1 Nuclear Radiation Detectors ................................ 1
1.1 Classification of Detectors ................................ 1
1.2 Ionization Chambers ........................................ 3
1.2.1 Ionization Chambers ................................. 3
1.2.2 Pulse Chambers ...................................... 3
1.2.3 Gas-Filled Pulse Counter ............................ 4
1.2.4 Variation of Pulse Sizes ............................ 5
1.3 Proportional Counter ....................................... 7
1.3.1 Construction ........................................ 7
1.4 Geiger Muller Counter ...................................... 7
1.4.1 Construction and Characteristics .................... 7
1.4.2 Pulse Formation and Decay ........................... 9
1.4.3 Quenching the Discharge ............................ 10
1.4.4 Scaling Circuits ................................... 12
1.5 Resolving Time ............................................ 12
1.5.1 Determination of Resolving Time: Double Source
Method ............................................. 13
1.6 Resolving Time of a Coincidence Circuit ................... 14
1.6.1 Determination of the Resolving Time of the
Coincidence Circuit ................................ 14
1.7 Semi-conductor Particle Detectors ......................... 19
1.7.1 Resolution ......................................... 19
1.7.2 Reversed Biased p-n Junction Particle Detector ..... 19
1.7.3 Advantages ......................................... 21
1.7.4 Applications ....................................... 22
1.7.5 Disadvantages ...................................... 22
1.8 Neutron Detectors ......................................... 23
1.8.1 Principle .......................................... 23
1.8.2 Desired Characteristics of Neutron Detectors ....... 24
1.8.3 Slow Neutron Detectors ............................. 24
1.8.4 Fission Detectors .................................. 27
1.8.5 Fast Neutron Detectors ............................. 27
1.8.6 Transmission Experiments ........................... 28
1.9 Scintillation Counter ..................................... 29
1.9.1 Construction ....................................... 29
1.9.2 Mechanism .......................................... 30
1.9.3 Desirable Characteristics of Luminescent
Materials .......................................... 30
1.9.4 Organic Scintillators .............................. 30
1.9.5 Inorganic Scintillators ............................ 31
1.9.6 Photo-Multiplier (PM) Characteristics .............. 32
1.9.7 Light Collection ................................... 32
1.9.8 Background ......................................... 32
1.9.9 Electronic Equipment ............................... 33
1.9.10 Gamma Ray Spectroscopy with Nal (TL) Scintillator .. 33
1.9.11 Applications and Advantages ........................ 36
1.10 Cerenkov Counters ......................................... 38
1.10.1 Focusing Type (Angular Selection Counters) ......... 38
1.10.2 Velocity Resolution δθ/δβ .......................... 40
1.10.3 Non-focusing Counters .............................. 40
1.10.4 Total Shower Absorption Cerenkov Counter ........... 41
1.10.5 Advantages ......................................... 41
1.10.6 Disadvantages ...................................... 42
1.11 Photographic Emulsions .................................... 43
1.11.1 Composition ........................................ 43
1.11.2 Latent Image ....................................... 43
1.11.3 Processing ......................................... 43
1.11.4 Techniques ......................................... 44
1.11.5 Advantages ......................................... 46
1.11.6 Limitations ........................................ 47
1.11.7 Discoveries Made with Photographic Emulsions ....... 48
1.12 Expansion Cloud Chamber ............................. 49
1.12.1 Principle .......................................... 49
1.12.2 The Stability of Charged Drops ..................... 49
1.12.3 Choice of Pressure ................................. 51
1.12.4 Choice of Gas ...................................... 51
1.12.5 Curvature Measurements ............................. 52
1.12.6 Multiplate Chamber ................................. 52
1.12.7 Counter Control .................................... 52
1.12.8 Temperature Control ................................ 52
1.12.9 Expansion Speed .................................... 52
1.12.10 Recycling Time .................................... 53
1.12.11 Discoveries ....................................... 53
1.13 Diffusion Cloud Chamber ................................... 53
1.13.1 Principle .......................................... 53
1.13.2 Choice of Liquid Vapor ............................. 55
1.13.3 Choice of Gas ...................................... 55
1.13.4 Operating Temperatures ............................. 55
1.13.5 Clearing Fields .................................... 55
1.13.6 Magnetic Field ..................................... 56
