The Scaling Law in the Fine-Structure Splitting of 1s²np States for the Lithium Isoelectronic Sequence

The 'full-core plus correlation' (FCPC) and the 'minimizing the expectation value of the Hamiltonian' methods are extended to calculate the fine-structure splitting of 1s²np (n=2–9) states for the lithium-like systems from Z=21 to 30. The leading order relativistic effect is included by using first-order perturbation theory. The higher-order relativistic and the quantum-electrodynamics contributions to the fine-structure splitting are investigated under a hydrogenic approximation with effective nuclear charges. Our results are compared with other theoretical calculations and experimental results. It is shown that the FCPC method is also effective to obtain the ionic structure for high nuclear ions of lithium-like systems. By fitting our theoretical results, the scaling law of the fine-structure splitting of the lithium isoelectronic sequence behaves like a quartic function of the screened nuclear charge Z^*.