Sub-barrier fusion in C-12+Mg-26,Mg-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 C-12+ Mg-24 (with a positive Q value for fusion) at sigma(fus) similar or equal to 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 C-12+ Mg-26 also having Q(fus) greater than or similar to 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 Mg-26 beam from the XTU Tandem accelerator of Laboratori Nazionali di Legnaro (LNL). The targets were thin C-12 evaporations isotopically enriched to 99.9%. The fusion-evaporation residues were detected at small angles by a E-Delta E-ToF detector telescope following an electrostatic beam deflector. Results: The fusion excitation function of C-12+ Mg-26 has been measured down to approximate to 5 mu b. The astrophysical S factor shows a maximum at an energy where the cross section is approximate to 0.03 mb, significantly lower than for C-12+ Mg-24. 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 approximate to 0.03 mb. The logarithmic slopes of the two excitation functions are superimposable to a large extent, with visible oscillations, more noticeable for C-12+ Mg-24. Conclusions: The hindrance phenomenon is clearly observed in C-12+ Mg-26. The difference between the corresponding threshold energies for C-12+ Mg-24,Mg-26 might (only qualitatively) be attributed to the alpha-like structure of Mg-24. In the Jiang's phenomenological systematics, the different behaviors of C-12+ (24,2)6Mg make the situation more complex, and call into question the extrapolation procedure toward the lighter systems of astrophysical interest.