Global Trends of Nuclear Radii and Binding Energies from the NUCLEI-PACK Framework

Abstract

I present a proof-of-concept study of nuclear radii and binding energies within NUCLEI-PACK, a novel semi-classical framework based on optimized sphere packing of nucleons and clusters. In this approach, proton and neutron positions are determined through a constrained packing algorithm with uniform nucleon radii, followed by global optimization across the nuclear chart ($1 \leq A \leq 250$). From these geometric configurations, I compute charge and matter radii, as well as binding energies. The model successfully reproduces global trends in nuclear size and stability, while maintaining transparency and computational efficiency. A fit of the Coulomb and surface terms of the semi-empirical mass formula shows remarkable agreement with theoretical expectations. These results establish the feasibility of NUCLEI-PACK as a systematic tool for describing nuclear bulk properties across the chart of nuclides.