter 55513.6 Film Dosimetry 55613.6.1 Radiographic Film 55613.6.1.1 Chemical Processing 55713.6.1.2 Optical Density of Film 55813.6.1.3 Processing Conditions 560

xiv Contents

13.6.1.4 Energy Dependence 56013.6.1.5 Dose-Rate Dependence 56113.6.1.6 Film Packaging and Air Traps 56113.6.1.7 Nuclear Track Emulsions 56213.6.2 Radiochromic Film 56213.6.2.1 Film Structure 56313.6.2.2 Measurement Principle 56313.6.2.3 Radiochromic Film Calibration 56413.6.2.4 Energy Dependence 56613.7 Gel Dosimetry 56813.7.1 Fricke Gels 56813.7.2 Polymer Gels 56913.7.3 Radiation Chemical Yield of Gels 57013.7.4 Gel Readout Techniques 57113.7.4.1 Magnetic Resonance Relaxometry 57113.7.4.2 X-ray Computed Tomography Imaging 57313.7.4.3 Optical Computed Tomography Imaging 57313.7.5 Energy Dependence 574

Exercises 574

14 Solid-State Detector Dosimetry 57714.1 Introduction 57714.2 Thermoluminescence Dosimetry 57714.2.1 TheThermoluminescence Process 57714.2.1.1 Materials 57714.2.1.2 Randall –Wilkins Theory 57914.2.1.3 Trap Stability 58014.2.1.4 Intrinsic Efficiency of TLD Phosphors 58214.2.2 TLD Readers 58214.2.3 TLD Phosphors 58314.2.4 TLD Forms 58614.2.5 Calibration of Thermoluminescent Dosimeters 58714.2.5.1 Form 58714.2.5.2 TLD Linearity and Dose-Rate Dependence 58714.2.5.3 TLD Energy Dependence 58714.2.6 Advantages and Disadvantages of TLDs 58914.2.6.1 Advantages 58914.2.6.2 Disadvantages 59014.3 Optically-Stimulated Luminescence Dosimeters 59114.3.1 OSLDMechanism 59114.3.2 OSLD Readout 59314.3.3 OSLDMaterials 59414.3.4 OSLD Energy Dependence 59514.4 Scintillation Dosimetry 59614.4.1 Introduction 59614.4.2 Light Output Efficiency 59714.4.3 Scintillator Types 598

Contents xv

14.4.4 Light Collection and Measurement 60014.4.4.1 Scintillator Enclosure 60014.4.4.2 Light Pipe or Fiber 60114.4.4.3 PM tube or photodetector 60414.4.4.4 Cerenkov Radiation 60514.4.5 Comparison with Ionization Chambers and Other

Detectors 60614.4.6 Pulse-Shape Discrimination 60614.4.7 β-Ray Dosimetry 60714.4.8 Energy Dependence of Plastic Fiber Scintillation

Dosimeters 60814.5 Semiconductor Detectors for Dosimetry 60914.5.1 Introduction 60914.5.2 Basic Operation of Reverse-Biased Semiconductor Junction

Detectors 61014.5.3 Diode Dosimeters 61114.5.3.1 Diode Construction and Functioning 61114.5.3.2 Diode Energy Dependence 61314.5.4 Lithium-Drifted and HP(Ge) Detectors for Spectroscopy 61514.5.5 Use of Si(Li) as an Ion-Chamber Substitute 61714.5.6 Use of Si(Li) Junctions with Reverse Bias as Counting Dose-Rate

Meters 61714.5.7 Fast-Neutron Dosimetry 61814.5.8 MOSFET Dosimeters 61814.5.8.1 MOSFET Construction and Functioning 61814.5.8.2 MOSFET Energy Dependence 62214.5.9 Diamond Detectors 62314.5.9.1 Diamond Detector Construction and Functioning 62414.5.9.2 Diamond Detector Energy Dependence 627

