Takigawa / Washiyama Fundamentals of Nuclear Physics

1. Auflage 2017
ISBN: 978-4-431-55378-6
Verlag: Springer Tokyo
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 277 Seiten, eBook

This book introduces the current understanding of the fundamentals of nuclear physics by referring to key experimental data and by providing a theoretical understanding of principal nuclear properties.It primarily covers the structure of nuclei at low excitation in detail. It also examines nuclear forces and decay properties. In addition to fundamentals, the book treats several new research areas such as non-relativistic as well as relativistic Hartree-Fock calculations, the synthesis of super-heavy elements, the quantum chromodynamics phase diagram, and nucleosynthesis in stars, to convey to readers the flavor of current research frontiers in nuclear physics. The authors explain semi-classical arguments and derivation of its formulae. In these ways an intuitive understanding of complex nuclear phenomena is provided.The book is aimed at graduate school students as well as junior and senior undergraduate students and postdoctoral fellows. It is also useful for researchers to update their knowledge of diverse fields of nuclear structure. The book explains how basic physics such as quantum mechanics and statistical physics, as well as basic physical mathematics, is used to describe nuclear phenomena. A number of questions are given from place to place as supplements to the text.

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.

Zielgruppe

Research

Autoren/Hrsg.

Takigawa, Noboru

Washiyama, Kouhei

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;1 Introduction;14
3.1;1.1 The Constituents and Basic Structure of Atomic Nuclei;14
3.2;1.2 Properties of Particles Relevant to Nuclear Physics;15
3.3;1.3 The Role of Various Forces;19
3.4;1.4 Useful Physical Quantities;20
3.5;1.5 Species of Nuclei;21
3.6;References;25
4;2 Bulk Properties of Nuclei;26
4.1;2.1 Nuclear Sizes;26
4.1.1;2.1.1 Rutherford Scattering;26
4.1.2;2.1.2 Electron Scattering;30
4.1.3;2.1.3 Mass Distribution;38
4.2;2.2 Number Density and Fermi Momentum of Nucleons;41
4.2.1;2.2.1 Number Density of Nucleons;41
4.2.2;2.2.2 Fermi Momentum: Fermi-Gas Model, Thomas--Fermi Approximation;41
4.3;2.3 Nuclear Masses;44
4.3.1;2.3.1 The Binding Energies: Experimental Data and Characteristics;45
4.3.2;2.3.2 The Semi-empirical Mass Formula (The Weizsäcker--Bethe Mass Formula)---The Liquid-Drop Model;55
4.3.3;2.3.3 Applications of the Mass Formula (1): The Stability Line, the Heisenberg Valley;56
4.3.4;2.3.4 Applications of the Mass Formula (2): Stability with Respect to Fission;59
4.3.5;2.3.5 Application to Nuclear Power Generation;70
4.3.6;2.3.6 Fission Isomers;73
4.4;References;77
5;3 The Nuclear Force and Two-Body Systems;78
5.1;3.1 The Fundamentals of Nuclear Force;78
5.1.1;3.1.1 The Range of Forces---A Simple Estimate by the Uncertainty Principle;78
5.1.2;3.1.2 The Radial Dependence;79
5.1.3;3.1.3 The State Dependence of Nuclear Force;80
5.2;3.2 The General Structure of Nuclear Force;84
5.2.1;3.2.1 Static Potentials (Velocity-Independent Potentials);84
5.2.2;3.2.2 Velocity-Dependent Potentials;86
5.3;3.3 The Properties of Deuteron and the Nuclear Force;87
5.3.1;3.3.1 The Effect of Tensor Force: The Wave Function in the Spin--Isospin Space;87
5.3.2;3.3.2 The Radial Wave Function: Estimate of the Magnitude of the Force Between Proton and Neutron;90
5.4;3.4 Nucleon--Nucleon Scattering;91
5.4.1;3.4.1 Low-Energy Scattering: Effective Range Theory;91
5.4.2;3.4.2 High-Energy Scattering: Exchange Force;94
5.4.3;3.4.3 High-Energy Scattering: Repulsive Core;96
5.4.4;3.4.4 Spin Polarization Experiments;98
5.5;3.5 Microscopic Considerations: Meson Theory, QCD;98
5.6;3.6 Phenomenological Potential with High Accuracy: Realistic Potential;101
5.6.1;3.6.1 Hamada--Johnston Potential;102
5.6.2;3.6.2 Reid Potential;104
5.7;3.7 Summary of the Nuclear Force in the Free Space;104
5.8;3.8 Effective Interaction Inside Nucleus;105
5.8.1;3.8.1 G-Matrix;105
5.8.2;3.8.2 Phenomenological Effective Interaction;107
5.9;References;109
6;4 Interaction with Electromagnetic Field: Electromagnetic Moments;110
6.1;4.1 Hamiltonian of the Electromagnetic Interaction ƒ;110
6.1.1;4.1.1 Operators for the Dipole and Quadrupole Moments;111
6.1.2;4.1.2 Various Corrections;113
6.1.3;4.1.3 Measurement of the Magnetic Moment: Hyperfine Structure;113
6.2;4.2 Electromagnetic Multipole Operators;115
6.3;4.3 Properties of the Electromagnetic Multipole Operators;116
6.3.1;4.3.1 Parity, Tensor Property and Selection Rule;116
