Giant Resonances

290 Pages·1998·41.199 MB·\290

by  P. F. Bortignon (Author), A Bracco (Author), R. A. Broglia (Author)

Giant
Resonances
Contemporary Concepts in Physics
A series edited by Associate Editors
Herman Feshbach Mildred S. Dresselhaus
Massachusetts Institute Massachusetts Institute
of Technology of Technology
Mai Ruderman
Founding Editor Columbia University
Henry Primakoff iman
s B Tre
(1914-1983) Princeton University
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Volume 6, ALGEBRAIC APPROACHES TO NUCLEAR STRUCTURE: Interacting
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Richard F. Casten, Pertti O. Lipas, David D. Warner, Takaharu Otsuka,
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Igal Talmi
Volume 8, NEUTRINOS IN PHYSICS AND ASTROPHYSICS
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Volume 9, THE HARMONIC OSCILLATOR IN MODERN PHYSICS
Marcos Moshinsky and Yuri F. Smirnov
Volume 10, GIANT RESONANCES: Nuclear Structure at Finite Temperature
P.F. Bortignon, A. Braceo and R.A. Broglia
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Giant Resonances
Nuclear Structure
at Finite Temperature
P. F. Bortignon
and
A. Bracco
Universita di Milano and lstituto Nazionale di Fisica Nuc/eare, Italy
R. A. Broglia
Universita di Milano and lstituto Nazionale di Fisica Nuc/eare, Italy
Niels Bohr Institute, University of Copenhagen, Denmark
Boca Raton London New York
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First published 1998 by Hardwood Academic Publishers
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British Library Cataloguing in Publication Data
Bortignon, P. F.
Giant resonances : nuclear structure at finite temperature.
- (Contemporary concepts in physics ; v. 10)
I .Nuclear magnetic resonance, Giant
I.Title II.Bracco, Angela III.Broglia, R. A.
538.3'62
For
Donatella, Gianandrea and Bettina
— AB andRAB
Inger-Marie and Ulla Maria
— PFB

Contents
Preface to the Series xi
Preface xiii
1 Introduction 1
1.1 Overview 1
1.2 Hot Nuclei 6
1.3 Single-Particle Motion 7
1.4 Giant Resonances 9
1.5 Low-Lying Vibrations 15
1.6 Rotations 17
Parti ZERO TEMPERATURE
2 Giant Vibrations 25
2.1 The Variety of Modes 25
2.2 The Giant Dipole Resonance 27
2.3 The Monopole and Quadrupole Vibrations 31
2.4 The Decay of Giant Resonances 35
2.5 Direct and Compound Particle-Decay 36
2.6 Gamma-Decay of Giant Resonances 39
2.6.1 Decay to Low-Lying States 39
2.6.2 The Ground-State Decay 40
2.7 Fission Decay of Giant Resonances 45
3 Random Phase Approximation 47
3.1 Mean Field Theory 47
3.1.1 Effective Mass (¿-mass) 49
viii CONTENTS
3.2 Random Phase Approximation (RPA) 51
3.2.1 Dispersion Relation 54
3.2.2 Sum Rules 58
3.2.3 Coupling Strength 61
3.2.4 Frequency of Dipole Vibrations 62
3.2.5 Frequency of Quadrupole Vibrations 65
3.3 Damping of Nuclear Motion 67
4 Beyond Mean Field 69
4.1 Doorway States 69
4.1.1 The Dynamical Shell Model 69
4.1.2 Effective Mass (co-mass) 76
4.2 Relaxation of Giant Vibrations 79
4.2.1 Giant Quadrupole Resonance 84
4.2.2 Compound Coupling 90
4.3 Particle-Decay of Giant Resonances 96
4.3.1 The Continuum-RPA Approach 96
4.3.2 The Doorway-State Projection-Operator Method 98
4.4 Gamma-Decay of Giant Resonances 103
Part 2 FINITE TEMPERATURE
5 Measurement of Giant Resonances 109
5.1 Overview 110
5.2 Experimental Techniques 113
5.2.1 Kinematic Relations 118
5.3 High-Efficiency Multidetector Arrays 118
5.4 Statistical Model of y-Decay 121
5.4.1 Simple Estimates 125
6 Dipole Oscillations: Experiment 129
6.1 Moderate Excitation Energies 129
6.1.1 A - 40 129
6.1.2 A« 110 130
6.1.3 A- 170 132
CONTENTS ix
6.2 Limiting Temperature 139
6.3 Fissioning Nuclei 143
6.4 The Pre-Fission y-Decay 144
6.5 Search for the Giant Monopole Resonance in Hot Nuclei.... 148
7 Concepts of Statistical Physics 151
7.1 The Variety of Ensembles 151
7.2 Level Density and Partition Function 153
7.2.1 The Fermi Gas Model :. . . 153
7.2.2 Role of Correlations 156
7.3 Applications of the SPA+RPA to Level Densities 159
7.3.1 A Schematic Model 160
7.3.2 A Realistic Model 161
7.3.3 The Monte-Carlo Shell Model Method 162
7.4 Use of Level Densities 163
8 Linear Response 165
8.1 Mean Field Theory 165
8.2 Shell Corrections 170
8.2.1 A Numerical Example 172
8.3 Sum Rules 174
8.4 Random Phase Approximation 176
8.4.1 Dispersion Relation 179
8.4.2 The Collective Response 179
9 Collisions 185
9.1 The Dynamical Shell Model 185
9.1.1 Single-Particle Width: Matsubara Formalism 186
9.1.2 Effective Mass (co-mass) 190
9.2 Relaxation of Giant Vibrations 191
9.3 Non-Perturbative Treatment of Collisions 195
9.3.1 Density-Matrix Formalism 195
9.3.2 The Time-Dependent Density-Matrix Formalism 197
9.3.3 Damping of Giant Vibrations 199