Exploring the half-lives of extremely long-livedαemitters

Abstract：

Naturally occurring αemitters with extremely long half-lives are investigated using the latest experimental data. Within the time-dependent perturbation theory, αdecay with a rather narrow width is treated as a quasi-stationary problem by dividing the potential between the αparticle and daughter nucleus into a stationary part and a perturbation. The experimental αdecay half-lives of seven available long-lived αemitters with $ T^{\rm{total}}_{1/2}>10^{14} $ 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 $ Q_\alpha $ values. Predictions of the αdecay half-lives of twenty naturally occurring nuclei are provided, namely, $ ^{142} $ Ce, $ ^{145,146} $ Nd, $ ^{149} $ Sm, $ ^{156} $ Dy, $ ^{162,164} $ Er, $ ^{168} $ Yb, $ ^{182,183,184,186} $ W, $ ^{187,188,189,190} $ Os, $ ^{192,195} $ Pt, and $ ^{204,206} $ Pb. These nuclei are energetically unstable to αdecay with low decay energies and extremely long decay half-lives. In particular, the candidates $ ^{187} $ Os and $ ^{149} $ Sm are strongly recommended for future experiments.