四原子分子中Majorana算子矩阵元的新计算公式

New Formulas of Matrix Element of MajoranaOperators of Four-atomic Molecules

李代数方法在研究双原子分子、三原子分子振-转光谱及相关问题等方面已被证明是一种有效方法[1～4], 并被成功推广到多原子分子[5～7]. 构造代数哈密顿量是此方法的关键, 这就要求选择合适的群链. 群链SU(4)SO(4)SO(3)SO(2)已被证明是合适的一条群链[3],并且可以推广到四原子分子[5]. 在代数哈密顿量中, Majorana算子扮演着重要角色. 我们首先研究了3个SO(4)的张量直积得到的耦合张量算子和Majorana算子及其关系, 然后应用广义维格纳-爱卡塔定理, 得到了耦合张量算子矩阵元的一般表达式. 作为特例, 我们计算了四原子分子中Majorana算子的矩阵元, 得到了比文献[4,5]更加简单的计算公式.

We first studied the relationship between coupling tensor operators of the product of three ten-sor operators of SO(4) and Majorana operators of four-atomic molecules. We have gained the general for-mulae of the matrix elements of the coupling tensor operators of product of three tensor operators by usingGeneralized Wigner-Eckart theorem. As an example, we calculated the matrix elements of Majorana oper-ators and gave the new simpler formulae of them.