  Relativistic coupled-cluster(RCC) theory has been employed to calculate the
life time of the $6 ^2P_{3/2}$ state of single ionized lead($^{207}Pb$) to an
accurac y of 3% and compared with the corresponding value obtained using second
order r elativistic many-body perturbation theory(RMBPT). This is one of the
very few ap plications of this theory to excited state properties of heavy
atomic systems. C ontributions from the different electron correlation effects
are given explicitl y.
