Abstract
The lifetimes of some heavy nuclei relative to the spontaneous emission of various clusters heavier than the alpha particle are estimated with a model extended from the fission theory of alpha decay, showing that this phenomenon is a new manifestation of the nuclear shell structure. A greater probability is obtained for parent-heavy-cluster combinations leading to a magic or almost magic daughter nucleus. The analytical formula obtained allows one to handle a large number of cases to search for new kinds of radioactivities.