Sub-barrier fusion in C12+Mg26,24 : Hindrance and oscillations

Background: The existence of fusion hindrance in the light heavy-ion systems of astrophysical interest is not well established, so investigating slightly heavier cases may allow a reliable extrapolation towards the lighter ones. The recent observation of a very high hindrance threshold in 12 C + 24 Mg (with a positive Q value for fusion) at σfus 0.75 mb, misses a valid interpretation within current theoretical models. Purpose: Our aim has been to search evidence for fusion hindrances in the nearby system 12 C + 26 Mg also having Qfus > 0, and to obtain information on the underlying physics from a comparison of the two cases and from coupled-channels calculations. Methods: The experiment was performed in inverse kinematics using the 26 Mg beam from the XTU Tandem accelerator of Laboratori Nazionali di Legnaro (LNL). The targets were thin 12 C evaporations 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: The fusion excitation function of 12 C + 26 Mg has been measured down to ≈5 μb. The astrophysical S factor shows a maximum at an energy where the cross section is ≈0.03 mb, significantly lower than for 12 C + 24 Mg. This difference is confirmed by the comparison of the two S factors. coupled channel calculations give a good account of the data, but they overpredict the cross sections below ≈0.03 mb. The logarithmic slopes of the two excitation functions are superimposable to a large extent, with visible oscillations, more noticeable for 12 C + 24 Mg. Conclusions: The hindrance phenomenon is clearly observed in 12 C + 26 Mg. The difference between the corresponding threshold energies for 12 C + 24,26 Mg might (only qualitatively) be attributed to the α-like structure of 24 Mg. In the Jiang’s phenomenological systematics, the different behaviors of 12 C + 24,26 Mg make the situation more complex, and call into question the extrapolation procedure toward the lighter systems of astrophysical interest.