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.

Background: The phenomenon of fusion hindrance may have important consequences on the nuclear processes occurring in astrophysical scenarios, if it is a general behaviour of heavy-ion fusion at extreme sub-barrier energies, including reactions involving lighter systems, e.g. reactions in the carbon and oxygen burning stages of heavy stars. The hindrance is generally identified by the observation of a maximum of the S factor vs. energy. Whether there is an S-factor maximum at very low energies for systems with a positive fusion Q-value is an experimentally challenging question.Purpose: Our aim has been to search for evidence of fusion hindrance in 12 C + 24 Mg which is a medium-light system with positive Q-value for fusion, besides the heavier cases where hindrance is recognised to be a general phenomenon. 12 C + 24 Mg is very close to the 16 O + 16 O and 12 C + 12 C systems that are important for the late evolution of heavy stars. Methods:The experiment has been performed in inverse kinematics using the 24 Mg beam from the XTU Tandem accelerator of LNL in the energy range 26-52 MeV with an intensity of 4-8 pnA. The targets were 12 C evaporations 50 µg/cm 2 thick, isotopically enriched to 99.9%. The fusion-evaporation residues were detected at small angles by a E-∆E-ToF detector telescope following an electrostatic beam deflector.Results: Previous measurements of fusion cross section for 12 C + 24 Mg were limited to above-barrier energies. In the present experiment the excitation function has been extended down to ≃15µb and it appears that the S factor develops a clear maximum vs. energy, indicating the presence of hindrance. This is the first convincing evidence of an S factor maximum in a medium-light system with a positive fusion Q-value. These results have been fitted following a recently suggested method, and a detailed analysis within the coupled-channels model that has been performed using a Woods-Saxon potential and including the ground state rotational band of 24 Mg. The CC calculations give a good account of the data near and above the barrier but overpredict the cross sections at very low energies. Conclusions:The hindrance phenomenon is clearly observed in 12 C + 24 Mg, and its energy threshold is in reasonable agreement with the systematics observed for several medium-light systems. The fusion cross sections at the hindrance threshold show that the highest value (σs=1.6mb) is indeed found for this system. Therefore it may even be possible to extend the measurements further down in energy to better establish the position of the S-factor maximum.

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Background: The fusion reaction 12 C + 30 Si is a link between heavier cases studied in recent years, and the light heavy-ion systems e.g. 12 C + 12 C, 16 O + 16 O that have a prominent role in the dynamics of stellar evolution. 12 C + 30 Si fusion itself is not a relevant process for astrophysics, but it is important to establish its behaviour below the barrier, where couplings to low-lying collective modes and the hindrance phenomenon may determine the cross sections. The excitation function is presently completely unknown below the barrier for the 12 C + 30 Si reaction, thus no reliable extrapolation into the astrophysical regime for the C+C and O+O cases, can be performed.Purpose: Our aim was to carry out a complete measurement of the fusion excitation function of 12 C + 30 Si from well below to above the Coulomb barrier, so as to clear up the consequence of couplings to low-lying states of 30 Si, and whether the hindrance effect appears in this relatively light system which has a positive Q-value for fusion. This would have consequences for the extrapolated behaviour to even lighter systems.Methods: The inverse kinematics was used by sending 30 Si beams delivered from the XTU Tandem accelerator of INFN-Laboratori Nazionali di Legnaro onto thin 12 C (50µg/cm 2 ) targets enriched to 99.9% in mass 12. The fusion evaporation residues (ER) were detected at very forward angles, following beam separation by means of an electrostatic deflector. Angular distributions of ER were measured at E beam = 45, 59 and 80 MeV, and they were angle-integrated to derive total fusion cross sections. Results:The fusion excitation function of 12 C + 30 Si has been measured with high statistical accuracy, covering more than five orders of magnitude down to a lowest cross section ≃3µb. The logarithmic slope and the S factor have been extracted and we have a convincing phenomenological evidence of the hindrance effect. These results have been compared with the calculations performed within the model that considers a damping of the coupling strength well inside the Coulomb barrier. Conclusions:The experimental data are consistent with the coupled-channels calculations. A better fit is obtained by using the Yukawa-plus-exponential potential and a damping of the coupling strengths inside the barrier. The degree of hindrance is much smaller than the one in heavier systems. Also a phenomenological estimate reproduces quite closely the hindrance threshold for 12 C + 30 Si, so that an extrapolation to the C+C and O+O cases can be reliably performed.

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