Feasibility study to search for the rare $\gamma $-decay mode in $^{12}$C

The triple $\alpha $ reaction plays a very important role in the $^{12}$C synthesis in the universe. Gamma-decay widths of excited states in $^{12}$C are the key parameters to determine the triple $\alpha $ reaction rate. The triple $\alpha $ process proceeds via the 0$_{2}^{+}$ state (Hoyle state) at normal stellar temperature. However, at high temperature T$_{9}$ \textgreater 1, the highly excited states such as the 3$_{1}^{-}$ and 2$_{2}^{+}$ states become dominant. Unfortunately, the $\gamma $-decay widths of these states are still unknown. We proposed to measure the $^{1}$H($^{12}$C, $^{12}$Cp) reaction to determine the radiative widths of the highly excited states in $^{12}$C. Recoil protons will be measured in coincidence with scattered $^{12}$C instead of $\gamma $-rays. The test experiment was carried out at the cyclotron facility in RCNP. In the present talk, we will report this result.