Resonance energies of n electrons in the field of N fixed nuclei are defined as discrete eigenvalues of non-selfadjoint operators which arise from the Hamiltonian H by a general class of complex distortions of R3 around the fixed nuclei. They are identified with the poles in the analytic continuation of resolvent matrix-elements between states of an explicitely given set A of analytic vectors, and thus shown to be independent of the particular choice of the distortion. Distortions are also used to derive local analyticity properties of bound state-and resonance energies in the nuclear coordinates. RESUME. On definit les energies de resonances de n electrons dans Ie champ de N noyaux fixes comme valeurs propres discretes d’operateurs non auto-adjoints obtenus a partir du Hamiltonien H par une classe générale de deformations complexes de R3 autour des noyaux fixes. On identifie ces energies avec les poles des prolongements analytiques des elements de matrice de la resolvante (4), (z entre des etats ~, ~r d’un ensemble A de vecteurs analytiques donne explicitement, montrant ainsi qu’elles sont independantes du choix particulier de la deformation. On utilise aussi ces deformations pour demontrer des proprietes d’analyticite locale des energies d’etats lies et de resonances par rapport aux coordonnées de noyaux. Annales de l’Institut Henri Poincaré Physique theorique 0246-0211 Vol. 45/86/04/339/20/S 4,00/(C) Gauthier-Villars 14
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