Acad Sinica, Inst High Energy Phys, Beijing 100039, Peoples R China
; Univ Three Gorges, Dept Phys, Yichang 443000, Peoples R China
In terms of the irreducible bases of the group space of the octahedral double group O' an analytic formula is obtained to combine the spin states \j, mu] into the symmetrical adapted bases belonging to a given row of a given irreducible representation of O'. This method is effective for an double point groups. However, for the subgroups of O' there is another way to obtain those combinations. As an example, the correlations of spin states for the tetrahedral double group T' are calculated explicitly.