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.
Categories: nucl-th