We investigate whether a single topological constraint Γvac = (α/2)·Ω·fG — where α is the fine-structure constant, Ω the closed solid angle of the nuclear surface, and fG a gauge-group weight derived from Lie-algebra dimension — accounts for empirical regularities across four nuclear decay modes. The hypothesis, termed Topological Density Functional Theory (T-DFT), predicts: (i) a Gamow-Teller quenching factor qGT = 0.759 from the eight generators of the SU(3) QCD vacuum; (ii) a 2.27% attenuation of electromagnetic transition rates and exact invariance of E2/M1 mixing ratios δ under SU(2); (iii) an a-decay pre-formation probability Pα = 0.759 from volumetric SU(3) confinement; and (iv) a topological lower bound on nuclear lifetimes Ttransit ~ 10-22s at the drip lines. We test these predictions against the full ENSDF database (incorporating 738,453 gamma, 7,547 beta, and 698 alpha decays) and the AME2020 atomic mass evaluation, employing a pipeline that integrates topological constraints with established nuclear structure effects. For alpha decay, incorporating proximity to magic numbers, the model achieves ρ = 0.963 for the Trans-Pb region (Z ≥ 83, N = 485). For beta decay, the observable log ft is decomposed into a Comparative Single-Particle estimate, a universal topological shift (Δ = +0.239), and a many-body quenching gap derived from published shell-model interactions; the 2nd-forbidden unique class serves as a consistency check of this decomposition, reproducing the empirical mean to within 0.22 log ft units with Qmb fixed independently from ab initio calculations. For drip-line unbound states, the topological lower limit (T1/2)exp ≥ (T1/2)topo is satisfied in all 12 cases with measured resonance widths (median ratio = 56.5). The T-DFT framework provides a no adjustable parameters estimate of the nuclear attempt frequency, with neutron emitters showing a mean barrier delay of 46.8× and proton emitters 86.6×, consistent with classical barrier penetrability.
Luis Rodrigues (Mon,) studied this question.