Unusual behavior in the systematics of $\alpha$-preformation factors above Z, $N=50$ doubly magic shell closures

Abstract

The systematics of $\alpha$-preformation factor ($P_\alpha$) above the Z, $N=50$ shell closures is investigated with the dynamical double-folding potential (DDFP) which incorporates the nuclear medium effect in $\alpha$ decay. With the accuracy of the DDFP verified in the half-life calculation, the $P_\alpha$ factors are deduced from the available experimental $\alpha$-decay energies and half-lives. The result suggests that the relative $\alpha$-reduced width $W_\alpha$ of $^{104}$Te is 6.54, which stands with the experimental conclusion $W_\alpha >5$ [Phys. Rev. Lett. 121, 182501, 2018], and is very close to the theoretical value 6.92 from the microscopic quartetting wavefunction approach (QWA) [Phys. Rev. C 101, 024316, 2020]. The $P_\alpha$ variations above Z, $N=50$ are found to show an unusual behavior which is different from the known $P_\alpha$ systematics above the $Z=82$, $N=126$ shell closures. The correlations of $P_\alpha$ factors with different types of two-nucleon correlated interactions are analyzed in detail, which suggests that the large enhancement of the proton–neutron interaction along with its positive correlation with the $P_\alpha$ value probably accounts for the unusual $P_\alpha$ systematics in this region. All these indications imply a likely predominant role played by the proton–neutron correlation against the pairing correlations in contributing to the $\alpha$-cluster formation for nuclei in the $^{100}$Sn neighboring region.