Exercises 628

15 Reference Dosimetry for External Beam RadiationTherapy 631

15.1 Introduction 63115.2 A Generalized Formalism 63215.2.1 Detector Calibration Coefficient and Beam Calibration 63215.2.2 Cross-Calibration of Ionization Chambers and Detectors 63515.3 Practical Implementation of Formalisms 63615.3.1 Dosimetry Protocols for Kilovoltage X-ray Beams Based on

Air-Kerma Standards 63815.3.1.1 Low-Energy kV x-ray Beams 64015.3.1.2 Medium-Energy kV x-ray Beams 64215.3.2 Dosimetry Protocols for Megavoltage Beams Based on Air-Kerma

Standards 64215.3.2.1 The ND,air Chamber Coefficient 64315.3.2.2 Dose Determination in Electron and Photon Beams 645

xvi Contents

15.3.2.3 Dose Determination in Protons and Heavier Charged-ParticleBeams 645

15.3.3 Dosimetry Codes of Practice Based on Standards of Absorbed Doseto Water 646

15.3.3.1 The Beam Quality Correction Factor, kQ,Q0647

15.3.3.2 The Qint Approach for Reference Qualities Differentfrom 60Co 648

15.3.4 Relation between NK –ND,air and ND,𝑤 Dosimetry Protocols 65115.4 Quantities Entering into the Various Formalisms 65115.4.1 Quantities for Kilovoltage X-ray Beams 65215.4.2 Quantities for High-Energy Beams 65615.4.2.1 Stopping-Power Ratios 65615.4.2.2 Impact of the I-Value for Water on Reference Dosimetry 66315.4.2.3 Perturbation Correction Factors 66415.5 Accuracy of RadiationTherapy Reference Dosimetry 66915.6 Addendum–Perturbation Correction Factors 67115.6.1 Departure of Practical Ionization Chambers from Bragg –Gray

Conditions 67315.6.2 The Correction for the Chamber Wall, pwall 67415.6.3 Correcting for the Finite Size of the Gas Cavity, pdis and pfl 67815.6.3.1 Averaging over the Cavity Volume, pdis 67815.6.3.2 Fluence Perturbation, pfl 68315.6.4 The Correction for the Central Electrode, pcel 68615.6.5 Perturbation Factors for kV X-ray Beams 687

Exercises 689

16 Dosimetry of Small and Composite Radiotherapy PhotonBeams 693

16.1 Introduction 69316.2 Overview 69416.3 The Physics of Small Megavoltage Photon Beams 69616.3.1 Charged-Particle Disequilibrium in Small Beams 69616.3.2 Source Size and Small Beams 69816.3.3 Spectral Changes in Small Beams 69916.4 Dosimetry of Small Beams 70116.4.1 Formalism 70216.4.2 Beam Quality Specification 70716.4.3 Stopping-Power Ratios for Small Beams 70916.4.4 Ionization Chamber Perturbation Effects in Small Beams 71116.5 Detectors for Small-Beam Dosimetry 71416.6 Dosimetry of Composite Fields 71716.6.1 Formalism 71816.6.2 Absence of CPE in Composite Field Dosimetry 72116.6.3 Correction Factors in Composite Field Dosimetry 72116.7 Addendum—Measurement in Plastic Phantoms 723

Exercises 726

Contents xvii

17 Reference Dosimetry for Diagnostic and InterventionalRadiology 729

17.1 Introduction 72917.2 Specific Quantities and Units 73017.2.1 Air Kerma versus Water Kerma 73317.3 Formalism for Reference Dosimetry 73617.3.1 Differences between the Diagnostic and Radiotherapy

Formalisms 73917.4 Quantities Entering into the Formalism 74017.4.1 Quantities for Monoenergetic Photons 74317.4.2 Quantities for Clinical X-ray Spectra 74517.4.3 Influence of PhantomThickness and Material 747

