Alternating Nucleon Model structures of stable nuclides from 2H to 64Zn
Abstract
The attached Master_data_ANM_H2_Zn64_v3 dataset provides three-dimensional Cartesian coordinates of quark and nucleon positions for 47 isotopes from ²H through ⁶⁴Zn predicted by the Alternating Nucleon Model (ANM). The predicted nuclear geometries were validated against experimental charge radii (R² = 0.984). Interactive 3D HTML visualizations display nucleon positions and inter-nucleon connections, enabling direct counting of nearest-neighbor nucleons within the strong force range (~1 fm). This structural parameter—the average coordination number (CAN)—accurately predicts the parabolic binding energy curve (R² = 0.992) via the regression BE/A = (5.9837 MeV) CAN - (0.6979 MeV) CAN ² - 4.0102 MeV, and correlates strongly with the EMC effect magnitude (R² = 0.965) through the linear relationship dR_EMC/dx = 0.1414CAN - 0.14. Reinterpreting this BE/A expression as Gibbs free energy (ΔG = ΔH - TΔS) partitions binding energy contributions into enthalpy-like (linear) and entropy-like (quadratic) terms. The linear coefficient (5.9837 MeV) represents the energetic benefit per nearest-neighbor interaction, while the quadratic penalty (0.6979 MeV) reflects entropic costs of increasing structural complexity and cross-linking with mass number. Converting the entropic coefficient to an effective temperature using the Boltzmann constant (kB = 8.62×10⁻⁵ eV/K) yields Teff = 8.1 × 10⁹ K (T₉,eff = 8.1), remarkably consistent with nuclear statistical equilibrium (NSE) conditions during explosive silicon burning in core-collapse supernovae (T₉ ≈ 5–10), where photodisintegration and reassembly reactions establish thermodynamic equilibrium among iron-peak nuclei. The ANM constructs nuclear structures from three empirical inputs: (1) proton charge radius rp = 0.8414 fm, defining nucleon spatial extent; (2) nucleon-nucleon potential minimum rNN ≈ 0.8 fm from Argonne v18, defining optimal separation distance; (3) prolate spheroidal geometry derived from the N→Δ(1232) quadrupole transition moment, representing intrinsic nucleon deformation. The model postulates that nucleons arrange to maximize nearest-neighbor connectivity while satisfying two constraints: (a) alternating isospin (reflecting the preferred stability of proton-neutron pairing), and (b) separation distances near the potential minimum. This geometric framework generates CAN as an emergent structural parameter that correlates with nuclear observables spanning multiple energy scales.
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 3 January 2026
- Document type
- Dataset