Green's Functions and the Nuclear Many-Body Problem

The properties of nuclei with extreme neutron to proton ratios are becoming available for experimental scrutiny at facilities like the Facility for Rare Isotope Beams (FRIB) on the campus of Michigan State University. Most of the experimental probes to study these exotic nuclei involve particles that interact strongly themselves making it difficult to extract the properties of individual protons or neutrons in these exotic systems. The present project overcomes this difficulty by providing a simultaneous description of positive energy nucleons related to probes and bound nucleons inside these exotic nuclei. The framework of the propagator method of quantum mechanics is employed to generate critical insights into the properties of very neutron-rich nuclei, and is therefore relevant for the physics of neutron stars by clarifying where neutrons are found with respect to the distribution of protons and how neutrons are captured by neutron-rich nuclei. The PI mentors graduate students in this research and collaborates with experimental colleagues who perform related experiments. The propagator method employs non-local potentials constrained by experimental data that allow for the accurate description of ground-state properties of nuclei by the method of dispersion relations. The resulting Dispersive Optical Model (DOM) is able to describe or predict all relevant experimental data for nuclei where data are available. Extrapolations of these potentials to exotic nuclei then generate predictions that can be tested experimentally at FRIB. The analysis of various nuclear reactions on these exotic nuclei benefit from using the ingredients of the DOM method in analogy to the successful analysis of electron-induced proton knockout reactions thereby elucidating the properties of protons and neutrons in exotic nuclei. Predictions of neutron distributions for nuclei with excess neutrons are intrinsic in this analysis. The propagator method will simultaneously be employed to calculate the properties of nuclei by starting from the underlying interactions between nucleons as constrained by the symmetries of the fundamental theory of quarks and gluons, Quantum Chromo Dynamics and the available data for the properties of two nucleons. Such calculations will be applied with a new strategy that allows the ab initio calculation of scattering properties off heavier nuclei. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.