准旋-角动量标量算子本征值与j壳层耦合态的完全分类计算

CALCULATIONSFOREIGENVALUESOFQUASISPIN ANGULAR MOMENTUNSCALAROPARATORANDCOMPLETE CLASSIFICATIONOFj SHELLCOUPLEDSTATES

应用二次量子化和不可约张量理论，由４ 个产生—湮灭算子耦合成准旋—角动量标量算子Ｚ（ Ｋ），Ｋ 为参数。计算表明：Ｚ（ Ｋ） 的本征值有很强的分类功能，能对ｊ≤１５／２ 壳层准旋—角动量耦合态完全分类（用准旋和角动量只能对ｊ≤７／２ 壳层耦合态完全分类）。讨论Ｚ（ Ｋ） 的构造和它的本征值的计算方法，给出ｊ≤１５／２ 壳层耦合态的完全分类。

By using the formalism ofsecond quantization and irreducible tensor,quasispin angular momentum scalaroperator Z( K) ,where K = 2 ,…,2j,isconstructedfrom 4 creation annihilation operators.Theeigenvalues of Z( K) havespecialability forclassification ofcoupled states,by angular momentum Jand quasispin Qthe com pleteclassification can be done only for j ≤7/2 ,but by eigenvalues of Z( K)the complete classification have be donefor j ≤15/2 .The methodsforcalculatingtheeigenvaluesof Z( K)are discussed,and thecompleteclassifica tionsfor j ≤15/2are presented.