principles of radiation interaction in matter and detection · xvi principles of radiation...
TRANSCRIPT
PRINCIPLES OF
h^m Intorartmi)IN Mattw Itowlinii
4th Edition
Claude LeroyUniversite de Montreal, Canada
Pier-Giorgio RancoitaIstituto Nazionale di Fisica Nucleare, Milan, Italy
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
Contents
Preface to the Fourth Edition vii
Preface to the Third Edition ix
Preface to the Second Edition xi
Preface to the First Edition xiii
Particle Interactions and Displacement Damage 1
1. Introduction 3
1.1 Radiation and Particle Interactions 5
1.2 Particles and Types of Interaction 7
1.2.1 Quarks and Leptons 9
1.3 Relativistic Kinematics 9
1.3.1 The Two-Body Scattering 13
1.3.2 The Invariant Mass 16
1.3.2.1 Lorentz-Invariant Quantities and Phase Space 18
1.3.3 Relativistic Doppler Effect 21
1.3.3.1 Redshift Parameter and Astronomy 24
1.4 Atomic Mass, Weight, Standard Weight and Mass Unit 26
1.5 Cross Section and Differential Cross Section 27
1.6 Coulomb Single-Scattering Differential Cross Section in
Laboratory and CoM Systems 30
1.6.1 Rutherford's Formula and Average Energy Transferred 35
1.7 Detectors and Large Experimental Apparata 39
1.7.1 Trigger, Monitoring, Data Acquisition, Slow Control. .
41
1.7.2 General Features of Particle Detectors and Detection
Media 41
1.7.3 Radiation Environments and Silicon Devices 48
XV
xvi Principles of Radiation Interaction in Matter and Detection
2. Electromagnetic Interaction of Charged Particles in Matter 51
2.1 Passage of Ionizing Particles through Matter 52
2.1.1 The Collision Energy-Loss of Massive Charged Particles 52
2.1.1.1 The Barkas-Andersen Effect 62
2.1.1.2 The Shell Correction Term 64
2.1.1.3 Energy-Loss Minimum, Density Effect and
Relativistic Rise 66
2.1.1.4 Restricted Energy-Loss and Fermi Plateau. .
69
2.1.2 Energy-Loss Formula for Compound Materials 73
2.1.3 Energy-Loss Fluctuations 75
2.1.3.1 5-Rays, Straggling Function, and Transport
Equation 75
2.1.3.2 The Landau-Vavilov Solutions for the
Transport Equation 78
2.1.3.3 The Most Probable Collision Energy-Loss for
Massive Charged Particles 80
2.1.3.4 Improved Energy-Loss Distribution and
Distant Collisions 84
2.1.3.5 Distant Collision Contribution to Energy
Straggling in Thin Silicon Absorbers 88
2.1.3.6 Improved Energy-Loss Distribution for
Multi-Particles in Silicon 91
2.1.4 Ionization Yield in Gas Media 92
2.2 Energy Loss of Light and Heavy Ions 94
2.2.1 Nuclear Stopping Power at Non-Relativistic Energies .97
2.2.1.1 Non-Relativistic Screened Nuclear Cross
Section 105
2.2.2 Nuclear Stopping Power at Relativistic Energies and
Energetic Recoil 109
2.2.3 Range of Heavy Charged Particles and Bragg Curve. .
118
2.3 Passage of Electrons and Positrons through Matter 124
2.3.1 Collision Losses by Electrons and Positrons 125
2.3.1.1 Most Probable Energy-Loss of Electrons and
Positrons 128
2.3.2 Practical Range of Electrons 130
2.3.3 Radiation Energy-Loss by Electrons and Positrons...
133
2.3.3.1 The Landau-Pomeranchuk-Migdal Effect and
Bremsstrahhmg Suppression 146
2.3.3.2 Collision and Radiation Stopping Powers. . 160
2.3.3.3 Radiation Yield and Bremsstrahlung AngularDistribution 160
