Table of Contents
1 Building blocks and interactions
1.1. What are the nuclei made of
1.2. Proton and neutron
1.3. Strong interactions
1.4. Electromagnetic interactions and charge distribution
1.5. Magnetic properties
1.6. Weak interactions
1.7. Neutron decay
1.8. Nuclear world
2 Isospin
2.1. Quantum numbers in the two-body problem
2.2. Introducing isospin
2.3. Isospin invariance
2.4. Space-spin symmetry and isospin invariance
2.5. Glimpse of a more general picture
2.6. Relations between cross sections
2.7. Selection rules
2.8. Isobaric mass formulae
3 Two-body dynamics and the deuteron
3.1. Low-energy nuclear forces
3.2. Example: Argonne potential
3.3. Meson exchange
3.4. Deuteron: Central forces and s-wave
3.5. Tensor forces and d-wave
3.6. Magnetic dipole moment
3.7. Electric quadrupole moment
4 Two-body scattering
4.1. Scattering problem
4.2. Phase shifts
4.3. Scattering length
4.4. Sign of the scattering length
4.5. Resonance scattering at low energies
4.6. Effective radius
4.7. Scattering of identical particles
4.8. Coulomb scattering
4.9. Coulomb-nuclear interference
5 Liquid drop model
5.1. Binding energies
5.2. Shape variables
5.3. Microscopic variables
5.4. Multipole moments
5.5. Kinetic energy and inertial parameters
5.6. Shape vibrations
5.7. Stability of the charged spherical liquid drop
6 Vibrations of a spherical nucleus
6.1. Sound waves
6.2. Isovector modes
6.3. Giant resonance and linear response
6.4. Classification of normal modes
6.5. Quantization of nuclear vibrational modes
6.6. Multiphonon excitations
6.7. Angular momentum classification
7 Fermi gas model
7.1. Mean field and quasiparticles
7.2. Perfect Fermi gas
7.3. Ground state
7.4. Correlation between particles
7.5. Asymmetric systems and chemical equilibrium
7.6. Pressure and speed of sound
7.7. Gravitational equilibrium.
8 Spherical mean field
8.1. Introduction
8.2. Magic numbers
8.3. Separation energy
8.4. Periodicity of nuclear spectra
8.5. Harmonic oscillator potential
8.6. Orbital momentum representation
8.7. Square well potential
8.8. Spin-orbit coupling
8.9. Realistic level scheme
8.10. Semiclassical origins of shell structure
9 Independent particle shell model
9.1. Shell model configurations
9.2. Particle-hole symmetry
9.3. Magnetic moment
9.4. Quadrupole moment
9.5. Recoil corrections
9.6. Introduction to group theory of multi-particle configurations
10 Light nuclei
10.1. A short walk along the beginning of the nuclear chart
10.2. Halo in quantum systems
10.3. Nuclear halos
10.4. One-body halos
10.5. Two-body halos
10.6. Efimov states
11 Many-body operator formalism
11.1 Secondary quantization
11.2. Physical observables: one-body operators
11.3. Two-body operators
11.4. Interparticle interaction
11.5. Interaction in a spherical basis.
11.6. Recoupling of angular momentum
12 Nuclear deformation
12.1. Idea of nuclear deformation
12.2. Collective model
12.3. Adiabatic approximation
12.4. Onset of deformation
12.5. Quadrupole deformation in the body-fixed frame
12.6. Quadrupole shape variables
12.7. Variety of quadrupole shapes
12.8. Empirical deformation
12.9. Single-particle quantum numbers
12.10. Anisotropic harmonic oscillator
12.11. Asymptotic quantum numbers
12.12. Nilsson potential
12.13. More examples
13 Pairing correlations
13.1. Physical evidence
13.2. Seniority scheme
13.3. Multipole moments in the seniority scheme
13.4. Degenerate model
13.5. Canonical transformation
13.6. BCS theory: Trial wave function
13.7. Energy minimization
13.8. Solution for the energy gap
13.9. Excitation spectrum
13.10. Condensation energy
13.11. Transition amplitudes
14 Gamma-radiation
14.1. Introduction
14.2. Electromagnetic field and gauge invariance
14.3. Photons
14.4. Interaction of radiation with matter
14.5. Radiation probability
14.6. Electric dipole radiation
14.7. Electric quadrupole radiation
14.8. Magnetic dipole radiation
14.9. Photoabsorption
14.10. Multipole expansion
15 Nuclear gamma-transitions
15.1. Single-particle transitions
