MEASUREMENT AND DETECTION OF RADIATION

MEASUREMENT AND DETECTION OF RADIATION Second Edition Nicholas Tsoulfanidis University of Missouri-Rolla Ж Taylor &Francis * Publishers since I79H

CONTENTS Preface to the First Edition Preface to the Second Edition xvii xxi 1 INTRODUCTION TO RADIATION MEASUREMENTS 1 1.1 What is Meant by Radiation? 1 1.2 Statistical Nature of Radiation Emission 2 1.3 The Errors and Accuracy and Precision of Measurements 3 1.4 Types of Errors 5 1.5 Nuclear Instrumentation 6 1.5.1 Introduction 6 1.5.2 The Detector 7 1.5.3 The NIM Concept 9 1.5.4 The High-Voltage Power Supply 9 1.5.5 The Preamplifier 11 1.5.6 The Amplifier 14 1.5.7 The Oscilloscope 16 1.5.8 The Discriminator or Single-Channel Analyzer (SCA) 17 1.5.9 The Scaler 20 1.5.10 The Timer 21 1.5.11 The Multichannel Analyzer 21 Bibliography 21 Reference 21 2 STATISTICAL ERRORS OF RADIATION COUNTING 23 2.1 Introduction 23 2.2 Definition of Probability 23 2.3 Basic Probability Theorems 25 2.4 Probability Distributions and Random Variables 28

viii CONTENTS 2.5 Location Indexes (Mode, Median, Mean) 30 2.6 Dispersion Indexes, Variance, and Standard Deviation 33 2.7 Covariance and Correlation 33 2.8 The Binomial Distribution 35 2.9 The Poisson Distribution 37 2.10 The Normal (Gaussian) Distribution 39 2.10.1 The Standard Normal Distribution 43 2.10.2 Importance of the Gaussian Distribution for Radiation Measurements 45 2.11 The Lorentzian Distribution 46 2.12 The Standard, Probable, and Other Errors 48 2.13 The Arithmetic Mean and Its Standard Error 49 2.14 Confidence Limits 52 2.15 Propagation of Errors 55 2.15.1 Calculation of the Average and Its Standard Deviation 55 2.15.2 Examples of Error Propagation Uncorrelated Variables 56 2.16 Goodness of Data x 2 Criterion Rejection of Data 58 2.17 The Statistical Error of Radiation Measurements 62 2.18 The Standard Error of Counting Rates 64 2.18.1 Combining Counting Rates 67 2.19 Methods of Error Reduction 68 2.19.1 The Background Is Constant and There Is No Time Limit for Its Measurement 68 2.19.2 There Is a Fixed Time Г Available for Counting Both Background and Gross Count 69 2.19.3 Calculation of the Counting Time Necessary to Measure a Counting Rate with a Predetermined Statistical Error 69 2.19.4 Relative Importance of Error Components 70 2.20 Minimum Detectable Activity 71 2.21 Counter Dead-Time Correction and Measurement of Dead Time 73 Problems 76 Bibliography 78 References 78 REVIEW OF ATOMIC AND NUCLEAR PHYSICS 79 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Introduction Elements of Relativistic Kinematics Atoms Nuclei Nuclear Binding Energy Nuclear Energy Levels Energetics of Nuclear Decays 3.7.1 Gamma Decay 3.7.2 Alpha Decay 3.7.3 Beta Decay 3.7.4 Particles, Antiparticles, and Electron-Positron Annihilation 3.7.5 Complex Decay Schemes The Radioactive Decay Law 79 79 83 86 88 91 92 94 96 97 102 103 103

