Energy Density Functional Description Of Low-Lying Spectra In Octupole Deformed Nuclei

As a quantum system, properties of octupole deformed nuclei have received much attention. Particularly, studying on the octupole deformed nuclei quantum phase transition, shape coexistence and shape evolution within low-lying spectrum has become one of the frontier areas of research in nuclear physics.The Covariant Energy Density Functional (CEDF) theory has achieved great success in the description of nuclear structure over almost the whole nuclide chart. In general, the framework based on the static nuclear mean field approximation can only describe ground-state properties. Excitation spectra and electromagnetic transition probabilities can only be calculated by including correlations beyond the static mean field through the restoration of rotational symmetries, parity symmetries and configuration mixing of symmetry-breaking product states. One effective approach is to construct a collective Hamiltonian with deformation dependent parameters determined from microscopic self-consistent mean-field calculations. By solving the collective Hamiltonian provides great description of low-energy excitation structure, which can be used over almost the whole nuclide chart.In this thesis, we have constructed the microscopic Quandrupole-Octupole collective Hamiltonian (QOCH) based on the covariant energy density functional and developed the corresponding Fortran code. The QOCH model is composed of three steps:1)The entire map of the energy surface as a function of the quadrupole and octupole deformation is obtained by imposing constraints on the axial mass quadrupole and octupole moments. The single-nucleon wave function, energy, and occupation factor at each deformed point provide the microscopic input for the parameters of the collective Hamiltonian.2) Nuclear microscopic collective potential and inertia parameters are calculated in the cranking approximation, and then one can obtain the collective Hamiltonian.3) By solving the collective Hamiltonian, one can yield the energy spectrum and the corresponding collective wave functions, from which various observables can be calculated and compared with experimental results.The QOCH model has been applied to study the following problems: 1) Studying on the low-energy excitation structure of Ra. The excited energies and electromagnetic transition rates of low-energy excitation states have been reproduced very well; 2) Systematic investigation of the low-energy excitation structure and shape evolution of even-even Ra isotopes.