Super-allowed β Decays And The Shape Coexistence Phenomena In Kr Isotopes With Point-coupling Covariant Density Functional

With the development of the new generation radioactive-beam facilities and detectors, more and more exotic nuclei far from theβ-stability line have been produced. In these nuclei, there present a lot of new physical phenomena, such as neutron halo, electronic dipole pygmy resonance, erosion of traditional magic numbers and appearance of new magic numbers. Thus, the study of exotic nuclei has become the frontier of nuclear physics. In recent years, many attentions have been paid to study the super-allowedβdecay and shape coexistence phonomenon, which provide rich information about iso-spin symmetry-breaking effects and exotic structure in atomic nuclei respectively.The covariant density functional theory has achieved a great success in the description for the ground-state properties of nuclei throughout the nuclear chart and has been one of the most important microscopical methods to systematically study the structure peoterties of medium-heavy and heavy nuclei. Particularly, the point-coupling covariant density functional has attracted more and more interests in recent years. To describe the properties of nuclear excited states, it is necessary to go beyond mean field approximation by employing Random Phase Approximation (RPA) or angular momentum projected Generator Coordinator Method (AMPGCM). Recently, the methods of RPA and AMPGCM based on the point-coupling covariant density functional have been successfully developed. These two methods have turned out to be successful in the studies of nuclear collective excitation with a small amplitude and nuclear collective motion with a large amplitude respectively.In this thesis, based on the point-coupling covariant density functional, two works concerning the above topics have been carried out. (1) The iso-spin symmetry-breaking corrections of 0+→0+ suple-allowedβdecays have been calculated with the charge-exchanged RPA. The unitarity of the Cabibbo-Kobayashi-Maskawa matrix in the standard model has been examined. (2) The shape coexistence phenomena in neutron-deficient 72,74,76,78Kr have been studied with the one-dimensional AMPGCM. Taking 74Kr for an example, the triaxiality effect has been studied with five-dimensional collective Bohr Hamiltonian.