Double-Folding Model Potentials with M3Y and São Paulo Interactions: Constructing Realistic Nucleus–Nucleus Potentials and Comparing Barrier Predictions

Abstract

The nucleus–nucleus interaction potential is the central quantity that governs elastic scattering, sub-barrier fusion, and the formation of compound and super-heavy systems. Among microscopic prescriptions, the double-folding model occupies a privileged position because it constructs the real part of the heavy-ion potential directly from the matter densities of the colliding nuclei and an effective nucleon–nucleon interaction, thereby minimising the number of adjustable parameters. This article develops the double-folding formalism in a self-contained manner and applies it with two of the most widely used effective interactions: the density-independent M3Y (Michigan three-range Yukawa) force in its Reid parametrisation, supplemented by a knock-on exchange term, and the São Paulo interaction, in which the folded potential is multiplied by a velocity-dependent factor that encodes the Pauli nonlocality. The folding integral is evaluated in momentum space, the resulting nuclear potential is combined with the Coulomb and centrifugal terms, and the fusion barrier height, radius, and curvature are extracted. For a representative set of eight systems spanning ^12C+^12C to ^48Ca+^208Pb, both interactions reproduce empirical barrier heights to within a few percent without any renormalisation, the São Paulo prescription tending to predict marginally higher and more compact barriers. Fusion excitation functions are further computed in the Wong approximation, and the sensitivity of the barrier to the surface diffuseness and to the energy dependence of the interaction is analysed. The results demonstrate that parameter-free folded potentials provide a reliable and physically transparent foundation for heavy-ion reaction studies....