三价原子的非相对论能级结构理论

本文以原子结构的拉卡方法为基础,从三价原子的拉卡基出发,反复利用三个角动量耦合的基本关系以及3j、6j、9j符号的性质,具体推导了(n1 l1)(n2 l2)(n3l3)和(n1 l1)2(n3l3)组态下三价原子非相对论哈密顿矩阵元的计算式,除径向部分用Slater-Condon径向积分表示以外,完成了所有的角向积分与自旋求和;简要举例说明了如何利用该矩阵元计算式推导三价原子非相对论谱项能量表达式以及利用变分原理确定其中的Slater-Condon径向积分,从而求出具体的谱项能量数值.可以说,本文已建立起三价原子非相对论性能级结构的一般理论.

Theory on the energy structure of atoms with three valence electrons

In this work, the non-relativistic energy structure theory for atoms with two valence electrons proposed by Racah is generalized to the case of three valence electrons atoms. We deduce the non-relativistic Hamiltonian matrix elements of atoms with three valence electrons with ( n1l1) (n2l2)(n3l3) and (n1l1)2 (n3l3) representation by using the fundamental principles of angular momentum coupling of atoms with three valence electrons and the nature of symbols 3j ,6j ,9j over and over from the Racah basis. We can say that the theory about non-relativistic energy level structure of three Valence electrons atoms is established through the works in this paper.