Reaserch Of Relativistic Symmetry In Nucleus By The Similarity Renormalization Group

Relativistic symmetries play important roles in the shell structure and its evolution. However, the origin of the symmetries and the corresponding breaking mechanism are still unclear up to now. In this thesis, we apply the similarity renormalization group into the covariant density functional theory and transform the Dirac Hamiltonian into a diagonal form by using continuous unitary transformation. By using the operator, we explore the origin and breaking mechanism of the symmetries, which include(1) the origin and breaking mechanism of the relativistic symmetries for spherical nuclei. We apply the similarity renormalization group into the covariant density functional theory describing the spherical nuclei and transform the Dirac Hamiltonian into a diagonal form, in which the upper (lower) diagonal element becomes an operator describing Dirac (anti-)particle, which holds the form of the Schr?dinger-like operator with the singularity and the coupling disappearing in every component. With this formalism, we have explored the origin and breaking mechanism of pseudospin symmetry. It is shown that the pseudospin energy splitting comes mainly from the contributions of the nonrelativistic, dynamical, and spin-orbit terms, while those from the modification of kinetic energy and the Darwin term are negligible. In addition, the pseudospin energy splitting depends on the shape of potential. For exotic nuclei, as the potential is more of diffusivity, the contribution of the dynamical term to the pseudospin symmetry evolves from destruction to an improvement. Hence, the pseudospin symmetry is better in exotic nuclei than that in usual nuclei.(2) the origin and breaking mechanism of relativistic symmetries for deformed nuclei. By applying the similarity renormalization group into the covariant density functional theory describing any deformed nuclei, we have obtained a diagonal Dirac Hamiltonian, in which the upper (lower) diagonal element becomes an operator describing Dirac (anti-)particle, which holds the form of the Schrodinger-like operator with the singularity and the coupling disappearing in every component. With this formalism, we have explored the origin and breaking mechanism of spin symmetry. It is shown that the the spin energy splitting arises almost entirely from the spin-orbit coupling. In addition, the energy splitting magnitude is different for the different doublets and for different deformations.(3) the origin and breaking mechanism of pseudospin symmetry for deformed nuclei. It is found that the pseudospin energy splitting is dominated by the nonrelativistic, dynamical, and spin-orbit terms. The nonrelativistic term always destroys the pseudospin symmetry and the spin-orbit coupling always improves the pseudospin symmetry, while the dynamical effect depends on nuclear deformation and the quantum numbers of the doublets as well as the position of the levels. The origin of pseudospin symmetry arises from these contributions of the nonrelativistic, dynamical, and spin-orbit terms, and the quality of pseudospin symmetry is associated with nuclear shape, the quantum numbers of the states, and the position of energy levels. In some cases, the position of the levels is more relevant to the quality of pseudospin symmetry.