Ab initio no core methods have become major tools for understanding the properties of light nuclei based on realistic nucleon-nucleon (NN) and three-nucleon (NNN) interactions.

A brief description is provided for the inter-nucleon interactions that fit two-body scattering and bound state data, as well as NNN interactions. Major new progress, including the goal of applying these interactions to solve for properties of nuclei, is limited by convergence issues. That is, with the goal of obtaining high precision

solutions of the nuclear many-body Hamiltonian with no core methods (all nucleons treated on the same footing), one needs to proceed to very large basis spaces to achieve a convergence pattern suitable for extrapolation to the exact result. This thesis investigates: (1) the similarity renormalization group (SRG) approach to soften the

interaction, while preserving its phase shift properties, and (2) adoption of a realistic basis space using Woods-Saxon (WS) single-particle wavefunctions. Both have their advantages and limitations, discussed here. For (1), SRG was demonstrated by applying it

to a realistic NN interaction, JISP16, in a harmonic oscillator (HO) representation. The degree of interaction softening achieved through a regulator parameter is examined. For (2), new results are obtained with the realistic JISP16 NN interaction in ab initio calculations of light nuclei ^4He, ^6He and ^{12}C, using a WS basis optimized to minimize the ground-state energy within the truncated no core shell model. These are numerically-intensive many-body calculations.

Finally, to gain insight into the potential for no core investigations of

heavier nuclei, an initial investigation was obtained for the odd mass

A = 47-49 region nuclei straddling ^{48}Ca. The motivation for selecting these nuclei stems from the aim of preparing for nuclear double beta-decay studies of ^{48}Ca.

In these heavier systems, phenomenological additions to the realistic NN interaction determined by previous fits to A = 48 nuclei are needed to fit the data. The modified Hamiltonian produces reasonable spectra for these odd mass nuclei. A look at future pathways opened up with the results presented here concludes this investigation.