Direct Observation of the Second \boldmath$J^\pi=2^+$ State in \boldmath${}^{12}\mathrm{C}$ and New Triple-\boldmath$\alpha$ Thermonuclear Reaction Rates

During core-collapse supernovae, the triple-$\alpha$ thermonuclear reaction rates at high temperatures can affect the outcome of explosive nucleo\-synthesis and the production of heavy elements. The question of the existence of a second $J^\pi=2^+$ state in ${}^{12}$C has led to a long-standing disagreement in the triple-$\alpha$ thermonuclear reaction rates at high temperatures. This $2^+_2$ state has been directly observed in the ${}^{12}\mathrm{C}(\gamma,\alpha){}^8\mathrm{Be}$ reaction using the intense, nearly mono\-energetic $\gamma$-ray beams available at the High Intensity $\gamma$ Source (HI$\gamma$S) facility. The $\alpha$ particles produced by the photo\-disintegration of ${}^{12}\mathrm{C}$ were detected using an optical time projection chamber (OTPC)\@. This allowed for the measurement of complete angular distributions which were used to determine the $E1$ and $E2$ amplitudes and their relative phases. The $2^+_2$ state was observed in the $E2$ cross section and confirmed in the behavior of the relative phases. This unique combination of a Compton-backscattered $\gamma$-ray beam and an active-target system made possible the first unambiguous identification of this $2^+$ state. New triple-$\alpha$ thermonuclear reaction rates have been calculated based on the results of this experiment, and simulations based on the $\nu p$ process~[1] have been performed illustrating the effect of the second $2^+$ state in ${}^{12}\mathrm{C}$ on the outcome of explosive nucleo\-synthesis.\\[4pt] [1] A.~Arcones, C.~Fr\"ohlich, and G.~Mart\'inez-Pinedo, ApJ \textbf{750}, 18 (2012)