平面反射对称操作对平均场Hamiltonian的约化

REDUCTION OF THE MEAN FIELD HAMILTONIAN BY REFLECTION SYMMETRY OPERATIONS WITH RESPECT TO A PLANE

研究了原子核平均场中本征能量的求解．当不存在任何几何对称性时，能量矩阵由２ Ｎ×２ Ｎ个复数矩阵元组成（ Ｎ 为基矢的大小）；如果空间存在１ 个反射对称平面，该２ Ｎ×２ Ｎ复矩阵可约化为１ 对互为共轭Ｎ×Ｎ复矩阵或１ 个２Ｎ×２Ｎ实矩阵；如果存在２ 个互相正交对称平面，则可约化为２ 个Ｎ×Ｎ实矩阵．

The solutions to the eigen energy problem in nuclear mean field are investigated. If there is no geometry symmetries in the coordinate space, the energy matrix is composed of 2 N×2N complex matrix elements( N is the size of the basis employed). If there exists one reflection symmetrical plane, this 2N×2N complex matrix can be reduced to a pair of conjugate N×N complex matrices or one 2N×2N real matrix. And if there are two perpendicular reflection planes, it can be further reduced to two N×N real matrices.