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The large-scale shell-model calculations have been performed for theneutron-rich nuclei in the south region of $^{208}$Pb in the nuclear chart. Theweak interaction properties, such as the $\log ft$, average shape factorvalues, half-lives, and neutron emission probabilities, are calculated forthese neutron-rich nuclei with the help of newly developed effectiveinteraction [Yuan et al., Phys. Rev. C 106, 044314 (2022)] for $^{208}$Pbregion. These calculations have been performed without truncation for aparticular model space, however, for some nuclei, a certain truncation has beenemployed and particle-hole excitations are included in the case ofcore-breaking nuclei. An extensive comparison with the experimental data hasbeen made and spin parities of several states have been proposed. In thisstudy, we have considered 270 transitions.

Shell-model study for allowed and forbidden $\beta^-$ decay properties in the "south" region of $^{208}$Pb