Construction of the energy matrix for complex atoms

Abstract

The continuation of the previous series of papers related to the construction of the energy matrix for complex atoms is presented. The contributions from the second-order perturbation theory concerning electrostatically correlated spin-orbit interactions (CSO), as well as electrostatically correlated hyperfine interactions (CHFS) to the atomic structure of $ nl^{N}$ , $ nl^{N}n_{1}l_{1}^{N_1}$ and $ nl^{N}n_{1}l_{1}^{N_1}n_{2}l_{2}^{N_2}$ configurations, are considered. This theory assumes that the electron excitation $ n_{0}l_{0}\rightarrow nl$ affects spin-orbit splitting and magnetic dipole and electric quadrupole hyperfine structure in the same way which will be discussed below. Part I of the series presented, in general terms, a method allowing the analysis of complex electronic systems. Parts II, III and IV provided a description of an electrostatic interaction up to second-order perturbation theory; they constitute the basis for the design of an efficient computer program package for large-scale calculations of accurate wave functions. Analyses presented in the entire series of our papers clearly demonstrate that obtaining the precise wave functions is impossible without considering the contribution from the second-order effects into fine and hyperfine atomic structure.