Probable Decay Modes of Superheavy Nuclei and Cluster Radioactivity

Cluster radioactivity is a very rare phenomenon. Among the various parameters that may determine the cluster radioactivity or cluster decay, the most important parameters are the binding energy $B\left(A,Z\right)$ of the parent nucleus and the binding energies of the nuclei that constitute the decay products. These parameters are crucial in determining the nuclear reaction energies (Q-values). Calculations for Q-values for even-even super heavy nuclei whose atomic numbers ($Z$ ) range from $Z=100$ to $Z=124$ were computed and the sign of the quantity of Q-values was used to determine whether the super heavy nuclei could undergo cluster radioactivity. The modified Bethe-Weizs？cker formula was used to calculate the binding energy of the nuclei involved in the cluster radioactivity, and the Coulomb energy was calculated using the modified Coulomb energy formula. It was found that nuclei whose Q-values are positive but relatively small fall under the category of super heavy nuclei which undergo cluster radioactivity while those nuclei whose Q-values are very high are significantly unstable, thus, they release energy that is sufficient to cause spontaneous fission. It is also noted that all the parent nuclei whose atomic numbers lie between $Z=100$ to $Z=124$ satisfy the conditions for spontaneous fission, however, for $Z>124$ the possibility for spontaneous fission diminishes. Based on our results, we conclude that nuclei with very high Q-values are significantly unstable, and the energy released is sufficient to cause spontaneous fission. Additionally, the boundary between cluster radioactivity and spontaneous fission remains elusive and an open question.