The Progressive Diagonalization Method And The Application Of The Nucleon-pair Shell Model

In this thesis,the progressive diagonalization method(PDM)for solving quan-tum many-body problems is outlined,and applied to the nuclear pairing model and the Dicke Model in description of a photon field interacting with N two-level atoms.Moreover,the nucleon-pair shell model(NPSM)is applied to describe 132-138Ce,130-136Ba,and 128-134Xe isotopes.Firstly,the PDM is introduced based on the algebraic Bethe Ansatz method.To illustrate the process of the PDM,the nuclear deformed mean-field plus pairing model is taken as an example.Then,the PDM is applied to the Dicke Model.Calculated results of ground-state energy,the photon number,the atomic inversion,and their fluctuations of the latter two quantities,entanglement measure,and the Shanon information entropy for finite N cases as functions of the coupling parameter are provided.The outcomes show that there are significant changes in the photon number,the atomic inversion,and their fluctuations near the critical point where the entanglement measure reaches its maximum value.Level statistics of the Dicke Model for finite N cases is investigated.The particle number statis-tics,the entanglement measure,and the Shannon information entropy at the resonance point as functions of the coupling parameter are calculated.It is shown that the entanglement measure based on the Von Neumann entropy reaches its maximum at the critical point of the quantum phase transition where the system is most chaotic.Noticeable change in the Shannon information entropy near or at the critical point of the quantum phase transition is also observed.In addition,the quantum phase transition may be observed in fluctuations of the ground state mean photon number and the atomic inversion.Finally,a three-parameter Hamiltonian of the NPSM truncated to an SD subspace is applied to describe typical 7-unstable nuclei 132-138Ce,130-136Ba,128-134Xe.The low-lying spectra,excited states,and the electromagnetic transition strengths of these nuclei are calculated and analyzed.The results show good agreement of the model calculations to the experimental data,which also indicates that the SD-pair approximation becomes better with the increasing of the number of pairs.