The current evaluation of the triple-$\alpha$ reaction rate assumes that the $\alpha$ decay of the 7.65 MeV, $0^{+}$ state in ${}^{12}\mathrm{C}$, commonly known as the Hoyle state, proceeds sequentially via the ground state of ${}^8\mathrm{Be}$. This assumption is challenged by the recent identification of two direct $\alpha$-decay branches with a combined branching ratio of $17(5)\%$. If correct, this would imply a corresponding reduction in the triple-$\alpha$ reaction rate with important astrophysical consequences. We have used the ${}^{11}\mathrm{B}({}^3\mathrm{He},d)$ reaction to populate the Hoyle state and measured the decay to three $\alpha$ particles in complete kinematics. We find no evidence for direct $\alpha$-decay branches, and hence our data do not support a revision of the triple-$\alpha$ reaction rate. We obtain an upper limit of $5\times {10}^{-3}$ on the direct $\alpha$ decay of the Hoyle state at $95\%$ C.L., which is 1 order of magnitude better than a previous upper limit.

• Received 27 February 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.202501