Abstract not provided.

We present an overview of recent results and developments of the no-core shell model (NCSM), an ab initio approach to the nuclear many-body problem for light nuclei. In this aproach, we start from realistic two-nucleon or two- plus three-nucleon interactions. Many-body calculations are performed using a finite harmonic-oscillator (HO) basis. To facilitate convergence for realistic inter-nucleon interactions that generate strong short-range correlations, we derive effective interactions by unitary transformations that are tailored to the HO basis truncation. For soft realistic interactions this might not be necessary. If that is the case, the NCSM calculations are variational. In either case, the ab initio NCSM preserves translational invariance of the nuclear many-body problem. In this review, we, in particular, highlight results obtained with the chiral two- plus three-nucleon interactions. We discuss efforts to extend the applicability of the NCSM to heavier nuclei and larger model spaces using importance-truncation schemes and/or use of effective interactions with a core. We outline an extension of the ab initio NCSM to the description of nuclear reactions by the resonating group method technique. A future direction of the approach, the ab initio NCSM with continuum, which will provide a complete description of nuclei as open systems with coupling of bound and continuum states is given in the concluding part of the review.

This book provides the first graduate-level, self-contained introduction to recent developments that lead to the formulation of the configuration-interaction approach for open quantum systems, the Gamow shell model, which provides a unitary description of quantum many-body system in different regimes of binding, and enables the unification in the description of nuclear structure and reactions. The Gamow shell model extends and generalizes the phenomenologically successful nuclear shell model to the domain of weakly-bound near-threshold states and resonances, offering a systematic tool to understand and categorize data on nuclear spectra, moments, collective excitations, particle and electromagnetic decays, clustering, elastic and inelastic scattering cross sections, and radiative capture cross sections of interest to astrophysics. The approach is of interest beyond nuclear physics and based on general properties of quasi-stationary solutions of the Schrödinger equation – so-called Gamow states. For the benefit of graduate students and newcomers to the field, the quantum-mechanical fundamentals are introduced in some detail. The text also provides a historical overview of how the field has evolved from the early days of the nuclear shell model to recent experimental developments, in both nuclear physics and related fields, supporting the unified description. The text contains many worked examples and several numerical codes are introduced to allow the reader to test different aspects of the continuum shell model discussed in the book.

The ab initio no-core shell model (NCSM) is extended to include a realistic three-body interaction in calculations for p-shell nuclei. They present results of first applications using the Argonne V8' nucleon-nucleon (NN) potential and the Tucson-Melbourne TM'(99) three-nucleon interaction (TNI). In addition to increase of binding energy, they observe a trend toward level-ordering and level-spacing improvement in comparison to experiment. With the TNI they obtain a correct ground-state spin for {sup 10}B contrary to calculations with NN potentials only. They also investigate neutrino-{sup 12}C exclusive cross sections and muon capture on {sup 12}C. They show that realistic nucleon-nucleon interactions underpredict the experimental cross sections by a factor of two or more. By including the TNI a much better agreement with experiment is achieved along with an encouraging trend.

The International Conference on Exotic Nuclei and Atomic Masses (ENAM) has gained the status of the premier meeting for the physics of nuclei far from stability. The selected and refereed papers presenting the main results constitute valuable proceedings that offer everyone working in this field an authoritative and comprehensive source of reference.

In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to a 4He+n+n description of 6He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core (4He) polarization effects.

Extensions to the No-Core Shell Model presents three extensions to the No-Core Shell Model (NCSM) that allow for calculations of heavier nuclei, 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 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. This thesis provides a detailed study of IT-NCSM calculations and compares them to full NCSM calculations to judge the accuracy of IT-NCSM in heavier nuclei. When IT-NCSM calculations are performed, one often needs to extrapolate the ground-state energy from the finite basis (or model) spaces to the full NCSM model space. In this thesis a careful investigation of the extrapolation procedures was performed. On a related note, extrapolations in the NCSM are commonplace, but up to recently did not have the ultraviolet (UV) or infrared (IR) physics under control. This work additionally presents a method that maps the NCSM parameters into an effective-field theory inspired framework, in which the UV and IR physics are treated appropriately. The NCSM is well-suited to describe 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 and the first extension of the NCSM.

This book provides a comprehensive overview of some key developments in the understanding of the nucleon-nucleon interaction and nuclear many-body theory. The main problems at the level of meson exchange physics have been solved, and we have an effective field theory using a phenomenological interaction pioneered by Achim Schwenk and Scott Bogner, which is nearly universally accepted as a unique low-momentum interaction that includes all experimental data to date.This understanding is based on a multi-step development in which different scientific insights and a wide range of physical and mathematical methodologies fed into each other. It is best appreciated by looking at the different 'steps along the way', starting with the pioneering work of Brueckner and his collaborators that was just as necessary and important as the insightful masterly improvements to Brueckner's theory by Hans Bethe and his students. Moving on from there, the off-shell effects that bedeviled Bethe's work — which had resulted in the 1963 Reference Spectrum Method — were treated relatively accurately by introducing an energy gap between initial bound states and an intermediate state. With their influential 1967 paper, Brown and Kuo prepared the effective field theory. Later, the introduction of 'Brown-Rho scaling' deepened understanding of saturation in the many-body system and fed directly into recent work on carbon-14 dating.

This book provides a comprehensive overview of some key developments in the understanding of the nucleon-nucleon interaction and nuclear many-body theory. The main problems at the level of meson exchange physics have largely been solved, and we now have an effective nucleon-nucleon interaction, pioneered in a renormalization group formalism by several of us at Stony Brook and our colleagues at Naples, which is nearly universally accepted as the unique low-momentum interaction that includes all experimental information to date.Our present understanding of these issues is based on a multi-step development in which different scientific insights and a wide range of physical and mathematical methodologies fed into each other. It is best appreciated by looking at the ‘steps along the way’, starting with the pioneering work of Brueckner and his collaborators that was just as necessary and important as the insightful improvements to Brueckner's theory by Hans Bethe and his students. Moving on from there, microscopic methods for nuclear structure calculations using the Brueckner G-matrix, and later low-momentum nucleon interactions, were developed and applied. With their influential 1967 paper, Brown and Kuo prepared the effective theory that allowed the description of nuclear properties directly from the underlying nucleon-nucleon interaction. Later, the addition of ‘Brown-Rho scaling’ to the one-boson-exchange model deepened the understanding of nuclear matter saturation, carbon-14 dating and the structure of neutron stars.