New perspective on complex cluster radioactivity of heavy nuclei

Abstract

Experimental data of complex cluster radioactivity $(^{14}\mathrm{C}\text{--}^{34}\mathrm{Si})$ are systematically analyzed and investigated with different models. The half-lives of cluster radioactivity are well reproduced by a new formula between half-lives and decay energies and by a microscopic density-dependent cluster model with the renormalized M3Y nucleon-nucleon interaction. The formula can be considered as a natural extension of both the Geiger-Nuttall law and the Viola-Seaborg formula from simple $\ensuremath{\alpha}$ decay to complex cluster radioactivity where different kinds of clusters are emitted. It is useful for experimentalists to analyze the data of cluster radioactivity. A new linear relationship between the decay energy of cluster radioactivity and the number of $\ensuremath{\alpha}$ particles in the cluster is found where the increase of decay energy for an extra $\ensuremath{\alpha}$ particle is between 15 and 17 MeV. The possible physics behind this new linear relationship is discussed.