1.13.7 Photography ........................................ 56
1.13.8 Advantages ......................................... 56
1.13.9 Limitations ........................................ 57
1.13.10 Discoveries ....................................... 58
1.14 Bubble Chamber ............................................ 58
1.14.1 Principle .......................................... 58
1.14.2 Bubble Chamber Liquids ............................. 58
1.14.3 Control of Temperature ............................. 59
1.14.4 Magnetic Field ..................................... 59
1.14.5 Track Distortion ................................... 60
1.14.6 Number of Tracks per Picture ....................... 60
1.14.7 Identification of Particles ........................ 60
1.14.8 Advantages ......................................... 61
1.14.9 Limitations ........................................ 62
1.14.10 Discoveries ....................................... 63
1.15 Spark Chamber ............................................. 63
1.15.1 Principle .......................................... 63
1.15.2 Mechanism of the Spark Discharge ................... 63
1.15.3 Detection Efficiency ............................... 63
1.15.4 Time Resolution .................................... 64
1.15.5 Spatial Resolution ................................. 65
1.15.6 Effect of Magnetic Fields .......................... 65
1.15.7 Recovery Time ...................................... 65
1.15.8 Gas Composition .................................... 65
1.15.9 Chamber Construction ............................... 66
1.15.10 Tracks Inclined to the Electric Field ............. 66
1.15.11 Applications ...................................... 66
1.15.12 Disadvantages ..................................... 67
1.15.13 Discoveries ....................................... 67
1.16 Calorimeters .............................................. 68
1.16.1 Introduction ....................................... 68
1.16.2 Electromagnetic Calorimeters ....................... 68
1.16.3 Hadron-Shower Calorimeters ......................... 71
1.17 Comparison of Various Experimental Techniques Used in
High Energy Physics ....................................... 72
1.18 Questions ............................................ 72
1.19 Problems ............................................. 75
References ................................................ 78
2 High Energy Accelerators .................................. 79
2.1 Introduction .............................................. 79
2.2 Electrostatic Accelerators ................................ 79
2.3 High Energy Accelerators .................................. 79
2.4 Cyclic Accelerators ....................................... 80
2.5 Cyclotron Accelerator ..................................... 80
2.5.1 Energy Limit ....................................... 82
2.5.2 Fringing Field ..................................... 84
2.6 Synchrocyclotron .......................................... 85
2.6.1 Phase Stability in Circular Motion ................. 85
2.6.2 Number of Orbits ................................... 91
2.7 AVF (Azimuthally Varying Field) Cyclotron ................. 91
2.8 Synchrotron ............................................... 93
2.8.1 Proton Synchrotron ................................. 93
2.8.2 Electron Synchrotron ............................... 99
2.9 Betatron ................................................. 100
2.10 Linear Accelerators ...................................... 103
2.10.1 Principle ......................................... 103
2.10.2 Total Length ...................................... 104
2.10.3 Phase Stability ................................... 104
2.10.4 Radial Focusing ................................... 105
2.11 Electron Linear Accelerators ............................. 106
2.12 Colliding Beam Accelerators .............................. 107
2.12.1 Cooling in p~p Colliders .......................... 109
2.13 Fixed Target Accelerators ................................ 110
2.13.1 Advantages ........................................ 110
2.13.2 Disadvantages ..................................... 111
2.14 Colliders ................................................ 111
2.14.1 Advantages ........................................ 111
2.14.2 Disadvantages ..................................... 111
2.15 Questions ................................................ 122
2.16 Problems ................................................. 123
References ............................................... 126
3 Elementary Particles ..................................... 127
3.1 Concepts and Nomenclature ................................ 127
3.1.1 Iso-spin ........................................... 128
3.2 Historical Development ................................... 129
3.3 Discovery and Properties of Elementary Particles ......... 135
3.3.1 Neutron ........................................... 135
3.4 Positron ................................................. 138
3.4.1 Discovery ......................................... 138