Contents xvii
2.3.3.4 Radiation Length and Complete ScreeningApproximation 162
2.3.3.5 Critical Energy 166
2.4 Scattering of Electrons on Nuclei 167
2.4.1 The Unscreened Mott Cross Section of Electrons and
Positrons on Nuclei 169
2.4.1.1 Approximate Solutions for the Mott Cross
Section 171
2.4.1.2 Improved Numerical Approach and 7£Mott
Interpolated Expression 174
2.4.2 Complete Treatment of Electron Scattering on Nucleus 179
2.4.2.1 Finite Nuclear Size 181
2.4.2.2 Finite Rest Mass of Target Nucleus 183
2.4.3 Nuclear Stopping Power of Electrons 185
2.5 Multiple and Extended Volume Coulomb Interactions 187
2.5.1 The Multiple Coulomb Scattering 187
2.5.2 Emission of Cerenkov Radiation 194
2.5.3 Emission of Transition Radiation 200
3. Photon Interaction and Electromagnetic Cascades in Matter 207
3.1 Photon Interaction and Absorption in Matter 207
3.1.1 The Photoelectric Effect 209
3.1.1.1 The Auger Effect 216
3.1.2 The Compton Scattering 217
3.1.2.1 The Klein-Nishina Equation for Unpolarized
Photons 220
3.1.2.2 Electron Binding Corrections to Compton and
Rayleigh Scatterings 228
3.1.2.3 The Thomson Cross Section 231
3.1.2.4 Radiative Corrections and Double Compton
Effect 234
3.1.2.5 Inverse Compton Scattering 235
3.1.2.6 Power Loss of Electrons due to Inverse Compton
Scattering 241
3.1.3 Pair Production 246
3.1.3.1 Pair Production in the Field of a Nucleus. .
246
3.1.3.2 Pair Production in the Electron Field 258
3.1.3.3 Angular Distribution of Electron and Positron
Pairs 260
3.1.4 Photonuclear Scattering, Absorption and Production . . 260
3.2 Attenuation Coefficients, Dosimetric and RadiobiologicalQuantities 264
xviii Principles of Radiation Interaction in Matter and Detection
3.3 Electromagnetic Cascades in Matter 279
3.3.1 Phenomenology and Natural Units of ElectromagneticCascades 280
3.3.2 Propagation and Diffusion of Electromagnetic Cascades
in Matter 281
3.3.2.1 Rossi's Approximation B and Cascade
Multiplication of Electromagnetic Shower . . 282
3.3.2.2 Longitudinal Development of the Electromag¬netic Shower 284
3.3.2.3 Lateral Development of ElectromagneticShowers 288
3.3.2.4 Energy Deposition in Electromagnetic Cascades 296
3.3.3 Shower Propagation and Diffusion in Complex Absorbers 297
4. Nuclear Interactions in Matter 299
4.1 General Properties of the Nucleus 299
4.1.1 Radius of Nuclei and the Liquid Droplet Model 302
4.1.1.1 Droplet Model and Semi-Empirical Mass
Formula 303
4.1.2 Form Factor and Charge Density of Nuclei 305
4.1.3 Angular and Magnetic Moment, Shape of Nuclei.... 308
4.1.4 Stable and Unstable Nuclei 309
4.1.4.1 The /3-Decay and the Nuclear Capture ....311
4.1.4.2 The a-Decay 313
4.1.5 Fermi Gas Model and Nuclear Shell Model 315
4.1.5.1 7 Emission by Nuclei 320
4.2 Phenomenology of Interactions on Nuclei at High Energy ....321
4.2.1 Energy and A-Dependence of Cross Sections 322
4.2.1.1 Collision and Inelastic Length 323
4.2.2 Coherent and Incoherent Interactions on Nuclei 327
4.2.2.1 Kinematics for Coherent Condition 327
4.2.2.2 Coherent and Incoherent Scattering 330
4.2.3 Multiplicity of Charged Particles and Angular Distribu¬
tion of Secondaries 335
4.2.3.1 Rapidity and Pseudorapidity Distributions.
.
