Search for $\alpha$-Cluster Structure in Exotic Nuclei with the Prototype Active-Target Time-Projection Chamber*

Some exotic nuclei appear to exhibit $\alpha$-cluster structure. While various theoretical models currently describe such clustering, more experimental data are needed to constrain model predictions. The Prototype Active-Target Time-Projection Chamber (PAT-TPC) has low-energy thresholds for charged-particle decay and a high luminosity due to its thick gaseous active target volume, making it well-suited to search for low-energy $\alpha$-cluster reactions. Radioactive-ion beams produced by the {\textit{TwinSol}} facility at the University of Notre Dame were delivered to the PAT-TPC to study nuclei including $^{14}$C and $^{14}$O via $\alpha$-resonant scattering. Differential cross sections and excitation functions were measured. Preliminary results from our recent experiments will be presented.