Abstract
A group-theoretical analysis of the states of first-row atoms and their internal electrostatic interactions is developed. The Hamiltonian is found to be completely expressible as a linear combination of operators that are diagonal in $U(3)$, operators diagonal in $O(4)$, and operators diagonal in both. This makes possible a simple and uniform treatment of the energy levels of first-row atoms. We use it here to analyze configuration mixing between the $2{s}^{2}2{p}^{x}$ and $2{p}^{x+2}$ configurations, and determine the contribution of configurations of $O(4)$ and $U(3)$ symmetry in several types of mixed-configuration wave functions.
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