Applications of the similarity renormalization group to the nuclear interaction

The Similarity Renormalization Group (SRG) is investigated as a powerful yet practical method to modify nuclear potentials so as to reduce computational requirements for calculations of observables. The SRG proves to be versatile and robust in its treatment of these interactions and opens the door to a deeper understanding of the renormalization process.;Chiral Effective Field Theory (chiEFT) provides a consistent and rigorous parametrization of the inter-nucleon interaction. While already softer than other available potentials, transformation via the Similarity Renormalization Group (SRG) brings numerous computational benefits. The hierarchy of many-body forces inherent in chiEFT's are also treated consistently by the SRG's simple formalism. The SRG is a natural partner to this modern program of formulating the nuclear interaction.;The key feature of SRG transformations that leads to computational benefits is the decoupling of low-energy nuclear physics from high-energy details of the internucleon interaction. We examine decoupling quantitatively for two-body observables and few-body binding energies. The universal nature of this decoupling is illustrated and errors from suppressing high-momentum modes above the decoupling scale are shown to be perturbatively small.;As implemented here, the SRG provides freedom to choose the form of its transformations and can be tailored to a given application. We explore the impacts of various choices and their decoupling properties, specifically a block-type transformation inspired by previous renormalization group techniques. Sharp and smooth block-diagonal forms of phase-shift equivalent nucleon-nucleon potentials in momentum space are generated as examples and compared to analogous low-momentum interactions ("Vlow k").;To explore the SRG evolution of many-body forces, we use as a laboratory a one-dimensional system of bosons with short-range repulsion and mid-range attraction, which emulates realistic nuclear forces. The free-space SRG is implemented for few-body systems in a symmetrized harmonic oscillator basis using a recursive construction analogous to no-core shell model implementations. This approach is fully unitary up to induced A-body forces when applied with an A-particle basis (e.g., A-body bound-state energies are exactly preserved). The oscillator matrix elements for a given A can then be used in larger systems. Errors from omitted induced many-body forces show a hierarchy of decreasing contribution to binding energies. An analysis of individual contributions to the growth of many-body forces demonstrates such a hierarchy and provides an understanding of its origins. Several other important sample calculations are explored in this model for future use in realistic systems.;Building on one-dimensional results we performed the first practical evolution of three-dimensional many-body forces within the No-Core Shell Model basis. Results for the 3H binding energy are consistent with previous calculations involving momentum-space evolution of only two-body forces, and validate expectations from calculations in the one-dimensional oscillator basis. When applied to 4He calculations, the two- and three-body oscillator matrix elements yield rapid convergence of the ground-state energy with a small net contribution of the induced four-body force. The radius of light nuclei is also explored in the three-dimensional basis.