Signature of shallow potentials in deep sub-barrier fusion reactions

We extend a recent study that explained the steep falloff in the fusion cross section at energies far below the Coulomb barrier for the symmetric dinuclear system ⁶⁴Ni+⁶⁴Ni to another symmetric system, ⁵⁸Ni+⁵⁸Ni, and the asymmetric system ⁶⁴Ni+¹⁰⁰Mo. In this scheme, the very sensitive dependence of the internal part of the nuclear potential on the nuclear equation of state determines a reduction of the classically allowed region for overlapping configurations and consequently a decrease in the fusion cross sections at bombarding energies far below the barrier. Within the coupled-channels method, including couplings to the low-lying 2⁺ and 3^- states in both target and projectile as well as mutual and two-phonon excitations of these states, we calculate and compare with the experimental data the fusion cross sections, S factors, and logarithmic derivatives for the above-mentioned systems and find good agreement with the data even at the lowest energies. We predict, in particular, a distinct double peaking in the S factor for the far sub-barrier fusion of ⁵⁸Ni+⁵⁸Ni, which should be tested experimentally.