中文摘要：

通过求解具有谐振子势的径向标量势与矢量势的Dirac方程,分别分析了原子核中赝自旋和自旋双重态的能级劈裂和波函数劈裂随着谐振子的振动频率参数ω和描述谐振子势阱底偏离中心参数r0的变化关系.研究发现,这些参数对于赝自旋和自旋双重态的能级劈裂和波函数劈裂都有着显著的影响.此外,也研究了能级劈裂和波函数劈裂随着量子数的变化关系.由于参数ω与核子数有关,而参数r0与形变核有关,所以以这些参数为变量对于赝自旋劈裂和自旋劈裂的研究是有意义的,研究的结果至少可以定性地应用到大部分原子核中.

英文摘要：

Pseudospin symmetry and spin symmetry in the relativistic harmonic oscillator are investigated systematically by solving the Dirac equation with scalar and vector potentials and are found to be a good approximation in realistic nuclei such as ^208Pb. The pseudospin breaking and spin breaking are shown in correlation with nuclear mean field. The harmonic oscillator frequency and the distance of well-bottom ＇deviation from the center of the potential play an important role in the splittings of energy and waveftinction. The energy-level crossing are found for all the pseudospin partners. The dependence of splittings with quantum numbers is also analyzed.