Symmetries in atomic nuclei : from isospin to supersymmetry / A. Frank, J. Jolie, P. Van Isacker.

Format:

Book

Author/Creator:

Frank, A. (Alejandro)

Contributor:

Jolie, J. (Jan)

Van Isacker, P.

Series:

Springer tracts in modern physics ; 230.

Springer tracts in modern physics, 1615-0430 ; v. 230

Language:

English

Subjects (All):

Nuclear physics.

Supersymmetry.

Physical Description:

xiii, 185 pages : illustrations ; 25 cm.

Place of Publication:

New York : Springer, [2009]

Summary:

Symmetries in Atomic Nuclei aims to present an overview of recent applications of symmetry to the description of atomic nuclei. Special care is given to a pedagogical introduction of symmetry concepts using simple examples. After a historical overview of the applications of symmetry in nuclear physics, progress in the field during the last decade is reviewed. Special emphasis is put on the introduction of neutron-proton and bosonfermion degrees of freedom. The combination leads to a supersymmetric description of pairs and quartets of nuclei.

Both theoretical aspects and experimental signatures of dynamical (super) symmetries are carefully discussed. Case studies show how these symmetries are displayed by real atomic nuclei which have been studied experimentally using state-of-the art spectroscopy.

Symmetries in Atomic Nuclei focuses on nuclear structure physics and has been written by active investigators in the field, but its scope is wider and is intended for final-year or post-graduate students and researchers interested in understanding the power and beauty of symmetry methods in physics.

Contents:

1 Symmetry and Supersymmetry in Quantal Many-Body Systems 1

1.1 Symmetry in Quantum Mechanics 2

1.1.2 Symmetry Transformations 4

1.1.3 Symmetry 5

1.1.4 Degeneracy and State Labeling 6

1.1.5 Dynamical Symmetry Breaking 7

1.1.6 Isospin in Nuclei 8

1.1.7 Selection Rules 16

1.2 Dynamical Symmetries in Quantal Many-Body Systems 18

1.2.1 Many-Particle States in Second Quantization 18

1.2.2 Particle-Number Conserving Dynamical Algebras 19

1.2.3 Particle-Number Non-conserving Dynamical Algebras 22

1.2.4 Superalgebras 24

1.3 The Algebraic Approach 26

2 Symmetry in Nuclear Physics 29

2.1 The Nuclear Shell Model 29

2.1.1 The SU(2) Pairing Model 31

2.1.2 The SU(3) Rotation Model 39

2.1.3 A Symmetry Triangle for the Shell Model 50

2.2 The Interacting Boson Model 51

2.2.1 Dynamical Symmetries 54

2.2.2 Geometry 57

2.2.3 Partial Dynamical Symmetries 64

2.2.4 Core Excitations 69

2.3 A Case Study: [superscript 112]Cd 71

2.3.1 Early Evidence for Vibrational Structures and Intruder Configurations 71

2.3.2 The [superscript 110]Pd([alpha],2n[gamma])[superscript 112]Cd Reaction and its Interpretation 71

2.3.3 Studies of [superscript 112]Cd Using the (n,n'[gamma]) Reaction 75

3 Supersymmetry in Nuclear Physics 79

3.1 The Interacting Boson-Fermion Model 80

3.2 Bose-Fermi Symmetries 82

3.3 Examples of Bose-Fermi Symmetries 84

3.4 Nuclear Supersymmetry 87

3.5 A Case Study: Detailed Spectroscopy of [superscript 195]Pt 89

3.5.1 Early Studies of [superscript 195]Pt 90

3.5.2 High-Resolution Transfer Studies Using (p,d) and (d,t) Reactions 93

3.6 Supersymmetry without Dynamical Symmetry 98

4 Symmetries with Neutrons and Protons 105

4.1 Pairing Models with Neutrons and Protons 106

4.2 Interacting Boson Models with Neutrons and Protons 111

4.2.1 s Bosons Only 112

4.2.2 s and d Bosons 114

4.3 The Interacting Boson Model-2 117

4.4 A Case Study: Mixed-Symmetry States in [superscript 94]Mo 123

4.4.1 The Discovery of Mixed-Symmetry States in Deformed Nuclei 123

4.4.2 Mixed-Symmetry States in Near-Spherical Nuclei 124

4.4.3 Mixed-Symmetry States in [superscript 94]Mo 125

5 Supersymmetries with Neutrons and Protons 133

5.1 Combination of F Spin and Supersymmetry 133

5.2 Examples of Extended Supersymmetries 136

5.3 One-Nucleon Transfer in Extended Supersymmetry 138

5.4 A Case Study: Structure of [superscript 196]Au 141

5.4.1 First Transfer Reaction Experiments 141

5.4.2 New Experiments at the PSI, the Bonn Cyclotron and the Munchen Q3D Spectrometer 143

5.4.3 Recent High-Resolution and Polarized-Transfer Experiments 147

5.4.4 Comparison with Theory 148

5.4.5 Two-Nucleon-Transfer Reactions 150

6 Supersymmetry and Supersymmetric Quantum Mechanics 155

6.1 The Supersymmetric Standard Model 155

6.2 Strings and Superstrings 156

6.3 Supersymmetric Quantum Mechanics 158

6.3.1 Potentials Related by Supersymmetry 159

6.3.2 The Infinite Square-Well Potential 161

6.3.3 Scattering Off Supersymmetric Partner Potentials 162

6.3.4 Long-Range Nucleon-Nucleon Forces and Supersymmetry 164

6.3.5 Matrix Approach to Supersymmetric Quantum Mchanics 167

6.3.6 Three-Dimensional Supersymmetric Quantum Mechanics in Atoms 168.

Notes:

Includes bibliographical references and index.

ISBN:

9780387874944

0387874941

038787495X

9780387874951

OCLC:

248979326