Isospin-breaking interactions in the nuclear shell model

The ever advancing scale of experimental nuclear physics has lit a fire under nuclear theorists. With the inevitable explosion in the number of exotic isotopes available for study at the soon to be operational Facility for Rare Isotope Beams and other rare isotope labs, the need for quantitative descriptions of nuclei far from stability is clear.The Nuclear Shell Model allows for the calculation of realistic nuclear wavefunctions using configuration-interaction theory. This theory examines only the valence nucleons in a restricted model space or "nuclear shell" and treats the filled shells in the core of the nucleus as inert. Interactions used in this theory usually take the form of one- and two-body terms which can be built up from fundamental theory using various many body methods and are continually being improved. The ab initio based methods now include three-body interactions together with improved methods for handling short-ranged correlations and model space truncations. This enables them to describe binding energies within several MeV and energy spectra within about 500 keV.One can phenomenologically improve upon these interactions by using the energy data for nuclei in a given mass region to obtain effective two-body matrix elements for a given model space. An effective method for doing this is to start with an ab initio based Hamiltonian and then to modify the best determined linear combinations of interaction parameters as determined by the energy data using what is called the singular value decomposition method. This can be thought of as a truncation of the allowed parameter space. The result is that both binding and excitation energies can be described to within 150-200 keV. The relatively small modifications to the ab initio interaction parameters reflect deficiencies in the many-body methods and their inputs.This method has resulted in widely used Hamiltonians for several model spaces. Universal effective sd-shell Hamiltonians have a history dating back to the 1970s, and the newest updates are presented in this dissertation. The USDC interaction, as it is called, and its companion interactions are the first effective sd-shell interactions that incorporate energies in the fitting protocol from proton rich nuclei and explicitly includes isospin-breaking terms. Apart from the addition of a Coulomb interaction, an isotensor term is added to the strong interaction in order to reproduce the oscillation found in the c-coefficients of the Isobaric Multiplet Mass Equation. A modified version of Coulomb is used in the USDCm interaction, which was constrained to better reproduce mirror energy differences.Experimental binding and excitation energies across the shell are reproduced by USDC, apart from the known island of inversion nuclei and the neutron-rich fluorine isotopes. A single-particle model of the Thomas-Ehrman shift is developed to account for coupling to the continuum not present in the shell model results for nuclei at or near the proton dripline. Using this model and the improved theoretical binding energies, new predictions for the proton and neutron driplines are presented. The possibility of 34Ca being a two-neutron emitter is explored.Isospin level mixing of isobaric analogue states with nearby states can significantly impact nuclear decays. Several cases with experimentally measured isospin mixing are explained with the new interactions. However, USDCm over predicts the strength of the associated matrix elements. This motivates a refinement of USDC in which an isovector term is added to the strong interaction and constrained to reproduce changes of mirror energy differences in the isobaric doublets. This is shown to provide the benefits of the modified Coulomb interaction without its detriments.An effective fp-shell interaction is presented tailored to the neutron rich calcium isotopes out to 60Ca. This is constrained with the nuclear interaction fitting code FINCH, developed during the creation of the USDC interactions. This interaction is shown to be a good renormalized fp-shell interaction and several predictions for unobserved states are presented. Using this and inter-model comparisons leads us to conclude that 60Ca is likely doubly-magic to a similar level as $. {68}$Ni.Following these successful implementations of effective universal configuration-interaction Hamiltonians, future research aims to develop an sdpf model space interaction for deeper study of the N=20, 28, and 42 islands of inversion.