Gorde:
| Egile nagusia: | |
|---|---|
| Formatua: | Recurso digital |
| Hizkuntza: | |
| Argitaratua: |
Zenodo
2026
|
| Gaiak: | |
| Sarrera elektronikoa: | https://doi.org/10.5281/zenodo.19199433 |
| Etiketak: |
Etiketa erantsi
Etiketarik gabe, Izan zaitez lehena erregistro honi etiketa jartzen!
|
Aurkibidea:
- <p>Nuclear spin-orbit coupling is essential to the nuclear shell model — it splits single-particle levels and generates the observed magic numbers 28, 50, 82, and 126 — yet in every existing shell-model formulation, the L·S operator is postulated, not derived. We show that the spin-orbit interaction emerges as an algebraic identity from the discrete symmetry Z<span>6 </span>= Z<span>2 </span>×Z<span>3 </span>of the vacuum manifold in Elastic Diffusive Cosmology (EDC).</p> <p>Starting from three axioms — a 5D Lorentzian manifold (P1), a thick brane with compact extra dimension (P2), and a density asymmetry across the brane (P3) — we derive:</p> <p>1. The vacuum manifold V<span>vac </span>= S<span>1 </span>×S<span>2 </span>carries topological defects with Z<span>6 </span>symmetry.</p> <p>2. The Complete Orthonormal Triad (COT) of the Z<span>6 </span>junction produces, by an algebraic identity, an isotropic second-moment matrix W<span>ij </span>= 2gδ<span>ij</span>.</p> <p>3. The resulting splitting operator is exactlyˆO<span>Z6 </span>= 2gL·S — the spin-orbit interaction.</p> <p>4. By Wigner–Eckart reduction, the splitting is ∆E<span>SO </span>= g(2l+ 1), matching 15 measured subshell splittings with correlation r= 0.9985.</p> <p>5. The Z<span>6 </span>spin-orbit reordering of harmonic oscillator shells reproduces all seven magic numbers 2, 8, 20, 28, 50, 82, 126 with zero free parameters.</p> <p>A negative-control calculation shows that a 2D hexagonal lattice fails to produce the L ·S structure (57.7% anisotropy), proving that the 3D COT geometry is essential.</p> <p>The derivation has one calibration (|g|= 2.11 MeV from the <span>16</span>O 1p splitting) and no tunable parameters beyond this overall energy scale.</p>