Perturbative calculation of transition amplitudes for cesium

We have done a many-body-perturbation-theory calculation, up to second order, for 6s→6${\mathit{p}}_{1/2}$ and 6s→6${\mathit{p}}_{3/2}$ transitions for Cs using the Dirac-Fock orbitals as single-particle wave functions. The results show that many-body-perturbation-theory calculations for transition amplitudes do not converge well unless some infinite subsets of diagrams are included. A systematic way of including infinite subsets of diagrams based on the Green’s-function formalism that preserves gauge invariance of transition amplitudes in each step is proposed for future work.