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In the present work, we report a comprehensive shell-model study of the $\logft$ values for the forbidden $\beta^-$ decay transitions in the north-eastregion of $^{208}$Pb. For this we have considered $^{210-215}$Pb $\rightarrow$$^{210-215}$Bi and $^{210-215}$Bi $\rightarrow$ $^{210-215}$Po transitions. Wehave performed shell-model calculation using KHPE interaction in valence shell82-126 for protons and 126-184 for neutrons without any truncation. We havealso calculated half-lives and Q-values for the concerned nuclei. Recentlyseveral $\log ft$ values are observed corresponding to $\beta^-$ decay from(8$^-$) isomeric state of $^{214}$Bi$^m$ at CERN-ISOLDE facility [Phys. Rev. C{\bf 104}, 054301 (2021)], and for the first time we have reported shell-modelresults for these transitions.

Shell-model description for the properties of the forbidden $\beta^-$ decay in the region "north-east" of $^{208}$Pb