Physics of Atomic Nuclei

Vladimir Zelevinsky is professor at the Department of Physics and Astronomy and at the National Superconducting Cyclotron Laboratory at Michigan State University, USA. In the 1980s he was Head of the Theory Division at the Budker Institute and Head of Theoretical Physics at Novosibirsk University, Russia. He spent three years as visiting professor at the Niels Bohr Institute in Copenhagen, Denmark. He is the author of over 250 scientific publications, deputy editor of the EPL journal and associate editor of the journal Nuclear Physics. He is also the author of Quantum Physics, 2 Volume Set, published with Wiley VCH in 2010.Alexander Volya is professor of Physics at the Florida State University, USA. His education includes diploma from Tallinn Tynismae Science School, Estonia; bachelor’s degree from St. Petersburg State University, Russia; doctoral degree in theoretical nuclear physics from Michigan State University; and postgraduate research work at the Argonne National Laboratory. In the fall of 2003, he joined the faculty at Florida State University where he currently leads a research program in theoretical nuclear physics and mesoscopic physics. He has published over 100 publications and has been regularly teaching nuclear physics courses at Florida State University.

• Dedication xiiiPreface xv1 Building Blocks and Interactions 11.1 What Are the Nuclei Made Of? 11.2 Proton and Neutron 31.3 Strong Interactions 41.4 Electromagnetic Interactions and Charge Distribution 51.5 Magnetic Properties 101.6 Weak Interactions 111.7 Neutron Decay 131.8 NuclearWorld 15References 192 Isospin 212.1 Quantum Numbers in the Two-Body Problem 212.2 Introducing Isospin 232.3 Isospin Invariance 252.4 Space–Spin Symmetry and Isospin Invariance 262.5 Glimpse of a More General Picture 302.6 Relations between Cross Sections 312.7 Selection Rules 352.8 Isobaric Mass Formulae 38References 413 Two-Body Dynamics and the Deuteron 433.1 Low-Energy Nuclear Forces 433.2 Example: Argonne Potential 453.3 Meson Exchange 483.4 Deuteron: Central Forces and s-Wave 513.5 Tensor Forces and d-Wave 553.6 Magnetic Dipole Moment 583.7 Electric Quadrupole Moment 59References 654 Two-Body Scattering 674.1 Scattering Problem 674.2 Phase Shifts 694.3 Scattering Length 714.4 Sign of the Scattering Length 784.5 Resonance Scattering at Low Energies 804.6 Effective Radius 824.7 Scattering of Identical Particles 834.8 Coulomb Scattering 864.9 Coulomb-Nuclear Interference 87References 895 Liquid Drop Model 915.1 Binding Energies 915.2 Shape Variables 955.3 Microscopic Variables 975.4 Multipole Moments 985.5 Kinetic Energy and Inertial Parameters 1005.6 Shape Vibrations 1025.7 Stability of the Charged Spherical Liquid Drop 104References 1116 Vibrations of a Spherical Nucleus 1136.1 SoundWaves 1136.2 Isovector Modes 1176.3 Giant Resonance and Linear Response 1196.4 Classification of Normal Modes 1216.5 Quantization of Nuclear VibrationalModes 1256.6 Multiphonon Excitations 1286.7 Angular Momentum Classification 132References 1347 Fermi Gas Model 1357.1 Mean Field and Quasiparticles 1357.2 Perfect Fermi Gas 1377.3 Ground State 1387.4 Correlation Between Particles 1427.5 Asymmetric Systems and Chemical Equilibrium 1437.6 Pressure and Speed of Sound 1467.7 Gravitational Equilibrium 1487.8 Nuclear Matter Equation of State 150References 1518 Spherical Mean Field 1538.1 Introduction 1538.2 Magic Numbers 1538.3 