6.3.2;4.3.2 Definition of the Electromagnetic Moments;117
6.4;References;119
7;5 Shell Structure;120
7.1;5.1 Magic Numbers;120
7.2;5.2 Explanation of the Magic Numbers by Mean-Field Theory;122
7.2.1;5.2.1 The Mean Field;122
7.2.2;5.2.2 Energy Levels for the Infinite Square-Well Potential;123
7.2.3;5.2.3 The Harmonic Oscillator Model;124
7.2.4;5.2.4 The Magic Numbers in the Static Potential Due to Short Range Force;125
7.2.5;5.2.5 Spin--Orbit Interaction;127
7.3;5.3 The Spin and Parity of the Ground and Low-Lying States of Doubly-Magic pm1 Nuclei;130
7.4;5.4 The Magnetic Dipole Moment in the Ground State of Odd Nuclei: Single Particle Model;132
7.4.1;5.4.1 The Schmidt Lines;133
7.4.2;5.4.2 Configuration Mixing and Core Polarization;134
7.4.3;5.4.3 [Addendum] The Anomalous Magnetic Moments of Nucleons in the Quark Model;136
7.5;5.5 Mass Number Dependence of the Level Spacing hbar?;137
7.6;5.6 The Magnitude and Origin of Spin--Orbit Interaction;138
7.7;5.7 Difference Between the Potentials for Protons and for Neutrons: Lane Potential;138
7.8;5.8 The Spin and Parity of Low-Lying States of Doubly-Magic pm2 Nuclei and the Pairing Correlation;140
7.8.1;5.8.1 The Spin and Parity of the Ground and Low Excited States of 210 82Pb;140
7.8.2;5.8.2 The Effect of ?-Type Residual Interaction: Pairing Correlation;141
7.9;References;146
8;6 Microscopic Mean-Field Theory (Hartree--Fock Theory);147
8.1;6.1 Hartree--Fock Equation;147
8.1.1;6.1.1 Equivalent Local Potential, Effective Mass;148
8.1.2;6.1.2 Nuclear Matter and Local Density Approximation;149
8.1.3;6.1.3 Saturation Property in the Well-Behaved Potential, Constraint to the Exchange Property;152
8.2;6.2 Skyrme Hartree--Fock Calculations for Finite Nuclei;153
8.2.1;6.2.1 Skyrme Force;153
8.2.2;6.2.2 Skyrme Hartree--Fock Equation;155
8.2.3;6.2.3 Energy Density and Determination of Parameters;156
8.2.4;6.2.4 Comparison with the Experimental Data;159
8.2.5;6.2.5 The Equation of State, Saturation, Spinodal Line, Surface Thickness;160
8.2.6;6.2.6 Beyond the Hartree--Fock Calculations: Nucleon--Vibration Coupling; ?-Mass;166
8.3;6.3 Relativistic Mean-Field Theory (??? Model);167
8.3.1;6.3.1 Lagrangian;168
8.3.2;6.3.2 Field Equations;169
8.3.3;6.3.3 The Mean-Field Theory;170
8.3.4;6.3.4 Prologue to How to Solve the Mean-Field Equations;170
8.3.5;6.3.5 Non-relativistic Approximation and the Spin--Orbit Coupling;172
8.3.6;6.3.6 Parameter Sets;173
8.4;6.4 Pairing Correlation;174
8.4.1;6.4.1 Overview;174
8.4.2;6.4.2 Multipole Expansion of the Pairing Correlation, Monopole Pairing Correlation Model and Quasi-Spin Formalism;175
8.4.3;6.4.3 BCS Theory;176
8.4.4;6.4.4 The Magnitude of the Gap Parameter;180
8.4.5;6.4.5 The Coherence Length;181
8.5;References;182
9;7 The Shapes of Nuclei;183
9.1;7.1 The Observables Relevant to the Nuclear Shape: Multipole Moments and the Excitation Spectrum;183
9.2;7.2 Deformation Parameters;186
9.3;7.3 The Deformed Shell Model;189
9.4;7.4 Nucleon Energy Levels in a Deformed One-Body Field: Nilsson Levels;192
9.5;7.5 The Spin and Parity of the Ground State of Deformed Odd Nuclei;194
9.6;7.6 Theoretical Prediction of Nuclear Shape;194
9.6.1;7.6.1 The Strutinsky Method: Macroscopic--Microscopic Method;194
9.6.2;7.6.2 Constrained Hartree--Fock Calculations;196
9.7;References;200
10;8 Nuclear Decay and Radioactivity;202
10.1;8.1 Alpha Decay;202
10.1.1;8.1.1 Decay Width;203
10.1.2;8.1.2 The Geiger--Nuttal Rule;211
10.2;8.2 Fission;211
10.3;8.3 Electromagnetic Transitions;214
10.3.1;8.3.1 Multipole Transition, Reduced Transition Probability;214
10.3.2;8.3.2 General Consideration of the Selection Rule and the Magnitude;216
10.3.3;8.3.3 Single-Particle Model Estimate: Weisskopf Units and Experimental Values;217
10.3.4;8.3.4 Connection Between Electromagnetic Transitions and the Shapes and Collective Motions of Nuclei;220
10.4;References;223
11;9 Synthesis of Elements;225
11.1;9.1 The Astrophysical S-Factor and Gamow Factor;225
11.2;9.2 Gamow Peak;227
11.3;9.3 Neutron Capture Cross Section;228
11.4;9.4 Synthesis of Heavy Elements: S-Process and R-Process;229
11.5;References;231
12;Appendix A Important Formulae and Their Derivation;232
13;Index;269

Introduction.- Bulk Properties of Nuclei.- The Nuclear Force and Two-Body Systems.- Interaction with Electromagnetic Field: Electromagnetic Moments.- Shell Structure.- Microscopic Mean-Field Theory (Hartree–Fock Theory).- The Shapes of Nuclei.- Nuclear Decay and Radioactivity.- Synthesis of Elements.

Über Autor(innen)

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.