CONTENTS ix 3.9 Nuclear Reactions 107 3.9.1 General Remarks 107 3.9.2 Kinematics of Nuclear Reactions 109 3.10 Fission 113 Problems 117 Bibliography 119 References 119 4 ENERGY LOSS AND PENETRATION OF RADIATION THROUGH MATTER 121 4.1 Introduction 121 4.2 Mechanisms of Charged-Particle Energy Loss 122 4.2.1 Coulomb Interactions 122 4.2.2 Emission of Electromagnetic Radiation (Bremsstrahlung) 123 4.3 Stopping Power Due to Ionization and Excitation 124 4.4 Energy Loss Due to Bremsstrahlung Emission 129 4.5 Calculation of de/dx for a Compound or Mixture 131 4.6 Range of Charged Particles 132 4.6.1 Range of Heavy Charged Particles (p, d, t, a; 1 < A < 4) 133 4.6.2 Range of Electrons and Positrons 138 4.6.3 Transmission of Beta Particles 142 4.6.4 Energy Loss after Traversing a Material of Thickness t < R 143 4.7 Stopping Power and Range of Heavy Ions (Z > 2, A > 4) 144 4.7.1 Introduction 144 4.7.2 The de/dx Calculation 145 4.7.3 Range of Heavy Ions 149 4.8 Interactions of Photons with Matter 150 4.8.1 The Photoelectric Effect 153 4.8.2 Compton Scattering or Compton Effect 154 4.8.3 Pair Production 157 4.8.4 Total Photon Attenuation Coefficient 158 4.8.5 Photon Energy Absorption Coefficient 161 4.8.6 Buildup Factors 162 4.9 Interactions of Neutrons with Matter 166 4.9.1 Types of Neutron Interactions 166 4.9.2 Neutron Reaction Cross Sections 166 4.9.3 The Neutron Flux 171 4.9.4 Interaction Rates of Polyenergetic Neutrons 172 Problems 173 Bibliography 174 References 175 5 GAS-FILLED DETECTORS 177 5.1 Introduction 177 5.2 Relationship Between High Voltage and Charge Collected 179 5.3 Different Types of Gas-Filled Detectors 180

X CONTENTS 5.4 Ionization Chambers 183 5.4.1 Pulse Formation in an Ionization Chamber 183 5.4.2 Current Ionization Chambers 187 5.5 Proportional Counters 189 5.5.1 Gas Multiplication in Proportional Counters 189 5.5.2 The Pulse Shape of a Proportional Counter 194 5.5.3 The Change of Counting Rate with High Voltage The High-Voltage Plateau 195 5.6 Geiger-Müller Counters 199 5.6.1 Operation of a GM Counter and Quenching of the Discharge 199 5.6.2 The Pulse Shape and the Dead Time of a GM Counter 200 5.7 Gas-Flow Counters 201 5.7.1 The Long-Range Alpha Detector (LRAD) 204 5.7.2 Internal Gas Counting 205 5.8 Rate Meters 206 5.9 General Comments about Construction of Gas-Filled Detectors 208 Problems 209 Bibliography 209 References 210 6 SCINTILLATION DETECTORS 211 6.1 Introduction 211 6.2 Inorganic (Crystal) Scintillators 212 6.2.1 The Mechanism of the Scintillation Process 212 6.2.2 Time Dependence of Photon Emission 215 6.2.3 Important Properties of Certain Inorganic Scintillators 216 6.3 Organic Scintillators 218 6.3.1 The Mechanism of the Scintillation Process 218 6.3.2 Organic Crystal Scintillators 220 6.3.3 Organic Liquid Scintillators 220 6.3.4 Plastic Scintillators 221 6.4 Gaseous Scintillators 222 6.5 The Relationship Between Pulse Height and Energy and Type of Incident Particle 222 6.5.1 The Response of Inorganic Scintillators 222 6.5.2 The Response of Organic Scintillators 223 6.6 The Photomultiplier Tube 224 6.6.1 General Description 224 6.6.2 Electron Multiplication in a Photomultiplier 227 6.7 Assembly of a Scintillation Counter and the Role of Light Pipes 228 6.8 Dead Time of Scintillation Counters 230 6.9 Sources of Background in a Scintillation Counter 231 6.10 The Phoswich Detector 232 Problems 233 Bibliography 233 References 234

