Consistent description of hindrance in sub-barrier fusion of 48Ca with 36S, 48Ca, and 96Zr

Recent fusion reaction data for the systems S-36 + Ca-48, Ca-48 + Ca-48, and Zr-96 + 48Ca are analyzed within the coupled-channel formalism. The heavy-ion entrance channel potential is calculated employing an improved double-folding prescription. The nonlocal kernel arising from the knock-on exchange component of the effective N-N interaction is localized within the lowest order of the Perey-Saxon approach, including full recoil. The single-particle densities entering the folding integrals are prescribed according to the density matrix expansion method. The investigation is more elaborated because each case is tested with four different types of N-N effective forces: The two standard parametrizations of the density-independent M3Y force (Reid and Paris) and two parametrizations of the density-dependent Gogny force (D1S and D1N). A consistent description of all three reactions is achieved by keeping fixed the nuclear structure input for Ca-48. The inclusion of 2(+) and 3(-) phonon states in the coupled-channel calculation, within an energy excitation window identical for all three reactions explains better the hindrance in extreme sub-barrier fusion cross sections. The interactions providing the best fit to the data are not pointing to a possible maximum in the astrophysical S factor, thereby confirming the conclusion reached by the Legnaro group for these cases.