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Nuclear Physics for Applications

ISBN: 978-3-527-40700-2
650 pages
October 2007
Nuclear Physics for Applications (3527407006) cover image
Written by a researcher and teacher with experience at top institutes in the US and Europe, this textbook provides advanced undergraduates minoring in physics with working knowledge of the principles of nuclear physics. Simplifying models and approaches reveal the essence of the principles involved, with the mathematical and quantum mechanical background integrated in the text where it is needed and not relegated to the appendices. The practicality of the book is enhanced by numerous end-of-chapter problems and solutions available on the Wiley homepage.
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Preface XIII

1 Introduction 1

1.1 Low-Energy 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 Model-based 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 Semi-Empirical Mass Formula and Applications to Radioactive Decay 109

5.1 Introduction 109

5.2 The Semi-Empirical Mass Formula 110

5.3 The Nuclear Mass Surface 115

5.4 The Semi-Empirical Mass Formula and β Decay 117

5.5 The Semi-Empirical Mass Formula and α Decay 123

5.6 The Semi-Empirical Mass Formula and Nuclear Fission 125

5.7 Discrepancies Between Experimental Masses and those Predicted by the Semi-Empirical 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 Many-Particle 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 Single-Particle Levels of Spherical Nuclei 189

7.4 Comparison of the Predictions of the Single-Particle 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 Odd-A 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 Half-Lives 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 Even-Even Nuclei 268

9.7 Angular Momentum Effects in α Decay 272

9.8 Decay of Odd-A 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 X-ray 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 β-Decay Schemes 320

10.13 β-Delayed 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 Liquid-Drop Model and Nuclear Fission: The Nuclear Potential Energy Surface 375

12.4 Empirical Data on Spontaneous and Neutron-Induced 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 γ-Rays 399

12.5.4 Summary of the Sources of Energy Release in Fission 399

12.6 Fission Barriers and Fission Probabilities 401

13 Low-Energy 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 First-Order Perturbation Theory 424

13.4 The Reciprocity Theorem 435

13.5 Qualitative Considerations of the Mechanisms of Low-Energy 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 Time-Dependent States 447

13.7 A Physical Approach to the Form of Cross Sections for Compound Nucleus Reactions: The Breit–Wigner Single-Level 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 S-Wave Scattering and Reactions in the Limit of the Spherical Potential Well Model 472

13.11 The Breit–Wigner Single-Level 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

First-Order Time-Dependent Perturbation Theory 611

Index 619

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Stanley G. Prussin received his Ph.D. degree in chemistry from the University of Michigan in 1964. After doing postdoctoral research at the Lawrence Berkeley National Laboratory from 1964 to 1966, he accepted a post at the Department of Nuclear Engineering at the University of California at Berkeley, where he still teaches in the position of a Professor of Graduate Studies. Professor Prussin is a member of the American Nuclear Society and of the American Association for the Advancement of Science. His areas of teaching expertise are low-energy nuclear physics, nuclear- and radiochemistry and applications, radiation protection and control, nuclear chemical engineering, and nuclear instrumentation.
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  • 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 end-of-chapter problems
  • Solutions manual available
  • From a researcher and teacher with experience at pinnacle institutions in the US and Europe
See More
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