Halo Nuclei Beyond the Shell Model: A Fractal-Dimensional Approach

Halo nuclei represent one of the most exotic classes of nuclear systems, characterized by extended matter distributions and weakly bound valence nucleons. This study systematically investigates known halo nuclei across the periodic table using a fractal nuclear model that incorporates self-similar geometric structures and fractal dimension ( D f) as a key parameter. Proton and neutron halos—including those in ⁶He, ⁸He, ¹¹Li, ¹¹Be, ¹⁹C, ²²N, and ³⁷Mg—are analyzed in terms of their spatial configurations, binding energies, and decay modes. This model demonstrates that halo structures correspond to elevated fractal dimensions ( D f>1.5), indicating geometric symmetry breaking and the emergence of loosely coupled nucleon clouds beyond the classical nuclear core. This study show that neutron-rich systems exhibit complex branching geometries consistent with chaotic fractals, while proton halos—such as in ¹⁷F and ⁸B—reveal linear, Coulomb-stretched configurations. By applying the fractal binding energy and decay rate formulations, the model accurately reproduces experimental observables, including half-lives and charge radii. This framework bridges shell model limitations by offering a geometric explanation for extended halo distributions and predicts conditions under which halo systems form and decay. The results provide new insights into weakly bound nuclear matter, with implications for nuclear astrophysics, r-process pathways, and the limits of nuclear stability.