Algebraic Approaches to Nuclear Structure: Interacting Boson and Fermion Models

ISBN-13: 9783718605378 / Angielski / Twarda / 1993 / 570 str.

R. Casten

Opis

This imponant book presents on approach to understanding the atomic nucleus that exploits simple algebraic techniques. The book focuses primarily on a panicular algebra:ic model, the Interacting Boson Model (IBM); ft outines the algebraic structure, or group theoretical basis, of the IBM and other algebraic models using simple examples. Both the compa6son of the IBM with empirical data and its microscopic basis are explored, as are extensions to odd mass nuclei and to phenomena not onginally encompassed within its purview. An impo@ant final chapter treats fermion algebraic approaches to nuclear structure which can be both more microscopic and more general, and which represent Dromisinq avenues for future research. Each of the cont6butors to t6is work i@ a leading expen in the field of algebraic models; together they have formulated an introducbon to the subject which will be an important resource for the series graduate student and the professional physicist alike.

Spis treści

Preface to the Series -- Preface -- Chapter 1 Introduction -- 1.1 Orientation -- 1.2 Nuclear Structure -- 1.3 Guide to the Text /Richard F. Casten -- Chapter 2 Group Theory of the IBM and Algebraic Models in General -- 2.1 Introduction: Why Groups? -- 2.2 Occupation-Number Representation -- 2.3 Isospin and Angular Momentum -- 2.4 The General Unitary Group U(n) -- 2.5 The Group U(6) in the IBM -- 2.6 Group Reductions -- 2.7 Dynamic Symmetries -- 2.8 Further Applications -- Appendix /Pertti O. Lipas -- Chapter 3 Empirical Tests of the IBM-1 -- Introduction -- 3.1 The 0(6) Symmetry -- 3.2 The U(5) Symmetry -- 3.3 The 51 /(3) Symmetry -- 3.4 Numerical Calculations in the IBM -- 3.5 E2 Transitions -- 3.6 The Consistent Q Formalism (CQF) -- 3.7 Practical Calculations -- 3.8 Ml Transitions -- 3.9 Transition Regions -- 3.10 Summary /Richard F. Casten and David D. Warner -- Chapter 4 Microscopic Basis and Introduction to IBM-2 -- 4.1 Shell Structure of Nucleus -- 4.2 Nuclear Surface and Nucleons -- 4.3 Effective Nucleon-Nucleon Interaction and Nuclear Deformation -- 4.4 S and D Nucleon Pairs—Truncation of the Shell Model -- 4.5 Mapping to SD Boson States -- 4.6 Proton Bosons, Neutron Bosons and Boson Number -- 4.7 Mapping of Nucleon Operators onto Boson Operators -- 4.8 Mapping in a Single-Orbit System -- 4.9 Spectrum of Mapped Boson System -- 4.10 Standard IBM-2 Hamiltonian: Phenomenology -- 4.11 F-spin -- 4.12 Scissors Mode and Other Mixed-Symmetry States -- 4.13 Ginocchio Model -- 4.14 Interacting Boson Models 3 and 4 -- 4.15 Concluding Remarks /Takaharu Otsuka -- Chapter 5 The IBFM and Bose-Fermi Symmetries -- 5.1 Core-Particle Coupling -- 5.2 The IBFM Hamiltonian -- 5.3 The Role of Symmetry -- 5.4 Symmetries Associated with f /B(6) x UF( 12) -- 5.5 Physical Requirements for Bose-Fermi Symmetry -- 5.6 Relationship with Other Models -- 5.7 Experimental Examples -- 5.8 Supersymmetry /David D. Warner -- Chapter 6 Extensions of the s-d Boson Model -- 6.1 Introduction -- 6.2 g-Bosons in the Interacting Boson Model -- 6.3 Negative Parity Bosons in the Interacting Boson Model -- 6.4 Triaxiality and Cubic Boson Interactions -- 6.5 Nucleon Excitations across Closed Shells: Intruder Excitations -- 6.6 Conclusion -- Appendix 6.1 /Kris Heyde -- Appendix 6.2 -- Chapter 7 Fermion Models -- 7.1 Fermions versus Bosons -- 7.2 Quantum Rotor and the SU(3) Model -- 7.3 Pseudo-Spin Symmetries -- 7.4 Fermion Dynamical Symmetry Model -- 7.5 Symplectic Shell Model /Jerry P. Draayer -- Index.

O autorze

Richard F. Casten was educated at the College of the Holy Cross and Yale University. He received the Humboldt Prize in 1983, and is a Fellow of the American Physical Society and the American Association for the Advancement of Science. Currently he is Senior Scientist and Nuclear Structure Physics Group Leader at Brookhaven National Laboratory, Upton, New York, USA. Pertti O. Lipas, Department of Physics, University of Jyvaskyla,SF-40351 Jyvaskyla, Finland. David D. Warner, Daresbury Laboratory, Warrington, CheshireWA4 4AD, UK. Takaharu Otsuka, Faculty of Science, Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan. Kris Heyde, Institute for Nuclear Physics, Proeftuinstraat 86, B-9000 Gent, Belgium.