The preformation of cluster radioactivity for heavy nuclei

The preformations of cluster radioactivities (¹⁴C, ^24,26Ne, ^28,30Mg, ³²Si and so on) have been analyzed in the framework of the preformed cluster model for even-even heavy nuclei. The nuclear potential is calculated by using the double folding model with the density-dependence nucleon-nucleon interaction. It is shown that the penetration probability sharply varies with the released energy in the cluster radioactivity. The penetration probability mainly determines the half-life of the cluster radioactivity. The shell effect plays an important role for the cluster preformation. The closer the residual daughter nuclei are to the magic number or the doubly magic number, the faster the cluster radioactivity preforms in the mother nuclei. The shell effect is clearly shown in the cluster radioactivity. The cluster radioactivity shows the characteristic of neutron-proton symmetry in trans-lead nuclei. The preformation factor can provide the information of nuclear structure.