Covariant Density Functional Study On Low-lying Spectra Of Odd-A Nuclei

The nuclear low-lying spectra, which reflect rich information about nuclear structure including nuclear quantum phase transition, evolution of shell structure, isomeric states as well as shape coexistence etc. have been one of the hot topics in nuclear physics. For even-even nuclei, since they are relatively stable and the pattern of low-lying spectra is comparatively simple, there are amounts of investigations about these nuclei. In the whole nuclide chart, nevertheless, the number of odd-A nuclei is nearly twice as much as the number of even-even nuclei. Along with that, polarization of the even-even core driven by the odd nucleon leads to more complicated pattern of low-lying spectra. The spectroscopic properties and related interesting structures of unstable odd-A nuclei, in particular, have become the hot topics and frontiers of nuclear research.Covariant density functional theory（CDFT） can provide a self-consistent description for the nuclear properties of the whole nuclide chart and has achieved great success in nuclear physics. The framework of static nuclear mean field approximation, however, can only describe ground-state properties of nucleus. To describe the exited spectrum and electromagnetic transition, it becomes necessary to include method of beyond-mean-field effect through the restoration of broken symmetries and taking shape fluctuation into consideration. The CDFT based five-dimensional collective Hamiltonian recently developed has realized the unified and self-consistent description of the spectrum of even-even nuclei. Furthermore, this method has been applied to the study of nuclear quantum phase transition, shape coexistence, octupole deformed nuclei, fission barrier as well as superdeformed bands and so on.In this thesis, we will extend the CDFT based collective Hamiltonian to the study of low-lying spectra of odd-A nuclei, i.e. core-quasiparticle coupling（CQPC） model based on CDFT will be implemented,. Taking the collective states and spherical single particle states of the neighboring even-even nuclei as basis, choosing proper coupling interaction between single particle and core, the core-quasiparticle coupling Hamiltonian can be constructed. Solving the CQPC Hamiltonian, the low-lying and electromagnetic transition of odd-A nuclei can be obtained. Furthermore, the CDFT based CQPC model is applied to the study of low-lying spectra of odd-neutron nucleus ¹⁵⁷Gd and odd-proton nucleus ¹⁵⁹Tb. The theoretical calculations are in good agreement with the experimental data.