Possible sub-barrier hindrance in the fusion of light nuclei

Fusion reactions between light nuclei have been studied because of the significance of their reactions for a wide variety of stellar burning processes. Since the experimental data are limited to energies higher than those of astrophysical interest, S-factors must be extrapolated using theoretical model calculations. Recently, an unexpected hindrance of heavy-ion fusion cross sections has been observed at sub-barrier energies, which could affect the astrophysically important fusion reactions. To investigate the hindrance effect, we have measured the cross sections for the $^{12}$C($^{13}$C, p)$^{24}$Na reaction through measurement of $\beta $-decay of $^{24}$Na by the $\beta \gamma $-coincidence method. We developed a cosmic-ray veto system required for the low background coincidence measurements. The background suppression achieved with the veto system allowed us to measure the fusion cross sections at extreme sub-barrier energies, below the lowest energies previously studied.