Extensions to the No-Core Shell Model: Importance-Truncation, Regulators and Reactions

The No-Core Shell Model (NCSM) is a first-principles nuclear structure technique, with which one can calculate the observable properties of light nuclei A ≤ 20. It is considered ab-initio as the only input to the calculation is the nuclear Hamiltonian, which contains realistic two or three-nucleon (NN or NNN) interactions. Provided the calculation is performed in a large enough basis space, the ground-state energy will converge. For A ≤ 4 convergence has been demonstrated explicitly. The NCSM calculations are computationally very expensive for A ≥ 6, since the required basis size for convergence often approaches on the order of a billion many-body basis states. In this thesis we present three extensions to the NCSM that allow us to perform larger calculations, specifically for the p-shell nuclei. The Importance-truncated NCSM, IT-NCSM, formulated on arguments of multi-configurational perturbation theory, selects a small set of basis states from the initially large basis space, in which the Hamiltonian is now diagonalized. Previous IT-NCSM calculations have proven reliable, however, there has been no thorough investigation of the inherent error in the truncated IT-NCSM calculations. We provide a detailed study of IT-NCSM calculations and compare them to full NCSM calculations in an attempt to judge the accuracy of IT-NCSM in heavier nuclei. Even when IT-NCSM calculations are performed, one often needs to extrapolate the ground-state energy from the finite basis (or model) spaces to the infinite model space. Such a procedure is common-place but does not necessarily have the ultraviolet (UV) or infrared (IR) physics under control. We present a potentially promising method that maps the NCSM parameters into an effective-field theory framework, in which the UV and IR physics is treated appropriately. The NCSM is well suited to describing bound-state properties of nuclei, but is not well adapted to describe loosely bound systems, such as the exotic nuclei near the neutron drip line. With the inclusion of the resonating group method (RGM), the NCSM/RGM can provide a first-principles description of exotic nuclei. The NCSM/RGM is also the first extension of the NCSM that can describe dynamic processes such as nuclear reactions