Studies Of Nuclei Shape Evolution And Octupole Vibration With Point-coupling Covariant Density Functional

Nuclear shapes and corresponding low-lying collective excitation modes are much related to the microscopic structures of atomic nuclei, and are therefore one of the most important subjects in the research of nuclear physics. In particular, the evolution of nuclear shape against isospin value reflects the change in single-particle shell structure, and becomes a hot topic in the study of nuclear structure physics. In recent years, the nuclear covariant density functional theory (DFT) combined with projected generator coordinate methods or collective Hamiltonian has been successfully applied to study the evolution of shell structure and shape of nuclei in different mass regions.In this thesis, the phenomena of shape evolution and shape coexistence in neutron-rich nuclei at N≈60, including Kr, Sr, Zr, and Mo isotopes are studied in the covariant DFT with the new parameter set PC-PK1. Pairing correlations are treated using the BCS approximation with a separable pairing force. Sharp rising in the charge radii of Sr and Zr isotopes at N=60 is observed and shown to be related to the rapid change in nuclear shapes. The shape evolution is moderate in neighboring Kr and Mo isotopes. Similar as the results of previous Hartree-Fock-Bogogliubov (HFB) calculations with the Gogny force, triaxiality is observed in Mo isotopes and shown to be essential to reproduce quantitatively the corresponding charge radii.In addition, the coexistence of prolate and oblate shapes is found in both98Sr and 100Zr. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi surfaces of neutron and proton respectively. Furthermore, the 5-dimensional collective Hamiltonian (5DCH) determined by the calculations of the PC-PK1 energy functional is solved for 98Sr and 100Zr. The resultant excitation energy of 02+ state and E0 transition strengthρ2(E0;02+�'01+) are in rather good agreement with the data. It is found that the lower barrier height separating the two competing minima along the y deformation in 100 Zr gives rise to the largerρ2(E0; 02+�'01+) than that in 98Sr.Compared with quadrupole deformation, nuclear octupole deformation has smaller contribution to binding energy for most atomic nuclei. However, it is responsible for nuclear collective excited states with negative parity and plays an important role in analysis of nuclear spectroscopic properties. Therefore, a 2D collective Hamiltonian including quadrupole and octupole vibrations based on a reflection asymmetry relativistic mean field is established to study nuclear low-lying octupole vibration states.