Exercises 751

18 Absorbed Dose Determination for Radionuclides 75318.1 Introduction 75318.2 Radioactivity Quantities and Units 75518.2.1 Decay Constant 75518.2.2 Activity 75518.2.3 Partial Decay Constants and Activity 75618.2.4 Half-Life and Mean Life 75618.2.5 Air-Kerma Rate Constant 75718.3 Dosimetry of Unsealed Radioactive Sources 76318.3.1 The Absorbed-Dose Fraction; Isotropic Dose Kernels 76418.3.2 Dosimetry of Radioactive Disintegration Processes 77318.3.2.1 Alpha Decay 77418.3.2.2 Beta Decay 77618.3.2.3 Electron Capture Decay 78018.3.2.4 Internal Conversion versus γ-Ray Emission 78218.3.3 Mean Energy Emitted Per Nuclear Transformation 78418.3.4 The MIRD Approach for Clinical Radionuclide Dose

Estimation 78618.4 Dosimetry of Sealed Radioactive Sources 78818.4.1 Dosimetry of Point and Linear Sources 78918.4.1.1 Point Isotropic Source 79218.4.1.2 Linear Source 79218.4.2 Specification of Brachytherapy Sources 79518.4.3 Air-Kerma Rate Measurement of Brachytherapy Sources 79618.4.4 Dosimetry of Brachytherapy Sources. The AAPM TG-43

Approach 79818.4.5 Analytical Approximation for the Dose-Rate Constant 80218.5 Addendum–The Reciprocity Theorem for Unsealed Radionuclide

Dosimetry 80418.5.1 Background 80418.5.2 The Reciprocity Theorem 805

Exercises 809

xviii Contents

19 Neutron Dosimetry 81319.1 Introduction 81319.2 Neutron Interactions in Tissue and Tissue-Equivalent Materials 81419.3 Neutron Sources 81819.4 Principles of Mixed-Field Dosimetry 82119.5 Neutron Detectors 82519.5.1 Absolute Instruments 82519.5.2 Dosimeters with Comparable Neutron and γ-Ray Sensitivities 82619.5.3 Neutron Dosimeters Insensitive to γ Rays 82719.6 Reference Dosimetry of Neutron Radiotherapy Beams 833

Exercises 838

A Data Tables 841A.1 Fundamental and Derived Physical Constants 841A.2 Data of Elements 843A.3 Data for Compounds and Mixtures 846A.4 Atomic Binding Energies for Elements 846A.5 Atomic Fluorescent X-ray Mean Energies and Yields for

Elements 857A.6 Interaction Data for Electrons and Positrons (Electronic Form) 863A.6.1 Electron Interaction Cross Sections 864A.6.2 Electron Stopping Powers and Related Data 865A.6.3 Restricted (Δ = 10 keV) and Unrestricted Mass Electronic Stopping

Powers 866A.6.4 Electron Mass Scattering Powers 867A.7 Interaction Data for Protons and Heavier Charged Particles

(Electronic Form) 868A.7.1 Properties of Heavy Charged Particles 868A.7.2 Proton Stopping Powers 869A.7.3 Proton Mass Scattering Powers 871A.7.4 He–Ar Ion Stopping Powers 872A.8 Interaction Data for Photons (Electronic Form) 874A.8.1 Compton Klein –Nishina Cross Sections for Free Electrons 875A.8.2 Photon Interaction Cross Sections 877A.8.3 Photon 𝜇/𝜌, 𝜇tr/𝜌, and 𝜇en/𝜌 Coefficients, and g Values 878A.9 Neutron Kerma Coefficients (Electronic Form) 879