CONTENTS xi 7 SEMICONDUCTOR DETECTORS 235 7.1 Introduction 235 7.2 Electrical Classification of Solids 236 7.2.1 Electronic States in Solids-The Fermi Distribution Function 236 7.2.2 Insulators 238 7.2.3 Conductors 238 7.3 Semiconductors 239 7.3.1 The Change of the Energy Gap with Temperature 241 7.3.2 Conductivity of Semiconductors 243 7.3.3 Extrinsic and Intrinsic Semiconductors The Role of Impurities 245 7.4 The p-n Junction 246 7.4.1 The Formation of a p-n Junction 246 7.4.2 The p-n Junction Operating as a Detector 250 7.5 The Different Types of Semiconductor Detectors 252 7.5.1 Surface-Barrier Detectors 252 7.5.2 Diffused-Junction Detectors 252 7.5.3 Silicon Lithium-Drifted [Si(Li)] Detectors 254 7.5.4 Germanium Lithium-Drifted [Ge(Li)] Detectors 258 7.5.5 Germanium (Ge) Detectors 258 7.5.6 CdTe and Hgl 2 Detectors 259 7.6 Radiation Damage to Semiconductor Detectors 260 Problems 261 Bibliography 262 References 262 8 RELATIVE AND ABSOLUTE MEASUREMENTS 265 8.1 Introduction 265 8.2 Geometry Effects 267 8.2.1 The Effect of the Medium between Source and Detector 267 8.2.2 The Solid Angle General Definition 268 8.2.3 The Solid Angle for a Point Isotropic Source and a Detector with a Circular Aperture 269 8.2.4 The Solid Angle for a Disk Source Parallel to a Detector with a Circular Aperture 273 8.2.5 The Solid Angle for a Point Isotropic Source and a Detector with a Rectangular Aperture 274 8.2.6 The Solid Angle for a Disk Source and a Detector with a Rectangular Aperture 274 8.2.7 The Use of the Monte Carlo Method for the Calculation of the Solid Angle 276 8.3 Source Effects 277 8.3.1 Source Self-Absorption Factor (f a ) 277 8.3.2 Source Backscattering Factor (f b ) 279 8.4 Detector Effects 282 8.4.1 Scattering and Absorption Due to the Window of the Detector 282 8.4.2 Detector Efficiency (e) 283

xii CONTENTS 8.4.3 Determination of Detector Efficiency 285 8.5 Relationship Between Counting Rate and Source Strength 287 Problems 289 References 291 9 INTRODUCTION TO SPECTROSCOPY 293 9.1 Introduction 293 9.2 Definition of Energy Spectra 293 9.3 Measurement of an Integral Spectrum with a Single-Channel Analyzer 295 9.4 Measurement of a Differential Spectrum with a Single-Channel Analyzer (SCA) 296 9.5 The Relationship Between Pulse-Height Distribution and Energy Spectrum 298 9.6 Energy Resolution of a Detection System 300 9.6.1 The Effect of Statistical Fluctuations: The Fano Factor 301 9.6.2 The Effect of Electronic Noise on Energy Resolution 303 9.6.3 The Effect of Incomplete Charge Collection 303 9.6.4 The Total Width Г 304 9.7 Determination of the Energy Resolution The Response Function 304 9.8 The Importance of Good Energy Resolution 305 9.9 Brief Description of a Multichannel Analyzer (MCA) 307 9.10 Calibration of a Multichannel Analyzer 310 Problems 314 References 315 10 ELECTRONICS 317 10.1 Introduction 317 10.2 Resistance, Capacitance, Inductance, and Impedance 317 10.3 A Differentiating Circuit 321 10.4 An Integrating Circuit 324 10.5 Delay Lines 325 10.6 Pulse Shaping 326 10.7 Timing 328 10.7.1 The Leading-Edge Timing Method 329 10.7.2 The Zero-Crossing Timing Method 330 10.7.3 The Constant-Fraction Timing Method 331 10.8 Coincidence-Anticoincidence Measurements 331 10.9 Pulse-Shape Discrimination 337 10.10 Preamplifiers 339 10.11 Amplifiers 342 10.12 Analog-to-Digital Converters (ADC) 344 10.13 Multiparameter Analyzers 347 Problems 349 Bibliography 350 References 350

