类重整化群对反核子谱相对论对称性的研究

发布时间：2018-12-23 18:57

【摘要】：相对论对称性是核结构理论中相当重要的一环,其起源与破缺机制也是目前的热点方向之一。本文从相对论对称性的发现出发,介绍了目前与之相关的一些研究,然后结合协变密度泛函理论(Covariant Density Functional Theory,CDFT)与类重整化群(Similarity Renormalization Group,SRG)方法,来探索球形核下反核子谱相对论对称性的起源与破缺机制。最后我们也对超形变核下核子谱的相对论对称性做了研究。主要内容有如下几点:一、简明介绍了相对论对称性的概念和当前研究中的进展及未解决问题。自自旋对称性与赝自旋对称性发现以来,它们在解释原子核壳结构和幻数等核物理现象起到了重要作用。二、详细阐明了类重整化群方法以及协变密度泛函理论的理论框架。三、分别对球形核下反核子谱的自旋和赝自旋对称性的研究。在描述球形核的协变密度泛函理论的框架下,运用类重整化群方法通过连续的么正变换将Dirac哈密顿算符转变为对角形式,分离出Dirac粒子与反粒子算符,分别得到动力学、自旋—轨道耦合等各个独立的厄米算符,从而避免了之前研究中所遇到的奇异性和算符耦合等问题。通过比较每一组分对自旋和赝自旋能级劈裂的贡献,发现在自旋能级劈裂中自旋—轨道耦合项占主导作用,而赝自旋能级劈裂主要来源于非相对论项和动力学项的贡献,同时势场形状及伙伴态量子数对自旋和赝自旋对称性的影响我们也给出了结论,从而揭示了相对论对称性的起源与破缺的机制。四、在相对论平均场框架下对超形变核的核子谱相对论对称性的研究。通过研究自旋和赝自旋对称性及其随形变变化的情况,发现超形变核态的自旋和赝自旋对称性与双重态的量子数和形变都相关,表明超形变态具有更好的对称性,是超形变核态具有较好稳定性的原因之一。
[Abstract]:Relativistic symmetry is an important part of nuclear structure theory, and its origin and breaking mechanism are also one of the hot topics. In this paper, based on the discovery of relativistic symmetry, some related studies are introduced, and then the covariant density functional theory (Covariant Density Functional Theory,CDFT) and the renormalization group (Similarity Renormalization Group,SRG) method are introduced. To explore the origin and breaking mechanism of relativistic symmetry of antinuclear spectrum in spherical nuclei. Finally, we also study the relativistic symmetry of the nuclear spectrum under superdeformed nuclei. The main contents are as follows: firstly, the concept of relativistic symmetry, the current research progress and unsolved problems are briefly introduced. Since the discovery of spin symmetry and pseudospin symmetry, they have played an important role in explaining nuclear physical phenomena such as nuclear structure and phantom number. Secondly, the quasi-renormalization group method and the theoretical framework of the covariant density functional theory are expounded in detail. Third, the spin symmetry and pseudospin symmetry of antinucleon spectra in spherical nuclei are studied respectively. In the framework of the covariant density functional theory describing spherical nuclei, the Dirac Hamiltonian is transformed into diagonal form by the method of quasi-renormalization group through continuous unitary transformation, and the Dirac particle and antiparticle operators are separated from each other to obtain the dynamics, respectively. Various independent Hermitian operators such as spin-orbit coupling can avoid the singularity and operator coupling problems encountered in previous studies. By comparing the contribution of each component to spin and pseudospin level splitting, it is found that the spin-orbit coupling term dominates the spin-orbit splitting, while the pseudo-spin level splitting mainly comes from the contribution of non-relativistic terms and kinetic terms. At the same time, the effects of the shape of potential field and the quantum number of partner states on the spin and pseudospin symmetry are also discussed, which reveals the origin and breaking mechanism of relativistic symmetry. Fourthly, the relativistic symmetry of superdeformed nuclei is studied under the framework of relativistic mean field. By studying the spin and pseudospin symmetries and their changes with deformation, it is found that the spin and pseudospin symmetry of superdeformed nuclear states are related to the quantum number and deformation of double states, which indicates that the superform metamorphosis has better symmetry. It is one of the reasons that the superdeformed nuclear state has good stability.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O571

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