Study of the hindrance effect in sub-barrier fusion reactions

In recent years, a hindrance model has been proposed to extrapolate heavy-ion fusion cross sections at sub-barrier bombarding energies. Compared to the single- and coupled-channel model, the hindrance model greatly reduces the fusion reaction rates in the stellar matter at temperatures T$\le $(3-10)x10$^{8}$ K. To test the hindrance model, we have measured the cross sections for the reaction $^{12}$C($^{13}$C,p)$^{24}$Na in the energy range E$_{c.m.}$= 3.08-4.80 MeV by counting the beta-gamma coincidence from the decay of $^{24}$Na which has a half life of 15 hours. Preliminary results will be presented.