  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.
