Analytical method for calculating atomic structures based on the variational method for many-electron atomic structure in plasmas

Within the framework of the Hartree–Fock method and the irreducible tensor theory, we have proposed an analytic formula for calculating the nonrelativistic energies of many-electron atoms. The relativistic mass, the one- and two-body Darwin, the spin–spin contact interaction, and the orbit–orbit interaction corrections to the energies are considered to make the results more precise. The angular interactions and spin sums involved in the formula are worked out explicitly using the irreducible theory. A program based on the variational method is developed to calculate the wave functions and atomic structure properties. The energies of the 1sns 1,3S (n = 1–4) and 1snp 1,3P (n = 2–4) states of the exemplary ions Ar16+, Fe24+, and Kr34+ in both Debye plasma and quantum plasma environments are given. Moreover, we analyzed the evolution of plasma screening parameters and provided some rules for practical and rapid evaluation in plasma applications.