中文摘要：

本文在空间格点上利用虚时间步长方法求解了球形Dirac方程,着重研究了出现的假态问题.利用三点数值导数公式离散方程中一阶导数项,可以证明对于量子数为κ和-κ的单粒子能级能量是完全相同的,其中一个为物理解,另一个为假态.通过在径向Dirac方程中引入Wilson项,可以解决假态问题,得到全部物理解.文章以Woods-Saxon势为例,考虑Wilson项后,得到与打靶法一致的结果.

英文摘要：

With the development of radioactive ion beam facilities, the study of exotic nuclei with unusual N/Z ratio has attracted much attention. Compared with the stable nuclei, the exotic nuclei have many novel features, such as the halo phenomenon. In order to describe the halo phenomenon with the diffused density distribution, the correct asymptotic behaviors of wave functions should be treated properly. The relativistic continuum Hartree-Bogoliubov（RCHB） theory which provides a unified and self-consistent description of mean field, pair correlation and continuum has achieved great success in describing the spherical exotic nuclei. In order to study the halo phenomenon in deformed nuclei, it is necessary to extend RCHB theory to the deformed case. However, solving the relativistic Hartree-Bogoliubov equation in space is extremely difficult and time consuming. Imaginary time step method is an efficient method to solve differential equations in coordinate space. It has been used extensively in the nonrelativistic case. For Dirac equation, it is very challenging to use the imaginary time step method due to the Dirac sea. This problem can be solved by the inverse Hamiltonian method. However, the problem of spurious states comes out. In this paper, we solve the radial Dirac equation by the imaginary time step method in coordinate space and study the problem of spurious states. It can be proved that for any potential, when using the three-point differential formula to discretize the first-order derivative operator, the energies of the single-particle states respectively with quantum numbers κ and-κ are identical. One of them is a physical state and the other is a spurious state. Although they have the same energies, their wave functions have different behaviors.The wave function of physical state is smooth in space while that of spurious state fluctuates dramatically. Following the method in lattice quantum chromodynamics calculation, the spurious state in radial Dirac equation can be removed by introducing the Wilson