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Half-lives of $α$ decay from natural nuclides and from superheavy elements

Recently, experimental researches on the $α$ decay with long lifetime are one of hot topics in the contemporary nuclear physics [e.g. N. Kinoshita {\sl et al.} (2012) and J. W. Beeman {\sl et al.} (2012) ]. In this study, we have systematically investigated the extremely long-lived $α$-decaying nuclei within a generalized density-dependent cluster model involving the experimental nuclear charge radii. In detail, the important density distribution of daughter nuclei is deduced from the corresponding experimental charge radii, leading to an improved $α$-core potential in the quantum tunneling calculation of $α$-decay width. Besides the excellent agreement between theory and experiment, predictions on half-lives of possible candidates for natural $α$ emitters are made for future experimental detections. In addition, the recently confirmed $α$-decay chain from $^{294}$117 is well described, including the attractive long-lived $α$-decaying $^{270}$Db, i.e., a positive step towards the "island of stability" in the superheavy mass region.