Exploring the half-lives of extremely long-lived α emitters * *Supported by the National Natural Science Foundation of China (11822503) and the Fundamental Research Funds for the Central Universities (Nanjing University)

Abstract

Naturally occurring α emitters with extremely long half-lives are investigated using the latest experimental data. Within the time-dependent perturbation theory, α decay with a rather narrow width is treated as a quasi-stationary problem by dividing the potential between the α particle and daughter nucleus into a stationary part and a perturbation. The experimental α decay half-lives of seven available long-lived α emitters with y are reproduced with a good accuracy. It is also found that the deformation effect should be treated carefully for long-lived nuclei, especially with low values. Predictions of the α decay half-lives of twenty naturally occurring nuclei are provided, namely, Ce, Nd, Sm, Dy, Er, Yb, W, Os, Pt, and Pb. These nuclei are energetically unstable to α decay with low decay energies and extremely long decay half-lives. In particular, the candidates Os and Sm are strongly recommended for future experiments.