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2p-2p pair correlation 3p electrons 3p_3p pair correlation angular integral B7 approximately basis set bound excited calculate the diagram Clementi reports configuration interaction consisting of unlinked correlations among 2p Coulomb interaction diagram of Fig electron pairs elements of Eq energy of argon equation exchange diagrams corresponding expect that three-body four-body Hamiltonian HF energy HF orbital hole lines Infinite number integration over continuum ionization potentials Is-ls lines drawn pointing linked graph ls-ls correlation energy ls-ls pair correlation many-body perturbation theory N-l particles Nesbet NEUTRAL ARGON ATOM number of bound orbital angular momentum pair correlation energy particle-particle ladder principal quantum number ring diagram RP of Eq Second-order pair correlations spherical harmon spin subshells sum rule Sums over bound Table Third-order correlation energies three matrix elements three-body contributions three-body correlations three-body diagrams total energy total three-body effects University of Virginia Value a.u. vanish unless wave function wave number Wigner 3~j symbol