Accurate many-body calculations on the lowestS2andP2states of the lithium atom

The many-body perturbation theory (MBPT) in the coupled-cluster formulation is applied to perform very accurate calculations on the $2^2$S and $2^2$P states of the lithium atom. The computational procedure is based on coupled one- and two-particle equations, which are solved iteratively. In this way it has been possible to evaluate almost all one- and two-particle effects—i.e., the core polarization and the pair correlation—to essentially all orders of perturbation theory. The main reasons for this work are to test the computational procedure and to determine the significance of genuine three-particle effects, which are not included in the calculation. The total energy, the valence electron binding energies, and the hyperfine-interaction parameters are calculated for the two states. The perturbation effect, i.e., the difference between the experimental value and the Hartree-Fock result, is in all cases reproduced within about 1%, except for the small hyperfine parameter of the $2^2$ $P_{3/2}$ state, where this discrepancy is about 4%, mainly due to some remaining error in the induced contact interaction. The quadrupole parameter of the $2^2$ $P_{3/2}$ state is expected to be accurate to a few tenths of a percent. No improved value of the quadrupole moment can be given, however, due to experimental uncertainty.