Theoretical Study of Interesting Fine-Structure Splittings Based on a Scenario for Precise Calculations

Based on the multi-configuration Dirac-Fock self-consistent field method, a scenario has been presented to calculate the fine-structure energy levels of C²⁺ and Si²⁺ excited states (3¹ D₂ and 3₃D_1,2,3). The Breit interactions and quantum electrodynamics corrections are added as perturbations. The present calculation results are found to be in excellent agreement with the experimental data. By means of the precise calculation procedure, we elucidate that four competitive mechanisms influence the interesting fine-structure splittings in C²⁺ and Si²⁺, such as spin-orbit interactions, relativistic corrections of exchange interactions, the Breit interactions and electron correlation effects. Furthermore, the mechanism of relativistic correction of exchange interactions has been studied clearly. We elucidate that the inner shell 2p_1/2,3/2 orbitals are essential to relativistic corrections of exchange interactions which are crucial for the final anomalous fine-structure splittings.