Symmetries in Atomic Nuclei: From Isospin to Supersymmetry

ISBN-13: 9783030219338 / Angielski / Miękka / 2020 / 209 str.

Alejandro Frank; Jan Jolie;Pieter Van Isacker

Opis

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 boson-fermion degrees of freedom. Their 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. This book 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.

Spis treści

1 Symmetry and Supersymmetry in Quantal Many-Body Systems

1.1 Symmetry in quantum mechanics

1.1.1 Some definitions

1.1.2 Symmetry transformations

1.1.3 Symmetry

1.1.4 Degeneracy and state labelling

1.1.5 Dynamical symmetry breaking

1.1.6 Isospin in nuclei 

1.1.7 Selection rules 

1.2 Dynamical symmetries in quantal many-body systems

1.2.1 Many-particle states in second quantization

1.2.2 Particle-number conserving dynamical algebras 

1.2.3 Particle-number non-conserving dynamical algebras

1.2.4 Superalgebras

1.3 The algebraic approach

 

2. Symmetry in Nuclear Physics : The  nuclear shell model 

2.1 The nuclear shell model

2.2 The SU(2) pairing model

2.3 Seniority conservation in a single-j shell 

2.4 The SU(3) rotation model 

2.5 A symmetry triangle for the shell model

2.6 A case study:  Seniority isomers in semi-magic nuclei 

3. Symmetry in Nuclear Physics: The interacting boson model 

3.1 Dynamical symmetries 

3.2 Geometry

3.3 Core excitations

3.4 Partial dynamical symmetries 

3.5 A case study: 112Cd

3.5.1 Early evidence for vibrational structures and intruder configurations

3.5.2 The 110Pd(\alpha

,2n)112Cd reaction and its interpretation

3.5.3 Studies of 112Cd using the (n,n´) reaction 

4 Supersymmetry in Nuclear Physics

4.1 The interacting boson-fermion model

4.2 Bose-Fermi symmetries

4.3 Examples of Bose-Fermi symmetries

4.4 Nuclear supersymmetry

4.5 A case study: Detailed spectroscopy of 195Pt

4.5.1 Early studies of 195Pt

4.5.2 High-resolution transfer studies using (p,d) and (d,t) reactions

4.6 Supersymmetry without dynamical symmetry

 

5 Symmetries with Neutrons and Protons

5.1 Pairing models with neutrons and protons

5.2 Interacting boson models with neutrons and protons

5.2.1 s bosons only

5.2.2 s and d bosons

5.3 The interacting boson model-2

5.4 A case study: Mixed-symmetry states in 94Mo

5.4.1 The discovery of mixed-symmetry states in deformed nuclei

5.4.2 Mixed-symmetry states in near-spherical nuclei

5.4.3 Mixed-symmetry states in 94Mo

 

6 Supersymmetries with Neutrons and Protons

6.1 Combination of F spin and supersymmetry

6.2 Examples of extended supersymmetries 

6.3 One-nucleon transfer in extended supersymmetry

6.4 A case study: Structure of 196Au

6.4.1 First transfer-reaction experiments

6.4.2 New experiments at the PSI, the Bonn cyclotron and the Munchen Q3D spectrometer

6.4.3 Recent high-resolution and polarized-transfer experiments

6.4.4 Comparison with theory

6.4.5 Two-nucleon transfer reactions

 

7 Supersymmetry and Supersymmetric Quantum Mechanics

7.1 The supersymmetric standard model 

7.2 Strings and superstrings 

7.3 Supersymmetric quantum mechanics

7.3.1 Potentials related by supersymmetry

7.3.2 The infinite square-well potential

7.3.3 Scattering off supersymmetric partner potentials

7.3.4 Long-range nucleon-nucleon forces and supersymmetry

7.3.5 Matrix approach to supersymmetric quantum mechanics

7.3.6 Three-dimensional supersymmetric quantum mechanics in atoms

8 Conclusion 

 

References

O autorze

Jan Jolie is Professor at the Institute of Nuclear Physics, University of Cologne. He performed several crucial experiments to test the applications of supersymmetry in atomic nuclei. For this work he was awarded the Leigh-Page Prize 2000 by Yale University.

Alejandro Frank is a Fellow of the American Physical Society and has received several distinctions including a Guggenheim Fellowship. He was head of the Department of Structure of Matter in the Institute of Nuclear Sciences of the National Autonomous University of Mexico (UNAM).  On March 3, 2016, he entered as a member of El Colegio Nacional, the highest academic institution in Mexico.

Piet van Isacker is a member of the Mexican Academy of Science and has written two previous books on the application of symmetry methods to nuclear physics.

Blurb

The revised edition of this established work presents an extended overview of recent applications of symmetry to the description of atomic nuclei, including a pedagogical introduction to symmetry concepts using simple examples. Following a historical overview of the applications of symmetry in nuclear physics, attention turns to more recent progress in the field. Special emphasis is placed on the introduction of neutron-proton and boson-fermion degrees of freedom. Their combination leads to a supersymmetric description of pairs and quartets of nuclei.

Expanded and updated throughout, the book now features separate chapters on the nuclear shell model and the interacting boson model, the former including discussion of recent results on seniority in a single-j shell. Both theoretical aspects and experimental signatures of dynamical (super)symmetries are carefully discussed.  

This book focuses on nuclear structure physics, but its broad scope makes it suitable for final-year or post-graduate students and researchers interested in understanding the power and beauty of symmetry methods in physics.

Review of the 1st Edition:

"The subject of this book, symmetries in physical systems, with particular focus on atomic nuclei, is of the utmost importance in modern physical science. In contrast to most treatments, frequently characterized by fearsome formalism, this book leads the reader step-by-step, in an easily understandable way, through this fascinating field...this book is remarkably accessible to both theorists and experimentalists. Indeed, I view it as essential reading for experimental nuclear structure physicists. This is one of the finest volumes on this subject I have ever encountered."

Prof. R.F. Casten, Yale University