Atomic Bethe-Goldstone equations. III. Correlation energies of ground states of Be, B, C, N, O, F, and Ne

A variational formulation of Brueckner's theory has been used to solve Bethe-Goldstone equations and to compute electronic pair-correlation energies for the atoms listed in the title. One-electron effective correlation energies, needed for open-shell atomic states, are also computed. An approximate Hartree-Fock function is used for the reference state in each case. Individual pair-correlation energies are computed to an expected accuracy of 0.001 Hartree a.u. The total correlation energies range from 98.5 to 100.3% of the empirical correlation energy. For comparison with many-particle perturbation theory, definitions of the hierarchy of nth-order Bethe-Goldstone equations and of the concepts of gross and net mean-value increments used in this work are restated in terms of linked Goldstone diagrams. © 1968 The American Physical Society.