Robustness Of Pair Structures For Nuclear Low-lying States

Atomic nuclei are complex quantum many-body systems composed of protons and neutrons.The nuclear shell model considers all correlations among valence nucleons,and is the fundamental theoretical model for nuclear low-lying states.The study on nuclear deformation and collectivity within the framework of the shell model is an important topic in nuclear structure.However,when it comes to deformed nuclei and transitional nuclei in middle-heavy and heavy regions,corresponding shell-model configuration spaces are too gigantic to handle.Pair truncation is a natural and efficient strategy to truncate shell-model configuration spaces.In the validity of pair truncations the optimization of structures of collective pairs is of great importance.Yet,one fundamental question whether or not the structures of relevant collective pairs are robust with respect to different low-lying states,has not been studied in a rigorous manner before.In this thesis,with the nucleon-pair approximation(NPA)and shell-model(realistic)effective interactions,we study yrast states of the deformed nuclei 28Si and 50Cr,as well as those of the transitional nucleus 132Xe,to study the robustness of pair structures along the yrast lines of deformed nuclei and transitional nuclei.Here,for each yrast state,a great number of full NPA calculations with varying pair structures are performed to find the energy minimum of this state and corresponding optimized pair structures,and the numerical optimization recipe of the conjugate gradient method is implemented.Our results suggest that optimized pair structures remain the same for all the states within a rotational band of a deformed nucleus.Our results also suggest that after the backbending,i.e.,the change of the intrinsic state,the structure of the S pair which is essential to build up the monopole pairing correlation still remains unchanged approximately,while the structures of the non-S D and G pairs which are essential to build up the quadrupole correlation change significantly.For the transitional nucleus 132Xe,a low-lying state is expected to be a mixture of spherical configurations and deformed ones,and the pattern in regards to the robustness of pair structures is consistent with the one for deformed nuclei and the one for spherical nuclei.