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
- 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
- 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 ∣Δnd∣=1
11.5 Comparison with experimental data of electric quadrupole transitions
11.6 Transitions with ∣Δnd∣= 0
11.7 Configurations with nd > τ
11.8 Quadrupole moments
- 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
- 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
- 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
- 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
- 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
- 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]
- References
- Index
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