$\alpha$-cluster structures above double shell closures via double-folding potentials from chiral effective field theory

$\alpha$-cluster structures above double shell closures are among the cornerstones for nuclear $\alpha$-cluster physics. Semi-microscopic cluster models (SMCMs) are important theoretical models to study their properties. A crucial ingredient of SMCM is the effective potential between the alpha cluster and the doubly magic nucleus. We derive new double-folding potentials between $\alpha$ clusters and doubly magic nuclei from soft local chiral nucleon-nucleon potentials given by chiral effective field theory ($\chi$EFT) at the next-to-next-to-leading order. The $\alpha$-cluster structures in ${}^{8}\text{Be}$, ${}^{20}\text{Ne}$, ${}^{44,52}\text{Ti}$, and ${}^{212}\text{Po}$ are explored to validate these new double-folding potentials. The $\alpha$ decay of ${}^{104}\text{Te}$ is also studied in the light of recent experimental results. Our study shows that double-folding potentials from $\chi$EFT are the new reliable effective potentials for the SMCM approach to $\alpha$-cluster structures above double shell closures, with both conceptual and phenomenological merits.