Fundamentals of Nuclear Physics (eBook)

Noboru Takigawa received his DSc in physics from the University of Tokyo in 1971. He subsequently worked as a postdoctoral researcher at the Institute for Nuclear Study of the University of Tokyo, 1971-1972, RIKEN, 1972-1973, Hahn Meitner Institut für Kernforschung Berlin GmbH, 1973-1975, the Technische Universität München, 1975, the University of Oxford, 1975-1976, the Institut de Physique Nucléaire d’Orsay of the Université Paris-Sud, 1976-1977, and the Universität Münster, 1977-1979. He served as a research associate (1979-1988) and as a professor of physics (1988-2007) at Tohoku University. Further, he has been a long-term visiting professor at the Technische Universität München, Academia Sinica at Taipei, Michigan State University, University of Wisconsin-Madison, University of Frankfurt, Université de Mons, Universidade de Sao Paulo, Australian National University, University of Catania, Institute for Nuclear Theory of the University of Washington, Tennessee Technological University and ECT* at Trento. He is now an emeritus professor at Tohoku University.Kouhei Washiyama received his DSc in physics from Tohoku University in 2007, and thereafter worked as a postdoctoral researcher at Grand Accélérateur National d'Ions Lourds, Université Libre de Bruxelles, and RIKEN Nishina Center. He is currently a researcher at Center for Computational Sciences, University of Tsukuba.

Preface 6
Contents 9
1 Introduction 14
1.1 The Constituents and Basic Structure of Atomic Nuclei 14
1.2 Properties of Particles Relevant to Nuclear Physics 15
1.3 The Role of Various Forces 19
1.4 Useful Physical Quantities 20
1.5 Species of Nuclei 21
References 25
2 Bulk Properties of Nuclei 26
2.1 Nuclear Sizes 26
2.1.1 Rutherford Scattering 26
2.1.2 Electron Scattering 30
2.1.3 Mass Distribution 38
2.2 Number Density and Fermi Momentum of Nucleons 41
2.2.1 Number Density of Nucleons 41
2.2.2 Fermi Momentum: Fermi-Gas Model, Thomas--Fermi Approximation 41
2.3 Nuclear Masses 44
2.3.1 The Binding Energies: Experimental Data and Characteristics 45
2.3.2 The Semi-empirical Mass Formula (The Weizsäcker--Bethe Mass Formula)---The Liquid-Drop Model 55
2.3.3 Applications of the Mass Formula (1): The Stability Line, the Heisenberg Valley 56
2.3.4 Applications of the Mass Formula (2): Stability with Respect to Fission 59
2.3.5 Application to Nuclear Power Generation 70
2.3.6 Fission Isomers 73
References 77
3 The Nuclear Force and Two-Body Systems 78
3.1 The Fundamentals of Nuclear Force 78
3.1.1 The Range of Forces---A Simple Estimate by the Uncertainty Principle 78
3.1.2 The Radial Dependence 79
3.1.3 The State Dependence of Nuclear Force 80
3.2 The General Structure of Nuclear Force 84
3.2.1 Static Potentials (Velocity-Independent Potentials) 84
3.2.2 Velocity-Dependent Potentials 86
3.3 The Properties of Deuteron and the Nuclear Force 87
3.3.1 The Effect of Tensor Force: The Wave Function in the Spin--Isospin Space 87
3.3.2 The Radial Wave Function: Estimate of the Magnitude of the Force Between Proton and Neutron 90
3.4 Nucleon--Nucleon Scattering 91
3.4.1 Low-Energy Scattering: Effective Range Theory 91
3.4.2 High-Energy Scattering: Exchange Force 94
3.4.3 High-Energy Scattering: Repulsive Core 96
3.4.4 Spin Polarization Experiments 98
3.5 Microscopic Considerations: Meson Theory, QCD 98
3.6 Phenomenological Potential with High Accuracy: Realistic Potential 101
3.6.1 Hamada--Johnston Potential 102
3.6.2 Reid Potential 104
3.7 Summary of the Nuclear Force in the Free Space 104
3.8 Effective Interaction Inside Nucleus 105
3.8.1 G-Matrix 105
3.8.2 Phenomenological Effective Interaction 107
References 109
4 Interaction with Electromagnetic Field: Electromagnetic Moments 110
4.1 Hamiltonian of the Electromagnetic Interaction ƒ 110
4.1.1 Operators for the Dipole and Quadrupole Moments 111
4.1.2 Various Corrections 113
4.1.3 Measurement of the Magnetic Moment: Hyperfine Structure 113
