Atomic Bethe-Goldstone Equations. II. The Ne Atom

The nonrelativistic electronic energy of $\mathrm{Ne}\left({}_{}{}^1{}_{}{}^{}S\right)$ is computed by the variational solution of generalized Bethe-Goldstone (BG) equations. The sum of all two-particle net energy increments (pair correlation energies) is -0.3822 atomic units (a.u.), or 97.3% of the empirical correlation energy. The three- and four-particle net energy terms expected to be most important are computed and found to be smaller than 0.001 a.u. The computed pair correlation energies are analyzed in terms of symmetries induced in the BG equations, and are found to be represented well within the accuracy of the present calculations by the somewhat smaller number of parameters needed to characterize the $L$ and $S$ eigenstates of all possible eight-particle subsystems of the ten-electron Hartree-Fock reference state.