The Current Status of Astrophysical S^*-factor Studies for the ¹²C+¹²C Fusion Reaction

Over the past two decades, astronomical observations of superbursts, initiated by the ¹²C+¹²C fusion reaction on the surfaces of neutron stars, have remained elusive by theoretical models based on the reaction rate of ¹²C+¹²C fusion reaction. Consequently, direct measurements for the cross section of the ¹²C+¹²C fusion reaction at energies well below Coulomb barriers have become a hot topic in nuclear astrophysics. For typical superbursts, the Gamow window energy of the ¹²C+¹²C fusion reaction is 1.5±0.3 MeV, significantly lower than the Coulomb barrier. This makes it a huge challenge to directly measure the extremely low cross section of the fusion reaction in the corresponding energy region. The experiment by the Trojan Horse Method (THM) is the only charged-particle measurement providing the excitation functions for all exit channels within the Gamow window. However, the experimental results still remain highly controversial at present. This work reviews the current status of direct measurement experiments for the ¹²C+¹²C fusion reaction and provides a novel interpretation of the data for THM. Combining the theory of identical boson systems, the compound nuclear excited states in ²⁴Mg extracted from THM are discussed. For the first time, a recommended average value of the dimensionless reduced width for the entrance channel of the ¹²C+¹²C fusion reaction is provided as \theta ^2 =0.031, which is consistent with theoretical predictions in the corresponding energy region from the antisymmetrized molecular dynamic (AMD). Furthermore, the reduced-width amplitude for the entrance channel of the ¹²C+¹²C fusion reaction within the Gamow window is suggested as \theta ^2 =0.031.