Cluster Structure and Three-Body Decay of ${}^{14}$C

Recent model calculations with most advanced methods for cluster states have shown the need of experimental data to probe the structure of light exotic nuclei, including those with $\alpha$-clustering, such as ${}^{14}$C. The prototype Active Target Time Projection Chamber (pAT-TPC) allows us to investigate these types of structures, giving access to the full excitation function with a single beam energy. This type of experiment measures resonances in ${}^{14}$C that can be compared to the models. Additionally, using a Dalitz-type analysis, three-body decays can be analyzed to determine probabilities of ``democratic" and ``sequential" decay. The measurement was carried out by resonant alpha-scattering of a ${}^{10}$Be beam at 40 MeV delivered by the \textit{TwinSol} facility at the University of Notre Dame. Preliminary results will be presented including event reconstruction using the Random Sample Consensus method.