Algebraic Solutions Of The Nuclear Pairing Models And The Nucleon-pair Shell Model

In this dissertation,the algebraic approaches to some nuclear pairing models and the nucleon-pair shell model are studied in detail.The spherical mean-field plus standard pairing model and extended monopole pairing model,together with the extended Heine-Stieltjes polynomial approach to the standard pairing model,axe introduced.Binding energies,the even-odd mass differences of 44-54 Ca and 42-52Ar,and the two-neutron separation energies of the even-even nuclei are calculated by using the extended Heine-Stieltjes polynomial approach in the spherical mean-field plus standard pairing model and compared with the experimental data.The results show that the spherical mean-field plus standard pairing model indeed describes the ground state of these near spherical nuclei very well.A spherical mean-field plus extended monopole pairing model is proposed.It is proven that the extended pairing interaction within a deformed mean-field theory is the special case of this model.As the application,binding energies and the even-odd mass differences of 12-28 O are fit,ted by using the model with 11 j-orbits up t.o the fifth major shell,of which the results are compared with those of ab initio calculations of the symmetry-adapted no-core shell model.The reasonably good fitting qualify elucidates the validity of the model.A simple and effective algebraic isospin projection procedure for constructing orthonormal basis vectors of irreducible representations of O(5)(?)OT(3)(?)ON(2)from those in the canonical O(5)(?)SUA(2)(?)SUI(2)basis is outlined.Explicit formulae for evaluating OT(3)-reduced matrix elements of O(5)generators are presented.An extended T = 1 pairing Hamiltonian within the seniority-zero symmetric subspace is proposed based on the standard T = 1 pairing formalism.As an example of the application,the average np-pairing interaction in even-even N~Z nuclei in A = 58-80 mass region are fitted.The shape phase crossover in the SD-pair shell model for like-nucleon sys-tem are investigated.It is shown once again that a few energy ratios of low-lying levels,and several B(E2)and B(M1)values can indeed be used as the order parameters in characterizing the crossover,and the shape phase transitional be-haviors shown in the interacting boson model can indeed be well reproduced by the SD-pair shell model.Finally,the crossover from vibration to γ-unstable shape phase and that from vibration to axially deformed rotational shape phase in the neutron-proton SD-pair shell model are analyzed with the single-particle energies of valence protons and neutrons are taken to be those suitable for describing nu-clei in the = 130 mass region.The results show that the model can reproduce the characters emerging in the vibration,rotation,and γ-unstable shape phases,and the crossover from vibration to γ-unstable shape phase or that from vibration to axially deformed rotational shape phase can be well reproduced with suitable model parameters,which not only elucidates the validity of the model,but also provides with a sound microscopic foundation for the interacting boson model of nuclei.