Alpha-Decay Systematics and a New Scaling Law in Heavy and Superheavy Nuclei

A systematic investigation of α-decay properties in even-even isotopic chains of Po (Z=84), Cm (Z=96), Hs (Z=108), and Fl (Z=114) is presented using a semi-classical approach. Ground-state properties, including binding energies and nucleon density distributions, are calculated by minimizing a Skyrme-based energy density functional augmented with microscopic corrections. The derived nuclear densities and Q_α-values are used to construct the α-decay deriving potential through the double-folding model (DFM). The α-decay dynamics are treated quantum mechanically based on the preformed cluster model (PCM) within the Wentzel-Kramers-Brillouin (WKB) approximation. The analysis reveals distinct signatures of spherical shell closures at N=126 and N=184, along with secondary anomalies near N = 148, 152, and 162, which are consistent with deformed sub-shell effects predicted by nuclear structure models. The signature of daughter nuclear stability is systematically observed through one or more of the following features: shortened α-decay half-lives, enhanced Q_α values, increased penetrabilities, and/or reduced assault frequencies. A new universal scaling relation, relating the decay half-lives and a scaled combination of nuclear charge and decay energy, is established, showing strong correlation across a wide mass range. Systematic comparisons demonstrate particular predictive advantages for superheavy nuclei, with the proposed method accurately reproducing observed half-life variations across all isotopic chains. The results confirm the sensitivity of α-decay observables to both spherical and deformed shell effects and reinforce the role of α-decay systematics as powerful tools for probing nuclear structure and guiding predictions in unexplored regions of the nuclear chart.