Elastic scattering between $\alpha$ particles and ${}^{12}\mathrm{C}$ nuclei plays a crucial role in understanding resonance phenomena in light nuclear systems. In this work, we construct inverse potentials for resonant states in $\alpha \text{−}{}^{12}\mathrm{C}$ elastic scattering using the variable phase approach, in tandem with a genetic-algorithm-based optimization technique. The reference function for the potential in the phase equation is chosen as a combination of three smoothly joined Morse-type functions. The parameters of the reference function are genetically evolved to minimize the the mean-squared error (MSE) between the numerically obtained scattering phase shifts and the expected values. To avoid overfitting and ensure model generalization, we employ a fivefold cross-validation strategy, where the genetic algorithm (GA) minimizes the average validation error across folds. The resulting inverse potentials accurately reproduce the resonance energies ($E_r$) and the resonance widths (${\mathrm{\Gamma }}_r$) for the ${\ell }^{\pi }$ states, $1^{-}$, $2^{+}$, $3^{-}$, and $4^{+}$, showing excellent agreement with experimental data. This computational approach to constructing inverse potentials serves as a complement to conventional direct methods for investigating nuclear-scattering phenomena.

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• Nuclear reactions
• 6 ≤ A ≤ 19
• A ≤ 5