Potential inversion with sub-barrier fusion data reexamined

Abstract

We invert experimental data for heavy-ion fusion reactions at energies well below the Coulomb barrier in order to directly determine the internucleus potential between the colliding nuclei. In contrast to the previous applications of the inversion formula, we explicitly take into account the effect of channel couplings on fusion reactions, by assuming that fusion cross sections at deep sub-barrier energies are governed by the lowest barrier in the barrier distribution. We apply this procedure to the $^{16}\mathrm{O}+^{144}\mathrm{Sm}$ and $^{16}\mathrm{O}+^{208}\mathrm{Pb}$ reactions, and find that the inverted internucleus potential are much thicker than phenomenological potentials. A relation to the steep fall-off phenomenon of fusion cross sections recently found at deep sub-barrier energies is also discussed.