群的对称性偶合系数计算的新方法

本文根据群G和子群g的不可约表示基向量标准化的性质,提出了直接计算子群g的V系数和W系数的新方法。对于SO(3)群-点群的情况,可由标准化基向量与尽可能低j值的SO(3)群-点群V系数和变换系数,以及3j、 6j符号等关系,分别导出计算点群V系数和W系数的公式。并以正二十四面体Ih群为例,计算了三角组分系、五角组分系的所有V系数和W系数,计算结果列于附表。

A New Calculation Method for Symmetry Coupling Coefficients of the Group

In terms of the standardization properties of the basic vectors in irreducible representations of group G and subgroup g, a new method for calculating directly the V and W coefficients of subgroup g has been put forward. With the three dimensional rotation group SO(3)-point group, the formulas for calculating point group V and W coefficients respectively have been derived on the basis of the relationship between the standardized basis vector and the V coefficients of low j value ,SO(3) group-point group, thetransformation coefficients Smiji , as well as the 3j, 6j symbols. Takingicosahedral Ih group as an example, we have calculated all the V and W coefficients of the trigonal and pentagonal component systems. The results obtained are listed per attached sheets.