Fusion of 32S+48Ca at deep sub-barrier energies, G. Montagnoli, University of Padova and INFN, Italy − In the interesting energy region below the Coulomb barrier, heavy-ion fusion cross sections result from a balance between the enhancement produced by couplings to internal degrees of freedom of the colliding nuclei and to nucleon transfers, and the limitation ("fusion hindrance") generally observed at very low energies.  This hindrance is conveniently represented by using the logarithmic derivative L(E) = dln(E*sigma)/dE (slope) which is very sensitive to the trend of the low-energy excitation function. This phenomenon is receiving much attention also from the theoretical side.  It has frequently been observed that hindrance is so strong that a maximum of the astrophysical S-factor develops as a function of the energy, as required by energy conservation for systems having negative Q-values for fusion.  In our recent study of the sub-barrier fusion excitation function of 40Ca + 48Ca an indication of an S-factor maximum in a system with a positive Q value has been observed for the first time.   As a matter of fact, it is known that for systems having Q>0 the presence of a maximum of the S-factor vs. energy is not needed.   If confirmed in other systems with positive Q values, this effect will play an important role in nuclear astrophysics where fusion reactions of light heavy-ion systems occur at very low energies which are presently unaccessible to laboratory studies and thus require extrapolations to estimate the reaction rates in stars.  The fusion excitation function of 32S+48Ca (Q=+7.66 MeV) has been experimentally studied in a wide energy range, from above the Coulomb barrier down to cross sections in the sub-microbarn region.  The measurements were done at Legnaro Naz. Laboratory of INFN, using the high-quality and intense 32S beam from the XTU Tandem accelerator.  The excitation function has a smooth behavior below the barrier, with a rather flat slope.  This slope does not reach the value expected for a constant S factor, which implies that no maximum of S vs. energy shows up in the measured energy range.  Of course it could be present at still lower energies.  However other interesting features of the dynamics of this system have shown up.  In particular, its barrier distribution has an unusual shape with two peaks of similar height on either side of the Akyuz-Winther (AW) barrier.  Preliminary coupled-channels calculations have been performed, including the lowest 2+ and 3- states of both projectile and target, and, additionally, the two-phonon quadrupole excitation of 32S.  The calculations employed a standard AW ion-ion potential.  The results strongly under predict the sub-barrier cross sections, although the slope of the excitation function is quite well reproduced.  Even the predicted barrier distribution is very different from experiment, in particular the high-energy peak is completely missing.  Since 32S+48Ca has several neutron pickup transfer channels with positive Q-values, further schematic calculations have been carried out including also a transfer coupling simulating the +2n pick up channel.  This produces a fusion excitation function and a barrier distribution in close agreement with the data.