协变密度泛函理论中的张量力效应

张量力是核子-核子相互作用的重要成分,被认为是理解奇特原子核中壳结构演化规律的关键要素。然而,目前对于核介质中的张量力及其效应的定量认识,仍存在很多亟待解决的关键问题。着重梳理了在原子核密度泛函理论框架下,研究有效相互作用中的张量力成分以及相应的张量力效应的相关工作,重点包括:基于相对论Hartree-Fock理论,以同位素链中的质子幻数壳演化为例,定量提取与分析其中的张量力效应;以及基于第一性原理的相对论Brueckner-Hartree-Fock理论,以中子滴单粒子能谱中的自旋-轨道劈裂演化为例,提出与张量力效应相关联的"准实验数据"。最后,展望原子核密度泛函理论今后可能的发展策略。Tensor force is one of the most important components of the nucleon-nucleon interaction. It plays a critical role in understanding the shell evolution in exotic nuclei. However, there are still several puzzles concerning the tensor force and its effects in the nuclear medium. In this paper, we mainly focus on the studies of tensor force in the effective interactions and its effects in finite nuclear systems within the scheme of nuclear density functional theory. In particular, we highlight the recent developments, including the quantitative analysis of tensor effects in the relativistic Hartree-Fock theory by taking the evolution of proton magic shells in the isotopic chains as an example, and the "meta-data" of tensor effects provided by the ab initio relativistic Brueckner-Hartree-Fock theory by taking the evolution of spin-orbit splitting in the single-particle spectra of neutron drops as an example. Perspectives are focused on the possible strategies for the future developments of nuclear density functional theory.     

原子核物理中的协变密度泛函理论

文章介绍了原子核协变密度泛函理论的历史发展、理论框架、对原子核基态和激发态的描述以及在一些交叉学科领域的应用。首先,通过回顾原子核物理研究中的几个重要里程碑并结合二十一世纪原子核物理面临的机遇和挑战,对当前核物理的研究热点和重要课题进行了介绍。随后系统介绍了原子核协变密度泛函理论,内容包括协变密度泛函理论的历史发展、一般理论公式、介子交换模型、点耦合模型、交换项、张量相互作用、物理观测量的计算公式等。协变密度泛函理论的应用包括原子核基态性质和激发态性质的描述以及在核天体物理与标准模型检验中的应用。其中,基态性质包括原子核结合能、半径、单粒子能级、共振态、磁矩、晕现象等。激发态性质包括原子核磁转动、低激发态性质、集体转动、量子相变、集体振动等。在核天体物理与标准模型检验的应用中,主要以核纪年法测算宇宙年龄和Cabibbo-Kobayashi-Maskawa矩阵的幺正性检验等为例,介绍协变密度泛函理论在交叉学科领域的应用。     

Solving the Dirac Equation with Nonlocal Potential by Imaginary Time Step Method

The imaginary time step （ITS） method is applied to solve the Dirac equation with the nonlocal potential in coordinate space by the ITS evolution for the corresponding Schrfdinger-like equation for the upper component. It is demonstrated that the ITS evolution can be equivalently performed for the Schrodinger-like equation with or without localization. The latter algorithm is recommended in the application for the reason of simplicity and efficiency. The feasibility and reliability of this algorithm are also illustrated by taking the nucleus ^16O as an example, where the same results as the shooting method for the Dirae equation with localized effective potentials are obtained.     

Perturbative pseudospin symmetry limit with linear spin-orbit potential

The pseudospin symmetry (PSS) limits which conserve substantial spin-orbit splitting are investigated. It is found that while the strength of the spin-orbit potential as well as the spin-orbit splitting increase, the pseudospin doublets, e.g., 2p_3/2 and 1f_5/2 states, are always degenerate. Furthermore, by examining the perturbation corrections to the single-particle energies, the perturbative nature of the proposed PSS limits is also discussed.     

First attempt to overcome the disaster of Dirac sea in imaginary time step method

Efforts have been made to solve the Dirac equation with axially deformed scalar and vector WoodsSaxon potentials in the coordinate space with the imaginary time step method. The results of the singleparticle energies thus obtained are consistent with those calculated with the basis expansion method, which demonstrates the feasibility of the imaginary time step method for the relativistic static problems.     

Stability of Strutinsky Shell Correction Energy in Relativistic Mean Field Theory

The single-particle spectrum obtained from the relativistic mean field （RMF） theory is used to extract the shell correction energy with the Strutinsky method. Considering the delicate balance between the plateau condition in the Strutinsky smoothing procedure and the convergence for the total binding energy, the proper space sizes used in solving the RMF equations are investigated in detail by taking ^208 Pb as an example. With the proper space sizes, almost the same shell correction energies are obtained by solving the RMF equations either on basis space or in coordinate space.     

Search for Ring-Like Nuclei under Extreme Conditions

The potential energy surfaces of 24Mg are studied within the adiabatic and diabatic constrained relativistic mean field approaches. The possible ring-like states are searched by analyzing the density distribution. It is found that in 24Mg the ring-like states are energetically favored at the extreme oblate condition ｜β2｜ ≥ 1.54 and a ring-like minimum is obtained with excitation energy Ex = 49.42 MeV and quadrupole deformation β2 = -0.93.     

First attempt to overcome the disaster of Dirac sea in imaginary time step method

Efforts have been made to solve the Dirac equation with axially deformed scalar and vector Woods-Saxon potentials in the coordinate space with the imaginary time step method. The results of the single-particle energies thus obtained are consistent with those calculated with the basis expansion method, which demonstrates the feasibility of the imaginary time step method for the relativistic static problems.