AI-Assisted analysis of $^{28}$Si$^*$ $\rightarrow$ 7$\alpha$ break-up data

Mid-weight $\alpha$-conjugate nuclei are predicted to possess exotic toroid-like resonances with high angular momenta. The search for these states in $^{28}$Si$^*$ is the main point of two published experimental investigations of the peripheral $^{28}$Si + $^{12}$C reaction by Cao and collaborators and by Hannaman and collaborators. In this work, we develop a novel Artificial Intelligence (AI)-based machine learning method utilizing the Gaussian Mixture Model (GMM) to analyze available experimental and theoretical data. We additionally study the reaction with the Hybrid $\alpha$-Cluster (H$\alpha$C) model. In all the examined data our results suggest the presence of underlying structure which is close to that predicted for toroidal states.