Stability and fine structure of $\alpha$ decay of isomers in the trans-tin region of the nuclear chart and their single-particle structure

The stability of nuclear isomers reflects a complex interplay of quantum-mechanical factors, influenced by the nuclear structure and the single-particle arrangement of nucleons within the nucleus. Here, we trace the factors behind the abundance and persistence of 1342 isomers over the trans-tin region of the nuclear chart from Sn to Tl, providing insight into the role of single-particle structure in controlling their stability and $\alpha$ decays. We found that nucleons originally belonging, or transferred, to the $\pi ,\nu 1h_{11/2}{}^{-}$ and $\nu 1i_{13/2}^{}+$ shell-model orbitals are directly connected to a substantial fraction of the observed isomers in this region, especially the more copious and more stable among them in addition to those of very high spin. They contribute either solely as odd valence nucleons or via a pure character of fully aligned configurations of a multiple of them, or with coupling to other valence nucleons, in addition to possible phonon coupling to lower spin states. A similar role is played by the $\pi 1g^{-1}{}_{7/2}^{+}$ ($\pi 3s_{1/2}^{+}$) proton hole for the copious and more stable Ta (Tl) isomers, by two protons reside outside the closed core of $Z_0=50$ in Te, by one (two) vacancies to the shell closure of $N_0=82$ for the isomers of $N=81$ (80), by valence $\nu 1h_{9/2}{}^{-}$ neutrons (hole) for $N=107$, and by a single lacked $\nu 3s_{1/2}^{+}$ neutron for $N=79$. The extracted $\alpha$-preformation probability is indicated to increase in isomers relative to their authentic ground states, when they release less energy. As in ground states, the stability of the isomeric states effectively increases with increasing the presupposed transfer of angular momentum, and, if the decay implicates a change in parity; lower value of the preformation probability is indicated in both cases. This clarifies the observed greater stability against $\alpha$ decay of many isomers of high spin relative to their ground states.

Figure 1

The number of observed isomers for nuclei of $50\le Z<82$, with larger or comparable stability relative to the corresponding ground states ($T_{\mathrm{iso}/\mathrm{gs}}\ge 0.001$), versus the proton and neutron number.

Figure 2

The partial half-lives against $\alpha$ decay ($T_{\alpha }$) on a logarithmic scale for (a) the observed favored decay modes of ground states and isomeric states of the nuclei with $65\le Z<81$ and $84\le N<109$, and for (b) the favored and unfavored $[l_{\min }\left(\alpha \right)=1\hslash ,3\hslash ,5\hslash ]$ decays from the ground states and (b) the favored and unfavored $[l_{\min }\left(\alpha \right)=2\hslash ,3\hslash ,8\hslash ]$ decays from the isomeric states of the nuclei of $84\le N<92$. Only the confirmed decay modes with well determined $\alpha$ intensity are considered.

Figure 3

The comparative preformation probability of an $\alpha$ particle, $S_{\alpha }\left(\mathrm{iso}/\mathrm{gs}\right)=S_{\alpha }^{\exp }\left(\mathrm{iso}\right)/S_{\alpha }^{\exp }\left(\mathrm{gs}\right)$, with $S_{\alpha }^{\exp }$ given by Eq. (2), for the decay modes from isomeric and ground states of a common value of $l_{\min }$, versus (a) the comparative released energy $Q_{\mathrm{iso}/\mathrm{gs}}=Q_{\alpha }\left(\mathrm{iso}\right)/Q_{\alpha }\left(\mathrm{gs}\right)$, and versus (b) the difference of energy between parent and daughter states ($E_P-E_D$). The solid trend lines are drawn according to the best coefficient of determination $R^2$.

Figure 4

The extracted preformation probability, $S_{\alpha }^{\exp }$, obtained using Eq. (2), for favored and unfavored decay modes from the ground and isomeric states of (a) the Ho, Tl, Tm, and Ta isotopes, and of (b) the $N=84$, 85, 100, and 109 isotones, against the minimum orbital angular momentum anticipated to be carried by the emitted $\alpha$ particle. The solid and dashed lines represent trend lines for the decays from ground states and from isomeric states, respectively, as obtained according to the best $R^2$ coefficient.