3.4.2 Sources ........................................... 139
3.4.3 Positronium ....................................... 140
3.5 Muon ..................................................... 140
3.5.1 Discovery ......................................... 140
3.5.2 Mass .............................................. 141
3.5.3 Lifetime .......................................... 142
3.5.4 μ-Decay Spectrum .................................. 143
3.5.5 Production ........................................ 144
3.5.6 Interactions ...................................... 144
3.5.7 Muon Scattering ................................... 145
3.5.8 Catalytic Reactions ............................... 145
3.5.9 Electric Dipole Moment ............................ 145
3.5.10 Spin .............................................. 145
3.6 Pions .................................................... 146
3.6.1 Discovery ......................................... 146
3.6.2 Artificial Production of Pions .................... 147
3.6.3 Threshold for Single Pion Production in N-N
Collisions ........................................ 149
3.6.4 Decay ............................................. 150
3.6.5 Mass .............................................. 151
3.6.6 Mean Life Time .................................... 152
3.6.7 Spin .............................................. 153
3.6.8 Isospin (T) of Pion ............................... 155
3.6.9 Primakoff Effect .................................. 155
3.7 Antiproton ............................................... 156
3.7.1 Discovery ......................................... 156
3.7.2 Charge ............................................ 157
3.7.3 Mass .............................................. 158
3.7.4 Production in Pairs ............................... 158
3.7.5 Decay Constant .................................... 158
3.7.6 IsotopicSpin ...................................... 158
3.7.7 Annihilation ...................................... 159
3.7.8 Interaction Cross-Sections ........................ 159
3.7.9 Elastic Scattering ................................ 160
3.7.10 Strange Particle Production ....................... 161
3.7.11 Anti-neutrons ..................................... 161
3.7.12 Antibaryons ....................................... 161
3.8 Strange Particles ........................................ 162
3.8.1 Production ........................................ 162
3.8.2 K+-Mesons (Kaons) ................................. 163
3.8.3 K--Mesons ......................................... 166
3.8.4 Σ Hyperons ........................................ 169
3.8.5 Λ-Hyperon ......................................... 171
3.8.6 Cascade Hyperon Ξ ................................. 172
3.8.7 Hyperfragments .................................... 173
3.8.8 Ω- (Omega Minus) Hyperon .......................... 175
3.9 Neutrino ................................................. 177
3.9.1 Introduction ...................................... 177
3.9.2 The Experimental Discovery ........................ 178
3.9.3 Experiment to Demonstrate that Neutrino and
Antineutrino Are Different Particles .............. 179
3.9.4 Muon Neutrino (νμ) is Different from Electron
Neutrino (νe) ..................................... 179
3.9.5 Mass of Neutrino .................................. 180
3.9.6 Charge ............................................ 181
3.9.7 Spin .............................................. 181
3.9.8 Quantum Numbers for Leptons ....................... 181
3.9.9 Helicity .......................................... 182
3.9.10 Neutrino Sources .................................. 182
3.9.11 Interactions of Neutrinos ......................... 184
3.10 Questions ................................................ 202
3.11 Problems ................................................. 204
References ............................................... 208
4 Conservation Laws and Invariance Principles .............. 209
4.1 Fundamental Interactions ................................. 209
4.2 Classification of Elementary Particles ................... 212
4.3 Conservation Laws ........................................ 213
4.3.1 Charge (Q/e) Conservation ......................... 214
4.3.2 Baryon Number (B) Conservation .................... 214
4.3.3 Lepton Conservation ............................... 214
4.3.4 Energy (E) Conservation ........................... 215
4.3.5 Linear Momentum Conservation ...................... 216
4.3.6 Angular Momentum Conservation ..................... 216
4.3.7 Isotopic Spin (Isospin or Isobaric Spin) .......... 216
4.4 Strangeness .............................................. 224
4.5 Isotopic Spin and Strangeness Conservation ............... 225
4.6 Invariance and Conservation Laws ......................... 228
4.7 Invariance and Operators ................................. 229
4.7.1 Translation ....................................... 230
4.7.2 Rotations ......................................... 230
4.7.3 Isospin Symmetry .................................. 231
