Absence of discrete spectrum in highly negative ions

Let Hsub(N) be the Hamiltonian for the Coulomb system consisting of N particles of like charge in the field of a fixed point charge Z. We show that if the particles are bosons, then Hsub(N) has no discrete spectrum when N >= N0 = cZ2 for some constant c. If the particles are fermions, then Hsub(N) is bounded below uniformly in N. These results can be extended to molecules and to other power law potentials. (orig.)