Shell model study of first-forbidden beta decay around ${}^{208}$Pb

In the present work, we report a systematic theoretical study of the $\log ft$ values for the forbidden ${\beta }^{-}$ decay transitions in the ${}^{208}$Pb region. For this, we have considered ${}^{206}$Hg $\to$ ${}^{206}$Tl, ${}^{208}$Hg $\to$ ${}^{208}$Tl, ${}^{206}$Tl $\to$ ${}^{206}$Pb and ${}^{208}$Tl $\to$ ${}^{208}$Pb transitions. We have performed shell model calculations using KHH7B interaction in valence shell 58-114 for protons and 100-164 for neutrons by considering $\mathit{1}p-\mathit{1}h$ excitations for both protons and neutrons simultaneously for daughter nuclei. This study presents the first shell model results of ${\beta }^{-}$-decay corresponding to the recent experimental data.