4.8 Parity ................................................... 235
4.8.1 Parity of Particles ............................... 236
4.8.2 Parity of a System of Particles ................... 236
4.8.3 Conservation of Parity in EM and Strong
Interactions ...................................... 237
4.8.4 Conservation of Parity in Electromagnetic
Interactions and Laporte Rule ..................... 239
4.8.5 Determination of Parity of Negative Pions ......... 239
4.8.6 Parity of Strange Particles ....................... 241
4.8.7 The Isospin Versus Parity ......................... 242
4.9 Spin of Neutral Pion ..................................... 242
4.10 Charge Conjugation (С) ................................... 244
4.10.1 Invariance of С in Strong Interactions ............ 245
4.10.2 Invariance of С in Electromagnetic Interactions ... 245
4.10.3 Eigen States of the Charge Conjugation Operator ... 245
4.10.4 С-Parity of Photons ............................... 246
4.10.5 Positronium Annihilation .......................... 246
4.11 G-Parity ................................................. 247
4.12 Time Reversal ............................................ 250
4.12.1 Г-Invariance in Strong Interactions ............... 251
4.12.2 Electric Dipole Moment (EDM) and Time Invariance .. 251
4.13 Charge Conservation and Gauge Invariance ................. 252
4.14 The CPT Theorem .......................................... 253
4.15 Questions ................................................ 262
4.16 Problems ................................................. 267
References ............................................... 269
5 Strong Interactions ...................................... 271
5.1 Resonances ............................................... 271
5.1.1 Dalitz Plot ........................................ 273
5.2 Baryon Resonances ........................................ 275
5.2.1 Nucleon Resonances ................................ 275
5.2.2 The Spin and Parity ............................... 276
5.2.3 Resonance Spin from Total Cross-Section ........... 278
5.2.4 Parity ............................................ 278
5.2.5 Isospin ........................................... 279
5.3 Hyperon Resonances ....................................... 279
5.3.1 Cascade Hyperon Resonance ......................... 280
5.4 Meson Resonances ......................................... 280
5.4.1 Pion Resonances ................................... 280
5.4.2 Kaon Resonances ................................... 283
5.5 Static Quark Model ....................................... 284
5.5.1 Predecessors to the Quark Model ................... 284
5.5.2 The Quark Model ................................... 285
5.6 Supermultiplets .......................................... 288
5.6.1 Baryon Decuplet ................................... 288
5.6.2 The Ω--Hyperon .................................... 289
5.6.3 States of the Decuplet ............................ 292
5.6.4 Baryon Octet (JP = 1+/2) .......................... 293
5.6.5 Gell-Mann-Okubo Mass Formula ...................... 294
5.6.6 Regge Trajectories ................................ 295
5.6.7 Magnetic Moments .................................. 296
5.6.8 Mass of Quarks from Magnetic Moments .............. 298
5.6.9 Meson Multiplets .................................. 298
5.6.10 U-Spin ............................................ 303
5.6.11 Mixing Angle ...................................... 304
5.6.12 Change of Flavour of Quarks ....................... 306
5.6.13 Quark Charge Assignment Test in Drell-Yan
Process ........................................... 307
5.7 Colour ................................................... 308
5.7.1 SU(3) Colour Group ................................. 309
5.7.2 Colour Singlet .................................... 309
5.7.3 Experimental Confirmation of Colour Hypothesis .... 310
5.8 Gluons ................................................... 311
5.8.1 Three Jet Events .................................. 314
5.9 Do Free Quarks Exist? .................................... 314
5.10 Quark Dynamics—Confinement ............................... 314
5.11 Hadron Decays and Zweig's Rule ........................... 316
5.12 The Fourth Quark (Charmed Quark) ......................... 318
5.12.1 Properties of the J/ψ ............................. 320
5.12.2 Charmonium ........................................ 322
5.12.3 The Positronium and Charmonium .................... 323
5.12.4 Charmed Hadrons ................................... 326
5.12.5 SU(4) Symmetry .................................... 327
5.13 The Fifth Quark (Bottom Quark) ........................... 329
5.14 The Sixth Quark (Top Quark) .............................. 332
5.15 Questions ................................................ 342
5.16 Problems ................................................. 344
References ............................................... 345
6 Electromagnetic Interactions ............................. 347
