Physics of Atomic Nuclei

This advanced textbook presents an extensive and diverse study of low-energy nuclear physics considering the nucleus as a quantum system of strongly interacting constituents. The contents guide students from the basic facts and ideas to more modern topics including important developments over the last 20 years, resulting in a comprehensive collection of major modern-day nuclear models otherwise unavailable in the current literature. The book emphasizes the common features of the nucleus and other many-body mesoscopic systems currently in the center of interest in physics. The authors have also included full problem sets that can be selected by lecturers and adjusted to specific interests for more advanced students, with many chapters containing links to freely available computer code. As a result, readers are equipped for scientific work in mesoscopic physics.

Table of Contents:
Dedication xiii Preface xv 1 Building Blocks and Interactions 1 1.1 What Are the Nuclei Made Of? 1 1.2 Proton and Neutron 3 1.3 Strong Interactions 4 1.4 Electromagnetic Interactions and Charge Distribution 5 1.5 Magnetic Properties 10 1.6 Weak Interactions 11 1.7 Neutron Decay 13 1.8 NuclearWorld 15 References 19 2 Isospin 21 2.1 Quantum Numbers in the Two-Body Problem 21 2.2 Introducing Isospin 23 2.3 Isospin Invariance 25 2.4 Space–Spin Symmetry and Isospin Invariance 26 2.5 Glimpse of a More General Picture 30 2.6 Relations between Cross Sections 31 2.7 Selection Rules 35 2.8 Isobaric Mass Formulae 38 References 41 3 Two-Body Dynamics and the Deuteron 43 3.1 Low-Energy Nuclear Forces 43 3.2 Example: Argonne Potential 45 3.3 Meson Exchange 48 3.4 Deuteron: Central Forces and s-Wave 51 3.5 Tensor Forces and d-Wave 55 3.6 Magnetic Dipole Moment 58 3.7 Electric Quadrupole Moment 59 References 65 4 Two-Body Scattering 67 4.1 Scattering Problem 67 4.2 Phase Shifts 69 4.3 Scattering Length 71 4.4 Sign of the Scattering Length 78 4.5 Resonance Scattering at Low Energies 80 4.6 Effective Radius 82 4.7 Scattering of Identical Particles 83 4.8 Coulomb Scattering 86 4.9 Coulomb-Nuclear Interference 87 References 89 5 Liquid Drop Model 91 5.1 Binding Energies 91 5.2 Shape Variables 95 5.3 Microscopic Variables 97 5.4 Multipole Moments 98 5.5 Kinetic Energy and Inertial Parameters 100 5.6 Shape Vibrations 102 5.7 Stability of the Charged Spherical Liquid Drop 104 References 111 6 Vibrations of a Spherical Nucleus 113 6.1 SoundWaves 113 6.2 Isovector Modes 117 6.3 Giant Resonance and Linear Response 119 6.4 Classification of Normal Modes 121 6.5 Quantization of Nuclear VibrationalModes 125 6.6 Multiphonon Excitations 128 6.7 Angular Momentum Classification 132 References 134 7 Fermi Gas Model 135 7.1 Mean Field and Quasiparticles 135 7.2 Perfect Fermi Gas 137 7.3 Ground State 138 7.4 Correlation Between Particles 142 7.5 Asymmetric Systems and Chemical Equilibrium 143 7.6 Pressure and Speed of Sound 146 7.7 Gravitational Equilibrium 148 7.8 Nuclear Matter Equation of State 150 References 151 8 Spherical Mean Field 153 8.1 Introduction 153 8.2 Magic Numbers 153 8.3 Separation Energy 155 8.4 Periodicity of Nuclear Spectra 156 8.5 Harmonic Oscillator Potential 157 8.6 Orbital Momentum Representation 160 8.7 SquareWell Potential 162 8.8 Spin–Orbit Coupling 163 8.9 Realistic Level Scheme 165 8.10 Semiclassical Origins of Shell Structure 166 References 168 9 Independent Particle