Exact Treatment of Continuum Couplings in Nuclear Optical Potentials via Feshbach Theory

We present the first numerically exact implementation of full-coupling Feshbach theory for deriving effective optical potentials in nuclear reactions, overcoming long-standing computational barriers that previously necessitated weak-coupling approximations. By integrating Feshbach projection operators with the Continuum-Discretized Coupled-Channels (CDCC) method, we rigorously incorporate all continuum-continuum interactions, previously considered intractable, to extract dynamic polarization potentials that capture virtual excitations and absorption in reactions with weakly bound nuclei. Application to deuteron-induced reactions on $^{58}$Ni demonstrates that our full-coupling effective potentials reproduce CDCC observables exactly, while weak-coupling and folding-model approaches show significant deviations. The method uniquely separates elastic breakup from breakup-fusion processes through the optical theorem, enabling precise determination of incomplete and complete fusion cross sections, critical for interpreting rare-isotope beam experiments at facilities like FRIB. The non-local polarization potentials provide insights into the energy-dependent interplay between reaction mechanisms, with our analysis suggesting an increasing relative importance of elastic breakup at higher energies while continuum absorption shows more complex behavior. This exact treatment eliminates systematic uncertainties from coupling approximations, providing predictive power for unstable nuclei far from stability where experimental data are scarce.