Advances in Nuclear Physics

VOLUME 27 CONTRIBUTORS TO THIS VOLUME

Stefan Scherer Igal Talmi Institut für Kernphysik The Weizmann Institute of Science Johannes Gutenberg-Universität Mainz Rehovot, Israel Mainz, Germany

A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher. ADVANCES IN NUCLEAR PHYSICS

Edited by J. W. Negele Center for Theoretical Physics Massachusetts Institute of Technology Cambridge, Massachusetts

E. W. Vogt Department of Physics University of British Columbia Vancouver, B.C., Canada

VOLUME 27

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Visit Kluwer Online at: http://kluweronline.com and Kluwer's eBookstore at: http://ebooks.kluweronline.com ARTICLES PUBLISHED IN EARLIER VOLUMES

Volume 1 The Reorientation Effect • J. de Boer and J. Eicher The Nuclear Model • M. Harvey The Hartree-Fock Theory of Deformed Light Nuclei • G. Ripka The Statistical Theory of Nuclear Reactions • E. Vogt Three-Particle Scattering—A Review of Recent Work on the Nonrelativistic Theory • I. Duck

Volume 2 The Giant Dipole Resonance • B. M. Spicer Polarization Phenomena in Nuclear Reactions • C. Glashausser and J. Thirion The Pairing-Plus-Quadrupole Model • D. R. Bes and R. A. Sorensen The Nuclear Potential • P. Signell Muonic Atoms • S. Devons and I. Duerdoth

Volume 3 The Nuclear Three-Body Problem • A. N. Mitra The Interactions of Pions with Nuclei • D. S. Koltun Complex Spectroscopy • J. B. French, E. C. Halbert, J. B. McGrory, and S. S. M. Wong Single Nucleon Transfer in Deformed Nuclei • B. Elbeck and P. O. Tjøm Isoscalar Transition Rates in Nuclei from the Reaction • A. M. Bernstein

Volume 4 The Investigation of Hole States in Nuclei by Means of Knockout and Other Reactions • Daphne F. Jackson High-Energy Scattering from Nuclei • Wieslaw Czyz Nucleosynthesis by Charged-Particle Reactions • C. A. Barnes Nucleosynthesis and Neutron-Capture Cross Sections • B. J. Allen, J. H. Gibbons, and R. L. Macklin Nuclear Structure Studies in the Z = 50 Region • Elizabeth Urey Baranger An s-d Shell-Model Study for A = 18 – 22 • E. C. Halbert, J. B. McGrory, B. H. Wildenthal, and S. P. Pandy

Volume 5 Variational Techniques in the Nuclear Three-Body Problem • L. M. Delves Nuclear Matter Calculations • Donald W. L. Sprung Clustering in Light Nuclei • Akito Arima, Hisashi Horiuchi, Kunihara Kubodera, and Noburu Takigawa

v vi Articles Published in Earlier Volumes Volume 6 Nuclear Fission • A. Michaudon The Microscopic Theory of Nuclear Effective Interactions and Operators • Bruce R. Barrett and Michael W. Kirson Two-Neutron Transfer Reactions and the Pairing Model • Ricardo Broglia, Ole Hansen, and Claus Riedel

Volume 7 Nucleon-Nucleus Collisions and Intermediate Structure • Aram Mekjian Coulomb Mixing Effects in Nuclei: A Survey Based on Sum Rules • A. M. Lane and A. Z. Mekjian The Beta Strength Function • P. G. Hansen Gamma-Ray Strength Functions • G. A. Bartholemew, E. D. Earle, A. J. Ferguson, J. W. Knowles, and M. A. Lone

Volume 8 Strong Interaction in A-Hypernuclei • A. Gal Off-Shell Behavior of the Nucleon-Nucleon Interaction • M. K. Strivastava and D. W. L. Sprung Theoretical and Experimental Determination of Nuclear Charge Distributions • J. L. Friar and J. W. Negele

Volume 9 One- and Two-Nucleon Transfer Reactions with Heavy Ions • Sidney Kahana and A. J. Baltz Computational Methods for Shell-Model Calculations • R. R. Whitehead, A. Watt, B. J. Cole, and I. Morrison Radiative Pion Capture in Nuclei • Helmut W. Baer, Kenneth M. Crowe, and Peter Truöl

