Coincident measurement of the ${}_{12}C+{}_{12}C$ fusion cross section via the differential thick-target technique

The ${}_{12}C+{}_{12}C$ fusion reaction is critical for the understanding and interpretation of the late phases of stellar evolution as well as the ignition and nucleosynthesis in cataclysmic binary systems such as type Ia thermonuclear supernovas and x-ray superbursts. Direct measurement of this reaction has been performed at the University of Notre Dame using particle-$\gamma$ coincidence and differential thick-target techniques with SAND (a silicon detector array) at the high-intensity 5U Pelletron accelerator. Partial cross section results for the channels of $p_1$ to $p_{10}$ and ${\alpha }_1$ at center-of-mass energies of 2.65–5 MeV that are relevant to nuclear astrophysics are reported. The total $S^{*}\left(E\right)$ factor is constructed by taking into account contributions from the missing channels. The recommended reaction rate and its impact on the carbon burning process under astrophysical scenarios will be discussed.