$\alpha$-cluster structure above double-shell closures and $\alpha$-decay of ${}^{104}$Te

Abstract

An analysis of the $\alpha$ + core properties of ${}^{104}$Te along with a global discussion on the $\alpha$-cluster structure above the double-shell closures is presented from the viewpoint of the local potential model. The $\alpha$ + core interaction is described by a nuclear potential of (1 + Gaussian)$\times$(W.S. + W.S.${}^3$) shape with two free parameters, which has been successfully tested in nuclei of different mass regions. The model produces $Q_{\alpha }$ values and $\alpha$-decay half-lives for ${}^{104}$Te in agreement with the 2018 experimental data of Auranen et al. in the energy range $5.13\mathrm{MeV}<Q_{\alpha }<5.3\mathrm{MeV}$ using an $\alpha$ preformation factor $P_{\alpha }=1$. The comparison of the calculated reduced $\alpha$-widths for the ground state bands of ${}^{104}$Te, ${}^{94}$Mo and ${}^{212}$Po indicates that ${}^{104}$Te has an $\alpha$-cluster degree significantly higher than ${}^{94}$Mo and much higher than ${}^{212}$Po. These results point to ${}^{104}$Te as a preferential nucleus for $\alpha$-clustering in the $N,Z=50$ region and corroborate the statement on the superallowed $\alpha$-decay in ${}^{104}$Te.

Comments: 11 pages, 3 figures. Accepted for publication in Physics Letters B