Triple-$\alpha$ Process in Hot Astrophysical Scenarios

The production of carbon in red giant stars relies significantly on the 1$^{st}$ 0$^{+}$ excited state of $^{12}$C at 7.65 MeV (the Hoyle state). The recent NACRE listing assumes a 2$^{+}$ resonance at 9.1 MeV,\footnote{Angulo \textit{et al}, Nucl. Phys. \textbf{A656} (1999)} which could be considered as the 2$^{+}$ member of a deformed rotational band built on the Hoyle state. At temperatures of several billion Kelvin in explosive scenarios like supernovae where the 3$\alpha $ process is also relevant, this state would increase the astrophysical reaction rate by an order of magnitude.\footnote{Fynbo \textit{et al}, Nature \textbf{433} (2005)} In order to determine this experimentally, the states of $^{12}$C were populated through $\beta $-decay of $^{12}$B and $^{12}$N mirror nuclei produced at the ATLAS in-flight facility at Argonne. The decay of $^{12}$C* into three alphas were detected in a twin ionization chamber, acting as a 4$\pi $ calorimeter. This minimized the effect of $\beta $-summing and allowed us to investigate the minimum between the 1$^{st}$ and the 2$^{nd}$ 0$^{+}$ state with much better accuracy than previously possible. An R-Matrix analysis was performed to determine an upper limit on the 2$^{+}$ resonance in the 8-11 MeV region. Our data analysis thus far shows no evidence of a 2$^{+}$ state in this region. This work is supported by U.S. DOE, and NSF grants.