3-Body Decay of Cluster States in $^{14}$C

The clustering of $\alpha$ particles in nuclei results in the self-organization of various geometrical arrangements, informing our understanding of nuclear structure and nuclear astrophysics. In a previous experiment, the Prototype Active-Target Time-Projection Chamber was used to investigate $^{14}$C cluster structures by way of a 38~MeV secondary $^{10}$Be beam incident on a 90:10 He:CO$_2$ active target gas at the University of Notre Dame. The $^{10}$Be beam was produced by TwinSol and delivered to the Prototype AT-TPC. In addition to measuring elastic and inelastic $^{10}\mathrm{Be}~+~\alpha$ resonances, evidence of 3-body decays of $^{14}$C were observed in the data. Thus, additional data were later taken with an updated trigger scheme more sensitive to 3-body $^{14}$C decay events. Preliminary analysis of this data will be discussed and presented.