Many-Body Contributions to Atomic Correlation Energies

Many-electron perturbation theory has been used to investigate the contribution to atomic correlation energies from high-order terms. The treatment analyzes several aspects of the inhomogeneous-electron-gas and the electron-pair approaches. It discusses in detail the coupling of electronic angular momenta with the multipolar components of the Coulomb interaction. The results are expressed in terms of renormalized propagators, which include partial perturbation summations to infinite order. Calculations have been carried out for the neon atom to ascertain the importance of contributions from many-body ring diagrams. Numerical results indicate that the ratio of many-body to two-body correlation energies is about 0.10 for the $2p$ subshell of NeI and that the many-body correlation energy has a positive sign.