340
4.2.4 Emission of Heavy Prongs 344
4.2.5 The Nuclear Spallation Process 347
4.2.6 Nuclear Temperature and Evaporation 350
4.3 Hadronic Shower Development and Propagation in Matter ..
. 354
4.3.1 Phenomenology of the Hadronic Cascade in Matter . . 355
4.3.2 Natural Units in the Hadronic Cascade 358
4.3.3 Longitudinal and Lateral Hadronic Development .... 360
Contents xix
5. Physics and Properties of Silicon Semiconductor 367
5.1 Structure and Growth of Silicon Crystals 368
5.1.1 Imperfections and Defects in Crystals 371
5.2 Energy Band Structure and Energy Gap 372
5.2.1 Energy Gap Dependence on Temperature and Pressure in
Silicon 375
5.2.2 Effective Mass 376
5.2.2.1 Conductivity and Density-of-States Effective
Masses in Silicon 378
5.3 Carrier Concentration and Fermi Level 384
5.3.1 Effective Density-of-States 385
5.3.1.1 Degenerate and Non-Degenerate
Semiconductors 391
5.3.1.2 Intrinsic Fermi-Level and Concentration of
Carriers 393
5.3.2 Donors and Acceptors 397
5.3.2.1 Extrinsic Semiconductors and Fermi Level. .
398
5.3.2.2 Compensated Semiconductors 405
5.3.2.3 Maximun Temperature of Operation of Extrin¬
sic Semiconductors 408
5.3.2.4 Quasi-Fermi Levels 409
5.3.3 Largely Doped and Degenerate Semiconductors 411
5.3.3.1 Bandgap Narrowing in Heavily Doped
Semiconductors 411
5.3.3.2 Reduction of the Impurity Ionization-Energy in
Heavily Doped Semiconductors 415
6. Transport Phenomena in Semiconductors 417
6.1 Thermal and Drift Motion in Semiconductors 418
6.1.1 Drift and Mobility 418
6.1.1.1 Mobility in Silicon at High Electric Fields or Up
to Large Doping Concentrations 422
6.1.2 Resistivity 428
6.2 Diffusion Mechanism 431
6.2.1 Einstein's Relationship 433
6.3 Thermal Equilibrium and Excess Carriers in Semiconductors . . 435
6.3.1 Generation and Recombination Processes, Carrier
Lifetimes 437
6.3.1.1 Bulk Processes in Direct Semiconductors. . .
437
6.3.1.2 Bulk Processes in Indirect Semiconductors. .
440
6.3.1.3 Surface Recombination 445
6.3.1.4 Lifetime of Minority Carriers in Silicon....
445
xx Principles of Radiation Interaction in Matter and Detection
6.4 The Continuity Equations 446
6.4.1 The Dielectric Relaxation Time and Debye Length . . . 450
6.4.2 Ambipolar Transport 451
6.4.3 Charge Migration and Field-Free Regions 454
6.4.3.1 Carrier Diffusion in Silicon Radiation Detectors 457
6.4.3.2 Measurement of Charge Migration in Silicon
Radiation Detectors 463
6.5 Hall Effect in Silicon Semiconductors 469
