ADVANCES IN

NUCLEAR PHYSICS

VOLUME 19

CONTRIBUTORS TO THIS VOLUME

c. J. Batty Rutherford Appleton Laboratory Chilton, England

E. Friedman Racah Institute of Physics The Hebrew University Jerusalem, Israel

H.J. Gils Kernforschungszentrum Karlsruhe Institut fiir Kernsphyslk Karlsruhe, Federal Republic of Germany

R. Machleidt Department of Physics University of California Los Angeles, California and Los Alamos National Laboratory Los Alamos, New Mexico

Present address: Department of Physics University of Idaho Moscow, Idaho

H. Rebel Kernforschungszentrum Karlsuhe Institut fiir Kernsphysik Karlsruhe, Federal Republic of 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

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

VOLUME 19

PLENUM PRESS • NEW YORK-LONDON

The Library of Congress cataloged the first volume of this title as follows:

Advances in nuclear physics. v. 1-New York, Plenum Press.

v. 24 cm. annual.

1968-

Editors: 1968- M. Baranger and E. Vogt.

1. Nuclear physics-Period I. Baranger, Michel, ed. II. Vogt, Erich W. 1929- ed.

QC173.A2545 539.7'05 67-29001

ISBN 978-1-4613-9909-4 ISBN 978-1-4613-9907-0 (eBook) DOI 10.1007/978-14613-9907-0

© 1989 Plenum Press, New York Softcover reprint of the hardcover 1 st edition 1989

A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013

All rights reserved

No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming,

recording, or otherwise, without written permission from the Publisher

ARTICLES PUBLISHED IN EARLIER VOLUMES

Volume 1 The Reorientation Effect • J. de Boer and J. Eichler The Nuclear SUa 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. Tjom Isoscalar Transition Rates in Nuclei from the (a, a') 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 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. Pandya

Volume 5 Variational Techniques in the Nuclear Three-Body Problem • L. M. Delves Nuclear Matter Calculations • Donald W. L. Sprung Clustering in Light Nuclei • Akita Arima, Hisashi Horiuchi, Kuniharu 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 Interactions 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 Truol

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

Volume 12 Hypemetted-Chain Theory of Matter at Zero Temperature • J. G. Zabolitzky Nuclear Transition Density Determinations from Inelastic Electron Scattering •

vii

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. lachello High-Energy Nuclear Collisions • S. Nagamiya and M. Gyulassy

Volume 14 Single-Particle Properties of Nuclei Through (e, e'p) 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-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 D. 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. Sainio, and A. Svarc Skyrmions in Nuclear Physics • UI/-G. Meissner and Ismail Zahed Microscopic Description 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 pp Interaction and the Quest for Baryonium • C. Amsler Radiative Muon Capture and the Weak Pseudoscalar Coupling in Nuclei. M. Gmitro and

P. TrutH Introduction to the Weak and Hypoweak Interactions. T. Goldman

ARTICLES PLANNED FOR FUTURE VOLUMES

Pion-Nucleus Scattering and Isobar Propagation in Nuclei. F. Lenz and E. J. Moniz Gamow-Teller Giant Resonances. C. D. Goodman and T. N. Taddeucci Relativistic Hamiltonian Dynamics in Nuclear and Particle Physics. B. D. Keister and

W. Polyzou Internuclear Cascade Methods for Relativistic Heavy-Ion Reactions. Zeev Fraenkel Electron Scattering and the Many-Body Problem. B. Frois, C. Papanicolas, and

V. Pandharipande The Quest for Signatures of Quark -Gluon Plasma Formation. M. Chu and T. Matsui Astrophysically Important Light Nuclear Reactions. G. Bliige and K. Langanke Solar Neutrinos. W. Haxton

ix

PREFACE

The two comprehensive reviews in this volume address two fundamental problems that have been of long-standing interest and are the focus of current effort in contemporary nuclear physics: exploring experimentally the density distributions of constituents within the nucleus and understand­ing nuclear structure and interactions in terms of hadronic degrees of freedom.

One of the major goals of experimental probes of atomic nuclei has been to discover the spatial distribution of the constituents within the nucleus. As the energy and specificity of probes have increased over the years, the degree of spatial resolution and ability to select specific charge, current, spin, and isospin densities have correspondingly increased. In the first chapter, Batty, Friedman, Gils, and Rebel provide a thorough review of what has been learned about nuclear density distributions using electrons, muons, nucleons, antinucleons, pions, alpha particles, and kaons as probes. This current understanding, and the limitations thereof, are crucial in framing the questions that motivate the next generation of experimental facilities to study atomic nuclei with electromagnetic and hadronic probes.

