Atomic Bethe-Goldstone Equations. I. The Be Atom

The nonrelativistic electronic energy of $\mathrm{Be}\left({}_{}{}^1{}_{}{}^{}S\right)$ is computed by a generalization of the method of Brueckner, through the variational solution of generalized Bethe-Goldstone equations. These equations describe clusters of two, three, or four electrons interacting with the remainder of an $N$-electron system. The three- and four-particle terms are found to be very small, but the sum of three-particle terms is nearly 0.001 atomic units (a. u.). The computed correlation energy is -0.0921 a. u., or 98.1% of the difference between experimental total energy and computed Hartree-Fock and relativistic energies.