7. Radiation Effects and Displacement Damage in Semiconductors 477
7.1 Energy Loss by Atomic Displacements 479
7.1.1 Damage Function, NIEL and Displacement StoppingPower 480
7.1.1.1 Knock-On Atoms and Displacement Cascade 486
7.1.1.2 Norgett-Robinson-Torrens Expression ....490
7.1.1.3 Displacement Threshold Energy and AnnealingEffects 491
7.1.1.4 Neutron Interactions 492
7.1.1.5 Interactions of Protons, cc-Particles, Light- and
Heavy-Ions 493
7.1.1.6 NIEL from Coulomb Scattering of Protons,
Q;-Particles, Light- and Heavy-Ions 498
7.1.1.7 Electron Interactions 500
7.1.1.8 NIEL from Electron-Nucleus Interactions. .
502
7.1.2 Damage Function for Neutrons, Charged Particles and
Photons 505
7.1.2.1 Damage Function for Neutrons 508
7.1.2.2 Damage Function for Protons, Light- and
Heavy-Ions 508
7.1.2.3 Damage Function for Electrons and Photons. 516
7.2 Radiation Induced Defects, Defect Clusters and NIEL 521
7.3 Ionization Energy-Loss and NIEL Processes 527
7.3.1 Imparted Dose in Silicon 528
7.3.2 Ionization Damage 532
7.4 Radiation Induced Defects and Modification of Silicon Bulk and
p— n Junction Properties 534
7.4.1 Displacement Damage Effect on Minority Carrier
Lifetime 535
7.4.2 Carrier Generation and Leakage Current 537
7.4.3 Diode Structure and Rectification Down to Cryogenic
Temperature 539
Contents xxi
7.4.3.1 Rectification Property Up to Large Fast-
Neutron Fluences at Room Temperature . . .540
7.4.3.2 Large Radiation Damage and p — i — n Structure
at Room Temperature 544
7.4.3.3 I — V Characteristics Down to Cryogenic
Temperature 546
7.4.4 Complex Impedance of Junctions and Cryogenic
Temperatures 550
7.4.5 Resistivity, Hall Coefficient and Hall Mobility at Large
Displacement Damage 558
7.4.6 AFM Structure Investigation in Irradiated Devices. . .
566
Radiation Environments and Particle Detection 569
8. Radiation Environments and Damage in Semiconductors 571
8.1 High-Luminosity Machines Environments for Particle
Physics Experiments 571
8.1.1 Ionization Process and LHC Collider
Environment 576
8.1.2 Non-Ionization Processes, NIEL Scaling Hypothesis and
Collider Environments 576
8.2 Space Radiation Environment 582
8.2.1 Solar Wind 584
8.2.2 Solar and Heliospheric Magnetic Field 591
8.2.3 Extension of the Heliosphere and the Earth
Magnetosphere 603
8.2.4 Propagation of Galactic Cosmic Rays through
Interplanetary Space 608
8.2.4.1 Diffusion Tensor 618
8.2.4.2 Modulated Differential Intensities of Cosmic
Rays and Drift Velocity 622
