$\alpha$-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. Semimicroscopic cluster models (SMCMs) are important theoretical models to study their properties. A crucial ingredient of SMCMs 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 ($\chi \mathrm{EFT}$) at the next-to-next-to-leading order. The $\alpha$-cluster structures in ${}^8\mathrm{Be}, {}^{20}\mathrm{Ne}, {}^{44,52}\mathrm{Ti}$, and ${}^{212}\mathrm{Po}$ are explored to validate these new double-folding potentials. The $\alpha$ decay of ${}^{104}\mathrm{Te}$ is also studied in the light of recent experimental results. Our study shows that double-folding potentials from $\chi \mathrm{EFT}$ are the new reliable effective potentials for the SMCM approach to $\alpha$-cluster structures above double shell closures, with both conceptual and phenomenological merits.

Figure 1

The double-folding potentials $U_{\text{DF}}\left(R\right)$ for various $\alpha +\text{doubly}\text{magic}\text{nucleus}$ systems from soft local chiral nucleon-nucleon potentials at the ${\text{N}}^2\text{LO}$. See text for details.

Figure 2

The joint experimental and theoretical analysis on $\alpha$-decay properties of ${}^{104}\mathrm{Te}$. The red solid line shows the relation between the $\alpha$-decay half-life and $Q_{\alpha }$ given by $\text{SMCM}+{\text{DF}}_{\chi }$ with the $\alpha$-formation probability $P_{\alpha }=1$. The light green and light yellow regions are the $1\sigma$ and $2\sigma$ bands from Ref. [17]. The light orange region is the parameter space allowed by Ref. [18]. The light red region estimates the $\text{SMCM}+{\text{DF}}_{\chi }$-allowed parameter space from the condition $P_{\alpha }\le 1$. The green, yellow, and orange regions are the overlaps of these four regions.