Stability and fine structure of α 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 α decays. We found that nucleons originally belonging, or transferred, to the π,ν1h11/2^- and ν1i13/2^+ 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 π1g^-17/2⁺ (π3s1/2⁺) proton hole for the copious and more stable Ta (Tl) isomers, by two protons reside outside the closed core of Z₀=50 in Te, by one (two) vacancies to the shell closure of N₀=82 for the isomers of $N=81$ (80), by valence ν1h9/2^- neutrons (hole) for $N=107$, and by a single lacked ν3s1/2⁺ neutron for $N=79$. The extracted α-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 α decay of many isomers of high spin relative to their ground states.