Nuclear and Particle Physics

Preface xi

Notes xiii

1 Basic concepts 1

1.1 History 1

1.1.1 The origins of nuclear physics 1

1.1.2 The emergence of particle physics: hadrons and quarks 6

1.1.3 The standard model of particle physics 9

1.2 Relativity and antiparticles 11

1.3 Space-time symmetries and conservation laws 13

1.3.1 Parity 14

1.3.2 Charge conjugation 16

1.3.3 Time reversal 17

1.4 Interactions and Feynman diagrams 20

1.4.1 Interactions 20

1.4.2 Feynman diagrams 21

1.5 Particle exchange: forces and potentials 24

1.5.1 Range of forces 24

1.5.2 The Yukawa potential 25

1.6 Observable quantities: cross-sections and decay rates 26

1.6.1 Amplitudes 27

1.6.2 Cross-sections 29

1.6.3 The basic scattering formulas 31

1.6.4 Unstable states 33

1.7 Units 36

Problems 1 37

2 Nuclear phenomenology 41

2.1 Mass spectroscopy 43

2.1.1 Deflection spectrometers 43

2.1.2 Kinematic analysis 45

2.1.3 Penning trap measurements 46

2.2 Nuclear shapes and sizes 51

2.2.1 Charge distribution 52

2.2.2 Matter distribution 56

2.3 Semi-empirical mass formula: the liquid drop model 59

2.3.1 Binding energies 59

2.3.2 Semi-empirical mass formula 60

2.4 Nuclear instability 64

2.5 Decay chains 67

2.6 β decay phenomenology 69

2.6.1 Odd-mass nuclei 70

2.6.2 Even-mass nuclei 71

2.7 Fission 72

2.8 γ decays 76

2.9 Nuclear reactions 76

Problems 2 81

3 Particle phenomenology 83

3.1 Leptons 83

3.1.1 Lepton multiplets and lepton numbers 83

3.1.2 Universal lepton interactions; the number of neutrinos 86

3.1.3 Neutrinos 88

3.1.4 Neutrino mixing and oscillations 90

3.1.5 Oscillation experiments 93

3.1.6 Neutrino masses and mixing angles 101

3.1.7 Lepton numbers revisited 103

3.2 Quarks 104

3.2.1 Evidence for quarks 104

3.2.2 Quark generations and quark numbers 106

3.3 Hadrons 109

3.3.1 Flavour independence and charge multiplets 109

3.3.2 The simple quark model 113

3.3.3 Hadron decays and lifetimes 117

3.3.4 Hadron magnetic moments and masses 119

3.3.5 Heavy quarkonia 126

3.3.6 Allowed and exotic quantum numbers 133

Problems 3 135

4 Experimental methods 139

4.1 Overview 139

4.2 Accelerators and beams 142

4.2.1 DC accelerators 142

4.2.2 AC accelerators 143

4.2.3 Neutral and unstable particle beams 150

4.3 Particle interactions with matter 152

4.3.1 Short-range interactions with nuclei 153

4.3.2 Ionisation energy losses 154

4.3.3 Radiation energy losses 157

4.3.4 Interactions of photons in matter 158

4.3.5 Ranges and interaction lengths 159

4.4 Particle detectors 160

4.4.1 Gaseous ionisation detectors 162

4.4.2 Scintillation counters 167

4.4.3 Semiconductor detectors 169

4.4.4 Cerenkov counters and transition radiation 170

4.4.5 Calorimeters 173

4.5 Detector Systems 176

Problems 4 182

5 Quark dynamics: the strong interaction 185

5.1 Colour 185

5.2 Quantum chromodynamics (QCD) 187

5.2.1 The strong coupling constant 190

5.2.2 Screening, antiscreening and asymptotic freedom 193

5.3 New forms of matter 194

5.3.1 Exotic hadrons 194

5.3.2 The quark–gluon plasma 201

5.4 Jets and gluons 204

5.4.1 Colour counting 205

5.5 Deep inelastic scattering and nucleon structure 207

5.5.1 Scaling 207

5.5.2 The quark-parton model 210

5.5.3 Scaling violations and parton distributions 211

5.5.4 Inelastic neutrino scattering 215

5.6 Other processes 217

5.6.1 Jets 219

5.6.2 Lepton pair production 221

5.7 Current and constituent quarks 224

Problems 5 226

6 Weak interactions and electroweak unification 229

6.1 Charged and neutral currents 229

6.2 Charged current reactions 231

6.2.1 W^±-lepton interactions 232

6.2.2 Lepton–quark symmetry and mixing 234

6.2.3 W-boson decays 238

6.2.4 Charged current selection rules 239

6.3 The third generation 242

6.3.1 More quark mixing 243

6.3.2 Properties of the top quark 246

6.4 Neutral currents and the unified theory 247

6.4.1 Electroweak unification 247

6.4.2 The Z⁰ vertices and electroweak reactions 250

