Развитие алгебраической теории коллективных движений атомных ядер Ганев Хубен Ганев

Краткое описание

Ганев, Хубен Ганев.
Развитие алгебраической теории коллективных движений атомных ядер = Development of an algebraic theory of the collective motions in atomic nuclei : Development of an algebraic theory of the collective motions in atomic nuclei : диссертация ... доктора физико-математических наук : 01.04.16 / Ganev Huben Ganev; [Место защиты: Объединенный институт ядерных исследований]. - Дубна, 2020. - 281 с. : ил.
Оглавление диссертациидоктор наук Ганев Хубен Ганев
Contents
1 Introduction
1.1 Actuality of the problem
1.2 The aim and tasks
1.3 Scientific novelty
1.4 Scientific and practical significance of the obtained results
1.5 Method
1.6 Approbation
1.7 Publications
1.8 Structure of the dissertation
1 The phenomenological approach
2 The Interacting Vector Boson Model
2.1 The building blocks
2.2 The algebraic structure
2.2.1 The Up(3) 0 Un(3) chain
2.2.2 The SU(3) 0 UT(2) chain
2.2.3 The O±(6) chain
2.2.4 The U(3, 3) chain
2.2.5 The model Hamiltonian
2.2.6 The dynamical symmetries of the IVBM
3 The unitary dynamical symmetry limit
3.1 Dynamical symmetry
3.1.1 The Basis
3.1.2 The Hamiltonian
3.1.3 Tensor operators
3.1.4 Matrix elements
3.2 Application
3.2.1 Energy spectra
3.2.2 Energy staggering
3.2.3 Transition probabilities
4 Geometrical structure of the IVBM
4.1 Shape structure
4.1.1 The Up(3) 0 Un(3) limit
4.1.2 The 0(6) limit
4.1.3 The SU(3) 0 Ut(2) limit
4.2 The generalized IVBM Hamiltonian and its phase diagram
5 Triaxial shapes in the IVBM
5.1 The shape of the SU*(3) limit
5.2 Perturbation of the SU*(3) dynamical symmetry
5.2.1 The Majorana perturbation
5.2.2 Phase transition between O(6) and SU*(3) limits
5.3 The energy surfaces of real nuclei
5.4 Angular momentum projected energy surfaces
6 The U(3, 3) dynamical symmetry limit
6.1 Dynamical symmetry
6.1.1 The Basis
6.1.2 The Hamiltonian
6.1.3 Tensor operators
6.1.4 Matrix elements
6.2 Application
6.2.1 Energy spectra
6.2.2 The energy staggering
6.2.3 Transition probabilities
7 The orthosymplectic extension of the IVBM
7.1 Fermion degrees of freedom
7.1.1 Fermion dynamical symmetries
7.1.2 Bose-Fermi symmetry
7.2 Dynamical supersymmetry
7.2.1 The Basis
7.2.2 The Hamiltonian
7.3 Odd mass nuclei
7.3.1 The even-even core
7.3.2 Energy spectra
7.3.3 Transition probabilities
7.4 Simultaneous description of even-even, odd-mass and doubly odd nuclei
8 Chiral doublet bands
8.1 The even-even core
8.2 The energy spectra of odd-mass and odd-odd nuclei
8.3 Electromagnetic transitions
8.3.1 E2 transitions
8.3.2 M1 transitions
8.3.3 Numerical results
8.4 The B(M1) staggering
II The microscopic shell-model approach
9 The Proton-Neutron Symplectic Model
9.1 The symplectic geometry
9.2 The dynamical content. Motion groups
9.3 The collective and intrinsic coordinates
9.4 The physical meaning of the collective variables
9.5 The wave functions
9.5.1 The collective wave functions
9.5.2 The intrinsic wave functions
9.5.3 The permutational symmetry
9.5.4 The spin part
9.6 The GCM(6) model
9.7 Shell-model representations of the proton-neutron symplectic model
9.7.1 The shell-model classification of nuclear collective states
9.7.2 Determination of the symplectic bandhead
9.8 Structure of the model Hamiltonian and many-particle Hilbert space
10 Many-particle limits of the PNSM
10.1 Contraction of the Sp(12,R) Algebra
10.2 The U(6)-Phonon Model
10.3 The Coupled Two-Rotor Model
11 The PNSM matrix elements
11.1 Some U(u1 + u2) D U(u) ® U(u2) isoscalar factors
11.1.1 Two-component boson system
11.1.2 The method of calculation
11.2 Tensorial properties of the Sp(12,R) generators
11.3 Matrix elements of the Sp(12,R) generators
11.4 Matrix elements of the collective potential
12 Structure of the low-lying positive-parity states
12.1 The model Hamiltonian
12.2 Application to 166Er
12.3 Application to 154Sm
12.4 Application to 238U
13 Structure of the low-lying negative-parity states
13.1 The model Hamiltonian
13.2 Application to 154Sm....................................................................23б
13.2.1 The energy spectra
13.2.2 The energy staggering
13.2.3 Transition probabilities
13.3 Application to 238U
13.3.1 The energy spectra
13.3.2 The energy staggering
13.4 The E1 transitions in the extended proton-neutron symplectic model
13.4.1 The PNSM collective observables
13.4.2 The wsp(12,R) algebra and its representations
13.4.3 Matrix elements of the dipole operator
13.4.4 Comparison of the B(E1) transition strengths with experiment for 154Sm
and 238U
14 Summary and conclusions 2бб
14.1 Main results of the dissertation
14.2 List of scientific publications on which the dissertation is based ......................2б0