References 881

Index 945

xix

Preface

The first edition of Frank Herbert Attix’s widely acclaimed book Introductionto Radiological Physics and Radiation Dosimetry was published in 1986 andreprinted in 2004. An update of its contents, taking into account the substantialdevelopments in dosimetry in the 30 years since its first appearance, was con-sidered essential. For the present authors it has been a formidable challenge tomaintain the high level and quality, raising the former as appropriate, consistentwith the current state of knowledge and the various applications. Other recentbooks of a comparable level are E. B. Podgorsak’s Radiation Physics for MedicalPhysicists (Springer, 2010), B. J. McParland’s Nuclear Medicine RadiationDosimetry – AdvancedTheoretical Principles (Springer, 2010), and N. J. Carron’sAn Introduction to the Passage of Energetic Particles through Matter (Taylor andFrancis, 2007).The scope of this second edition, which we abbreviate to FIORD (from Fun-

damentals of IOnizing Radiation Dosimetry) can be stated as follows: Given a(ionizing) radiation field from whatever source, be it a radionuclide, an x-raygenerator or an accelerator, this book will enable the reader to understand theprinciples/essentials/fundamentals of the determination of the physical quantityof interest from the interaction of the radiation field with the medium. In thiscontext, we often refer to absorbed dose as a surrogate of the quantity fluence,although it should be understood that energy transfer from a radiation field canmanifest itself in ways other than dose. The text is pitched at senior undergrad-uate or graduate level, and for the latter a number of advanced topics have beenincluded as addenda to some of the chapters.We concur with the sentiment expressed by Attix et al. (1966) in their edition

of the classic text Radiation Dosimetry, “Although the present work is called asecond edition, it is in many respects a new start.” Compared with the first edi-tion, a major change in FIORD is the order of the different chapters; for example,the description of particle interactions with matter (Chapters 2 and 3) is placedbefore the definition of radiation quantities (Chapter 4). Radiation interactionsare covered at a somewhat higher level than that of the first edition, the rationalebeing the extended use of theMonte Carlo (MC)method (Chapter 8) in radiationdosimetry today, as most MC codes include certain interaction types and detailsnot considered in the majority of books at undergraduate level. More generally,this edition contains everything the student and the practising radiation physi-cist might need to know about the interactions of radiation with matter in order

xx Preface

to understand the theory and practice of radiation dosimetry as covered here.Following the description of the interactions of single particles, Chapters 5 and6 are devoted to what we choose to call ‘macroscopic aspects,’ i.e. the interac-tion of radiation fields and beams with matter.This is followed by the descriptorscommonly used to characterize beam quality (Chapter 7), mostly of applicationin radiation therapy and radiodiagnostics. Cavity theory (Chapter 9) provides thegrounds for the theoretical aspects of dosimetry, which is followed by a generaloverview of radiation detector principles (Chapter 10). The description of theprimary measurement standards in current use for the absolute determinationof air kerma and absorbed dose (Chapter 11) is followed by separate chapterson the most important types of radiation detectors used for dose determination,namely ionization chambers (Chapter 12), chemical dosimeters (Chapter 13),and solid state detectors (Chapter 14). Practical applications of dosimetry in thedifferent areas are covered in subsequent chapters: reference dosimetry for radi-ation therapy and dosimetry protocols are dealt with from a general perspective(Chapter 15), complemented by the current status of dosimetry for small andcomposite photon beams (Chapter 16), which, at the time of writing, is a topicof considerable research. This is followed by the dosimetry of kilovoltage x-raybeams used in diagnostic radiology and interventional procedures (Chapter 17).The dosimetry of radionuclide sources in Chapter 18 follows very closely the orig-inal text of the first edition, being complemented by the fundamentals of thedosimetry of unsealed (e.g., for nuclear medicine) and sealed (for brachytherapy)sources. Finally, Chapter 19 provides an update on the dosimetry of neutronbeams, nowadays far less frequently employed.It should be noted that extensive data tables are not provided in the printed

edition; the tabulated data are mostly restricted to fundamental constants anddata. The reason for this approach is that direct internet access to most of thedata needed for numerical calculations, including periodic updates, makes dataretrieval more dynamic. For this purpose internet links are provided throughoutthe various chapters. The most commonly-used practical data, including thoseless accessible on the web, are however made available via an internet siteprovided by the editor (http://www.wiley-vch.de/ISBN9783527409211). Weconsider that the book should not include a compendium of data replacing thosein original references. Instead, the use of a large number of figures that provideinformation on the trends and dependencies of the data has been preferred.As the book is addressed also to graduate and practising physicists, the authors

