Conforming the measured lifetimes of the $5d{}^2{D}_{3/2,5/2}$ states in Cs with theory

We find very good agreement between our theoretically evaluated lifetimes of the $5d{}^2{D}_{3/2}$ and $5d{}^2{D}_{5/2}$ states of Cs with the experimental values reported by DiBerardino et al. [Phys. Rev. A 57, 4204 (1998)], which were demonstrated to disagree with an earlier rigorous theoretical study [Safronova and Clark, Phys. Rev. A 69, 040501(R) (2004)] and with the other available precise measurement [Hoeling et al., Opt. Lett. 21, 74 (1996)]. In this work, we carry out calculations of the radiative transition matrix elements using many variants of relativistic many-body methods, mainly in the coupled-cluster theory framework, and analyze the propagation of electron correlation effects to elucidate their roles in accurate evaluations of the matrix elements. We also demonstrate contributions explicitly from Dirac-Coulomb interactions, frequency-independent Breit interaction, and lower order quantum electrodynamics effects. Uncertainties in these matrix elements due to different possible sources of errors are estimated. By combining our calculated radiative matrix elements with the experimental values of the transition wavelengths, we obtain the transition probabilities due to both the allowed and the lower order forbidden channels. Adding these quantities together, the lifetimes of the above two states are determined precisely and plausible reasons for the reported inconsistencies between the earlier theoretical calculations and the experimental results are pointed out.