With the opening of new facilities, such as the Facility for Rare Isotope Beams, exotic nuclei will be increasingly accessible. Many exotic nuclei are strongly coupled to the continuum resulting in interesting structure formations, such as halo nuclear states or nuclear resonances. In this thesis, the Gamow Shell Model framework is used to describe nuclei as Open Quantum Systems. This framework is a configuration-interaction shell model implemented in the Berggren basis which includes bound, resonant, and scattering states on equal footing. Two case studies are presented to highlight the impact of continuum effects on nuclear structure. Spectroscopic Factors are calculated for 8,9C, 8B, 8,9Li, and 8He using a traditional Shell Model approach (ignoring the continuum) and the Gamow Shell Model. The results from both methods are compared and demonstrate Spectroscopic Factors in these nuclei are dependent on the continuum. The newly discovered ephemeral nucleus 9N will be presented, which is unique with over half of its nucleons lying in the continuum. A projection method will be outlined to extract the continuum effects from the Gamow Shell Model to understand and directly quantify the effects of continuum coupling. Finally, a new outreach and community engagement demonstration, designed to educate the general public about nuclear structure and decays, will be discussed.
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