Green's Functions and the Nuclear Many-Body Problem

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The properties of nuclei with large or small neutron to proton ratios are becoming available for experimental scrutiny at facilities like the Facility for Rare Isotope Beams (FRIB) under construction 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. This project aims at overcoming this difficulty by providing a simultaneous description of positive energy nucleons, the domain of elastic scattering, and bound nucleons, the domain of nuclear structure, using the framework of the propagator method of quantum mechanics. This approach will provide critical insight 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. The PI will mentor graduate students in this research and collaborate with experimental colleagues who will perform related experiments.The propagator method will be utilized with 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. Simultaneously, this implementation will be able to describe or predict all relevant experimental data in the continuum including elastic scattering cross sections. It will therefore be possible to study various nuclear reactions using the ingredients of this method in analogy to the successful analysis of electron-induced proton knockout reactions, thereby clarifying the properties of protons and neutrons in exotic nuclei as well as suggesting relevant new experiments. In particular, the prediction of the neutron distribution for nuclei with excess neutrons will be of critical importance for experiments at Jefferson Lab and future experiments at FRIB. The propagator method will also 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 scheme that allows the ab initio calculation of properties of heavier nuclei that have not been studied in this way to date.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.