α-α folding cluster model for α-radioactivity

The $ \alpha$-decay half-lives are calculated for heavy and superheavy nuclei for $ 52\leq Z\leq112$ and $ 108\leq A\leq 285$ from the ground state to ground state $ \alpha$ transitions within the framework of the Wentzel-Kramers-Brillouin (WKB) method and the Bohr-Sommerfeld quantization. In the calculations, the $ \alpha$-$ \alpha$ single folding cluster potential obtained with the folded integral of the $ \alpha$-$ \alpha$ potential with the $ \alpha$ -cluster density distributions is used in order to model the nuclear interaction between the $ \alpha$ -particle and core nucleus. While the results show very good agreement with the experimental ones in the heavy-nuclei region, especially for even-even nuclei, smaller values than the experimental ones are obtained for superheavy nuclei. As both the density of the core and the interaction term in the folding integral include the $ \alpha$-clustering effects and, in this way, all cluster effects are taken into account in the model, the results of calculations are more physical and reasonable than the calculations done in the other models. The present method could be applied to light nuclei with different types of nuclear densities