  Within the framework of nonrelativisitic quantum electrodynamics we consider
a single nucleus and $N$ electrons coupled to the radiation field. Since the
total momentum $P$ is conserved, the Hamiltonian $H$ admits a fiber
decomposition with respect to $P$ with fiber Hamiltonian $H(P)$. A stable atom,
resp. ion, means that the fiber Hamiltonian $H(P)$ has an eigenvalue at the
bottom of its spectrum. We establish the existence of a ground state for $H(P)$
under (i) an explicit bound on $P$, (ii) a binding condition, and (iii) an
energy inequality. The binding condition is proven to hold for a heavy nucleus
and the energy inequality for spinless electrons.
