Experimental interest in nuclei far from stability, especially due to proposed advancements in rare isotope facilities, has stimulated improvements in theoretical predictions of exotic isotopes. However, standard techniques developed for nuclear structure calculations, Configuration Interaction theory and Energy Density Functional methods, lack either the generality or the accuracy necessary for reliable calculations away from stability. Hybrid methods, which combine Configuration Interaction theory and Energy Density Functional methods in order to exploit their beneficial properties, are currently under investigation for improved theoretical capabilities.A new technique to produce nuclear Hamiltonians has been developed, implementing renormalization group methods, many-body perturbative techniques, and Energy Density Functional methods. Connection to the underlying physics is a primary focus, limiting the number of free parameters necessary in the procedure. The main benefit of this approach is the improvement in the quality of effective interactions outside of standard model spaces.In the Hybrid Renormalization Procedure developed in this dissertation, Skyrme energy density functionals provide a realistic single particle basis that accounts for the long tail of loosely bound orbits, especially significant for valence orbits of exotic isotopes. A microscopic nucleon-nucleon potential is softened with renormalization group techniques to eliminate the hard core of the nuclear interaction. Many-body perturbative techniques, in the form of Rayleigh-Schrodinger theory, implement the realistic basis to convert the low-momentum interaction into a model space of interest.The basis is an important ingredient in the renormalization and greatly affects the results obtained with the Hybrid Renormalization Procedure, specifically through the single particle energies derived from Skyrme functionals. A comparison of the standard harmonic oscillator basis and the realistic basis derived from energy density functional methods illustrates the necessity of a realistic basis when a microscopic nucleon-nucleon potential is renormalized into the nuclear medium. Because Skyrme single particle energies are unreliable, other sources are desired for the determination of this component of the effective interaction.An sd shell interaction is produced for a proof of principle, and extensive results are obtained in the island of inversion region and for 42Si. One hundred nuclei are calculated near the island of inversion region of the nuclear chart. Binding energies and low-lying excitations agree well with available experimental data. The neutron dripline is determined theoretically for isotopic chains near the island of inversion. The boundaries of the island of inversion region are mapped out, suggesting an extension to lighter and more neutron-rich isotopes than measured experimentally thus far. Reactions in the island of inversion region have also been studied and reproduce experimental behavior, such that conclusions can be reached regarding the evolution of shell structure and the properties of states of particular interest. The known states of 42Si are reproduced with effective interactions derived from the Hybrid Renormalization Procedure, but the detection of the 0+2 and 4+1 states are important to distinguish between different theoretical approaches.The viability of the Hybrid Renormalization Procedure is evident from the results in the island of inversion region. Applications to other exotic regions of the nuclear chart are desired for future research.
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