The goals of nuclear physics are to understand:
- how simplicity emerges from complexity
- the origin of the elements in the universe
- the fundamental particles of nature and their interactions

Nuclear theory divides into several major methods:
- Ab-initio
- Configuration Interaction (CI)
- Energy Density Functional (EDF)
- Collective
- Cluster
- Reaction and Time Dependent

With these methods, most properties of all nuclei can be understood with varying degrees of accuracy. The theory group at the NSCL has expertise in all of these theoretical methods. Collaboration among the members of group and with the experimental program at the NSCL provide the resources and interactions needed to make advances toward the overall goals of nuclear physics.

One of the major uncertainties lies in the properties of the nuclei far from stability. This unknown region is shown by the orange area in the figure. The neutron drip line is where the orange area stops to the right. The other colors indicate the known energies of the 2⁺ states for the even-even nuclei with low to high values indicated by purple-blue-aqua-green-yellow-orange-red. The high energies and ridges are due to the spherical properties that come from nuclear magic numbers shown by the grey lines at neutron and protons numbers 8, 20, 28, 50, 82 and 126. Nuclei inside the ovals in the figure require collective methods for their understanding. In these regions most of the nucleons move coherently. The region outside of the ovals can be considered by the CI method. In these regions the structure for the lowest-lying states is dominated by the properties of a few single-particle orbitals and their interactions. In the following I will gives some examples of the CI method in collaboration with experiment [1] and in collaboration with other methods.

Many experiments at the NSCL are designed to find new nuclei and their properties in the unexplored regions of the nuclear chart. Theory and experiment collaborate before an experiment to determine the best possible measurements for improving the applicable theoretical methods. After the experiment, theory and experiment again collaborate to understand the outcome and its consequence for improving the models and methods.

For example, CI theory for the sd shell predicted properties of nuclei near the neutron drip line in the oxygen isotopes. Many of these have been verified. But other results show the need to go beyond the sd shell in terms of including higher-energy orbitals and coupling to the continuum. [2] Future experiments will consider, for example, neutron-rich nuclei near the islands of inversion [3] , the regions ⁶⁰Ca, ⁷⁸Ni and ¹⁰⁰Sn. The unknown properties of the single-particle degrees of freedom are most transparent in these regions near these potentially double-magic nuclei.

Other experiments are designed to explore uncertain aspects of nuclear resonances at high excitation energy. For example, the ⁵⁶Ni to ⁵⁶Cu charge-exchange reaction revealed the properties of the Gamow-Teller resonance that constrained the pf shell Hamiltonian. This constraint improves the theoretical electron capture rates used for electron capture in supernovae [4].

Even in well studied regions of the nuclear chart all theoretical methods have limitations. For example, the theoretical uncertainty for binding energies and low-lying excitation energies ranges from about 150 keV for the CI method to about one MeV for the EDF method. However, there are some astrophysical rates that require an energy precision of 10 keV or less. The goal of some experiments is to measure the required energy precisely. Collaboration with theory is often required to provide the decay properties of these levels for the rate. A recent example is the ⁵⁷Cu(p,gamma)⁵⁸Zn reaction rate that determines the rp-process flow through this mass region. [5].

The CI method usually starts from some ab-initio input. Up until recently a major problem has been the unknown three-body interactions that has resulted in the need for significant phenomenological adjustments. A major advance in the last decade has been the development of better ab-initio methods that include the three-body interaction. This new starting point will result in significant improvements in the CI methods over the next decade. Ab-initio methods can also be used to constrain the parameters of the EDF models, in particular, for the neutron equation of state and the related symmetry energy. [6] Another example for collaboration between methods is in the use of EDF models to constrain the single-particle and monopole part of the CI Hamiltonians. [7]

References

[1] NSCL experimental collaborations link to publications

[2] Oxygen Isotopes Beyond the Neutron Drip Line [link to webpage]

[3] Islands of Shell Breaking [link to webpage]

[4] Gamow-Teller Transition Strengths from ⁵⁶Ni M. Sasano et al., Phys. Rev. Lett. 107, 202501 (2011). [link to paper]

[5] Determining the rp-Process Flow through ⁵⁶Ni: Resonances in ⁵⁷Cu(p,g)⁵⁸Zn Indentified with GRETINA, C. Langer et al. Phys. Rev. Lett. 113, 032502 (2014). [link to paper]

[6] The Neutron Equation of State [link to webpage]

[7] Configuration Interactions Constrained by Energy Density Functionals [link to webpage]