The starting point of nuclear theory is the two-nucleon interaction. Several interactions already in use satisfy the criterion of fitting the two-nucleon data, and we will use them in the ab initio theory of light nuclei. For ab initio calculations beyond mass 4, there are three well-proven methodologies: Green's Function Monte Carlo (GFMC), the No-Core Shell Model (NCSM), and the Coupled Cluster (CC) method, and we will use all three of them.

Fundamentally, Kohn-Sham Energy Density Functional (EDF) can be derived by systematically studying truncation effects in the full many-body theory. A candidate functional will be constructed by making use of EFT ideas.

By DFT theory we mean a theory based on an energy functional of orbital variables, such as the well-known Kohn-Sham density functional theory in condensed matter. In practice this approach is identical to the self-consistent mean-feld theory, apart from the fact that the EDF has a strong ab initio underpinning, in which the Hamiltonian is modified to take into account correlation effects. Mean-feld theory has long been an essential tool for understanding nuclei. From the early days of restricted application to magic nuclei and to the qualitative justification of the phenomenological shell model, the theory blossomed in the 1990s to become a powerful quantitative tool for all aspects of nuclear structure in medium to heavy nuclei. Present self-consistent mean-field theories are much like the EDF theory of condensed matter. We believe we can make an order-of-magnitude improvement in the reliability and accuracy of the theory with another generation of functionals coupled with the high-performance computing that is now available. These improvements are urgently needed for several reasons. EDF theory is the microscopic method of choice for calculating masses and for interpreting data from the upcoming generation of exotic beam facilities. Further, it is the basis of theories of dynamic processes describing fission and low-energy reactions.

Long-range correlation effects are not describable by Kohn-Sham functionals and should be treated as additive contributions to the energy. Even in condensed matter theory, it is recognized that correlation effects, such as the van der Waals interaction, need to be treated separately. In nuclear theory, there are indications that explicit correlation effects must be included to achieve the desired accuracy for predicting nuclear masses, but so far these have been treated only phenomenologically. There are a number of very different ways to treat correlations. Our project will pursue a number of these independently, compare them, and explore whichever are the most reliable and effcient. Included in these theories are two that have been used for a long time, the Generator Coordinate Method (GCM), and the Quasiparticle Random Phase Approximation (QRPA). We plan to consider also Fock-space methods, the coupled cluster (CC) theory, and the Configuration-Interaction (CI) method to guide the construction of the correlation term.. We expect to use these extensions without introducing additional parameters into the EDFs.

The theory of low-energy nuclear reactions has been well-developed for many years from a formal point of view. In particular we have the Hauser-Feshbach (HF) theory for very low energy neutron reactions; the Feshbach-Kerman-Koonin (FKK) theory for medium energy neutron-induced reactions; and the optical model both for elastic scattering and as an essential ingredient in the other theories. These theories have been applied successfully to analyze and predict a large body of experimental data. However, as currently used, they include many phenomenological parameters, and this weakens their predictive power and our ability to assess uncertainties. The DFT theory will play an essential role in replacing the phenomenological inputs with theoretical predicted ones. The primary interface between the structure and reaction theories are the transition densities and overlaps between states. These, along with the optical potential and the projectile interaction, are the ingredients of the coupled-channel reaction theory that will be applied. The transition densities will be generated between the ground state and a set of low-lying excited states, but later between any pair of levels. The level structure and its density will be exactly those states calculated by QRPA elaborations of the structure theories. In conjunction with these approaches we will also explore various incarnations of the Continuum Shell Model. Obviously, one important task of the project will be to coordinate the structure calculations with the needs of the reaction theory.

Both HF and FKK theories rely on the knowledge of nuclear level densities, and this is another place where EDF theory will provide needed input. Now the methodologies for calculating level densities are limited to medium mass nuclei, but with petascale computing it will become possible to calculate them across the whole chart of nuclides.