f壳层耦合态的完全分类与准旋标量算符本征值

The Complete Classification of f-shell Coupled States and the Eigenvalues of Quasispin Scalar Operator

本文用二次量子化方法,对l壳层引进准旋、自旋、轨道为(1/2,1/2,l)阶不可约张量的产生-湮灭算符b_(qsm)^(1/2 1/2 t),由4个这种算符按下式耦合成准旋、自旋、轨道标量算符, (?)Y (K_1,k_2,k_3) 与准旋、自旋、轨道算符对易,可用于对耦合态进一步分类。利用Y(k_1,k_2,k_3)与准旋、自旋、轨道算符的适当结合,本文给出了对f壳层完全分类的算符(组),给出了与G.Racah对f壳层分类一致的算符组。

In the second quantization methed we introduce the creation-annihilstion operatorb_q3m^1/2/1/21, which is triple tensor of rank (1/2, 1/2, 1) for Q (quasispin), S (spin), L(orbit angular-momentum), and a triple scalar operatorv (k_1,k_2,k_3) ie constructed bycoupling of triple tensor, Y (k_1,k_2,k_3)=((bb)a^k_1~k_2~k_3 (bb)~k_1~k_2~k_3)~000, the Y (k_1,k_2,k_3) commutates with (?) and(?), then it can be used to further ciassify the coupledstates. By appropriate combining Y (k_1,k_2,k_3) with(?), the set of operatorswhich can clessify completely f-shell is obtained, and the set of operators which can clas-sify in agreement with those of Recah is also obtained.