The Application Of Nuclear Shell Model For Large-scale Calculations In Neutron-rich Nuclei

Thanks to the development of experimental technology，a number of experiment data havebeen accumulated for the neutron-rich nuclei mass region in the recent years, which creates a goodcondition for the people to study the characteristic of nuclear force away from the β-decay stableline. With the help of computer technology, applying shell model in nuclear systems for large-scalecalculations under a quite large model space is an important method in nuclear physics research. Inthis thesis, we mainly make use of large-scale shell-model calculation programs to do the structureresearches for the mid-heavy neutron-rich mass regions through the extended paring force plusmultipole force plus monopole correction model(EPQQM model).Firstly, this thesis briefly introduces the basic ideas of large-scale shell-model calculation,M-scheme and J-scheme two approaches for constructing basic vectors, the Lanczos method forthe diagonalization process when solving the eigenvalue and the common ways to determine theeffective interaction for the system under a given model space. We focus on discussing how to getthe residual two-body matrix elements for the EPQQM model. Based on EPQQM model, we carryout our works as follow:In the mass region of132Sn, we determine a new effective interaction using EPQQM mod-el and perform large-scale shell-model calculations for the neutron-rich nuclei with a few nu-cleons beyond132Sn. This interaction provides a systematical description for energy levels ofA=133135nuclei from low spins up to high-spin core-excitation states and reproduces avail-able experiment data of electromagnetic transitions. The calculations show the existence of hex-adecupole correlation in addition to octupole correlation in this mass region.By modifying the existing EPQQM interaction parameters, we do the large-scale shell-modelcalculations for the neutron-rich5762Mn isotopes within the fpg9/2model space. We systemat-ically calculate the energy levels of both positive and negative parities up to J=27/2for theodd-mass57,59,61Mn and J=16for the odd-odd58,60,62Mn. The importance of neutron g9/2ex-citations is emphasized for the energy spectrums of these nuclei. The investigation for the rotationbands of negative parity in58,60,62Mn highlights that the g9/2excitations are the main contributionfor the onset of collectivity in this neutron-rich mass region. The monopole interaction can influence the effective single-particle energies of the neutron-rich systems, which leads to the shell evolutions and change the structures of the system. Underthe frame of EPQQM model, we discuss the effects of monopole interaction to the shell evolu-tions and structures for the neutron-rich nuclei. As two examples, we find the signature inversionsof neutron-rich58,60Mn and the rigid triaxial deformation of76Ge are sensitive to monopole cor-rections, which demonstrates the roles the monopole corrections of EPQQM model play in thelarge-scale calculations of neutron-rich nuclei.The researches in this thesis show that the effective interaction derived from EPQQM modelis a valid method for the large-scale shell-model calculations in neutron-rich nuclei. By meansof this kind of effective interaction, we can explain the exotic structures of neutron-rich nucleiexperimentally and give the prediction well. The present researches are closely related to thenuclear structure experiments in neutron-rich mass regions ongoing internationally. They are alsosignificant to the understanding of the nuclear force under extreme condition and the researchesfor elements abundances in r process of nuclear astrophysics.