### The Interacting Boson Model (IBM) of the Atomic Nucleus, an Introduction

- Preface
- 1 Introduction
- 2 Characteristics of the IBM
- 3 Many-body configurations
- 3.1 Many-boson states
- 3.2 Symmetric states of two and three
*d*-bosons - 3.3 The seniority scheme, rules defining
*J*

- 4 Many-boson states with undefined angular momentum
- 4.1 two- and three-
*d*-boson states - 4.2 General "primitive" many-boson states

- 4.1 two- and three-
- 5 Operators and matrix elements
- 5.1 Matrix elements of the single-boson operator
- 5.2 Creation and annihilation operators
- 5.3 Single- and two-boson operators represented by creation and annihilation operators

- 6 Applications of the creation and annihilation operators
- 6.1 Many-boson configurations represented by operators
- 6.2 Generating boson pairs with total angular momentum zero
- 6.3 Tensor operators annihilating bosons
- 6.4 Annihilating boson pairs with total angular momentum zero
- 6.5 Number operators for bosons

- 7 The Hamilton operator of the IBM1
- 7.1 The components of the Hamiltonian
- 7.2 The operator of the boson-boson interaction formulated with defined angular momentum
- 7.3 The basic form of the Hamilton operator
- 7.4 The conservation of boson number

- 8 The angular momentum operator of the IBM1
- 8.1 The angular momentum operator in quantum mechanics
- 8.2 The angular momentum operator expressed in terms of
*d*-boson operators - 8.3 The conservation of angular momentum

- 9 The Hamiltonian expressed in terms of Casimir operators
- 10 The
*u*(5)- or vibrational limit- 10.1 The Hamiltonian of the vibrational limit. The spherical basis

10.2 Eigenvalues of the seniority operator

10.3 Energy eigenvalues. Comparison with experimental data

- 10.1 The Hamiltonian of the vibrational limit. The spherical basis
- 11 Electromagnetic transitions in the
*u*(5)-limit- 11.1 Multipole radiation

11.2 The operator of the electromagnetic interaction

11.3 Transition probabilities

11.4 Reduced matrix elements for ∣Δ*n*∣=1_{d}

11.5 Comparison with experimental data of electric quadrupole transitions

11.6 Transitions with ∣Δ*n*∣= 0_{d}

11.7 Configurations with*n*> τ_{d}

11.8 Quadrupole moments

- 11.1 Multipole radiation
- 12 The treatment of the complete Hamiltonian of the IBM1
- 12.1 Eigenstates

12.2 Matrix elements of the Hamiltonian

12.3 Electric quadrupole radiation

12.4 Comparison with experimental data

12.5 An empirical Hamilton operator

- 12.1 Eigenstates
- 13 Lie algebras
- 13.1 Definition

13.2 The*u*(*N*)- and the*su*(*N*)-algebra

13.3 The*so*(*N*) algebra

13.4 Dimensions of three classical algebras

13.5 Operators constituting Lie algebras, their basis functions and their Casimir operators

13.6 Properties of operators

- 13.1 Definition
- 14 Group theoretical aspects of the IBM1
- 14.1 Basis operators of the Lie algebras in the IBM1

14.2 Subalgebras within the IBM1

14.3 The spherical basis as function basis of Lie algebras

14.4 Casimir operators of the*u*(5)- or vibrational limit

14.5 Casimir operators of the*su*(3)- or rotational limit

14.6 Casimir operators of the*so*(6)- or γ -instable limit

- 14.1 Basis operators of the Lie algebras in the IBM1
- 15 The proton-neutron interacting boson model IBM2
- 15.1 The complete Hamiltonian of the IBM2

15.2 Basis states and the angular momentum operator of the IBM2

15.3 A reduced Hamiltonian of the IBM2

15.4 Eigenenergies and electromagnetic transitions within the IBM2

15.5 Comparisons with experimental data

15.6 Chains of Lie algebras in the IBM2

- 15.1 The complete Hamiltonian of the IBM2
- 16 The interacting boson-fermion model IBFM
- 16.1 The Hamiltonian of the IBFM

16.2 The*u*(5)-limit of the IBFM

16.3 Numerical treatment of the IBFM. Comparison with experimental data

- 16.1 The Hamiltonian of the IBFM
- Appendix
- A1 Clebsch-Gordan coefficients and 3-
*j*symbols

A2 Symmetry properties of coupled spin states of identical objects

A3 Racah-coefficients and 6-*j*symbols

A4 The 9-*j*symbol

A5 The Wigner-Eckart theorem

A6 A further multipole representation of the Hamiltonian

A7 The program package PHINT

A8 Commutators of operators such as [*d*^{ +}×*d*^{ ~}]^{(J)}_{M}

A9 The commutator [[*d*^{ +}×*d*^{ ~}]^{(J')}_{M' }, [*d*^{ +}×*d*^{ +}]^{(J)}_{M}]

- A1 Clebsch-Gordan coefficients and 3-
- References
- Index