Separation Energy 1558.4 Periodicity of Nuclear Spectra 1568.5 Harmonic Oscillator Potential 1578.6 Orbital Momentum Representation 1608.7 SquareWell Potential 1628.8 Spin–Orbit Coupling 1638.9 Realistic Level Scheme 1658.10 Semiclassical Origins of Shell Structure 166References 1689 Independent Particle Shell Model 1699.1 Shell Model Configurations 1699.2 Particle–Hole Symmetry 1719.3 MagneticMoment 1729.4 Quadrupole Moment 1749.5 Recoil Corrections 1779.6 Introduction to Group Theory of Multiparticle Configurations 178References 18310 Light Nuclei 18510.1 A ShortWalk along the Beginning of the Nuclear Chart 18510.2 Halo in Quantum Systems 19010.3 Nuclear Halos 19210.4 One-Body Halo 19310.5 Two-Body Halos 19510.6 Efimov States 199References 20211 Many-Body Operator Formalism 20311.1 Secondary Quantization 20311.2 Physical Observables: One-Body Operators 20811.3 Two-Body Operators 20911.4 Interparticle Interaction 21011.5 Interaction in a Spherical Basis 21311.6 Recoupling of Angular Momentum 215References 22212 Nuclear Deformation 22312.1 Idea of Nuclear Deformation 22312.2 Collective Model 22412.3 Adiabatic Approximation 22612.4 Onset of Deformation 22812.5 Quadrupole Deformation in the Body-Fixed Frame 23012.6 Quadrupole Shape Variables 23212.7 Variety of Quadrupole Shapes 23312.8 Empirical Deformation 23512.9 Single-Particle Quantum Numbers 23912.10 Anisotropic Harmonic Oscillator 24012.11 Asymptotic Quantum Numbers 24512.12 Nilsson Potential 24612.13 More Examples 247References 25013 Pairing Correlations 25113.1 Physical Evidence 25113.2 Seniority Scheme 25613.3 Multipole Moments in the Seniority Scheme 26013.4 Degenerate Model 26113.5 Canonical Transformation 26513.6 BCS Theory: TrialWave Function 26913.7 Energy Minimization 27113.8 Solution for the Energy Gap 27313.9 Excitation Spectrum 27613.10 Condensation Energy 27813.11 Transition Amplitudes 279References 28114 Gamma-Radiation 28314.1 Introduction 28314.2 Electromagnetic Field and Gauge Invariance 28314.3 Photons 28514.4 Interaction of Radiation with Matter 28814.5 Radiation Probability 29114.6 Electric Dipole Radiation 29214.7 Electric Quadrupole Radiation 29514.8 Magnetic Dipole Radiation 29614.9 Photoabsorption 29814.10 Multipole Expansion 299References 30315 Nuclear Gamma-Transitions and Related Electromagnetic Processes 30515.1 Single-Particle Transitions 30515.2 Collective Transitions 30815.3 Nuclear Isomerism 31015.4 Isospin 31215.5 Structural Selection Rules 31515.6 Monopole Transitions 31815.7 Internal Electron Conversion 32015.8 Coulomb Excitation 32215.9 Nuclear Photoeffect 32615.10 Electron Scattering 330References 33516 Nuclear Rotation 33716.1 Introduction: Rotational Bands 33716.2 Finite Rotations 34516.3 Rotation Matrices as Functions on the Group 34616.4 Euler Angles 34716.5 Angular Momentum in Euler Angles 35116.6 Eigenfunctions of Angular Momentum 35416.7 Rigid Rotor 35516.8 Symmetry Properties 35716.9 Simplest Solutions 35816.10 Ground-State Band 35916.11 Intensity Rules 36016.12 Electric Quadrupole Moment 36316.13 MagneticMoment 36616.14 Symmetry Properties Revisited 36716.15 Coriolis Mixing and Decoupling Parameter 36816.16 Classical Rotation and Routhian 37016.17 Cranked Rotation 37216.18 Moment of Inertia 37516.19 Adiabatic Expansion 37716.20 Rotation of a Perfect Fermi Gas 37916.21 Perfect Bose Gas and Ideal Liquid 38116.22 Pairing Effects 38416.23 Band Crossing 385References 38817 