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We prove a HVZ theorem for a general class of no-pair Hamiltonians describingan atom or positively charged ion with several electrons in the presence of aclassical external magnetic field. Moreover, we show that there existinfinitely many eigenvalues below the essential spectrum and that thecorresponding eigenfunctions are exponentially localized. The novelty is thatthe electrostatic and magnetic vector potentials as well as a non-localexchange potential are included in the projection determining the model. As amain technical tool we derive various commutator estimates involving spectralprojections of Dirac operators with external fields. Our results apply to allnuclear charges less than or equal to 137.

SPECTRAL THEORY OF NO-PAIR HAMILTONIANS