用初等方法导出原子能级的精细结构公式

A DERIVATION TO FINE STRUCTURE FORMULA OF ATOMIC ENERGY LEVELS BY ELEMENTARY METHOD

在初等原子物理和量子力学书中,原子能级的精细结构公式都是用矢量模型导出的.而在专门的书籍中,则采用约化矩阵的理论.本文从兰德(Landé)公式出发,用初等量子力学方法,就两个价电子原子导出精细结构的公式,并且求出用单电子的精细结构分裂因子表示两个价电子原子的分裂因子的公式.

In the present paper,fine structure formula of atomic energy levels concerning an atom with two valence electrons is derived by means of elemen- tary quantum meChanics instead of vector model and reduced matrix.Firstly, it is proved that the spin-orbit interactive matrix elements of two electrons can be replaced by those of two different particles.Then in the SLM_sM_L repre- sentation the Landé formula is used for S and A respectively.As a result the fine structure formula is obtained;and for an atom with two valence electrons,the splitting factor expressed by that for one valence electron is also obtained.