High Order Corrections in the Relativistic Perturbation Theory with the Model Zeroth Approximation, Mg-Like and Ne-Like Ions

The relativistic perturbation theory is applied to the solution of the many-electron Dirac equation. The theoretical consideration is accomplished for some Mg-like ions: S V, Ca IX, Ti XI and Fe XV; the energies of all the states 1 s 2 2 s 2 2 p 6 3 l 1 j 1 , 3 l 2 j 2 are calculated. The Ne-like spectra are calculated for the ions with Z = 16-26; all the states of configurations 1 s 2 2 s 2 2 p 5 3 s , 3 p , 3 d and 1 s 2 2 s 2 p 6 3 s , 3 p , 3 d are considered. The Dirac equation with the central one-particle model potential V c ( r ) is accepted as a zeroth approximation; the model potential imitates the core potential of the closed shells. The empirical information about the energy structures of one electron above the core or one vacancy inside the core is used here to construct the zeroth approximation. The perturbation theory first order correction is calculated exactly, the high order contributions are accounted for effectively. Two main types of high order corrections are investigated: "polarization" interaction of two "above core" particles and effect of the mutual screening of these particles.