We extend the modified two-potential approach to give an identical description of α-decay and cluster radioactivity in trans-tin nuclei within the density-dependent cluster model. The cluster-preformation factor (Pc) is well considered in two ways, respectively, based on some available experimental cases and a simple model for the reduced width. To obtain the fitted parameters of Pc expressions, various cluster emissions in trans-lead nuclei, with available experimental data, are initially investigated. Meanwhile, these calculated results are found to agree well with the measured values in this research. This can be considered as an active response to present calculations, which use the same formulae of the preformation factor to predict the cluster emission above the double-magic nucleus 100Sn. The experimental half-lives of α-decay are well reproduced, and some predictions for light α-emitters are also made. In addition, this work on cluster radioactivity in the light-mass region is also compared with other theoretical calculations. These calculated results may be useful for future experiments.

The recently proposed cluster-formation model (CFM) (Ahmed et al 2013 J. Phys. G: Nucl. Part. Phys. 40 065105) is extended to calculate the α preformation factors of odd-A and odd-odd nuclei. The extraction process of the formation energy of a preformed α cluster is analyzed in detail, which is crucial for determining the realistic α preformation factor in CFM. With an adaptive modification in the formation energy, we investigate the α preformation factors of odd-A and odd-odd heavy nuclei, and our results show a good agreement with both theoretical prospects and experimental extracted values. This work confirms the validity of the CFM in α preformation factor calculation and can be a useful reference for microscopic calculation in the future.

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