have opted for the use of in-text citations to references in a style following thatof many scientific journals. The large number of ‘classic’ references given is anattempt to address the apparent shortening of ‘scientific historical memory,’resulting in the link to important original sources being progressively lost. Somesections therefore include reviews of certain topics with a sufficient numberof references to map the evolution of these topics. The comprehensive list ofreferences makes liberal use of international publications, for example, fromthe International Commission on Radiation Units and Measurements (ICRU)and the International Atomic Energy Agency (IAEA), in an attempt to provide aglobal view of radiation dosimetry. This view also justifies the prominent use ofinternationally accepted symbols for the various quantities.

Preface xxi

This second edition is dedicated to the memory of Frank H. Attix, one ofthe great pioneers in radiation dosimetry and an important contributor tothis book. The authors wish to express their gratitude to colleagues who haveprovided suggestions for improvements to various chapters of the book, inparticular F. Ballester, H. Bouchard, D. Emfietzoglou, C. Kessler, B. Mijnheer,J. Perez-Calatayud, F. Salvat, A. Sanchez-Crespo, J. Sempau, and S. Vynckier.Finally, we thank our respective families for their patience and understandingduring this seemingly never-ending task.

June 23, 2016 Pedro AndreoDavid T. BurnsAlanE.NahumJan Seuntjens

xxiii

Quantities and Symbols1

Roman letter symbols

A, a

A atomic mass, mass number (nucleon number)distance between the reference plane and the collector of afree-air ionization chamber

activity of a radionuclide time-integrated activity (MIRD, formerly called cumulated

activity)L activity per unit lengthapp apparent activitym specific (or mass) activityAF absorbed-dose fraction (radionuclide point isotropic source)AFm specific absorbed-dose fractiona surface area

B, b

B magnetic field vectorB buildup factor in broad photon beams, also denoted by B(𝜇 r),

B(k, r) or B(k, 𝜃)Bmed backscatter factor in kV x-ray beams in medium ‘med’BMol Molière’s expansion parameterBm magnetic field strengthb impact parameter

number of bits in the integer representation of computer data(computer word length)

1 Some Roman and Greek symbols that appear with more than one description are used in ratherindependent sections; thus, there should be no confusion in their meaning. Symbols appearing onlyonce in the text, for example, in a single equation – usually related to a change of variable – orgeneral mathematical functions – for example, the gamma function Γ(x)–have not been included inthe list.

xxiv Quantities and Symbols

C, c

C electrical capacitancecema

CΔ restricted cemaC(𝛽) shell correction in the stopping-power expressionCi concentration of species i (radiation chemistry)CK CT air-kerma indexCw,c composite conversion factor in graphite calorimetryCTDI CT dose indexc speed of light in vacuumcm specific heat capacity of a material ‘m’corgan,𝔮 organ dose conversion coefficient calculated for the quantity 𝔮

D, d

D absorbed doseDdet,Dmed absorbed dose to the radiation-sensitive volume of a detector, or

to a medium ‘med’Dw,Q(z) absorbed dose to water at a depth z in a beam of quality QDpl,Q(zeq-pl) absorbed dose to plastic at the equivalent depth zeq-plDx absorbed dose due to a radionuclide disintegration of type xD mean absorbed doseDIsoE isoeffective absorbed dose by protons and heavier charged

particlesDSSD(z) absorbed dose at depth z with constant SSD (DSDD(z) for constant

