Using a simplified multi-configuration Dirac–Fock (SMCDF) scheme based on the multi-configuration Dirac–Fock (MCDF) theory, we study the systematic variations of the fine-structure splittings of n2D3/2,5/2 Rydberg series along the sodium-like isoelectronic sequence, i.e. the fine-structure orderings vary with increasing atomic number Z. The competition between the spin-orbit interactions and the exchange interactions due to relativistic effects of the nd orbital wavefunctions well explain such variations. Furthermore, the effect of Breit interactions which plays the secondary role is studied.

In theoretical simulations and analysis of diagnostic measurements for hot dense plasmas in the inertial confinement fusion(ICF) researches, it is usually necessary to consider thousands of ionic energy states and transition arrays between these energy states. Average atom(AA) models are generally adopted for practical purposes. In order to calculate ionic populations of hot dense plasmas more accurately, we propose a method beyond the AA model, which can calculate the ionic populations of plasma in local thermal equilibrium with satisfactory accuracy, and may also deal effectively with the ionic populations of plasma in non-local thermal equilibrium.

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For practical purposes, the ionic stage and populations of hot dense plasma are often described by the average atom(AA) model instead of the detailed average configuration accounting(DCA) model, which is more close to the reality. According the atomic self-consistent field theory, we calculate the DCA reduced photonionization cross-sections of every subshell of Br ions in different ionic stages. Comparing these DCA reduced cross-sections with the reduced photonionization cross-secion of the corresponding average electronic orbital in the AA model, we deduce the inherent rules between the reduced cross-sections. Based on the AA reduced photonionization cross-section, the DCA reduced photonionization cross-sections and detailed configuration rate coefficients of photonionizaiton and radiative recombination can be calculated. This work is a necessary preparation for accurate description of non-local thermal equilibrium(n-LTE) plasma.