Prediction for cluster radioactivity in even-even naturally occurring isotopes

Abstract

For the first time, a systematic investigation of cluster radioactivity in all even-even naturally occurring isotopes is performed by employing the universal decay law (UDL). Based on the calculated half-lives and the adopted criterion $T_{1/2}^{UDL}<{10}^{30}$ yr, twelve α-emitting candidates are suggested, with ¹⁷⁶Hf being the shortest-lived case ($T_{1/2}^{UDL}=2.79\times {10}^{18}$ yr). The systematic analysis presented in this work reveals that: (1) the known and predicted natural α emitters below $Z=82$ serve as a stringent benchmark for semiempirical decay laws in the extremely low-Q regime, and (2) naturally occurring isotopes offer a distinct advantage in rare-event searches, despite their much longer expected half-lives than those of non-natural isotopes. For heavier cluster decays, among those nuclei with N ≤ 126, only the doubly magic ⁴⁸Ca emission from ¹⁸⁶Os gives a half-life within the 10³⁰-yr limit. In contrast, for ^230,232Th and ^234,238U with N > 126, the $T_{1/2}^{UDL}$ values for many cluster-emission channels fall within this limit. These findings provide promising candidate cluster emitters among naturally occurring isotopes and therefore motivate future experimental searches.