15.2. Collective transitions
15.3. Nuclear isomerism
15.4. Isospin
15.5. Structural selection rules
15.6. Monopole transitions
15.7. Internal electron conversion
15.8. Coulomb excitation
15.9. Nuclear photoeffect
15.10. Electron scattering
16 Nuclear rotation
16.1. Introduction: rotational bands
16.2. Finite rotations
16.3. Rotation matrices as functions on the group
16.4. Euler angles
16.5. Angular momentum in Euler angles
16.6. Eigenfunctions of angular momentum
16.7. Rigid rotor
16.8. Symmetry properties
16.9. Simplest solutions
16.10. Ground state band
16.11. Intensity rules
16.12. Electric quadrupole moment
16.13. Magnetic moment
16.14. Symmetry properties revisited
16.15. Coriolis mixing and decoupling parameter
16.16. Classical rotation and Routhian
16.17. Cranked rotation
16.18. Moment of inertia
16.19. Adiabatic expansion
16.20. Rotation of a perfect Fermi gas
16.21. Perfect Bose gas and ideal liquid
16.22. Pairing effects
16.23. Band crossing
17 Self-consistent field
17.1. Exchange interaction
17.2. Hartree-Fock equations
17.3. Operator formulation
17.4. Single-particle density matrix
17.5. Hartree-Fock-Bogoliubov approximation
17.6. General canonical transformation
17.7. Solutions
17.8. Generalized density matrix
17.9. Pairing and particle number conservation
17.10. Effective interaction
17.11. Skyrme functionals
17.12. Generalization
to non-zero temperature
18 Collective modes
18.1. Schematic model
18.2. Random phase approximation
18.3. Canonical form of the RPA
18.4. Model with factorized forces
18.5. Collective modes as bosons
18.6. Mapping of dynamics
18.7. Normalization and the mass parameter
18.8. Symmetry breaking
18.9. Generator coordinate method
19 Bosons, symmetries and group models
19.1. Introduction
19.2. Low-lying quadrupole excitations as interacting bosons
19.3. Algebra of boson operators
19.4. Subgroups and Casimir operators
19.5. s-d model
19.6.Irreducible representations and quantum numbers
19.7. Vibrational limit
19.8. O(6) limit
19.9. SU(3) limit
19.10. Shapes and phase transitions in IBM
20 Statistical properties
20.1. Introduction
20.2. Level density: general properties
20.3. Darwin-Fowler method
20.4. Relation to statistical thermodynamics
20.5. Thermodynamics of a nuclear Fermi gas.
20.6. Statistics of angular momentum
20.7. Shell Model Monte Carlo approach
20.8. Thermodynamics of compound reactions
20.9. Statistical description of resonances
21 Nuclear fission
21.1. Introduction
21.2. Alpha-decay
21.3. Neutron fission
21.4. Photofission
21.5. Fission as a large-amplitude collective motion
21.6. Non-adiabatic effects and dissipation
21.7. Fission isomers
21.8. Parity violation in fission
22 Heavy ion reactions: Selected topics
22.1. Introduction
22.2. Experimental indications
22.3. Macroscopic description
22.4. Equilibration as a diffusion process
22.5. Towards a microscopic description
22.6. Sketch of a more general approach
22.7. A simple model
22.8. Nuclear multifragmentation
22.9. More about fusion reactions
23 Configuration interaction approach
23.1. Center-of-mass problem
23.2. Matrix elements of two-body interactions
23.3. Ab-initio approach
23.4. Three-body forces
23.5. Semiempirical effective interactions
23.6. Hamiltonian matrix, properties and solutions
23.7. Effective non-Hermitian Hamiltonian
23.8. Realistic nuclear calculations
24 Weak interactions
24.1. Introduction
24.2. Beta spectrum in the simplest case
24.3. Nuclear transitions
24.4. Dirac formalism
24.5. Four-fermion theory
24.6. Nuclear structure effects
24.7. Parity violation
24.8. Electric dipole moment
24.9. Nuclear enhancement
24.10. On the way to electroweak theory
24.11. Higgs mechanism
24.12. Neutrino: oscillations
24.13. Neutrino: Majorana or Dirac?
25 Nucleus as chaotic system
25.1. Introduction
25.2. Strength function
25.3. Level density revisited
25.4. Complexity of wave functions
25.5. Correlations between classes of states
25.6. Invariant entropy
25.7. Random matrix ensembles
25.8. Thermalization