4.2 Electromagnetic Multipole Operators 115
4.3 Properties of the Electromagnetic Multipole Operators 116
4.3.1 Parity, Tensor Property and Selection Rule 116
4.3.2 Definition of the Electromagnetic Moments 117
References 119
5 Shell Structure 120
5.1 Magic Numbers 120
5.2 Explanation of the Magic Numbers by Mean-Field Theory 122
5.2.1 The Mean Field 122
5.2.2 Energy Levels for the Infinite Square-Well Potential 123
5.2.3 The Harmonic Oscillator Model 124
5.2.4 The Magic Numbers in the Static Potential Due to Short Range Force 125
5.2.5 Spin--Orbit Interaction 127
5.3 The Spin and Parity of the Ground and Low-Lying States of Doubly-Magic pm1 Nuclei 130
5.4 The Magnetic Dipole Moment in the Ground State of Odd Nuclei: Single Particle Model 132
5.4.1 The Schmidt Lines 133
5.4.2 Configuration Mixing and Core Polarization 134
5.4.3 [Addendum] The Anomalous Magnetic Moments of Nucleons in the Quark Model 136
5.5 Mass Number Dependence of the Level Spacing hbar? 137
5.6 The Magnitude and Origin of Spin--Orbit Interaction 138
5.7 Difference Between the Potentials for Protons and for Neutrons: Lane Potential 138
5.8 The Spin and Parity of Low-Lying States of Doubly-Magic pm2 Nuclei and the Pairing Correlation 140
5.8.1 The Spin and Parity of the Ground and Low Excited States of 210 82Pb 140
5.8.2 The Effect of ?-Type Residual Interaction: Pairing Correlation 141
References 146
6 Microscopic Mean-Field Theory (Hartree--Fock Theory) 147
6.1 Hartree--Fock Equation 147
6.1.1 Equivalent Local Potential, Effective Mass 148
6.1.2 Nuclear Matter and Local Density Approximation 149
6.1.3 Saturation Property in the Well-Behaved Potential, Constraint to the Exchange Property 152
6.2 Skyrme Hartree--Fock Calculations for Finite Nuclei 153
6.2.1 Skyrme Force 153
6.2.2 Skyrme Hartree--Fock Equation 155
6.2.3 Energy Density and Determination of Parameters 156
6.2.4 Comparison with the Experimental Data 159
6.2.5 The Equation of State, Saturation, Spinodal Line, Surface Thickness 160
6.2.6 Beyond the Hartree--Fock Calculations: Nucleon--Vibration Coupling ?-Mass
6.3 Relativistic Mean-Field Theory (??? Model) 167
6.3.1 Lagrangian 168
6.3.2 Field Equations 169
6.3.3 The Mean-Field Theory 170
6.3.4 Prologue to How to Solve the Mean-Field Equations 170
6.3.5 Non-relativistic Approximation and the Spin--Orbit Coupling 172
6.3.6 Parameter Sets 173
6.4 Pairing Correlation 174
6.4.1 Overview 174
6.4.2 Multipole Expansion of the Pairing Correlation, Monopole Pairing Correlation Model and Quasi-Spin Formalism 175
6.4.3 BCS Theory 176
6.4.4 The Magnitude of the Gap Parameter 180
6.4.5 The Coherence Length 181
References 182
7 The Shapes of Nuclei 183
7.1 The Observables Relevant to the Nuclear Shape: Multipole Moments and the Excitation Spectrum 183
7.2 Deformation Parameters 186
7.3 The Deformed Shell Model 189
7.4 Nucleon Energy Levels in a Deformed One-Body Field: Nilsson Levels 192
7.5 The Spin and Parity of the Ground State of Deformed Odd Nuclei 194
7.6 Theoretical Prediction of Nuclear Shape 194
7.6.1 The Strutinsky Method: Macroscopic--Microscopic Method 194
7.6.2 Constrained Hartree--Fock Calculations 196
References 200
8 Nuclear Decay and Radioactivity 202
8.1 Alpha Decay 202
8.1.1 Decay Width 203
8.1.2 The Geiger--Nuttal Rule 211
8.2 Fission 211
8.3 Electromagnetic Transitions 214
8.3.1 Multipole Transition, Reduced Transition Probability 214
8.3.2 General Consideration of the Selection Rule and the Magnitude 216
8.3.3 Single-Particle Model Estimate: Weisskopf Units and Experimental Values 217
8.3.4 Connection Between Electromagnetic Transitions and the Shapes and Collective Motions of Nuclei 220
References 223
9 Synthesis of Elements 225
9.1 The Astrophysical S-Factor and Gamow Factor 225
9.2 Gamow Peak 227
9.3 Neutron Capture Cross Section 228
9.4 Synthesis of Heavy Elements: S-Process and R-Process 229
References 231
Appendix A Important Formulae and Their Derivation 232
Index 269