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

Recent fusion reaction data for the systems {sup 36}S+{sup 48}Ca, {sup 48}Ca+{sup 48}Ca, and {sup 96}Zr+{sup 48}Ca 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 {sup 48}Ca. The inclusion of 2{sup +} and 3{sup -} 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 themore » Legnaro group for these cases.« less