SDD)Dfield

w,Qfieldabsorbed dose to water in a specific field

Dpb(z, r) dose distribution of a pencil beam as a function of depth andradius

Dbb(z,R) central-axis depth–dose distribution of a broad beam of radius Rd collision diameter in particle interaction (closest distance of

approach)d distance (as a generic variable)

electrode separation in a free-air ionization chamberd80 depth of the 80% depth dose for a photon beamd𝜎∕dΩ differential cross section per unit solid angled𝜎∕dE differential cross section per energyd𝜎∕dΩ dE double differential cross section, per unit solid angle and per

energy%dd(10) percent depth dose at a depth of 10 cm (photon beam quality

specifier)%dd(10)x as above, in the absence of electron contamination, that is, filtered

by 1 mm Pb

E, e

E electrical field vectorE kinetic energy of charged particles

Quantities and Symbols xxv

Etot total energy of charged particles (rest energy plus kinetic energy)E+,E− positron and electron kinetic energy

Ea kinetic energy of the recoil atom in photon interactionsEn neutron kinetic energyEtrap energy depth of TLD trapE mean energy of a spectrumEΦ,EΨ,EKair

mean energy of a spectrum averaged over a fluence, energyfluence, and air-kerma spectrum, respectively

Ez mean energy of an electron spectrum at the depth z (E0 at thesurface)

Eabs energy absorbed (water calorimetry)Eheat energy appearing as heat (water calorimetry)Eh Hartree energyEi mean energy of an i-type particle emitted in a nuclear transitionE𝛽max

maximum energy of a beta decay spectrumE𝛽

mean energy of a beta decay spectrumEp plasma energy of a medium (also denoted by ℏ𝜔p)E(xn) expected value of x, that is, the nth moment of f (x)E∕A specific energy (heavy charged particles)e elementary charge, absolute value of the electron charge

F, f

F atomic form factorFelec calibration factor of an electrometerFGS Goudsmit–Saunderson angular distribution for multiple elastic

scatteringFMol Molière’s angular distribution for multiple elastic scatteringFk fraction of a detector signal produced by photons of energy

between k and k + dkF(r, 𝜃) anisotropy function for a radioactive line sourceF(x) cumulative probability distribution function (CPD)F(E, r) scaled absorbed dose kernel (radionuclide point isotropic source)F𝛽

Fermi function in beta decayf efficiency of charge collection in an ionization chamber

enhancement factor of a gas (humid air)fd field size at the distance d (SSD or SDD) in MV photon beamsfi oscillator strength of the i-shell of an atomffel free-electron efficiency of charge collectionfref conventional broad reference beam (10 cm × 10 cm)fmsr machine-specific reference (msr) field)fpcsr plan-class-specific reference (msr) field)f (Q,W ) generalized oscillator strength (GOS)f (W ) optical oscillator strength (OOS)f (x) probability distribution function (PDF) of a continuous variable xfC(Z) Coulomb correction factorfE(𝛽) Elwert factor (in bremsstrahlung)

xxvi Quantities and Symbols

f𝜇

detector signal fraction by photons with attenuation coefficientbetween 𝜇 and 𝜇 + d𝜇

fm,F factor to correct for different radiation interaction coefficients inFricke dosimetry

fmed,det,Q generic cavity-theory factor (fmed,det = Dmed∕Ddet) for radiationquality Q

G, g

G chamber geometric factor (recombination in pulsed andcontinuous radiation)

G(x) radiation chemical yield; related to the G-valueG(Fe3+) radiation chemical yield of ferric ions in a Fricke dosimeterGL(r, 𝜃) geometry function for a radioactive line source; GP(r) for a point

source generic quantityg radiative fraction; related to radiation yield, Y (E)ge free-electron Landé factorgL(r) radial-dose function for a radioactive line source; g

P(r) for a point

source

H, h

H Hamiltonian operatorHI homogeneity index of a radiotherapy dose distributionHVL half-value layer of a kV x-ray spectrumHVL1,HVL2 first and second half-value layersHi heat of formation for species i (radiation chemistry)h relative humidityhd heat defect (water calorimetry)hi homogeneity index of a kV x-ray spectrum (HVL1∕HVL2)hn+γ for a neutron detector, response to the photons in a mixed n + γ

field relative to its response in a photon calibration beamhni for a neutron-insensitive detector, response to the photons in a

mixed n + γ field relative to its response in a photon calibrationbeam

hT TLD heating rate (K s−1)ℏ reduced Planck’s constant

I, i

I, Imed mean excitation energy of a medium (known as the I-value)IE first ionization energy of an atomI𝓁 intensity of a light beami ionization current measured by a detector

