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We present the study of weakly bound, neutron-rich nuclei using the nuclearshell model employing the complex Berggren ensemble representing the boundsingle-particle states, unbound Gamow states, and the non-resonant continuum.In the proposed Gamow Shell Model, the Hamiltonian consists of a one-bodyfinite depth (Woods-Saxon) potential and a residual two-body interaction. Wediscuss the basic ingredients of the Gamow Shell Model. The formalism isillustrated by calculations involving {\it several} valence neutrons outsidethe double-magic core: $^{6-10}$He and $^{18-22}$O.Comment: 19 pages, 20 encapsulated PostScript figure

Gamow shell model description of weakly bound nuclei and unbound nuclear states