Jian Constant and α-Cluster Hierarchical Phenomenological Model: Unveiling Intrinsic Geometric Characteristics of Nuclear Cluster Structure

Based on the nuclear α-cluster model, this paper constructs a hierarchical phenomenological model and defines for the first time the Jian constant j — a dimensionless geometric characteristic parameter describing the intrinsic structure of α-clusters. The model divides nuclear structure into two layers: the intrinsic core layer and the external perturbation layer. In the intrinsic core layer, the quantum correlation of four nucleons inside the α-particle (4He) is idealized as an effective average configuration with regular tetrahedral symmetry, leading to the ideal geometric eigenvalue of the Jian constant j0=26/3≈1.633 (uniquely determined by 3D regular tetrahedral symmetry without artificial fitting parameters). Considering the proton-neutron non-identity effect in real α-particles, systematic intrinsic perturbation correction is completed, and the physically corrected range of the Jian constant is jphys=1.632∼1.634, verifying the strong robustness of the ideal geometric value and its underlying universality for all nuclei containing α-clusters. The macroscopic observable properties of nuclei are the superposition of the intrinsic core term and quantifiable external perturbation correction terms. Using the generalized nuclear radius formula derived in this paper, quantitative calculations are performed on typical nuclides: for pure α-cluster nuclei, the relative errors between model calculations and experimental values are all within 6%; for weakly bound nuclei with external nucleons, the intrinsic core rule remains valid, and macroscopic deviations can be reasonably explained by perturbation corrections. This model provides a concise geometric symmetry-based explanation for the intrinsic stability of α-clusters, offers a fitting-free geometric preferred value for the equilibrium spacing of α-particles in the Brink model, and presents a novel, universally applicable geometric perspective for the study of nuclear cluster structure.