Atomic Bethe-Goldstone Equations. IV. Valence-Shell Correlation Energies of Ground States of Na, Mg, Al, Si, P, S, Cl, and Ar

Abstract

Correlation energies for $M$-shell and mixed $\mathrm{LM}$-shell electron pairs have been computed for the ground states of the atoms listed in the title. For open-shell atomic states, one-electron effective correlation energies are also computed. The method used is a formulation of Brueckner's theory in which one- and two-particle Bethe-Goldstone equations are solved by a variational procedure that uses $N$-particle trial wave functions expressed as linear combinations of Slater determinants. Individual pair-correlation energies are computed to an expected accuracy of a few percent, based on previous calculations on $L$-shell atoms. The computed correlation-energy data are used to analyze the various energy contributions to the first ionization potentials of the atoms considered.