Three-electron atoms from a Bethe-Salpeter equation approach

The two-electron Bethe-Salpeter equation is reviewed. The transition to a Hamiltonian form is discussed, and the criterion that the first-order energy shift vanish is used to determine the electron-electron potential that appears in the Hamiltonian. A similar program is carried through for the three-electron case. The fundamental idea of Feldman and Fulton is used for the transition to the Hamiltonian form, although some changes are necessary. The optimum two-electron interaction is the same as that in the two-electron case.