Stability and $\alpha$ decay of translead isomers and the related preformation probability of $\alpha$ particles

Nuclear isomers provide an opportunity to investigate the role of the single-particle configuration and its exotic rearrangements in nuclear stability, away from the shell closures. We explored the configurations of translead isomers from Pb to U and their stability relative to ground states, and then we investigated their well-defined $\alpha$-decay modes relative to the ground-state decays. The $\alpha$-preformation probability $S_{\alpha }$ is deduced from the experimental half-life and that calculated without implementing $S_{\alpha }$, within the preformed cluster model based on the Wentzel–Kramers–Brillouin tunneling penetrability and assault frequency in terms of the Skyrme $\alpha +$ core potential. We found that the single valence $Z=83,85,87$ protons ($\pi 1h^{1,3,5}{}_{{9/2}^{-}}$) and $N=127$ neutron ($\nu 2g^1{}_{{9/2}^{+}}$) outside the doubly magic Pb core play a main role in enhancing the stability of translead isomers, whether they last in the original orbital or promote to another one, solely or coupled to another valence nucleon. The spin-gap isomers of high spin may be attributed to coupling of two protons or neutrons to stretched large spin, and then they jointly couple with a single valence nucleon. For favored $\alpha$ decays, the isomers indicate larger $\alpha$-preformation probability than ground states. The decays from isomeric states of lower energy to higher daughter states and that involve a change in parity exhibit not only less $S_{\alpha }$ but also less relative stability than the higher-to-lower decays and those keep the parity unchanged, respectively. Increasing the difference in spin of the isomer relative to its daughter nucleus is found to enhance its stability, yielding larger half-live and smaller preformation probability.

Figure 1

The comparative half-lives $T_{1/2}\left(\text{iso/gs}\right)=T_{1/2}\left(\text{iso}\right)/T_{1/2}\left(\text{gs}\right)$ of the isomeric states for (a) the isotopes of Bi, Po, and At isotopes and for (b) the isotones of $N=115$, 126, 127 and 128 relative to their ground states.

Figure 2

The decimal logarithm of the partial half-life time (${log}_{10}{T}_{\alpha }$) for the observed favored ($l_{\alpha }=0$) and unfavored [$l_{\min }\left(\alpha \right)=5\hslash ,8\hslash$] $\alpha$-decay modes from (a) the ground states and from (b) the isomeric states of the investigated translead nuclei from Pb to U as function of ${\left(Q_{\alpha }^{-1}\right)}^{1/2}$.

Figure 3

The preformation probability $S_{\alpha }^{\text{expt}}$ as extracted from the $T_{\alpha }^{\text{expt}}$ and $T_{\alpha }^{\text{calc}}$ (without $S_{\alpha }$) for (a) the decay modes of Bi isotopes, in ground and isomeric states, against the energy of the parent state, and for (b) the favored and unfavored decay modes of Bi and At isomers, against the difference in energy between parent and daughter energy states. (c) $S_{\alpha }^{\text{expt}}$ for the unfavored decays of Bi and At isomers, versus the minimum transfer of the orbital angular momentum, carried by the emitted $\alpha$ particle, according to the conservation of angular momentum.