Mid-weight $\alpha$-conjugate nuclei are predicted to possess exotic toroid like resonances with high angular momenta. The search for these states in ${}^{28}\mathrm{Si}^{*}$ is the main point of two published experimental investigations of the peripheral ${}^{28}\mathrm{Si}$ $+$ ${}^{12}\mathrm{C}$ 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 $\left(\mathrm{H}\alpha \mathrm{C}\right)$ model. In all the examined data, our results suggest the presence of underlying structure which is close to that predicted for toroidal states.

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• Breakup reactions
• Nuclear reactions
• Machine learning
• Nuclear data analysis & compilation