Exploration Of The Relativistic Symmetry In Antinucleon Spectrum By Similarity Renormalization Group

Spin symmetry and pseudospin symmetry are two of the most important concepts in the nuclear structure and its related theory.The origin of the symmetries and their breaking mechanism are still arouse our interest.In this thesis,on the basis of predecessors’ work,we apply the similarity renormalization group into the covariant density functional theory to explore the origin and breaking mechanism of the relativistic symmetries for the antinucleon spectrum.Then the relativistic symmetries for superdeformed nuclei was clarified.This paper is mainly summarized as follows:Firstly,the origin of relativistic symmetries and some of the recent achievements is elaborated.After the discovery of spin symmetry and pseudospin symmetry,they have successfully explained the existence of magic numbers and other numerous phenomena in nuclear structure and its evolution.Secondly,the theory basis of this work,which includes the Covariant Density Functional Theory and the Similarity Renormalization Group Method,are introduced in details.Thirdly,we explore the spin symmetry and pseudospin symmetry for the antinucleon spectrum respectively.By applying the similarity renormalization group into the covariant density functional theory describing the spherical nuclei,we can 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 dynamical term,the spin-orbit coupling and other operators.By comparing the contribution of every component to the spin and pseudospin splittings,it is found that the energy splitting of spin doublets is dominated by the spin-orbit coupling while the pseudospin breaking comes mainly from these contributions of the nonrelativistic term and the dynamical term.In addition,the dependencies of the spin and pseudospin symmetries on the shape of the potential and the quantum numbers of the doublets are clarified.Fourthly,the exploration of the relativistic symmetries for superdeformed nuclei is clarified.It is found that the spin and pseudospin symmetry of the superdeformed nuclei are related to the quantum numbers of the doublets and deformation of the nuclei by studying the spin and pseudospin symmetries and its variation with the deformation.