Fusion Hindrance and Pauli Blocking in ⁵⁸Ni + ⁶⁴Ni

Abstract

58Ni +64Ni is the first case where the influence of positive Q-value transfer channels on sub-barrier fusion was evidenced, in a very well known experiment by Beckerman et al., by comparing with the two systems 58Ni +58Ni and 64Ni +64Ni. Subsequent measurements on 64Ni +64Ni showed that fusion hindrance is clearly present in this case. On the other hand, no indication of hindrance can be observed for 58Ni +64Ni down to the measured level of 0.1 mb. In the present experiment the excitation function has been extended by two orders of magnitude downward. The cross sections for 58Ni + 64Ni continue decreasing very smoothly below the barrier, down to ≃1 μb. 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-channels (CC) calculations using a Woods-Saxon potential and including inelastic excitations only, underestimate the sub-barrier cross sections by a large amount. Good agreement is found by adding two-neutron transfer couplings to a schematical level. This behaviour is quite different from what already observed for 64Ni+64Ni (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. No hindrance effect is observed in 58Ni+64Ni in the measured energy range. This trend at deep sub-barrier energies reinforces the recent suggestion that the availability of several states following transfer with Q >0, effectively counterbalances the Pauli repulsion that, in general, is predicted to reduce tunneling probability inside the Coulomb barrier.

The slopes of sub-barrier heavy-ion fusion excitation functions shed light on the dynamics of quantum tunnelling

“…Once more, we note that inelastic couplings do not change the slope of the excitation functions, while strong transfer couplings do. Looking in more detail, we note that the data of 58 Ni + 64 Ni are very near to those of the group of "inelastic" systems down to Eσ ≈15 MeV mb, corresponding to E/V b ≈0.93 [24]. Below that, the points for this system have a fast decrease, leading to the overlap with 40 Ca + 96 Zr for lower Eσ.…”

“…In the original papers it was remarked that fusion hindrance appears at different cross section levels for the two Mg + C systems as well as for 30 Si + 12 C, on the basis of the comparison with CC calculations using a Woods-Saxon potential. However, we note that the large uncertainties for 24 Mg + 12 C and the presence of oscillations weaken this statement.…”

“…Its excitation function was measured down to ≃2µb [23] with a regular trend not evidencing any sign of hindrance. CC analyses performed for those two systems (see [24,35] and Refs. therein) indicated that the absence of hindrance should be attributed to strong couplings to quasi-elastic neutron transfer with positive Q-values.…”

“…Fig. 12, as an example, shows the results of measurements of 58 Ni + 64 Ni fusion [24], performed using the electrostatic deflector set-up of INFN-Laboratori Nazionali di Legnaro (LNL) [4]. The ER events are identified in twodimensional plots of time-of-flight T OF vs energy loss ∆E.…”

“…We analyze here the two cases of 26,24 Mg + 12 C, whose fusion excitation functions have been recently measured down to a few µb [41,42]. Their behaviour in the representation d(Eσ)/dE vs Eσ is similar, as shown in the top panel of Fig.…”