Woods-Saxon势下的赝自旋对称性

通过求解具有Woods-Saxon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双重态能级劈裂和波函数下分量劈裂随着Woods-Saxon势参数的变化关系, 其中Wood-Saxon势中的参数a以及R对于赝自旋能级劈裂和波函数劈裂的影响最大, 而势阱深度V₀只产生微小的影响. 随着平均场的变化, 赝自旋双重态会出现能级反转现象. 具有较大n或l的赝自旋双重态能级劈裂对于参数的变化更敏感. 赝自旋波函数下分量劈裂随着参数a和R的增大向核表面扩散, 并且在核表面附近达到最大. 赝自旋波函数劈裂随着参数a的增大而增大, 但是随着参数R或V₀的增大它却在减小的. 由于在特定的同位素链中, 参数R和V₀都与核子数有关系, 而参数a又是描述核的表面性质的, 所以以这些参数为变量对于赝自旋劈裂的研究是有意义的, 研究的结果至少在定性上可以应用到大部分原子核中.

Pseudospin Symmetry in the Dirac Equation with (Scalar and Vector) Woods-Saxon Potential

The pseudospin symmetry is systematically investigated by solving the Dirac equation with an (scalar and vector) Woods-Saxon potential. We find that the splittings of pseudospin energy and the lower component of pseudospin doublets are sensitive to the nuclear radius and the nuclear diffusivity, but to the depth of nuclear potential. The splitting of pseudospin energy with larger n~ or l~ is more sensitive to the values of the parameters. The energy level crossing is also found for some pseudospin partners with variation of the nuclear mean field. With the increasing of nuclear radius and nuclear diffusibility, the splitting of the lower component of pseudospin doublets diffuses toward the nuclear surface and reaches the largest value on the nuclear surface. The splitting of pseudospin doublets increases with increasing nuclear diffusibility but decreases with increasing nuclear radius and the depth of nuclear potential. Because the variations of the parameters R and V0 are related with the number of nucleon and the characteristics of nuclear surface can be described by the parameter of diffusibility, the conclusions obtained are meaningful for analyzing nuclear properties.