Systematic study of the half-lives of nuclear bound-state $β^-$ decay
Nuclear bound-state $β^-$ decay ($β_{\text b}$ decay) is a novel weak-interaction process that becomes possible when atoms are highly ionized, such as in stellar environments or heavy-ion storage rings. In this work we present a systematic theoretical calculations for the $β_{\text b}$-decay half-lives of interesting candidates for the first time, where both allowed Gamow-Teller transitions and first-forbidden transitions are taken into account by the microscopic projected shell model, and the lepton phase space is calculated by the Takahashi-Yokoi model. We analyzed the structure informations for hundreds of nuclei near the $β$-stability line, and select 16 interesting candidates belonging to two categories, i.e., nuclei with negative $Q$ values and positive $Q$ values in neutral atoms respectively. Among these candidates, we recommend $^{243}\mathrm{Am}^{95+}$, $^{194}\mathrm{Os}^{76+}$, $^{227}\mathrm{Ac}^{89+}$, $^{228}\mathrm{Ra}^{88+}$, $^{241}\mathrm{Pu}^{94+}$, $^{247}\mathrm{Cm}^{96+}$ and $^{250}\mathrm{Cm}^{96+}$ as promising ones for future studies of storage-ring experiments because their $β_{\text{b}}$-decay half-lives are predicted to be much shorter than the half-lives in neutral atoms. These findings provide essential nuclear inputs for astrophysical models and identify specific candidates where experimental verification would be most valuable.