Potential inversion with sub-barrier fusion data reexamined

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.

Figure 1

(a) The experimental fusion barrier distribution for the ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ reaction defined as $d^2(E{\sigma }_{\mathrm{fus}})/{\mathit{dE}}^2$. The experimental data are taken from Ref. [5]. (b) The first derivative of $E{\sigma }_{\mathrm{fus}}$ for the ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ reaction. (c) The same as (b), but normalized so that it is 0.5 at the energy of the lower peak in the barrier distribution shown in (a) (the filled circle). The open circles are obtained in a similar way, but by taking into account the energy dependence of the effective moment of inertia as given by Eq. (9).

Figure 2

The adiabatic potential for the ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ reaction obtained with the inversion method. The dashed line is a barrier due to a phenomenological Woods-Saxon potential.

Figure 3

Same as Fig. 2, but for the ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ reaction.