6.1 Feynman Diagrams ......................................... 347
6.2 Basic Electromagnetic Processes .......................... 349
6.3 Actual Process ........................................... 350
6.3.1 Moller Scattering ................................. 351
6.3.2 e+ - e- Annihilation .............................. 352
6.3.3 Pair Production у = e+ + e- ....................... 353
6.3.4 Photoelectric Effect and Bremsstrahlung ........... 354
6.4 Second-Order Diagrams .................................... 354
6.5 Scattering of Electrons .................................. 355
6.5.1 Elastic Scattering of Spinless Electrons by
Nuclei ............................................ 355
6.6 Form Factors ............................................. 356
6.7 Four-Momentum Transfer ................................... 357
6.8 Elastic Scattering of Electrons with Spin by Spinless
Nuclei (Mott Scattering) ................................. 358
6.8.1 Elastic Scattering of an Electron by a Point-
Like Dirac Particle of Mass M ..................... 359
6.9 Rosenbluth Formula ....................................... 359
6.10 The Scaling Law .......................................... 360
6.11 Muon Pair Production in e+e- Annihilation ................ 361
6.12 Bhabha Scattering e + e- → e + e- ........................ 362
6.13 Tests of QED ............................................. 363
6.13.1 The Lamb Shift .................................... 363
6.13.2 Hyperfine Structure in Muonium and Positronium .... 364
6.13.3 The g-Factors ..................................... 364
6.14 Electrodynamics of Quarks and Hadrons .................... 365
6.15 Hadron Production in e+-e- Scattering .................... 366
6.16 Natural Units ............................................ 367
6.16.1 Conversion Factors ................................ 368
6.16.2 Restoration of Practical Units .................... 369
6.17 Deep Inelastic Lepton-Hadron Scattering .................. 369
6.18 Bjorken Scaling and Parton Model ......................... 373
6.19 Parton Spin and Callan-Gross Relation .................... 377
6.19.1 Parton Charges .................................... 378
References ............................................... 379
7 Weak Interactions ........................................ 381
7.1 Characteristics .......................................... 381
7.2 Leptonie Decays .......................................... 381
7.3 Semileptonic Decays ...................................... 382
7.4 Non-leptonic Decay ....................................... 383
7.5 Weak Interaction and Quarks .............................. 383
7.6 Charge Current and Neutral Current Weak Interactions ..... 384
7.7 Basic Vertices for W±-Lepton Interactions ................ 387
7.8 Coupling Strength of the Charged Current ................. 388
7.8.1 The Decay of the Muon ............................. 389
7.9 Neutrino-Electron Scattering ............................. 390
7.10 Universality of the Weak Interaction ..................... 391
7.11 Lepton-Quark Symmetry .................................... 392
7.12 The Cabibbo Theory ....................................... 394
7.13 Selection Rules in Weak Decays ........................... 397
7.13.1 Semi Leptonic Decays .............................. 397
7.13.2 Pure Hadronic Decays .............................. 398
7.13.3 Decay of Charmed Particles ........................ 399
7.14 Leptonie Decays of Vector Mesons ......................... 399
7.15 Non Conservation of Parity ............................... 400
7.16 Experiment of Wu and Her Collaborators (1957) ............ 401
7.16.1 Parity Non-conservation in β-Decay ................ 402
7.16.2 Parity Non-conservation in Λ-Decay ................ 402
7.17 The Dirac Equation ....................................... 403
7.17.1 Free-Particle Equation ............................ 404
7.18 Free-Particle Solutions .................................. 406
7.19 Parity of Particle and Antiparticle ...................... 407
7.20 Left-Handed and Right-Handed Fermions .................... 407
7.21 Useful Relations ......................................... 408
7.22 Currents ................................................. 409
7.23 Application of the Dirac Theory to Beta Decay ............ 411
7.24 Helicity ................................................. 411
7.25 Fermi's Theory of β-Decay-Revisited ...................... 412
7.25.1 Electron Energy Spectrum .......................... 413
7.25.2 Electron-Neutrino Correlations .................... 413
7.25.3 'ƒt Values' and Coupling Constants ................ 414
7.26 Parity Non-conservation in β-Decay ....................... 415
7.27 β-Decay Theory After Parity Non-conservation ............. 416
7.28 Helicity Conservation in Vector Interactions ............. 417
7.29 Helicity of Electron Neutrino ............................ 418
7.29.1 Helicity of Muon Neutrino ......................... 420
7.30 Pion and Muon Decay ...................................... 420
