Generalization of the Geiger-Nuttall law and alpha clustering in heavy nuclei

A generalization of the Geiger-Nuttall law is deduced, which is valid for the radioactivity of all clusters (including α particles), by considering the clusterization and subsequent decay of nucleons within the nucleus. This universal decay law (UDL) is a linear relation between the half-lives of the decaying clusters and the corresponding Q-values. In this universal decay law (UDL) the penetrability is still a dominant quantity. By using three free parameters only, one finds that all known ground state to ground state radioactive decays are explained rather well. This allows us to search for new cluster decay modes and to carry out a simple and model-independent study of the decay properties of nuclei over the whole nuclear chart. It also helps in distinguishing the role played by pairing collectivity in the clustering process in heavy nuclei.