Volume 10 Phenomena in Fast Rotating Heavy Nuclei • R. M. Lieder and H. Ryde Valence and Doorway Mechanisms in Resonance Neutron Capture • B. J. Allen and A. R. de L. Musgrove Lifetime Measurements of Excited Nuclear Levels by Doppler-Shift Methods • T. K. Alexander and J. S. Forster

Volume 11 Clustering Phenomena and High-Energy Reactions • V. G Neudatchin, Yu. F. Smirnov, and N. F. Golovanova Pion Production in Proton-Nucleus Collisions • B. Holstad Fourteen Years of Self-Consistent Field Calculations: What Has Been Learned • J. P. Svenne Hartree-Fock-Bogoliubov Theory with Applications to Nuclei • Alan L. Goodman Hamiltonian Field Theory for Systems of Nucleons and Mesons • Mark Bolsterli Articles Published in Earlier Volumes vii Volume 12 Hypernetted-Chain Theory of Matter at Zero Temperature • J. G. Zabolitzky Nuclear Transition Density Determinations from Inelastic Electron Scattering • Jochen Heisenberg High-Energy Proton Scattering • Stephen J. Wallace

Volume 13 Chiral Symmetry and the Bag Model: A New Starting Point for Nuclear Physics • A. W. Thomas The Interacting Boson Model • A. Arima and F. Iachella High-Energy Nuclear Collisions • S. Nagamiya and M. Gyullasy

Volume 14 Single-Particle Properties of Nuclei Through (e, ) Reactions • Salvatore Frullani and Jean Mougey

Volume 15 Analytic Insights into Intermediate-Energy Hadron-Nucleus Scattering • R. D. Amado Recent Developments in Quasi-Free Nucleon Scattering • P. Kitching, W. J. McDonald, Th. A. J. Maris, and C. A. Z. Vasconcellos Energetic Particle Emission in Nuclear Reactions • David H. Boal

Volume 16 The Relativistic Nuclear Many-Body Problem • Brian Serot and John Dirk Walecka

Volume 17 P-Matrix Methods in Hadronic Scattering • B. L. G. Bakker and P. J. Mulders Dibaryon Resonances • M. P. Locher, M. E. Saino, and A. Švarc Skrymions in Nuclear Physics • Ulf-G. Meissner and Ismail Zahed Microscopic Descriptions of Nucleus-Nucleus Collisions • Karlheinz Langanke and Harald Friedrich

Volume 18 Nuclear Magnetic Properties and Gamow-Teller Transitions • A. Arima, K. Shimizu, W. Bentz, and H. Hyuga Advances in Intermediate-Energy Physics with Polarized Deuterons • J. Arvieux and J. M. Cameron Interaction and the Quest for Baryonium • C. Amsler Radiative Muon Capture and the Weak Pseudoscalar Coupling in Nuclei • M. Gmitro and P. Truöl Introduction to the Weak and Hypoweak Interactions • T. Goldman viii Articles Published in Earlier Volumes Volume 19 Experimental Methods for Studying Nuclear Density Distributions • C. J. Batty, E. Friedman, H. J. Gils, and H. Rebel The Meson Theory of Nuclear Forces and Nuclear Structure • R. Machleidt

Volume 20 Single-Particle Motion in Nuclei • C. Mahaux and R. Sartor Relativistic Hamiltonian Dynamics in Nuclear and Particle Physics • B. D. Keister and W. N. Polyzou

Volume 21 Multiquark Systems in Hadronic Physics • B. L. G. Bakker and I. M. Narodetskii The Third Generation of Nuclear Physics with the Microscopic Cluster Model • Karlheinz Langanke The Fermion Dynamical Symmetry Model • Cheng-Li Wu, Da Hsuan Feng, and Mike Guidry

Volume 22 Nucleon Models • Dan Olof Riska Aspects of Electromagnetic Nuclear Physics and Electroweak Interaction • T. W. Donnelly Color Transparency and Cross-Section Fluctuations in Hadronic Collisions • Gordon Baym Many-Body Methods at Finite Temperature • D. Vautherin Nucleosynthesis in the Big Bang and in the Stars • K. Langanke and C. A. Barnes

