Fusion Hindrance and Pauli Blocking in 58Ni + 64Ni

Background: $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ is the first case where the influence of positive $Q$-value transfer channels on subbarrier fusion was evinced, in a very well known experiment by Beckerman et al. [Phys. Rev. Lett. 45, 1472 (1980)], by comparing with the two systems $^{58}\mathrm{Ni}+^{58}\mathrm{Ni}$ and $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$. Subsequent measurements on $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$ showed that fusion hindrance is clearly present in this case. On the other hand, no indication of hindrance can be observed for $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ down to the measured level of 0.1 mb.Purpose: Measuring deep subbarrier fusion cross sections for $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$, where the influence of positive $Q$-value transfer channels on near-barrier fusion was evidenced previously, in order to investigate whether hindrance shows up.Methods: 167--200 MeV $^{58}\mathrm{Ni}$ beams from the XTU Tandem Accelerator of INFN-Laboratori Nazionali di Legnaro were used, bombarding thin metallic $^{64}\mathrm{Ni}\phantom{\rule{4pt}{0ex}}(50\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{g}/{\mathrm{cm}}^{2})$ enriched to $99.6%$ in mass 64. An electrostatic beam deflector allowed fusion evaporation residues to be detected at very forward angles in a detector telescope.Results: The excitation function has been extended by two orders of magnitude downward. The cross sections for $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ continue decreasing very smoothly below the barrier, down to $\ensuremath{\simeq}1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{b}$. The logarithmic slope of the excitation function increases slowly, showing a tendency to saturate at the lowest energies. No maximum of the astrophysical $S$ factor is observed. Coupled-channel (CC) calculations using a Woods-Saxon potential and including inelastic excitations only underestimate the subbarrier cross sections by a large amount. Good agreement is found by adding two-nucleon transfer couplings to a schematical level. This behavior is quite different from what already observed for $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$ (no positive $Q$-value transfer channels available), where a clear low-energy maximum of the $S$ factor appears, and whose excitation function is overestimated by a standard Woods-Saxon CC calculation.Conclusions: No hindrance effect is observed in $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ in the measured energy range. This trend at deep subbarrier energies reinforces the recent suggestion that the availability of several states following transfer with $Qg0$ effectively counterbalances the Pauli repulsion that, in general, is predicted to reduce tunneling probability inside the Coulomb barrier.