Consistent description of hindrance in sub-barrier fusion ofCa48withS36,Ca48, andZr96

Abstract

Recent fusion reaction data for the systems ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, and ${}^{96}\mathrm{Zr}+{}^{48}\mathrm{Ca}$ 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 $N\ensuremath{-}N$ 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 $N\ensuremath{-}N$ 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 $^{48}\mathrm{Ca}$. The inclusion of 2${}^{+}$ and 3${}^{\ensuremath{-}}$ 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.