Investigating 3-body Decays of Cluster States with the PAT-TPC

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. With an improved Micromegas pad plane with a circular backgammon design we are able to investigate 3-body decays in addition to 2-body scattering. The measurements were carried out by resonant alpha-scattering on $^{10}$Be beam delivered by the {\textit{TwinSol}} facility at the University of Notre Dame. We also observed the 3-body decay of the Hoyle State in $^{12}$C from a $^{12}$N or $^{12}$B beam with the same device. Preliminary results will be presented.