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 $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$ to another symmetric system, $^{58}\mathrm{Ni}+^{58}\mathrm{Ni}$, and the asymmetric system $^{64}\mathrm{Ni}+^{100}\mathrm{Mo}$. 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 ${3}^{\ensuremath{-}}$ 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 $^{58}\mathrm{Ni}+^{58}\mathrm{Ni}$, which should be tested experimentally.