CONTENTS xiü 11 DATA ANALYSIS METHODS 353 11.1 Introduction 353 11.2 Curve Fitting 353 11.3 Interpolation Schemes 355 11.4 Least-Squares Fitting 359 11.4.1 Least-Squares Fit of a Straight Line 360 11.4.2 Least-Squares Fit of General Functions 361 11.5 Folding and Unfolding 364 11.5.1 Examples of Folding 365 11.5.2 The General Method of Unfolding 368 11.5.3 An Iteration Method of Unfolding 371 11.5.4 Least-Squares Unfolding 372 11.6 Data Smoothing 373 Problems 377 Bibliography 378 References 378 12 PHOTON (GAMMA-RAY AND X-RAY) SPECTROSCOPY 381 12.1 Introduction 381 12.2 Modes of Energy Deposition in the Detector 381 12.2.1 Energy Deposition by Photons with E < 1.022 MeV 382 12.2.2 Energy Deposition by Photons with E > 1.022 MeV 385 12.3 Efficiency of X-Ray and Gamma-Ray Detectors: Definitions 389 12.4 Detection of Photons with Nal(Tl) Scintillation Counters 392 12.4.1 Efficiency of Nal(Tl) Detectors 392 12.4.2 Analysis of Scintillation Detector Energy Spectra 395 12.5 Detection of Gammas with an NE 213 Organic Scintillator 398 12.6 Detection of X-Rays with a Proportional Counter 399 12.7 Detection of Gammas with Ge Detectors 400 12.7.1 Efficiency of Ge Detectors 401 12.7.2 Energy Resolution of Ge Detectors 411 12.7.3 Analysis of Ge Detector Energy Spectra 412 12.7.4 Timing Characteristics of the Pulse 418 12.8 CdTe and Hgl 2 Detectors as Gamma Spectrometers 419 12.9 Detection of X-Rays with a Si(Li) Detector 420 12.10 Detection of X-Rays with a Crystal Spectrometer 421 12.10.1 Types of Crystal Spectrometers 426 12.10.2 Energy Resolution of Crystal Spectrometers 428 Problems 430 Bibliography 431 References 431 13 CHARGED-PARTICLE SPECTROSCOPY 433 13.1 Introduction 13.2 Energy Straggling 433 434

xiv CONTENTS 13.3 Electron Spectroscopy 439 13.3.1 Electron Backscattering 439 13.3.2 Energy Resolution and Response Function of Electron Detectors 441 13.3.3 Energy Calibration of Electron Spectrometers 442 13.3.4 Electron Source Preparation 444 13.4 Alpha, Proton, Deuteron, and Triton Spectroscopy 445 13.4.1 Energy Resolution and Response Function of Alpha Detectors 446 13.4.2 Energy Calibration 446 13.4.3 Source Preparation 446 13.5 Heavy-Ion (Z > 2) Spectroscopy 447 13.5.1 The Pulse-Height Defect 447 13.5.2 Energy Calibration: The Schmitt Method 450 13.5.3 Calibration Sources 452 13.5.4 Fission Foil Preparation 452 13.6 The Time-of-Flight Spectrometer 453 13.7 Detector Telescopes {EdE/dx Detectors) 455 13.8 Magnetic Spectrometers 456 13.9 Electrostatic Spectrometers 458 13.10 Position-Sensitive Detectors 459 13.10.1 Position-Sensitive Semiconductor Detectors 459 13.10.2 Multiwire Proportional Chambers 461 Problems 462 Bibliography 463 References 463 14 NEUTRON DETECTION AND SPECTROSCOPY 467 14.1 Introduction 467 14.2 Neutron Detection by (n, Charged Particle) Reaction 468 14.2.1 The BF 3 Counter 469 14.2.2 Boron-Lined Counters 473 14.2.3 6 Li Counters 474 14.2.4 3 He Counters 475 14.3 Fission Chambers 476 14.4 Neutron Detection by Foil Activation 478 14.4.1 Basic Equations 478 14.4.2 Determination of the Neutron Flux by Counting the Foil Activity 482 14.5 Measurement of a Neutron Energy Spectrum by Proton Recoil 484 14.5.1 Differentiation Unfolding of Proton Recoil Spectra 487 14.5.2 The FERDOR Unfolding Method 488 14.5.3 Proportional Counters Used as Fast-Neutron Spectrometers 489 14.5.4 Organic Scintillators Used as Fast-Neutron Spectrometers 494 14.6 Detection of Fast Neutrons Using Threshold Activation Reactions 496 14.6.1 The Code SAND-II 501 14.6.2 The Code SPECTRA 502 14.6.3 The Relative Deviation Minimization Method (RDMM) 502 14.6.4 The LSL-M2 Unfolding Code 503 14.7 Neutron Energy Measurement with a Crystal Spectrometer 503

