Recently, experimental researches on the α decay with long lifetime are one of hot topics in the contemporary nuclear physics [e.g. N. Kinoshita et al. (2012) [2] and J.W. Beeman et al. (2012) [4] ]. 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.
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