STUDY OF NUCLEAR SHELL STRUCTURE AND MAGIC NUMBERS

Abstract

The nuclear shell model has been instrumental in explaining the stability patterns observed in atomic nuclei, particularly through the concept of magic numbers. These numbers, corresponding to fully filled proton or neutron shells, are associated with enhanced nuclear stability, reduced deformation, and distinctive spectroscopic properties. In this study, we explore the theoretical foundations of the nuclear shell structure, emphasizing the spin-orbit coupling and its role in producing experimentally observed magic numbers. We analyze experimental data from nuclear binding energies, separation energies, and nuclear radii across isotopic chains to identify signatures of shell closures. Furthermore, modern approaches—including mean-field theories and ab-initio calculations—are employed to investigate shell evolution in exotic nuclei far from stability. Our findings confirm the persistence of traditional magic numbers in stable isotopes while revealing potential modifications in neutron-rich systems, suggesting the emergence of new magic numbers in regions of high isospin asymmetry. These results have implications for nuclear astrophysics, particularly in the r-process nucleosynthesis pathway, and for the synthesis of super heavy elements.