Fusion of 48Ca + 48Ca far below the Coulomb barrier

We have measured the fusion excitation function of the system 48Ca + 48Ca from near the barrier to very low energies, where the phenomenon known as 'fusion hindrance' should show up. We have extended the range of measured data from σ ∼150 μb [1] down to ∼0.6 μb. Fusion hindrance has been proposed to be a consequence of the saturation properties of nuclear matter, that inhibit a large overlap of the colliding nuclei. The case of 36S + 48Ca appeared to be an exception since no clear-cut indication of fusion hindrance was found well below the Coulomb barrier [2]. This has been tentatively linked to the positive Q-value for compound nucleus formation. Measuring the near-by system 48Ca + 48Ca appeared to be very interesting, since Q is negative in this case. We stress that both systems are composed of spherical magic nuclei. The experiment has been performed using the 48Ca Tandem beam of LNL and the electrostatic beam separator for evaporation residue detection, with an increased efficiency (see [2] for details). The results are shown in the Figure (left panel) together with the previously measured cross sections. Overall, the complete excitation function covers about six orders of magnitude. Also reported are the results of coupled-channels calculations [3] using a Woods-Saxon bare potential with parameters V0=76.5 MeV, ro=1.10 fm and a=0.80 fm giving a barrier Vb=51.9 fm very near to the Akyuez-Winther value. The 2+ and 3- states of both nuclei were included in the coupling scheme, with adopted strengths. The fit to the measured cross sections is quite nice. A smaller diffuseness like a=0.66 fm leads to calculate a slope definitely too flat, below the barrier. The right panel of the Figure is a comparison of the log-slopes for 36S + 48Ca and 48Ca + 48Ca, plotted vs. the fusion cross section. The behavior of the two systems is very similar (and the same is true in the usual representation of the log-slope vs. energy), so that the sign of the Q-value appears to be irrelevant in the measured energy range.(author)