Experiments to Further the Understanding of the Triple-$\alpha$ Process in Hot Astrophysical Scenarios

The first 0$^{+}$ state of $^{12}$C at 7.654 MeV (the Hoyle state) is the most relevant in the triple-$\alpha$ process for carbon nucleosynthesis. In explosive scenarios such as supernovae, the interference of the Hoyle state with the second 0$^{+}$ state located at 10.3 MeV in $^{12}$C becomes significant. The recent NACRE listing assumes a 2$^{+}$ resonance at 9.117 MeV for which no experimental evidence exists. The states above 7.654 MeV level in $^{12}$C were populated through the $\beta$-decay of $^{12}$B and $^{12}$N produced at the ATLAS in-flight facility at ANL. The decay of $^{12}$C into three alphas is detected in a twin Frisch grid ionization chamber, acting as a calorimeter. This minimizes the effects of $\beta$-summing and allowed us to investigate the minimum above the Hoyle state with much higher accuracy than previously possible. A detailed data analysis will include an R-matrix fit to determine an upper limit on the 2$^{+}$ resonance. Work is supported by U.S. DOE, ONP under contracts DE-AC02-06CH11357 (ANL), DE-FG02-04R41320 (WMU), NSF grant PHY01-40324, and JINA NSF-PFC grant PHY02-16783.