This paper presents a comprehensive investigation of quantum correlations in radiative-capture reactions through a unified lens of quantum information theory and nuclear physics. By combining density matrix formulations with open quantum system dynamics, we can establish universal scaling laws governing the relationship between quantum discord (D), entanglement entropy (S), and fundamental nuclear properties. The analysis reveals the inverse power-law dependencies \(D \propto \Gamma ^{-0.83 \pm 0.04}\) and \(S \propto \Gamma ^{-1.12 \pm 0.06}\) between these quantum metrics and the decay width ( \(\Gamma\) ), maintained across fourteen nuclear systems spanning six decades in \(\Gamma\) and masses \(2 \le A \le 56\) . A machine learning architecture that integrates physical constraints with deep residual networks achieves 92% prediction accuracy for coherence lengths \(L_c\) while identifying shell structure effects that enhance quantum correlations near magic numbers. The persistent quantum discord ( \(D > 0.3\) ) observed in systems with sub-attometer coherence lengths suggests nuclear spins maintain non-classical correlations through internal degrees of freedom rather than spatial coherence. The developed phase diagram categorizes nuclear reactions into three quantum technology regimes: memory ( \(Q > 10^{20}\) s \(\phantom{0}^{-1}\) ), sensing ( \(10^{18}< Q < 10^{20}\) s \(\phantom{0}^{-1}\) ), and foundational tests ( \(Q < 10^{18}\) s \(\phantom{0}^{-1}\) ), with \(\phantom{0}^{56}\) Fe \((n,\gamma )\) and \(\phantom{0}^6\) Li \((n,\gamma )\) identified as optimal candidates for applications. These results bridge nuclear physics with quantum information science, providing both theoretical insights into decoherence mechanisms and practical tools for quantum material design. The proposed methodology establishes radiative capture reactions as a novel platform for exploring emergent quantum phenomena in strongly interacting systems.
