Nuclear Physics for ApplicationsISBN: 9783527407002
650 pages
October 2007

Preface XIII
1 Introduction 1
1.1 LowEnergy Nuclear Physics for Applications 1
1.2 Some General Observations and Notations 3
1.3 Overview of Radioactive Decay Processes and Nuclear Reactions 4
1.3.1 Alpha Decay 4
1.3.2 Beta Decay 5
1.3.3 Spontaneous Fission 7
1.3.4 Gamma Decay 8
1.3.5 Nuclear Reactions 9
1.4 The Modelbased Character of this Text 10
1.5 Sources of Nuclear Data 11
2 Nuclear Masses and Energetics of Radioactive Decay and Nuclear Reactions 13
2.1 Introduction 13
2.2 Review of the Special Theory of Relativity 13
2.3 Masses of Atoms and Particles 18
2.4 Comments Concerning “Nuclear Stability” and Energetics 21
2.4.1 Spontaneous Transformations and Nuclear Masses 21
2.4.2 Nuclear Stability 24
2.5 Bound and Unbound States and Their Energetics: Potential Wells 25
2.6 Nuclear and Atomic Masses and Binding Energies 29
2.6.1 β– Decay 30
2.6.2 β+ Decay or Positron Emission 32
2.6.3 Electron Capture Decay 34
2.6.4 Competitive Decay Modes 35
2.6.5 α Decay 36
2.6.6 Spontaneous Fission 37
2.7 Nuclear Reactions 38
3 Phenomenology of Radioactive Decay and Nuclear Reactions 41
3.1 Introduction 41
3.1.1 The Phenomenology of Radioactive Decay 41
3.1.2 Units for Describing Radioactive Decay 45
3.1.3 Radioactive Growth and Decay 45
3.1.4 Simple Decay Schemes and Decay Chains 51
3.2 Statistical Considerations in Radioactive Decay 54
3.2.1 The Binomial Distribution 54
3.2.2 The Poisson Distribution 56
3.2.3 Application of Statistical Analysis to Common Experimental Conditions 61
3.2.4 Propagation of Errors 62
3.3 Reaction Cross Sections 66
4 Nuclear Binding Energies: Empirical Data and the Forces in Nuclei 75
4.1 Empirical Masses and Average Binding Energies of Nucleons 75
4.2 The Forces Acting Between Nucleons 77
4.3 The Average Nuclear Interaction Between Nucleons in the Nucleus and Nuclear Radii 83
4.4 Quantization of the Nucleus: Pairing of Identical Nucleons 92
4.5 Quantization of the Nucleus: Asymmetry Energy 100
5 The SemiEmpirical Mass Formula and Applications to Radioactive Decay 109
5.1 Introduction 109
5.2 The SemiEmpirical Mass Formula 110
5.3 The Nuclear Mass Surface 115
5.4 The SemiEmpirical Mass Formula and β Decay 117
5.5 The SemiEmpirical Mass Formula and α Decay 123
5.6 The SemiEmpirical Mass Formula and Nuclear Fission 125
5.7 Discrepancies Between Experimental Masses and those Predicted by the SemiEmpirical Mass Formula 128
6 Elements of Quantum Mechanics 133
6.1 Introduction 133
6.2 Elements of Quantum Mechanics 134
6.2.1 The Schrödinger Equation and Conservation Laws 134
6.2.2 Elementary Properties of Operators 135
6.2.3 Elementary Properties of Wave Functions 137
6.2.4 Operators, Eigenfunctions and Conservation Laws 138
6.2.5 Parity 146
6.3 Angular Momentum in Quantum Mechanics 147
6.3.1 Operators for Orbital Angular Momentum 148
6.3.2 Angular Momentum and Magnetic Moments 150
6.4 The Vector Model for Angular Momentum 152
6.5 The Wave Functions of ManyParticle Systems 158
7 Nuclear Structure: The Spherical Shell Model 161
7.1 Introduction 161
7.2 The Independent Particle Model 161
7.2.1 The Angular Equations: Angular Momentum and Parity 164
7.2.2 Some Properties of the Wave Functions 170
7.2.3 The Radial Equation and the Centrifugal Potential 172
7.2.4 Models for the Average Central Potential in the Independent Particle Approximation 175
7.2.5 The Infinite Spherical Potential Well 178
7.2.6 The Isotropic Harmonic Oscillator 185
7.3 The SingleParticle Levels of Spherical Nuclei 189
7.4 Comparison of the Predictions of the SingleParticle Model with Experiment 195
8 Nuclear Shapes, Deformed Nuclei and Collective Effects 205
8.1 Introduction 205
8.2 Collective Excitations 212
8.3 Rotational Excitations in (Even,Even) Nuclei 213
8.4 Rotational Excitations in OddA Nuclei 219
8.5 Vibrational Excitations in Nuclei 222
8.6 Nuclear Structure in a Deformed Potential 229
8.7 The Nilsson Model 234
9 α Decay and Barrier Penetration 245
9.1 Introduction 245
9.2 Qα and α Decay HalfLives 248
9.3 Binding of Valence Nucleons and the Potential for Interaction Between an α Particle and a Heavy Nucleus 253
9.4 The Wave Functions for Particles in Finite Potential Wells and Barrier Penetration 258
9.5 A Simple Model for α Decay 266
9.6 Application of the Model to the Decay of EvenEven Nuclei 268
