Relativistic matrix elements of the electrostatic interaction energy operator in the case of two subshells of equivalent electrons

Abstract

The article is devoted to obtaining the relativistic matrix elements of the energy operator of electrostatic interaction of electrons. The case of configuration-diagonal matrix elements for atoms (ions) with two unfilled subshells of equivalent electrons is considered. The function of bound moments of the state of atoms (ions) with two unfilled subshells of equivalent electrons is obtained by the method of irreducible tensor operators in the representation of secondary quantization. In this case, the state function of one N subshell of equivalent electrons is obtained by coupling the N moments (ranks) of identical electron creation operators. The state function of two subshells of equivalent electrons is obtained by coupling the resulting moments (ranks) N1(N2) of the electron creation operators corresponding to the first (second) subshell of equivalent electrons. The matrix elements of the electrostatic interaction energy operator in the case of two subshells take into account the interaction energies of electrons inside the subshells and direct and exchange interactions between electrons of different subshells, which leads to the need for slope coefficients and radial integrals that depend on both angular and radial quantum numbers. Radial integrals represent linear combinations of Slater-type integrals but depend on the larger and smaller components of the Dirac-type relativistic wave functions. Recursive relations connecting two subshell configurations with different numbers of electrons in subshells are obtained for direct and exchange angular coefficients.