CONTENTS XV 14.8 The Time-of-Flight Method 505 14.8.1 The Neutron Velocity Selector (Neutron Chopper) 508 14.8.2 Pulsed-Ion Beams 509 14.9 Compensated Ion Chambers 510 14.10 Self-Powered Neutron Detectors (SPND) 511 14.10.1 SPNDs with Delayed Response 512 14.10.2 SPNDs with Prompt Response 517 14.11 Concluding Remarks 518 Problems 519 Bibliography 520 References 520 15 ACTIVATION ANALYSIS 523 15.1 Introduction 523 15.2 Selection of the Optimum Nuclear Reaction 524 15.3 Preparation of the Sample for Irradiation 526 15.4 Sources of Radiation 528 15.4.1 Sources of Neutrons 528 15.4.2 Sources of Charged Particles 529 15.4.3 Sources of Photons 529 15.5 Irradiation of the Sample 530 15.6 Counting of the Sample 531 15.7 Analysis of the Results 532 15.8 Sensitivity of Activation Analysis 534 15.9 Interference Reactions 536 15.10 Advantages and Disadvantages of the Activation Analysis Method 537 Problems 537 Bibliography 538 References 538 16 HEALTH PHYSICS FUNDAMENTALS 541 16.1 Introduction 541 16.2 Units of Exposure and Absorbed Dose 542 16.3 The Relative Biological Effectiveness The Dose Equivalent 544 16.4 Dosimetry for Radiation External to the Body 547 16.4.1 Dose Due to Charged Particles 547 16.4.2 Dose Due to Photons 549 16.4.3 Dose Due to Neutrons 552 16.5 Dosimetry for Radiation Inside the Body 555 16.5.1 Dose from a Source of Charged Particles Inside the Body 555 16.5.2 Dose from a Photon Source Inside the Body 556 16.6 Internal Dose Time Dependence Biological Half-Life 558 16.7 Biological Effects of Radiation 562 16.7.1 Basic Description of the Human Cell 563 16.7.2 Stochastic and Nonstochastic Effects 564

xvi CONTENTS 16.8 Radiation Protection Guides and Exposure Limits 567 16.9 Health Physics Instruments 570 16.9.1 Survey Instruments 571 16.9.2 Thermoluminescent Dosimeters 572 16.9.3 Solid-State Track Recorders (SSTRs) 576 16.9.4 The Bonner Sphere (the Rem Ball) 579 16.9.5 The Neutron Bubble Detector 580 16.9.6 The Electronic Personal Dosimeter 581 16.9.7 Foil Activation Used for Neutron Dosimetry 582 16.10 Proper Use of Radiation 582 Problems 585 Bibliography 587 References 587 APPENDIXES 589 A Useful Constants and Conversion Factors 589 В Atomic Masses and Other Properties of Isotopes 591 С Alpha, Beta, and Gamma Sources Commonly Used 595 D Tables of Photon Attenuation Coefficients 599 E Table of Buildup Factor Constants 605 INDEX 607