Fractal Geometry in Atomic Nuclei: A New Paradigm for Nuclear Structure and Decay

The liquid drop and shell models have long described nuclear structure. Yet, certain phenomena—such as magic numbers, exotic decays, and the stability of superheavy nuclei—suggest an underlying geometric order beyond these traditional frameworks. This paper proposes a fractal-based model of atomic nuclei, where the fractal dimension ( 𝐷f ) emerges as a fundamental parameter governing nuclear stability, binding energy, and decay modes. This study demonstrates that magic nuclei exhibit a critical fractal dimension (𝐷f ≈1.44), corresponding to closed-shell symmetries, while exotic nuclei (e.g., neutron halos, proton-rich systems) deviate from this ideal, with 𝐷f correlating to their decay lifetimes and deformation. A unified formula for binding energy, incorporating 𝐷f reproduces experimental values with remarkable accuracy (±0.3%) and predicts new islands of stability for superheavy elements (Z≥114).this study introduce a fractal dimension parameter 𝐷f that correlates with nuclear stability, binding energy, and decay half-lives. Through comparative analysis with experimental data—including alpha, beta, and electron capture decays.