In this work, a microscopic effective nucleon-nucleon interaction based on the Dirac-Brueckner-Hartree-Fock $G$ matrix starting from a bare nucleon-nucleon interaction is used to explore the $\alpha$-decay half-lives of nuclei above doubly magic nucleus ${}^{100}\mathrm{Sn}$. Specifically, the $\alpha$-nucleus potential is constructed by doubly folding the effective nucleon-nucleon interaction with respect to the density distributions of both the $\alpha$-cluster and the daughter nucleus. Moreover, the $\alpha$-cluster preformation factor is extracted by a cluster formation model. It is shown that the calculated half-lives within the Wentzel-Kramers-Brillouin approximation can reproduce the experimental data well. Then, the $\alpha$-decay half-lives that are experimentally unavailable for the nuclei around ${}^{100}\mathrm{Sn}$ are predicted, which are helpful for searching for the new candidates of $\alpha$ decay in future experiments. In addition, by analyzing the proton-neutron correlation energies and two proton–two neutron correlation energies of nuclei above doubly magic nuclei ${}^{100}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$, the $\alpha$-cluster preformation factor evolution with $N$ is explained. It is found that the two proton–two neutron interaction plays a more important role in an $\alpha$-cluster preformation than the proton-neutron interaction. However, the two proton–two neutron correlation energies of nuclei near ${}^{100}\mathrm{Sn}$ are much larger than those near ${}^{208}\mathrm{Pb}$, which results in a larger preformation factor for the nuclei around ${}^{100}\mathrm{Sn}$. Meanwhile, the proton-neutron interaction results in the odd-even effect of the $\alpha$-cluster preformation factor.

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• Alpha decay
• Binding energy & masses
• Lifetimes & widths
• Nucleon-nucleon interactions
• 90 ≤ A ≤ 149