Properties of the Lithium Sequence

It is shown that in a perturbation description based upon a zero-order single-particle Hamiltonian, the diagonal and off-diagonal matrix elements of a single-particle operator for an $N$-particle system are essentially just linear combinations of matrix elements for two-particle systems. A similar statement applies to a restricted class of two-particle operators. The theory is applied to the calculation of the leading terms in the relativistic and mass-polarization corrections for the lithium sequence and to the calculation of the $2s-2p$ and $3s-3p$ dipole transition probabilities of the lithium sequence. Comparison of the transition probabilities with experimental data and with the results of refined variational calculations shows that high accuracy can be obtained.