Volume 23 Light Front Quantization • Matthias Burkardt Nucleon Knockout by Intermediate Energy Electrons • James J. Kelly Volume 24 Nuclear Charge-Exchange Reactions at Intermediate Energy • W. P. Alford and B. M. Spicer Mesonic Contributions to the Spin and Flavor Structure of the Nucleon • J. Speth and A. W. Thomas Muon Catalyzed Fusion: Interplay between Nuclear and Atomic Physics • K. Nagamine and M. Kamimura

Volume 25 Chiral Symmetry Restoration and Dileptons in Relativistic Heavy-Ion Collisions • R. Rapp and J. Wambach Fundamental Symmetry Violation in Nuclei • H. Feshbach, M. S. Hussein, A. K. Kerman, and O. K. Vorov Nucleon-Nucleus Scattering: A Microscopic Nonrelativistic Approach • K. Amos, P. J. Dortmans, H. V. von Geramb, S. Karataglidis, and J. Raynal Articles Published in Earlier Volumes ix Volume 26 The Spin Structure of the Nucleon • B. W. Filippone and Xiangdong Ji Liquid-Gas Phase Transition in Nuclear Multifragmentation • S. Das Gupta, A. Z. Mekjian, and M. B. Tsang High Spin Properties of Atomic Nuclei • D. Ward and P. Fallon The Deuteron: Structure and Form Factors • M. Garçon and J. W. Van Orden PREFACE

This volume contains two major articles, one providing a historical retrospec- tive of one of the great triumphs of nuclear physics in the twentieth century and the other providing a didactic introduction to one of the quantitative tools for understanding strong interactions in the twenty-first century. The article by Igal Talmi on “Fifty Years of the Shell Model – the Quest for the Effective Interaction”, pertains to a model that has dominated nuclear physics since its infancy and that developed with astonishing results over the next five decades. Talmi is uniquely positioned to trace the history of the Shell Model. He was active in developing the ideas at the shell model’s inception, he has been central in most of the subsequent initiatives which expanded, clar- ified and applied the shell model and he has remained active in the field to the present time. Wisely, he has chosen to restrict his review to the dominat- ing issue: the choice of the effective interactions among valence nucleons that determine the properties of low lying nuclear energy levels. The treatment of the subject is both bold and novel for our series. The ideas pertaining to the effective interaction for the shell model are elucidated in a historical sequence. In a massive article, which will be valued both for its completeness and its sound judgment of the various contributions to the subject, Talmi succeeds without use of a single figure comparing model results with each other or with experimental data. Instead, the compelling flow of ideas and results for the Shell Model are described in a manner that makes clear why this magnificent edifice has had such great resilience. Many of the ideas of the Shell Model are very elegant. They converge on a picture of nuclear states that is so all-encompassing that there has been very little room, so far, for the intrusion of subnucleon physics. Talmi takes us right up to the most recent decade in which very large computers have been able to verify and ex- pand upon earlier views of the effective interaction by directly diagonalizing the matrices pertaining to the myriad of nuclear states that arise from several valence nucleons beyond closed shells. This review is then a celebration of a most successful model of atomic nuclei and of its underlying ideas.

xi xii Preface

The second article of this volume is also massive and pertains to a subject that has become very important for the field. Chiral Perturbation Theory has been one of the few quantitative tools for coping with the theory of the strong interactions, QCD, which is both remarkably simple to express as a fundamental Lagrangian and notoriously intractable to solve. Chiral Perturbation Theory is particularly useful for the nucleon-nucleon and the nucleon-meson interactions. Stefan Scherer has worked on the theory for more than a decade and has taught a course on it at the University of Mainz. He has chosen in his present review to write a didactic article which should be especially helpful for nuclear physicists who are entering the field. The subject has had major critics who have worried about the convergence of the theory and also about its relation to effective interactions. These subjects are dealt with clearly in this review. Our series has now produced twenty-seven volumes and the technology producing it, which began thirty five years ago with an article set in the hot lead of linotype machines, has now evolved to electronic formatting and production. Having recently concentrated our effort in the successful transition to this new technology, we are now positioned to devote renewed effort to the commissioning of review articles. With the ever increasing breadth on contem- porary nuclear physics and related fields, the need for insightful, pedagogical reviews has never been greater.