The second chapter, by Machleidt, reviews our current understanding of nuclear forces and structure in terms of hadronic degrees of freedom, that is, in terms of mesons and nucleons. Such an understanding in terms of hadronic variables is crucial for two reasons. First, since effective hadronic theories are quite successful in describing a broad range of phenomena in low-energy nuclear physics, and there are clear experimental signatures of meson exchange currents in nuclei, we must understand their foundations. Second, a viable hadronic theory is an essential prerequisite for establishing the framework within which one investigates quark and gluon degrees of freedom in nuclear systems. In addressing these issues, this contribution reviews the foundations of the meson theory of hadronic interactions, and applies this theory to nuclear matter and to finite nuclei.

xi

J. W. NEGELE

E. W. VOGT

CONTENTS

Chapter 1

EXPERIMENTAL METHODS FOR STUDYING NUCLEAR DENSITY DISTRIBUTIONS

C. J. Batty, E. Friedman, H. J. Gils, and H. Rebel

l. Introduction

2. Nuclear Charge Distributions 2.l. Electron Scattering 2.2. Muonic Atoms 2.3. Electronic X Rays 2.4. Optical Isotope Shifts 2.5. Comparisons and Comments

3. Information on Specific Orbitals 3.l. Coulomb Displacement Energies 3.2. Nucleon Transfer Reactions 3.3. Charge-Exchange Reactions to Analog States 3.4. Magnetic Scattering of Electrons 3.5. Comparisons and Comments

4. Information on the Periphery of the Nucleus 4.l. Kaonic and Antiprotonic Atoms 4.2. Pionic Atoms 4.3. K- and p Reactions with Nuclei 4.4. Comments

5. Information on the Nuclear Surface 5.l. Total and Reaction Cross Sections at High Energies

xiii

1

8 8

12 16 19 27

29 29 33 42 46 48

49 51 58 58 68

68 70

xiv Contents

5.2. Model-Independent Methods for the Analysis of Scattering Experiments . . . . . . . . . . . . . . . . . 79

5.3. Folding Model Approaches to the Optical Potential . .. 87 5.4. Low- and Medium-Energy Proton Scattering . . . . .. 95 5.5. Diffraction Scattering of Low- and Medium-Energy Alpha

Particles ............. 102 5.6. Scattering of Intermediate-Energy Pions 112 5.7. Scattering of Low-Energy Antiprotons 115

6. Toward the Nuclear Interior ...... 120 6.1. Intermediate-Energy Alpha-Particle Scattering 120 6.2. Double-Folding versus Single-Folding in Analyses of Com-

plex Particle Scattering and the Choice of the Interaction 134 6.3. Scattering of Intermediate-Energy Protons 141 6.4. Scattering of Low-Energy Pions ......... 155

7. Future Methods and Probes 161 7.1. Combined Analysis of Different Types of Experiments 161 7.2. K+ Scattering 164

8. Concluding Remarks 168

Acknowledgments 171

References . . . . . . 172

Chapter 2

1.

2.

THE MESON THEORY OF NUCLEAR FORCES AND NUCLEAR STRUCTURE

R. Machleidt

Introduction

Historical Overview 2.1. The "Hypothetical" Period 2.2. The Pion as the Quantum 2.3. "Dispersive" Approaches 2.4. A Tale of Two Cities 2.5. More Recent Developments

189

190 190 194 199 202 204

Contents xv

3. Pedagogical Introduction ......... 205 3.1. Empirical Features of the Nuclear Force 205 3.2. The Idea of Massive-Particle Exchange 209 3.3. Field Theory, Perturbation Theory, and Feynman

Diagrams ............ 210 3.4. Various Boson Fields and their Role in NN 212

4. The One-Boson Exchange Model . . . . . . . 220 4.1. Covariant Equations . . . . . . . . . . 220 4.2. Meson Parameters and Two-Nucleon Properties 225

5. Advanced Meson Exchange Models 235 5.1. Models for the 21T Exchange 235 5.2. 1Tp Contributions ..... 239 5.3. Other Two-Meson-Exchange Contributions 244 5.4. Results . . . . 245 5.5. Off-Shell Aspects 247

6. Charge Dependence 253 6.1. Introduction 253 6.2. Empirical Evidence 254 6.3. Some Results from Theory 257

7. Nucleon-Nucleon Scattering above the Inelastic Threshold 265 7.1. At Intermediate Energies . . 265 7.2. The Ge V Region ..... 279

8. Some Related Hadronic Interactions 280 8.1. Pion-Nucleon Scattering 281 8.2. The NN Potential . . . . . 283 8.3. Strange Nuclear Interactions 287

9. Nuclear Matter I-Conventional 288 9.1. Introduction ...... 289 9.2. History of the Conventional Many-Body Problem 291 9.3. Conventional Theories . . . . . 292 9.4. Results and Problems ..... 297

10. Nuclear Matter II-Beyond Convention 304 10.1. Possible Extensions . . . . 304 10.2. Meson Degrees of Freedom 310 10.3. Isobar Degrees of Freedom 318 10.4. Many-Body Forces 322 10.5. Relativistic Effects 328

11. Finite Nuclei ..... 336 11.1. The Three-Nucleon System 336 11.2. The Ground State of Closed-Shell Nuclei 339 11.3. Excited States ............ 340

xvi

12. Summary, Conclusions, and Outlook

Acknowledgments . . . . . . . . . . . Appendix A: One-Boson Exchange Potentials

AI. Interaction Lagrangians and OBE Amplitudes A2. Relativistic Momentum Space OBEP A3. Coordinate Space Potentials

Appendix B: Models Including Isobar Degrees of Freedom

Appendix C: Deuteron Wave Functions

References

Contents

340

342 342 342 345 348

351

355

363