The α-decay half-lives of recently synthesized superheavy nuclei (SHN) are investigated by employing a unified fission model (UFM) and Royer’s analytical formula (2000 J. Phys. G: Nucl. Part. Phys. 26 1149). The good agreement with the experimental data indicates the UFM and the analytical formula are useful tools to investigate these α-decays. A modified formula is proposed for determining the spontaneous fission half-lives based on Swiatecki’s formula, including the microscopic shell correction and isospin effect.The spontaneous fission half-lives for heavy and SHN in regions from Th to Fl are calculated systematically. Experimental data are well reproduced by the modified Swiatecki formula. The competition between α-decay and spontaneous fission is analyzed in detail and the decay modes are predicted for the unknown cases.

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Half-lives of cluster radioactivity treated as very asymmetric spontaneous fission are investigated by the WKB barrier penetration probability. The potential barrier is constructed by a generalized liquid-drop model(GLDM), taking into account the nuclear proximity, the mass asymmetry, the accurate nuclear radius, the phenomenological pairing correction, and the microscopic shell correction. The calculated cluster emission half-lives reproduce accurately the experimental data. Predictions are provided for possible cluster radioactivity within the GLDM using the up-to-data atomic mass table AME2011, which may be used for the future experiments.