J.W. NEGELE E.W. VOGT CONTENTS

Chapter 1 FIFTY YEARS OF THE SHELL MODEL – THE QUEST FOR THE EFFECTIVE INTERACTION Igal Talmi

1. Introduction 2 2. The (Re)Emergence of the Shell Model 11 2.1. Single Nucleon Orbits 12 2.2. The Supermultiplet Scheme 19 3. Early Calculations 26 3.1. Energy Levels of Simple Configurations 26 3.2. Nuclear Magnetic Moments 37 3.3. Electromagnetic Moments and Transitions. Beta Decay 44 3.4. Seniority and the 53 3.5. Applications of the to Even-Even and Odd-Odd Nuclei 58 3.6. Simple Potential Interactions. Configuration Mixing 62 3.7. The Beta Decay of 68 3.8. Simple Potential Interactions. Ignoring the Hard Core 73 3.9. The Pb Region I 85 4. Effective Interactions from Experimental Nuclear Energies 89 4.1. Simple Configurations 91 4.2. Protons and Neutrons in Different Orbits. 102 4.3. The Zr Region I 109

xiii xiv Contents

4.4. The Shell 115 4.5. Mixed Configurations in the Shell 121 4.6. The Nickel Isotopes 133 4.7. The Pb Region II 140 4.8. The Zr region II 144 4.9. The Shell 168 4.10. The Complete and Beyond 175 4.11. “Pseudonium Nuclei” 179 5. Some Schematic Interactions and Applications 181 5.1. The Pairing Interaction 181 5.2. The Surface Delta Interaction, the Quasi-Spin Scheme and Extensions 193 5.3. The SU (3) Scheme 202 6. Seniority and Generalized Seniority in Semi-Magic Nuclei 215 6.1. The Seniority Scheme and Applications 215 6.2. Generalized Seniority 220 7. Large Scale Shell Model Calculations 232 7.1. The and Beyond 232 7.2. The 241 7.3. Nuclei in which N = 20 Loses Its Magicity 249 8. What have we learned? Where do we stand? 253 References 265

Chapter 2 INTRODUCTION TO CHIRAL PERTURBATION THEORY Stefan Scherer

1. Introduction 278 1.1. Scope and Aim of the Review 278 1.2. Introduction to Chiral Symmetry and Its Application to Mesons and Single Baryons 279 2. QCD and Chiral Symmetry 290 2.1. Some Remarks on SU(3) 290 Contents xv

2.2. The QCD Lagrangian 293 2.3. Accidental, Global Symmetries of 297 2.4. Green Functions and Chiral Ward Identities 310 3. Spontaneous Symmetry Breaking and the Goldstone Theorem 323 3.1. Degenerate Ground States 324 3.2. Spontaneous Breakdown of a Global, Continuous, Non-Abelian Symmetry 330 3.3. Goldstone’s Theorem 335 3.4. Explicit Symmetry Breaking: A First Look 338 4. Chiral Perturbation Theory for Mesons 339 4.1. Spontaneous Symmetry Breaking in QCD 340 4.2. Transformation Properties of the Goldstone Bosons 347 4.3. The Lowest-Order Effective Lagrangian 352 4.4. Effective Lagrangians and Weinberg’s Power Counting Scheme360 4.5. Construction of the Effective Lagrangian 365 4.6. Applications at Lowest Order 370 4.7. The Chiral Lagrangian at Order 380 4.8. The Effective Wess-Zumino-Witten Action 384 4.9. Applications at Order 388 4.10. Chiral Perturbation Theory at 405 5. Chiral Perturbation Theory for Baryons 417 5.1. Transformation Properties of the Fields 418 5.2. Lowest-Order Effective Baryonic Lagrangian 423 5.3. Applications at Tree Level 427 5.4. Examples of Loop Diagrams 440 5.5. The Heavy-Baryon Formulation 449 5.6. The Method of Infrared Regularization 483 6. Summary and Concluding Remarks 496 Appendix 501 A.1. Green Functions and Ward Identities 501 A.2. Dimensional Regularization: Basics 507 A.3. Loop Integrals 512 A.4. Different Forms of in SU(2) × SU(2) 522 References 529

Index 539