The reaction ${}^3\text{He}+{}^{11}\text{B}\to d+{}^{12}{\text{C}}^{*}$ has been used to populate resonances in ${}^{12}\mathrm{C}$ up to an excitation energy of $15$ MeV. The subsequent breakup to three $\alpha$ particles has been measured in complete kinematics. Dalitz plots are used to visualize and analyze the data. The Dalitz plot intensity distribution exhibits zero points characteristic of the total spin and parity of the $3\alpha$ system allowing us to determine the spin and parity of a state in ${}^{12}\mathrm{C}$ at $13.35$ MeV whose quantum numbers were hitherto not well established. The Dalitz plot intensity distributions of the $2^{-}$ state at $11.83$ MeV and the $1^{+}$ state at $12.71$ MeV are compared with the predictions of a recent three-body calculation as well as with simpler models. All are able to reproduce the gross structures seen in the Dalitz plot, but none give an accurate description of the detailed profile of the distributions.

• Received 3 May 2010

DOI:https://doi.org/10.1103/PhysRevC.81.064313