8.2.4.3 Heliosphere Modulation: the HelMod Model.
627
8.2.5 Solar, Heliospheric and Galactic Cosmic Rays in the
Interplanetary Space 633
8.2.6 Trapped Particles and Earth Magnetosphere 638
8.3 Neutron Spectral Fluence in Nuclear Reactor Environment. . .
645
8.3.1 Fast Neutron Cross Section on Silicon 646
8.3.2 Energy Distribution of Reactor Neutrons and
Classification 647
9. Scintillating Media and Scintillator Detectors 649
xxii Principles of Radiation Interaction in Matter and Detection
9.1 Scintillators 650
9.1.1 Organic Scintillators 651
9.1.2 Inorganic Scintillators 653
9.1.2.1 Novel Inorganic Scintillators 656
9.2 The Cerenkov Detectors 662
9.2.1 Threshold Cerenkov Detectors 665
9.2.2 Differential Cerenkov Detectors 670
9.2.3 Ring Imaging Cerenkov (RICH) Detectors 671
9.3 Wavelength Shifters 673
9.4 Transition Radiation Detectors (TRD) 674
9.5 Scintillating Fibers 676
9.6 Detection of the Scintillation Light 679
9.7 Applications in Calorimetry 684
9.8 Application in Time-of-Flight (ToF) Technique 685
10. Solid State Detectors 689
10.1 Standard Planar Float-Zone and MESA Silicon Detectors
Technologies 690
10.1.1 Standard Planar Float-Zone Technology 690
10.1.2 MESA Technology 692
10.2 Basic Principles of Operation 694
10.2.1 Unpolarized p— n Junction 695
10.2.2 Polarized p— n Junction 700
10.2.3 Capacitance 701
10.2.4 Charge Collection Measurements 703
10.2.5 Charge Transport in Silicon Diodes 704
10.2.6 Leakage or Reverse Current 715
10.2.7 Noise Characterization of Silicon Detectors 717
10.3 Charge Collection Efficiency and Hecht Equation 719
10.4 Spectroscopic Characteristics of Standard Planar Detectors. . .
725
10.4.1 Energy Resolution of Standard Planar Detectors .... 726
10.4.2 Energy Resolution and the Fano Factor 729
10.5 Microstrip Detectors 731
10.6 Pixel Detector Devices 736
10.6.1 The Medipix-Type Detecting Device 737
10.6.2 Examples of Application of Medipix2: Particle Physics 740
10.6.2.1 Electrons and Photons 741
10.6.2.2 Neutrons 741
10.6.2.3 Muons, Pions and Protons 744
10.6.2.4 a-Particles and Heavier Ions 744
10.6.2.5 Charge Sharing 744
Contents xxiii
10.6.2.6 Luminosity and Induced Radioactivity-
Measurement with Medipix Family Detectors 748
10.7 The Timepix Detecting Device 751
10.7.1 The Timepix Time-over-Threshold (ToT) Mode of
Operation 752
10.7.2 The Pattern Recognition of Tracks with Timepix ....754
10.7.2.1 Reliability of Track Pattern Recognition of
Timepix Validated with Radioactive Sources.
