Nonlinear SU(3)-Modified Shell Model for Neutron-Rich Exotic Nuclei: Analytical Predictions of Magic Numbers and Deformation-Driven Spin Anomalies

Background: The conventional nuclear shell model faces significant challenges in describing exotic neutron-rich nuclei, particularly in predicting magic numbers, deformation-driven spin anomalies, and binding energy systematics. These discrepancies arise from the neglect of nonlinear effects induced by extreme neutron excess, such as three-body correlations and density-dependent spin-orbit interactions. Objective: We propose a fundamental modification of the shell model through the introduction of a nonlinear potential derived from the SU(3) Lie algebra structure, specifically tailored to address the physics of neutron-drip line nuclei. Methods: By synthesizing systematics from international nuclear databases (NNDC, ENSDF) and analytically solving the modified Hamiltonian via group-theoretic techniques, we develop a non-perturbative framework. The nonlinear potential Vnl = αρ2/3+β( ∇ρ) 2 , where ρ denotes the nucleonic density, is incorporated into the Hamiltonian while preserving SU(3) symmetry constraints on quadrupole deformation. Results: Our model predicts (i) the emergence of new magic numbers at N = 16 (exemplified by 24O) and N = 34 (for 54Ca), resolving long-standing discrepancies in single-particle level ordering; (ii) quantitative reproduction of anomalous J π = 3/2 − ground states in 31Ne through SU(3) multiplet splitting; (iii) enhanced stability predictions for superheavy nuclei near Z ≈ 120, N ≈ 184, driven by renormalized spin-orbit coupling. Significance: This SU(3)-modified formalism provides a unified description of stable and exotic nuclei without recourse to phenomenological adjustments. The derived analytical relations establish testable predictions for nextgeneration rare isotope facilities (FRIB, FAIR), while offering insights into deformation effects critical for r-process nucleosynthesis modeling.