6.5 Gauge invariance and the Higgs boson 252

6.5.1 Unification and the gauge principle 253

6.5.2 Particle masses and the Higgs field 255

6.5.3 Properties of the Higgs boson 257

6.5.4 Discovery of the Higgs boson 259

Problems 6 266

7 Symmetry breaking in the weak interaction 271

7.1 P violation, C violation, and CP conservation 271

7.1.1 Muon decay symmetries 273

7.1.2 Parity violation in electroweak processes 275

7.2 Spin structure of the weak interactions 277

7.2.1 Left-handed neutrinos and right-handed antineutrinos 277

7.2.2 Particles with mass: chirality 279

7.3 Neutral kaons: particle–antiparticle mixing and CP violation 281

7.3.1 CP invariance and neutral kaons 281

7.3.2 CP violation in K⁰_L decay 283

7.3.3 Flavour oscillations and CPT invariance 285

7.4 CP violation and flavour oscillations in B decays 289

7.4.1 Direct CP violation in decay rates 290

7.4.2 B⁰ − B⁰ mixing 291

7.4.3 CP violation in interference 295

7.5 CP violation in the standard model 299

Problems 7 302

8 Models and theories of nuclear physics 305

8.1 The nucleon–nucleon potential 305

8.2 Fermi gas model 308

8.3 Shell model 310

8.3.1 Shell structure of atoms 310

8.3.2 Nuclear shell structure and magic numbers 312

8.3.3 Spins, parities, and magnetic dipole moments 315

8.3.4 Excited states 318

8.4 Nonspherical nuclei 319

8.4.1 Electric quadrupole moments 319

8.4.2 Collective model 322

8.5 Summary of nuclear structure models 323

8.6 α decay 324

8.7 β decay 327

8.7.1 V − A theory 327

8.7.2 Electron and positron momentum distributions 329

8.7.3 Selection rules 330

8.7.4 Applications of Fermi theory 332

8.8 γ decay 337

8.8.1 Selection rules 337

8.8.2 Transition rates 339

Problems 8 340

9 Applications of nuclear and particle physics 343

9.1 Fission 343

9.1.1 Induced fission and chain reactions 344

9.1.2 Thermal fission reactors 348

9.1.3 Radioactive waste 352

9.1.4 Power from ADS systems 354

9.2 Fusion 357

9.2.1 Coulomb barrier 357

9.2.2 Fusion reaction rates 358

9.2.3 Nucleosynthesis and stellar evolution 361

9.2.4 Fusion reactors 366

9.3 Nuclear weapons 371

9.3.1 Fission devices 371

9.3.2 Fission/fusion devices 374

9.4 Biomedical applications 377

9.4.1 Radiation and living matter 377

9.4.2 Radiation therapy 380

9.4.3 Medical imaging using ionising radiation 385

9.4.4 Magnetic resonance imaging 390

9.5 Further applications 395

9.5.1 Computing and data analysis 395

9.5.2 Archaeology and geophysics 396

9.5.3 Accelerators and detectors 397

9.5.4 Industrial applications 398

Problems 9 398

10 Some outstanding questions and future prospects 401

10.1 Overview 401

10.2 Hadrons and nuclei 402

10.2.1 Hadron structure and the nuclear environment 402

10.2.2 Nuclear structure 405

10.3 Unification schemes 407

10.3.1 Grand unification 407

10.3.2 Supersymmetry 412

10.3.3 Strings and things 417

10.4 The nature of the neutrino 418

10.4.1 Neutrinoless double beta decay 420

10.5 Particle astrophysics 426

10.5.1 Neutrino astrophysics 427

10.5.2 Cosmology and dark matter 432

10.5.3 Matter–antimatter asymmetry 438

10.5.4 Axions and the strong CP problem 441

A Some results in quantum mechanics 445

A.1 Barrier penetration 445

A.2 Density of states 447

A.3 Perturbation theory and the Second Golden Rule 449

A.4 Isospin formalism 452

A.4.1 Isospin operators and quark states 452

A.4.2 Hadron states 454

Problems A 456

B Relativistic kinematics 457

B.1 Lorentz transformations and four-vectors 457

B.2 Frames of reference 459

B.3 Invariants 461

Problems B 463

C Rutherford scattering 465

C.1 Classical physics 465

C.2 Quantum mechanics 467

Problems C 469

D Gauge theories 471

D.1 Gauge invariance and the standard model 471

D.1.1 Electromagnetism and the gauge principle 471

D.1.2 The standard model 474

D.2 Particle masses and the Higgs field 478

Problems D 481

E Short answers to selected problems 483

References 487

Index 491

Inside Rear Cover: Table of constants and conversion factors