General decay law for emission of charged particles and exotic cluster radioactivity

For the emission of charged particles from metastable nuclei, a general decay formula is developed based on the basic phenomenon of resonances occurring in quantum scattering process under Coulomb-nuclear potential. It relates the half-lives of monopole radioactive decays with the Q-values of the outgoing elements in different angular momentum states as well as the masses and charges of the nuclei involved in the decay. The relation is found to be a generalization of the Geiger-Nuttall law in α radioactivity and it explains well all known emission of charged particles including clusters, alpha and proton carrying angular momenta.