Based on the framework of the nuclear α-cluster model, this paper constructs a hierarchical phenomenological model of α-clusters and defines for the first time a dimensionless geometric characteristic parameter describing the intrinsic structure of α-clusters: Jian Constant j. 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 among the four nucleons inside the α-particle (⁴He) can be idealized as an effective average configuration with regular tetrahedral symmetry. The ideal geometric eigenvalue of the Jian Constant is derived as j₀=2631. 633, which is uniquely determined by the three-dimensional regular tetrahedral symmetry without artificial fitting parameters. For the proton-neutron non-identity effect in real α-particles, a systematic intrinsic perturbation correction is completed, and the physically corrected range of the Jian Constant is obtained as j₇ₘₒ=1. 6321. 634, proving the strong robustness and underlying universality of the ideal geometric value. The macroscopic observable properties of atomic nuclei are the superposition of the intrinsic core term and the quantifiable external perturbation correction term. Using the revised generalized nuclear radius formula, quantitative calculations are performed for 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 macroscopic deviations can be reasonably explained by the perturbation correction term. This model provides a concise interpretation for the intrinsic stability of α-clusters based on geometric symmetry, offers a fitting-free geometric constraint for the equilibrium spacing of α-particles in the Brink model, and presents a novel and universally applicable geometric perspective for the study of nuclear cluster structure.
Jian Wen (Sat,) studied this question.