Proc. Int. Conf. "Horizons of Innovative Theories, Experiments and Supercomputing in Nuclear Physics", June 4-7, 2012, New Orleans, Luisiana, USA; 10 pages, 4 figuresInternational audienceStructure of weakly bound/unbound nuclei close to particle drip lines is different from that around the valley of beta stability. A comprehensive description of these systems goes beyond standard Shell Model and demands an open quantum system description of the nuclear many-body system. We approach this problem using the Gamow Shell Model which provides a fully microscopic description of bound and unbound nuclear states, nuclear decays, and reactions. We present in this paper the first application of the GSM for a description of the elastic and inelastic s...