Self-Consistent Field 39117.1 Exchange Interaction 39117.2 Hartree–Fock Equations 39517.3 Operator Formulation 39717.4 Single-Particle Density Matrix 39817.5 Hartree–Fock–Bogoliubov Approximation 40017.6 General Canonical Transformation 40217.7 Solutions 40417.8 Generalized Density Matrix 40717.9 Pairing and Particle Number Conservation 40917.10 Effective Interaction 41117.11 Skyrme Functionals 41317.12 Generalization to Nonzero Temperature 418References 41918 Collective Modes 42118.1 Schematic Model 42118.2 Random Phase Approximation 42618.3 Canonical Form of the RPA 42718.4 Model with Factorized Forces 43018.5 Collective Modes as Bosons 43218.6 Mapping of Dynamics 43318.7 Normalization and the Mass Parameter 43518.8 Symmetry Breaking 43818.9 Generator Coordinate Method 444References 44619 Bosons, Symmetries and Group Models 44719.1 Introduction 44719.2 Low-Lying Quadrupole Excitations as Interacting Bosons 44819.3 Algebra of Boson Operators 45019.4 Subgroups and Casimir Operators 45219.5 s–d Model 45519.6 Irreducible Representations and Quantum Numbers 45819.7 Vibrational Limit 46119.8 óG(6) Limit 46619.9 óKóM(3) Limit 46819.10 Shapes and Phase Transitions in the IBM 470References 47320 Statistical Properties 47520.1 Introduction 47520.2 Level Density: General Properties 47820.3 Darwin–FowlerMethod 48020.4 Relation to Statistical Thermodynamics 48220.5 Thermodynamics of a Nuclear Fermi Gas 48320.6 Statistics of Angular Momentum 48620.7 Shell Model Monte Carlo Approach 48820.8 Thermodynamics of Compound Reactions 49020.9 Statistical Description of Resonances 492References 49721 Nuclear Fission 49921.1 Introduction 49921.2 Alpha-Decay 50221.3 Neutron Fission 50521.4 Photofission 50921.5 Fission as a Large-Amplitude Collective Motion 51021.6 Nonadiabatic Effects and Dissipation 51221.7 Fission Isomers 51421.8 Parity Violation in Fission 518References 52222 Heavy-ion Reactions: Selected Topics 52522.1 Introduction 52522.2 Experimental Indications 52622.3 Macroscopic Description 53022.4 Equilibration as a Diffusion Process 53422.5 Toward a Microscopic Description 54022.6 Sketch of a More General Approach 54122.7 A Simple Model 54522.8 Nuclear Multifragmentation 54722.9 More about Fusion Reactions 550References 55323 Configuration Interaction Approach 55523.1 Center-of-Mass Problem 55523.2 Matrix Elements of Two-Body Interactions 55823.3 Ab initio Approach 55923.4 Three-Body Forces 56423.5 Semiempirical Effective Interactions 56523.6 Shell-Model Hamiltonian, Properties and Solutions 57023.7 Effective Non-Hermitian Hamiltonian 57123.8 From Isolated to Overlapping Resonances 57623.9 Realistic Nuclear Calculations 581References 58324 Weak Interactions 58524.1 Introduction 58524.2 Beta-Spectrum in the Simplest Case 58724.3 Nuclear Transitions 59024.4 Dirac Formalism 59524.5 Four-Fermion Theory 59924.6 Nuclear Structure Effects 60124.7 Parity Violation 60424.8 Electric Dipole Moment 60724.9 Nuclear Enhancement 60924.10 On theWay to ElectroweakTheory 61224.11 Higgs Mechanism 61624.12 Neutrino: Oscillations 61824.13 Neutrino:Majorana or Dirac? 620References 62325 Nucleus as a Chaotic System 62725.1 Introduction 62725.2 Strength Function 62825.3 Level Density Revisited 63325.4 Complexity ofWave Functions 63625.5 Correlations between Classes of States 63925.6 Invariant Entropy 64325.7 Random Matrix Ensembles 64625.8 Thermalization 650References 652General Nuclear Data Resources 655Index 657