Density variation effects in α + Pb208 and O16 + Pb208 fusion reactions

Abstract

We propose a hybrid approach between the sudden model and the adiabatic model to explain the fusion hindrance in heavy-ion fusion reactions at deep subbarrier energies. Due to the strong Pauli blocking effects at the density overlap region, the $\ensuremath{\alpha}$ particle approaching the target $^{208}\mathrm{Pb}$ becomes enlarged and its density distribution gets changed. By introducing energy dependence into this density variation effect, the potentials at different colliding energies are diverse. With the decrease of colliding energies, the significantly enhanced density variation effects make the nuclear potential more attractive and result in a deeper pocket in the inner part. A reasonable description of the experimental fusion cross sections is achieved for the $\ensuremath{\alpha} + ^{208}\mathrm{Pb}$ reaction. On account of highlighting the influence of density variation effects on the fusion process at deep subbarrier energies, we further investigate the density variation effects in the $^{16}\mathrm{O} + ^{208}\mathrm{Pb}$ fusion reaction based on the $\ensuremath{\alpha}$-cluster structures in $^{16}\mathrm{O}$ nuclei. The fusion hindrance at deep subbarrier energies is described well by considering the density variation effects. In addition, an astrophysical $S$ factor between the sudden model and adiabatic model is predicted at the energies below the experimental data.