Estimates of radioactive decay by the emission of nuclei heavier than α-particles

Abstract

We estimate the lifetimes for radioactive decay of a nucleus by the emission of α-particles or heavier fragments like 14C, by treating these processes as extreme cases of spontaneous fission. The lifetime is accordingly written as a frequency factor of the order of collective nuclear oscillations (10 −21−10 −22 sec) times a Gamow penetrability factor for the appropriate deformation-energy barrier. For the very asymmetric decays, an approximation to the barrier is obtained by combining the Coulomb repulsion between the fragments with the nuclear proximity potential (up to contact) and interpolating smoothly between the contact configuration and the configuration of the parent nucleus. We give a closed formula for the penetrability factor and find that, to within about one power of ten, we can account for the recently observed branching ratios between α-particle and 14C emissions from 222,223,224Ra. We apply our method to calculate branching ratios for other exotic decays (involving isotopes of O and Ne among others) and estimate that there may be a number of such decays that will be accessible to observation.