754
10.7.2.2 Heavy Tracks Recognition 755
10.7.2.3 Single Track Analysis 758
10.7.3 Dependence of the Cluster shape on the Applied Bias
Voltage 759
10.7.4 The Timepix Time-of-Arrival (ToA) Mode of Operation 761
10.8 Photodiodes, Avalanche Photodiodes and Silicon Photomultipliers 762
10.8.1 Photodiodes 762
10.8.1.1 Photodiode and Electrical Model 764
10.8.2 Avalanche Photodiodes 770
10.8.3 Geiger-mode Avalanche Photodiodes and Silicon
Photomultiplier Detectors 772
10.8.4 Electrical Characteristics of SiPM Devices as Function of
Temperature and Frequency 781
10.8.4.1 Capacitance Response 782
10.8.4.2 Current-Voltage Characteristics 785
10.8.4.3 Electrical Model for SiPMs 785
10.9 Photovoltaic Solar Cells 790
10.10 Neutrons Detection with Silicon Detectors 797
10.10.1 Principles of Neutron Detection with Silicon Detectors.
797
10.10.1.1 Signal in Silicon Detectors for Thermal
Neutrons 799
10.10.1.2 Signals in Silicon Detectors by Fast Neutrons 806
10.10.2 3-D Neutron Detectors 811
11. Displacement Damages and Interactions in Semiconductor Devices 813
11.1 Displacement Damage in Irradiated Bipolar Transistors 816
11.1.1 Transit Time of Minority Carriers Across the Base. . .
819
11.1.2 Gain Degradation of Bipolar Transistors and
Messenger-Spratt Equation 820
11.1.3 Surface and Total Dose Effects on the Gain Degradation
of Bipolar Transistors 824
11.1.4 Generalized Messenger-Spratt Equation for Gain
Degradation of Bipolar Transistors 826
xxiv Principles of Radiation Interaction in Matter and Detection
11.1.4.1 Experimental Evidence of Approximate NIEL
Scaling 827
11.1.5 Transistor Gain and Self-Annealing 830
11.1.6 Radiation Effects on Low-Resistivity Base Spreading-Resistance 832
11.2 Radiation Effects on Silicon Semiconductor Detectors 834
11.2.1 MESA Radiation Detectors 836
11.2.1.1 Electrical Features of Planar MESA Detectors 837
11.2.1.2 Spectroscopic Characteristics of MESA
Detectors 838
11.2.2 Results of Irradiation Tests of Planar MESA Detectors 839
11.2.3 Irradiation with Low-Energy Protons in High-Resistivity
Silicon Detectors and NIEL 844
11.3 NIEL Dose Dependence for GaAs Solar Cells 850
11.3.1 Single Junction Solar Cells 851
11.3.2 Triple Junction Solar Cells 854
11.4 Single Event Effects 855
11.4.1 Classification of SEE 856
11.4.2 SEE in Spatial Radiation Environment 858
11.4.3 SEE in Atmospheric Radiation Environment 859
11.4.4 SEE in Terrestrial Radiation Environment 860
11.4.5 SEE Produced by Radioactive Sources 861
11.4.6 SEE in Accelerator Radiation Environment 864
11.4.7 SEE Generation Mechanisms 864
11.4.7.1 Direct Ionization 864
11.4.7.2 Indirect Ionization 866
11.4.7.3 Linear Energy Transfer (LET) 868
11.4.7.4 Sensitive Volume 869
11.4.7.5 Critical Charge 869
11.4.8 SEE Cross Section 873
11.4.8.1 Calculation of SEU Rate for Ions 875
11.4.8.2 Calculation of SEU Rate for Protons and
Neutrons 877
11.4.9 SEE Mitigation 880
12. Gas Filled Chambers 881
12.1 The Ionization Chamber 881
12.2 Recombination Effects 884
12.2.1 Germinate or Initial Recombination 885
12.2.2 Columnar Recombination 885
12.2.3 The Box Model 886
12.2.4 Recombination with Impurities 887
Contents xxv
12.3 Example of Ionization Chamber Application: the a-Cell 890
12.3.1 The a-Cell 890
12.3.2 Charge Measurement with the a-Cell 893
12.3.3 Examples of Pollution Tests Using the a-Cell 898
12.4 Proportional Counters 901
12.4.1 Avalanche Multiplication 901
12.5 Proportional Counters: Cylindrical Coaxial Wire Chamber. . . 903
12.6 Multiwire Proportional Chambers (MWPC) 910
12.7 The Geiger-Mueller Counter 912
13. Principles of Particle Energy Determination 915
13.1 Experimental Physics and Calorimetry 915
13.1.1 Natural Units in Shower Propagation 919
13.2 Electromagnetic Sampling Calorimetry 919
13.2.1 Electromagnetic Calorimeter Response 919
13.2.2 The e/mip Ratio 922
13.2.2.1 e/mip Dependence on Z-Values of Readout and
Passive Absorbers 926
13.2.2.2 e/mip Dependence on Absorber Thickness. .
930
13.2.3 e/mip Reduction in High-Z Sampling Calorimeters:
