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 $\rightarrow$ $^{206}$Tl, $^{208}$Hg $\rightarrow$ $^{208}$Tl, $^{206}$Tl $\rightarrow$ $^{206}$Pb and $^{208}$Tl $\rightarrow$ $^{208}$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 ${\it 1p-1h}$ 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.