Mapping the Invisible: Modeling Nuclear Densities for Rare Isotope Analysis

Understanding the internal structure and dynamics within atomic nuclei is a fundamental quest for rare isotope research. This two-phase project focuses on the development of a python based framework to reconstruct matter density distributions of exotic and stable isotopes from experiments conducted by the MoNA Collaboration at the Facility for Rare Isotope Beams (FRIB) of Michigan State University. In the first phase, the nucleon density distributions for Magnesium-33, Carbon-12, Iron-56, and Lead-208 were computed by adjusting parameters such as the nuclear radius (R0), central density (𝜌0), and surface diffuseness (a), These density functions are then transformed into nuclear form factors via zeroth order, and spherical Bessel-integrated Fourier transforms. Their sensitivity to variations in R0 was studied showing a downward shift of the minima of diffraction when R0 increases. In the second phase, our calculations were compared and adjusted to reproduce the measured form factor of 33Mg obtained from the MoNA-LISA-Sweeper setup used during experiment e16027. This work is the first to demonstrate the possibility to extract matter radii of rare isotopes by the MoNA Collaboration, paving the way for a new exciting scientific program centered on the size of the nuclear matter.