Abstract
A new numerical calculation method has been used to solve the relativistic Hartree-Fock （RHF） equation of atomic system. The retardation term in Breit interaction was given in a explicit and succinct formulation. The established theoretical method and computational program have been used to study the fine structure of nd（n=17—31） series of sodium. We obtained the fine structures by using RHF method in a self- consistent procedure for the first time, rather than perturbation method often used by other authors. The results show that the exchange interaction between the core and valence electrons in the frame of relativity is the main reason of abnormal fine structure. By combining the effect of Breit interaction, it is shown that a relativistic calculation reproduces the inverted fine structure of sodium exactly and our work is far better than other theoretical results.
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