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 gener