原子核的相对论对称性

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.

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。

对称性是反映微观多体系统结构、特征和性质的重要方面。本项目利用相似重整化群方法结合协变密度泛函理论研究原子核的相对论对称性，取得了一些重要进展。.分别在球形和形变情况下，实现了协变密度泛函理论框架下Dirac哈密顿算符的解析对角化，上下对角元变成类Schrödinger 算符，分别对应于Dirac粒子和反粒子算符。尤其，这个类Schrödinger 算符由5个具有独立物理意义的算符组成，分别对应于非相对论项、动力学项、自旋-轨道耦合项、Darwin项和动能的相对论修正项。利用这个算符研究了原子核的核子和反核子谱的相对论对称性，弄清了这些对称性的起源和破坏机制。自旋对称性几乎完全归因于自旋-轨道耦合，而赝自旋对称性与非相对论项、动力学效应和自旋轨道耦合都相关。解析分解了包含张量耦合的Dirac哈密顿算符，研究了张量耦合对自旋和赝自旋对称性的贡献，揭示了相对论对称性的张量耦合效应。结合复动量表象方法，研究了原子核单粒子共振态的自旋和赝自旋对称性，指出自旋和赝自旋对称性主要存在于连续阈附近的低轨道角动量态。与能级存在的对称性相比，波函数的自旋和赝自旋对称性保持得更好。发展了描述球形和形变核的复动量表象方法，研究了19C，31Ne等若干不稳定核的奇特结构，揭示了19C，31Ne晕的形成机制，预言了几个较重丰中子核可能存在晕结构。发展了相对论的复动量表象方法，研究了Ca，Ni，Zr，Sn和Pb同位素，发现在极端丰中子区可能存在晕或巨晕结构；研究了37Mg形变晕的形成机制，指出它是p波晕核。发展了复标度格林函数方法，研究了原子核的单粒子共振态，获得了比耦合道方法更丰富的共振态信息。这些结果对实验探测原子核的奇特结构与奇特核有参考价值。培养博士研究生3名，硕士研究生15名，支持5名青年教师科研工作。