Correlation Effects in Atoms

The applicability of many-body perturbation theory in calculating electron correlations in atoms has been investigated. It was found that, in order for results to agree well with experiment, certain classes of diagrams, representing terms of the perturbation series, must be included to many orders. The higher order diagrams were found to be more important in calculating correlations among the outer electrons than among inner electrons. Methods for summing various classes of these diagrams were found. The total correlation energy in beryllium was calculated by perturbation theory, by the use of an IBM 7090 computer, to be -2.48±0.11 eV. The value obtained from experiment is -2.59 eV. The calculated correlation energies for the different electronic shells were found to be -1.19 eV among $2s$ electrons, -1.15 eV among $1s$ electrons, and -0.135 eV between the $1s$ and $2s$ shells.