Lowest energy states in nonrelativistic QED: atoms and ions in motion

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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.