Microscopic mechanism of charged-particle radioactivity and generalization of the Geiger-Nuttall law

TLDR

The authors propose a linear relation for charged‑particle emissions derived from the microscopic mechanism of radioactive decay. The relation links the logarithm of decay half‑lives to two variables, χ′ and ρ′, which are functions of the Q values, masses, and charges of the emitting nuclei. This universal decay law accurately describes all known cluster decays, generalizes the Geiger‑Nuttall law, predicts likely emissions across the nuclear chart, and shows that heavier clusters predominantly occur in the trans‑lead region while equal‑proton‑neutron clusters can be emitted from neutron‑deficient nuclei with Z ≥ 54.

Abstract

A linear relation for charged-particle emissions is presented starting from the microscopic mechanism of the radioactive decay. It relates the logarithms of the decay half-lives with two variables, called ${\ensuremath{\chi}}^{'}$ and ${\ensuremath{\rho}}^{'}$, which depend upon the $Q$ values of the outgoing clusters as well as the masses and charges of the nuclei involved in the decay. This relation explains well all known cluster decays. It is found to be a generalization of the Geiger-Nuttall law in $\ensuremath{\alpha}$ radioactivity, and therefore we call it the universal decay law. Predictions of the most likely emissions of various clusters are presented by applying the law over the whole nuclear chart. It is seen that the decays of heavier clusters with nonequal proton and neutron numbers are mostly located in the trans-lead region. The emissions of clusters with equal protons and neutrons, like $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$, are possible in some neutron-deficient nuclei with $Z\ensuremath{\geqslant}54$.