Fusion hindrance for the positive $Q$-value system $^{12}\mathrm{C}+^{30}\mathrm{Si}$
Résumé
Background: The fusion reaction C12+Si30 is a link between heavier cases studied in recent years, and the light heavy-ion systems, e.g., C12+C12, O16+O16 that have a prominent role in the dynamics of stellar evolution. C12+Si30 fusion itself is not a relevant process for astrophysics, but it is important to establish its behavior 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 C12+Si30 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 C12+Si30 from well below to above the Coulomb barrier, so as to clear up the consequence of couplings to low-lying states of Si30, 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 behavior to even lighter systems. Methods: The inverse kinematics was used by sending Si30 beams delivered from the XTU Tandem accelerator of INFN-Laboratori Nazionali di Legnaro onto thin C12 (50μg/cm2) 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 Ebeam=45, 59, and 80 MeV, and they were angle integrated to derive total fusion cross sections. Results: The fusion excitation function of C12+Si30 was 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 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 C12+Si30, so that an extrapolation to the C+C and O+O cases can be reliably performed.