9.7 Angular Momentum Effects in α Decay 272
9.8 Decay of OddA Nuclides and Structure Effects 274
10 β Decay 281
10.1 Introduction 281
10.2 β Decay and Conservation Laws: The Neutrino and the Weak Interaction 282
10.3 The Fermi Golden Rule No. 2 285
10.4 The Fermi Theory of Allowed β Decay 287
10.5 β Spectra 292
10.6 Decay Probabilities for β– and β+ Decay 296
10.7 Some Implications of the Simple Theory of Allowed β Decay 300
10.7.1 Angular Momentum Effects 300
10.7.2 Nuclear Matrix Elements: Fermi Transitions 302
10.7.3 Nuclear Matrix Elements: Gamow–Teller Transitions 305
10.8 Classification of β Transitions and Experimental Log10ft 306
10.9 Electron Capture Decay 307
10.9.1 Xray Emission 308
10.9.2 Auger Electron Ejection 311
10.10 Elementary Theory of Electron Capture 314
10.11 Ratio of Electron Capture to Positron Emission 318
10.12 βDecay Schemes 320
10.13 βDelayed Particle Emission 325
10.14 Comments on Fermi Transitions 327
11 γ Decay and Internal Conversion 331
11.1 Introduction 331
11.2 The Angular Momentum of Photons and Conservation Laws 332
11.3 Introduction to the Theory of Photon Emission 334
11.3.1 The Radiation Field and Matrix Elements for Photon Emission 334
11.3.2 Matrix Elements and Transition Rates 341
11.4 Examples of Nuclear Isomerism 347
11.5 Some General Observations 350
11.5.1 E1 Transitions 350
11.5.2 E2 and M1 Transitions 351
11.5.3 Other Transitions 351
11.6 Internal Conversion 351
11.6.1 Elementary Theory of Internal Conversion 353
11.7 Decay Schemes 357
12 Nuclear Fission 373
12.1 Introduction 373
12.2 The Discovery of Nuclear Fission 374
12.3 The LiquidDrop Model and Nuclear Fission: The Nuclear Potential Energy Surface 375
12.4 Empirical Data on Spontaneous and NeutronInduced Fission 383
12.5 Energy Release in Fission 392
12.5.1 Fission Fragment Kinetic Energy 392
12.5.2 Kinetic Energy of Prompt Neutrons 395
12.5.3 The Spectrum of Prompt γRays 399
12.5.4 Summary of the Sources of Energy Release in Fission 399
12.6 Fission Barriers and Fission Probabilities 401
13 LowEnergy Nuclear Reactions 405
13.1 Introduction 405
13.2 Kinematics of Nonrelativistic Reactions 407
13.2.1 Kinematics of Elastic Scattering in the Laboratory Coordinate System 408
13.2.2 Kinematics of Elastic Scattering in the Center of Mass Coordinate System 412
13.2.3 Kinematics of General Nonrelativistic Nuclear Reactions 418
13.3 Cross Sections for Nuclear Reactions from FirstOrder Perturbation Theory 424
13.4 The Reciprocity Theorem 435
13.5 Qualitative Considerations of the Mechanisms of LowEnergy Nuclear Reactions 440
13.5.1 Potential Scattering 440
13.5.2 The Compound Nucleus 441
13.5.3 Direct Reactions 446
13.6 The Properties of TimeDependent States 447
13.7 A Physical Approach to the Form of Cross Sections for Compound Nucleus Reactions: The Breit–Wigner SingleLevel Formula 451
13.8 Scattering in Quantum Mechanics: Partial Wave Analysis 457
13.9 Extension of the Partial Wave Analysis to Nuclear Reactions 468
13.10 SWave Scattering and Reactions in the Limit of the Spherical Potential Well Model 472
13.11 The Breit–Wigner SingleLevel Formula and Experimental Cross Sections 478
13.12 About Fission Cross Sections 487
14 The Interaction of Ionizing Radiation with Matter 493
14.1 Introduction 493
14.2 The Interaction of Photons with Matter 495
14.2.1 Elastic Scattering of Photons on Unbound Electrons 496
14.2.2 Compton Scattering 502
14.2.3 The Photoelectric Effect 516
14.2.4 Pair Production 519
14.2.5 Total Cross Sections and Attenuation Coefficients 520
14.3 The Interaction of Charged Particles with Matter 524
14.3.1 The Stopping of Heavy Charged Particles in Matter 525
14.3.2 The Stopping of Electrons and Positrons in Matter 538
Appendix 1
Atomic Masses 545
Appendix 2
Nuclide Table 565
Appendix 3
Physical Constants 607
Appendix 4
FirstOrder TimeDependent Perturbation Theory 611
Index 619

Conveying a working understanding of the essentials of nuclear physics to advanced undergraduate students minoring in physics

Simplifying models and approaches to reveal their essence

Mathematical and Quantum Mechanical Background not in appendices but in the text where needed

Numerous endofchapter problems

Solutions manual available

From a researcher and teacher with experience at pinnacle institutions in the US and Europe