the Local Hardening Effect 930
13.3 Principles of Calorimetry with Complex Absorbers 934
13.3.1 The Filtering Effect and How to Tune the e/mip Ratio 936
13.3.2 e/mip Reduction by Combining Local Hardening and
Filtering Effects 941
13.4 Energy Resolution in Sampling Electromagnetic Calorimetry .943
13.4.1 Visible Energy Fluctuations 943
13.4.1.1 Calorimeter Energy Resolution for Dense Read¬
out Detectors 945
13.4.1.2 Calorimeter Energy Resolution for Gas Readout
Detectors 949
13.4.2 Effect of Limited Containment on Energy Resolution.
953
13.5 Homogeneous Calorimeters 957
13.5.1 General Considerations 957
13.5.2 Energy Measurement 960
13.6 Position Measurement 967
13.7 Electron Hadron Separation 971
13.8 Hadronic Calorimetry 972
13.8.1 Intrinsic Properties of the Hadronic Calorimeter....
972
13.8.1.1 The e/h, e/ir, h/mip and n/mip Ratios. . . 973
13.8.1.2 Compensating Condition e/h = e/n = 1 and
Linear Response 977
xxvi Principles of Radiation Interaction in Matter and Detection
13.9 Methods to Achieve the Compensation Condition 981
13.9.1 Compensation Condition by Detecting Neutron Energy 982
13.9.2 Compensation Condition by Tuning the e/mip Ratio.
988
13.10 Compensation and Hadronic Energy Resolution 998
13.10.1 Non-Compensation Effects and the (j)(e/ir) Term ....1004
13.10.2 Determination of Effective Intrinsic Resolutions.... 1006
13.10.3 Effect of Visible-Energy Losses on Calorimeter Energy
Resolution 1008
13.11 Calorimetry at Very High Energy 1009
13.11.1 General Considerations 1009
13.11.2 Air Showers (AS) and Extensive Air Showers (EAS) . .1013
13.11.3 Electromagnetic Air Showers 1016
13.11.3.1 Longitudinal Development 1016
13.11.3.2 Lateral Development 1017
13.11.4 Hadronic Extensive Air Showers 1019
13.11.5 The Muon Component of Extensive Air Showers .... 1021
14. Superheated Droplet (Bubble) Detectors and CDM Search 1023
14.1 The Superheated Droplet Detectors and their Operation ....1026
14.1.1 Neutron Response Measurement 1030
14.1.2 a-Particle Response Measurement 1034
14.1.3 Radon Detection 1037
14.1.4 Spontaneous Nucleation 1038
14.1.5 Signal Measurement with Piezoelectric Sensors 1039
14.2 Search of Cold Dark Matter (CDM) 1040
14.2.1 Calculation of the Neutralino-Nucleon Exclusion Limits 1041
14.2.1.1 Spin-Independent or Coherent Cross Section.
1042
14.2.1.2 Spin-Dependent or Incoherent Cross Section.
1045
14.2.1.3 Calculation of (5P) and (Sn) in Nuclei....
1050
14.2.1.4 Shell Models Calculation and Validation of (Sp)and (Sn) 1055
14.2.2 The PICASSO Experiment, an Example 1055
14.2.3 Status of Dark Matter Searches 1057
14.3 Double Beta Decay 1059
15. Medical Physics Applications 1065
15.1 Single Photon Emission Computed Tomography (SPECT) . . .1067
15.2 Positron Emission Tomography (PET) 1082
15.2.1 Use of Silicon in PET Imagers 1088
15.2.1.1 Example of Silicon Microstrip Detectors
Used in Scanners 1088
Contents xxvii
15.2.1.2 Example of Silicon Pad Detectors Used in
Scanners 1089
15.2.1.3 Example of Silicon Pixel Detectors Used in
Scanners 1089
15.2.1.4 Example of Silicon Photomultipliers (SiPM)Detectors Used in Scanners 1091
15.3 X-Ray Medical Imaging 1095
15.3.1 The Contrast 1096
15.3.2 The Modulation Transfer Function 1096
15.3.3 The Detective Quantum Efficiency 1097
15.4 Magnetic Resonance Imaging (MRI) 1099
15.4.1 Physical Basis of MRI 1099
15.4.2 Forming an Image 1102
15.4.2.1 Spin-Echo 1102
15.4.2.2 Gradient-Echo 1103
15.4.2.3 Space Positioning 1103
15.4.2.4 Flows 1104
15.4.2.5 Functional MRI 1105
Appendix A General Properties and Constants 1107
A.l Physical Constants 1108
A.2 Periodic Table of Elements 1113
A.3 Conversion Factors 1115
A.4 Electronic Structure of the Elements 1127
A.5 Interpolating Parameter for 7£Mott 1130
A.6 Isotopic Abundances 1148
A.7 Commonly Used Radioactive Sources 1150
A.8 Free Electron Fermi Gas 1151
A.9 Gamma-Ray Energy and Intensity Standards 1154
A. 10 Screened Relativistic NIEL for Electrons and Protons in GaAs and
Si media 1158
Appendix B Mathematics and Statistics 1167
B.l Probability and Statistics for Detection Systems 1168
B.2 Table of Integrals 1180
Bibliography 1183
Index 1261