Convergence of all-order many-body methods: Coupled-cluster study for Li

We present and analyze results of the relativistic coupled-cluster calculation of energies, hyperfine constants, and dipole matrix elements for the $2s$, 2p1∕2, and 2p3∕2 states of Li atom. The calculations are complete through the fourth order of many-body perturbation theory for energies and through the fifth order for matrix elements and subsume certain chains of diagrams in all orders. A nearly complete many-body calculation allows us to draw conclusions on the convergence pattern of the coupled-cluster method. Our analysis suggests that the high-order many-body contributions to energies and matrix elements scale proportionally and provide a quantitative ground for semiempirical fits of ab initio matrix elements to experimental energies.