Cluster radioactivity using modified generalized liquid model with a statistical cluster preformation probability

The cluster radioactivity of various heavy nuclei have been studied using the modified generalized liquid drop model (MGLDM) with a new statistical cluster preformation probability of Dong et al. [Eur. Phys. J. A 41, 197 (2009)]. The statistical preformation factor obtained obeys the relation for preformation factor or spectroscopic factor, $S=S_{\alpha }^{(A_2-1)/3}$ of Blendowske et al. [Phys. Rev. Lett. 61, 1930 (1988)] with $S_{\alpha }$=0.063, exactly the same value reported. The predicted half-lives using MGLDM are in agreement with experimental data with standard deviation $\sigma$=1.16 and also consistent with other empirical formula predictions. Predictions on decay modes of nuclei, which are energetically allowed but not yet observed, are also done which will be helpful for scientists to design new experiments on cluster radioactivity.