Shell Model 169 9.1 Shell Model Configurations 169 9.2 Particle–Hole Symmetry 171 9.3 MagneticMoment 172 9.4 Quadrupole Moment 174 9.5 Recoil Corrections 177 9.6 Introduction to Group Theory of Multiparticle Configurations 178 References 183 10 Light Nuclei 185 10.1 A ShortWalk along the Beginning of the Nuclear Chart 185 10.2 Halo in Quantum Systems 190 10.3 Nuclear Halos 192 10.4 One-Body Halo 193 10.5 Two-Body Halos 195 10.6 Efimov States 199 References 202 11 Many-Body Operator Formalism 203 11.1 Secondary Quantization 203 11.2 Physical Observables: One-Body Operators 208 11.3 Two-Body Operators 209 11.4 Interparticle Interaction 210 11.5 Interaction in a Spherical Basis 213 11.6 Recoupling of Angular Momentum 215 References 222 12 Nuclear Deformation 223 12.1 Idea of Nuclear Deformation 223 12.2 Collective Model 224 12.3 Adiabatic Approximation 226 12.4 Onset of Deformation 228 12.5 Quadrupole Deformation in the Body-Fixed Frame 230 12.6 Quadrupole Shape Variables 232 12.7 Variety of Quadrupole Shapes 233 12.8 Empirical Deformation 235 12.9 Single-Particle Quantum Numbers 239 12.10 Anisotropic Harmonic Oscillator 240 12.11 Asymptotic Quantum Numbers 245 12.12 Nilsson Potential 246 12.13 More Examples 247 References 250 13 Pairing Correlations 251 13.1 Physical Evidence 251 13.2 Seniority Scheme 256 13.3 Multipole Moments in the Seniority Scheme 260 13.4 Degenerate Model 261 13.5 Canonical Transformation 265 13.6 BCS Theory: TrialWave Function 269 13.7 Energy Minimization 271 13.8 Solution for the Energy Gap 273 13.9 Excitation Spectrum 276 13.10 Condensation Energy 278 13.11 Transition Amplitudes 279 References 281 14 Gamma-Radiation 283 14.1 Introduction 283 14.2 Electromagnetic Field and Gauge Invariance 283 14.3 Photons 285 14.4 Interaction of Radiation with Matter 288 14.5 Radiation Probability 291 14.6 Electric Dipole Radiation 292 14.7 Electric Quadrupole Radiation 295 14.8 Magnetic Dipole Radiation 296 14.9 Photoabsorption 298 14.10 Multipole Expansion 299 References 303 15 Nuclear Gamma-Transitions and Related Electromagnetic Processes 305 15.1 Single-Particle Transitions 305 15.2 Collective Transitions 308 15.3 Nuclear Isomerism 310 15.4 Isospin 312 15.5 Structural Selection Rules 315 15.6 Monopole Transitions 318 15.7 Internal Electron Conversion 320 15.8 Coulomb Excitation 322 15.9 Nuclear Photoeffect 326 15.10 Electron Scattering 330 References 335 16 Nuclear Rotation 337 16.1 Introduction: Rotational Bands 337 16.2 Finite Rotations 345 16.3 Rotation Matrices as Functions on the Group 346 16.4 Euler Angles 347 16.5 Angular Momentum in Euler Angles 351 16.6 Eigenfunctions of Angular Momentum 354 16.7 Rigid Rotor 355 16.8 Symmetry Properties 357 16.9 Simplest Solutions 358 16.10 Ground-State Band 359 16.11 Intensity Rules 360 16.12 Electric Quadrupole Moment 363 16.13 MagneticMoment 366 16.14 Symmetry Properties Revisited 367 16.15 Coriolis Mixing and Decoupling Parameter 368 16.16 Classical Rotation and Routhian 370 16.17 Cranked Rotation 372 16.18 Moment of Inertia 375 16.19 Adiabatic Expansion 377 16.20 Rotation of a Perfect Fermi Gas 379 16.21 Perfect Bose Gas and Ideal Liquid 381 16.22 Pairing Effects 384 16.23 Band Crossing 385 References 388 17 Self-Consistent Field 391 17.1 Exchange Interaction 391 17.2 Hartree–Fock Equations 395 17.3 Operator Formulation 397 17.4 Single-Particle Density Matrix 398 17.5 Hartree–Fock–Bogoliubov Approximation 