J, j

J particle current density (vector fluence rate)J IA Compton profile

Quantities and Symbols xxvii

Jair specific charge (charge per unit mass of air)j phase-space current density (also termed energy distribution of

vector particle radiance, angular current density, or directionalflux)

K, k

K kermaKel electronic kerma (also known as collision kerma, Kcol)Krad radiative kermaKair,E air-kerma spectrum or differential air kermaKair(t) air kerma attenuated by an absorber of thickness t[Kair,Q]med air kerma at the quality Q determined in medium ‘med’Kair,e entrance-surface air kermaKair,i incident air kermaKair air-kerma rateKR reference-air-kerma rate of a radioactive sourceKrel(𝜃) correction factor to account for relativistic and spin effects

(in 𝜎elast)Kscr(𝜃) correction factor to account for the screening by atomic electrons

(in 𝜎elast)kV kilovoltage (tube potential), for x-ray spectra produced by

electrons with energies in the keV rangek wave number (k = p∕ℏ)k photon energyk mean energy of a photon spectrumkB Boltzmann constantkeff effective photon energy of a spectrumkmax maximum photon energy of a spectrumki correction factors for ionization chamber measurements (generic)ka correction factor for photon attenuation in a free-air ionization

chamberkan correction factor for the axial non-uniformity of the electrical field

within an ionization chamberkcav correction factor for the perturbation of the electron fluence in an

ionization chamberke electron-loss correction factor in a free-air ionization chamberkfl fluorescence correction factor in a free-air ionization chamberkh correction factor for air humiditykhd correction factor for heat defect in a water calorimeterkht correction factor for heat transfer in a water calorimeterkn+γ for a neutron detector, response to the neutrons and photons in a

mixed n + γ field relative to its response in a photon calibrationbeam

kni for a neutron-insensitive detector, response to the neutrons andphotons in a mixed n + γ field relative to its response in a photoncalibration beam

xxviii Quantities and Symbols

kp perturbation correction factor for non-water materials in a watercalorimeter

ks correction factor for recombination (or saturation)ks,fel correction factor for free-electron recombination (or saturation)ksc correction factor for photon scattering in a free-air ionization

chamberkppth photon threshold energy for pair productionktpth photon threshold energy for triplet productionkwall correction factor for photon attenuation and scattering in an ion

chamber wallkP correction factor for pressurekT correction factor for temperaturek+, k− mobility of positive and negative ions (recombination in pulsed

radiation)kw,plQ plastic phantom dose conversion factor to waterkQ,Q0

beam quality correction factor; kQ if Q0 = 60Co γ rays

kffield, frefQfield,Qrefcorrection factor to account for the difference between theconventional broad reference beam fref (10 cm × 10 cm) and themsr or the pcsr field

kfclin, ffieldQclin,Qfieldoutput correction factor for a beam clin relative to themsr field orto the pcsr field

L, l

optical path length in a Fricke dosimeterL orbital angular momentum operatorL length of the region from which charge is measured in a free-air

ionization chamberlength of a radioactive source line

L(𝛽) stopping numberLΔ(E) linear energy transfer (LET)(LΔ∕𝜌)med

det Spencer–Attix stopping-power ratio med/det, also denoted bysSAmed,det

l length, scattering length𝓁 orbital-angular-momentum quantum number𝓁 mean chord length of a convex volume

M, m

air molar mass of dry airvap molar mass of water vaporM atomic molar massMfi matrix element of an interactionMair,Q detector reading in air, corrected for influence quantities, in a

beam of quality QMw,Q(z) detector reading at a depth z in water, corrected for influence

quantities