Symmetries in Atomic Nuclei: From Isospin to Supersymmetry

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 

1.2.4 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 

3.2 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

6.4.4 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

7.3.6 Three-dimensional supersymmetric quantum mechanics in atoms

8 Conclusion 

References