7.30.1 The π → μ and π → e Branching Ratios .............. 421
7.31 Decay of Neutral Kaons ................................... 424
7.31.1 Behaviour of Neutral Particles Under the Joint
Action of CP ...................................... 425
7.31.2 Strangeness Oscillations .......................... 427
7.31.3 The K0 Regeneration Phenomenon .................... 429
7.31.4 CP Violation in K0-Decay .......................... 430
7.32 Neutrino Oscillations .................................... 432
7.32.1 Solar Neutrino Problem ............................ 433
7.32.2 Standard Solar Model (SSM) ........................ 433
7.32.3 SSM Predictions of Solar Neutrinos on Earth ....... 434
7.32.4 Neutrino Oscillations ............................. 436
References ............................................... 438
8 Electroweak Interactions ................................. 439
8.1 Neutral Currents ......................................... 439
8.2 Layout of Neutrino Beam .................................. 440
8.3 The Basic Vertices ....................................... 441
8.4 The GIM Model and Charm .................................. 443
8.5 The Cabibbo-Kolayashi-Maskawa (CKM) Matrix ............... 444
8.6 The Electroweak Unification .............................. 446
8.6.1 Weak Spin ......................................... 446
8.7 The Weinberg Angle ....................................... 447
8.8 The Unification Condition ................................ 448
8.9 W± and Z0 Bosons ......................................... 449
8.9.1 Detection of W± and Z0 Bosons ..................... 450
8.9.2 The Z0 Events ..................................... 451
8.9.3 W± Events ......................................... 453
8.10 Electroweak Reactions .................................... 454
8.11 Decays of the Z0 Boson ................................... 456
8.12 Types of Neutrinos ....................................... 458
8.13 Decay of W± Bosons ....................................... 459
8.14 Spontaneous Symmetry Breaking ............................ 459
8.15 The Standard Model of Particle Physics ................... 461
8.16 Experimental Tests of the Standard Model ................. 461
8.16.1 Neutral Current ................................... 461
8.16.2 Weak-Electromagnetic Interference in,
е+е- → μ+μ-, Reaction .............................. 461
8.16.3 Parity Non-conservation in Inelastic Electron
Scattering ........................................ 462
8.16.4 Experimental Discovery of Heavy Bosons ............ 464
8.17 Grand Unification Theories (GUTS) ........................ 464
8.18 Questions ................................................ 471
8.19 Problems ................................................. 473
8.20 Open Questions ........................................... 475
References .................................................... 477
Appendix A .................................................... 479
A.1 Relativistic Kinematics .................................. 479
A.2 Expressions for Production Threshold ...................... 479
A.3 Expressions for γc and γ* ................................. 480
A.4 Relation Between Lab and CMS Angles ....................... 480
Appendix В .................................................... 483
B.1 Composition of Angular Momenta and the Clebsch Gordon
Coefficients ............................................. 483
References ............................................... 485
Appendix С .................................................... 487
C.1 Special Functions ........................................ 487
C.l.l Bessel Functions .................................. 487
C.1.2 Asymptotic Expressions ............................ 488
С.1.3 Spherical Bessel Functions ........................ 488
С.1.4 Spherical Harmonics ............................... 489
C.1.5 Associated Legendre Functions ..................... 490
C.1.6 Ortho-normal Properties ........................... 490
Appendix D .................................................... 491
D.l Table of Physical Constants .............................. 491
Appendix E .................................................... 493
E.l Dalitz Plots ............................................. 493
E.l.l Three Similar Particles ........................... 493
E.l.2 Dalitz Plots Involving Three Dissimilar
Particles ......................................... 498
References .................................................... 499
Appendix F .................................................... 501
F.I Properties of Selected Particles and Resonances ......... 501
F.1.1 Gauge Bosons (J = 1) .............................. 501
F.1.2 Leptons (J = 1/2) ................................. 501
F.1.3 Baryons (Jp = 1/2+) ............................... 502
F.1.4 Baryon Resonances (Jp = 3/2+) ..................... 502
F.1.5 Mesons (Jp = 0-) .................................. 502
F.1.6 Mesons (Jp = 1-) .................................. 503
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