Abstract
The newly discovered $\ensuremath{\alpha}$ decay of ${}^{209}\mathrm{Bi}$ [Marcillac et al., Nature (London) $422,$ 876 (2003)] is investigated in the cluster model of $\ensuremath{\alpha}$ decay. It is found that the cluster model can reproduce the data of this longest-lived $\ensuremath{\alpha}$ emitter in all known $\ensuremath{\alpha}$-decay nuclei. This decay belongs to a special class of $\ensuremath{\alpha}$ decays occurring in odd-$A$ nuclei with an extra nucleon outside a closed shell. By combining the cluster model of $\ensuremath{\alpha}$ decay with a microscopic model of preformation $\ensuremath{\alpha}$ cluster, we can successfully describe the half-lives of odd-$A$ $N=127$ isotones. The cluster model of the favored $\ensuremath{\alpha}$ decays is interestingly generalized to the hindered $\ensuremath{\alpha}$ decays of odd-$A$ nuclei.
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