400 17.6 General Canonical Transformation 402 17.7 Solutions 404 17.8 Generalized Density Matrix 407 17.9 Pairing and Particle Number Conservation 409 17.10 Effective Interaction 411 17.11 Skyrme Functionals 413 17.12 Generalization to Nonzero Temperature 418 References 419 18 Collective Modes 421 18.1 Schematic Model 421 18.2 Random Phase Approximation 426 18.3 Canonical Form of the RPA 427 18.4 Model with Factorized Forces 430 18.5 Collective Modes as Bosons 432 18.6 Mapping of Dynamics 433 18.7 Normalization and the Mass Parameter 435 18.8 Symmetry Breaking 438 18.9 Generator Coordinate Method 444 References 446 19 Bosons, Symmetries and Group Models 447 19.1 Introduction 447 19.2 Low-Lying Quadrupole Excitations as Interacting Bosons 448 19.3 Algebra of Boson Operators 450 19.4 Subgroups and Casimir Operators 452 19.5 s–d Model 455 19.6 Irreducible Representations and Quantum Numbers 458 19.7 Vibrational Limit 461 19.8 óG(6) Limit 466 19.9 óKóM(3) Limit 468 19.10 Shapes and Phase Transitions in the IBM 470 References 473 20 Statistical Properties 475 20.1 Introduction 475 20.2 Level Density: General Properties 478 20.3 Darwin–FowlerMethod 480 20.4 Relation to Statistical Thermodynamics 482 20.5 Thermodynamics of a Nuclear Fermi Gas 483 20.6 Statistics of Angular Momentum 486 20.7 Shell Model Monte Carlo Approach 488 20.8 Thermodynamics of Compound Reactions 490 20.9 Statistical Description of Resonances 492 References 497 21 Nuclear Fission 499 21.1 Introduction 499 21.2 Alpha-Decay 502 21.3 Neutron Fission 505 21.4 Photofission 509 21.5 Fission as a Large-Amplitude Collective Motion 510 21.6 Nonadiabatic Effects and Dissipation 512 21.7 Fission Isomers 514 21.8 Parity Violation in Fission 518 References 522 22 Heavy-ion Reactions: Selected Topics 525 22.1 Introduction 525 22.2 Experimental Indications 526 22.3 Macroscopic Description 530 22.4 Equilibration as a Diffusion Process 534 22.5 Toward a Microscopic Description 540 22.6 Sketch of a More General Approach 541 22.7 A Simple Model 545 22.8 Nuclear Multifragmentation 547 22.9 More about Fusion Reactions 550 References 553 23 Configuration Interaction Approach 555 23.1 Center-of-Mass Problem 555 23.2 Matrix Elements of Two-Body Interactions 558 23.3 Ab initio Approach 559 23.4 Three-Body Forces 564 23.5 Semiempirical Effective Interactions 565 23.6 Shell-Model Hamiltonian, Properties and Solutions 570 23.7 Effective Non-Hermitian Hamiltonian 571 23.8 From Isolated to Overlapping Resonances 576 23.9 Realistic Nuclear Calculations 581 References 583 24 Weak Interactions 585 24.1 Introduction 585 24.2 Beta-Spectrum in the Simplest Case 587 24.3 Nuclear Transitions 590 24.4 Dirac Formalism 595 24.5 Four-Fermion Theory 599 24.6 Nuclear Structure Effects 601 24.7 Parity Violation 604 24.8 Electric Dipole Moment 607 24.9 Nuclear Enhancement 609 24.10 On theWay to ElectroweakTheory 612 24.11 Higgs Mechanism 616 24.12 Neutrino: Oscillations 618 24.13 Neutrino:Majorana or Dirac? 620 References 623 25 Nucleus as a Chaotic System 627 25.1 Introduction 627 25.2 Strength Function 628 25.3 Level Density Revisited 633 25.4 Complexity ofWave Functions 636 25.5 Correlations between Classes of States 639 25.6 Invariant Entropy 643 25.7 Random Matrix Ensembles 646 25.8 Thermalization 650 References 652 General Nuclear Data Resources 655 Index 657

About the Author :
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.