Research Program: One of the fundamental outstanding problems in the field of physics is to understand the structure and properties of the atomic nucleus starting from the basic interactions among the neutrons and protons (collectively called nucleons) and employing only quantum mechanical many-body theory. Great progress has been made in solving this problem in the last ten years due to new developments in nuclear many-body theory and advances in computer technology. One of these developments is the so-called No Core Shell Model (NCSM), in which all the nucleons in a nucleus are treated as being active, instead of only a few valence nucleons outside an assumed inert core. The NCSM approach simplifies the structure of the many-body problem to be solved and has had considerable success in describing the properties of light nuclei, up to masses near oxygen, i.e., nucleon number 16. This same NCSM approach can be and is being now applied to nuclear reaction theory. One of the fundamental advances following from these investigations is the understanding of the importance of not only pair-wise interactions among nucleons in determining nuclear structure, but also of triplet (or three-nucleon) interactions. More work needs to be done to determine whether or not four-nucleon and higher-nucleon interactions are also necessary. Another important problem is to understand the relationship between the energy required in the two-nucleon system relative to the energy available for all the nucleons in a nucleus.
Broader Impact: Our NCSM approach not only has wide applications in theoretical nuclear physics but also in atomic and molecular physics and in condensed matter physics, such as, the problem of a small number of fermions, e.g., electrons, constrained by an harmonic oscillator trap. In addition, our research program is actively educating and mentoring a new generation of young nuclear theorists. For example, during the previous award period, our research group included two undergraduate students, two graduate students, and three post-doctoral research associates. The principal investigator also teaches undergraduate and graduate nuclear physics courses at the University of Arizona and lectures on nuclear structure theory at international summer schools, workshops and symposia.
The overall goal of my research efforts is to establish a first principles formailism for calculating the properties of atomic nuclei, e.g., binding energies, radii, transitions strengths, etc. In this regard my collaborators and I have, over the last 20 years, developed the so-called No-Core Shell Model (NCSM), which is an ab initio approach for microscopically calculating nuclear properties. It is called the NCSM because all A nucleons (protons and neutrons) in a nucleus are treated as active, as opposed to the Standard Shell Model of an inert core of nucleons plus a few valence nucleons. The NCSM has been successfully applied to nuclei up to around mass A = 16 (e.g., oxygen), but it is difficult to apply it to heavier nuclei, because of the huge increase with increasing A in the size of the configuration space that must be used in the numerical calculations. Consequently, in the current grant period my research has focused on how to improve the NCSM and how to extend it to nuclei heavier than mass 16, as follows: 1. In order to treat loosely bound and unbound nuclei (especially those far from stability--so-called exotic nuclei), we have now included the continuum in the NCSM, using the Berggren basis, which contains configurations in the complex energy plane. This approach, which we call the No-Core Gamow Shell Model, has been successfully applied to the unbound 5He nucleus. Thus, we can now calculate the properties of exotic nuclei near the proton and neutron driplines, which will be produced and studied at the growing number of rare isotope beam accelerators worldwide. 2. For nuclei with A>16 we have developed the "NCSM-with-a-core" method, which allows us to use the NCSM to calculate microscopically the input for standard shell model calculations, which can then be used for investigating the properties of nuclei in an entire nuclear major shell. Our approach has now been adopted by other research groups but using their own particular numerical methods. To date, the results obtained by all of these research groups are consistent with one another. In addition, we have developed our own version of "Importance Truncation", which truncates the basis space to a more manageable size, based on physical input. 3. Another exciting project is the development of a formalism for using Chiral Effective Field Theory to relate the symmetries of Quantum Chromodynamics (QCD) directly to the construction of effective interactions in a model space, such as in the NCSM approach. This is more fundamental and direct than first constructing a nucleon-nucleon potential, which is then used to construct the model-space effective interaction. This is especially true, because potentials are not physical observables. First applications of this approach have been quite successful, particularly for few-body systems in a harmonic trap. Other research groups have now taken up our approach and applied it their problems of interest. During the current grant period, I have worked with three post-doctoral research associates, one PhD student and two undergraduate students and contributed to their education, training and scientific development.
