Search for a Broad 9.11 MeV $2^+$ in $^{12}C$*

Carbon is formed during stellar helium burning in the ``triple- alpha process''-- the $^8Be(\alpha,\gamma)^{12}C$ reaction that is mostly governed by the $0^+$ state at 7.654 MeV. At high temperatures (T $>$ 3 GK) higher lying states in $^{12}C$ may contribute. A broad $(\Gamma_\alpha = 560 \ keV, \Gamma_\gamma = 0.2 \ eV) \ 2^+$ state at 9.11 MeV in $^{12}C$ was included in the NACRE compilation following theoretical prediction for the $2^+$ member of the rotational band built on top of the $0^+ $ state at 7.654 MeV. It increases the production of carbon at temperatures in excess of 1 GK by up to a factor of 15. An Optical-Readout Time Projection Chamber (O-TPC) operating with $CO_2$ gas that is being used at the High Intensity $\gamma$-ray Source (HI$\gamma$S) at TUNL is ideally suited for a search of such a state via the identification of triple alpha events from the $^{12}C(\gamma,3\alpha)$ reaction. We have studied this reaction at $E_{\gamma}$ = 9.55, 10.54, 10.84 and 11.14 MeV. Only 4 triple alpha events were observed during a 10 hour long measurement at 9.55 MeV which are consistent with the known broad $1^-$ state at 10.84 MeV in $^{12}C$. Using the known cross section of the $^{16}O(\gamma,\alpha)^{12}C$ (= 4.2 $\mu $b) we place the upper limit of $\Gamma_{\gamma} (0^+_{g.s.} \rightarrow 2^+) \ <$ 1.28 meV at $E_\gamma = 9.55$ MeV, hence $B(E2: 2^+ \rightarrow 0^+_{g.s.}) \ < \ 4 \times 10^{-3}$ W.u.\\ $^*$Work supported by the U.S. Department of Energy grant No. DE- FG02-94ER40870 and DE-FG02-97ER41033.