奇特核的壳层结构及其演化规律，传统幻数消失和新幻数形成的物理根源是当前核物理领域的主要前沿课题之一。相对论对称性在原子核的壳层结构及其演化规律中扮演着重要角色。本项目拟进一步将相似重整化群(SRG)方法和协变密度泛函理论(CDFT)结合，退耦CDFT框架下的Dirac哈密顿算符，分离出描述Dirac粒子和反粒子算符，分解出动力学、自旋轨道耦合等每个有独立物理意义的组分，探索它们对自旋和赝自旋对称性的贡献，揭示相对论对称性的起源和破坏机制，弄清相对论对称性在原子核的壳层结构及其演化规律中扮演的重要角色；退耦包括张量耦合的Dirac哈密顿算符，探索每个张量组分与相对论对称性的关系，弄清它们对奇特核幻数改变的影响，预言超重核幻数；退耦包括推转项的Dirac哈密顿算符，研究原子核的集体转动，给出赝自旋伙伴带的判据，预言若干可能存在的赝自旋伙伴带，为实验探测赝自旋伙伴带提供理论依据。

The shell structure and its evolution in exotic nuclei, together with the disappearing of traditional magic numbers and the formation of new magic numbers is one of the hottest topics in the field of nuclear physics. Relativistic symmetries in nuclei play important roles in the shell structure and its evolution. In this project we further explore the relativistic symmetries by the similarity renormalization group for the spherical, axially and non-axially deformed nuclei, in which the Dirac Hamiltonian derived from the covariant density functional theory is transformed into a diagonal form by using continuous unitary transformation. Moreover, the upper (lower) diagonal element becomes an operator describing Dirac (anti-)particle, which holds the form of the Schrödinger-like operator with the singularity and the coupling disappearing in every component. Furthermore, in the Schrödinger-like operator, the spin-orbit coupling term, the dynamical item, and the other terms with special physics are isolated from the coupling Dirac operator. By using this Hamiltonian, we compare the contributions of each component to the relativistic symmetries, analyze the relationship between the relativistic symmetries and the quantum numbers of single-particle states, check the influence of the shape of the potential and the relativistic effect on the relativistic symmetries, and explore the effects of the spin-orbit coupling, the dynamics, the tensor coupling, and the deformation on the relativistic symmetries. Based on these studies, we will obtain this knowledge on the shell structure and its evolution， and predict the magic numbers for exotic nuclei and superheavy nuclei. Further, we decouple the Dirac Hamiltonian with rotational term for nuclear collective rotation, present the judgment of pseudospin partner bands, and predict the pseudospin partner bands for the exploration of experiment.