Many-body calculations for the heavy atoms. III. Pair correlations

Corrections to the interaction integrals of 4f electrons, which are due to the interaction of configurations for which two f electrons are excited, are calculated with a pair function approach. Using first-order pair functions of this kind, second order and third order ladder diagrams are evaluated. The third order diagrams are quite small. This indicates a satisfactory convergence of the theory and means that an exact pair treatment is not necessary to deal with correlation effects among the f electrons. It is found that the second order results obtained in the Hartee-Slater potential introduced by Lindgren (1971) agree quite closely with Hartree-Fock results. Since the pair equation can more easily be solved in a local potential, the Hartree-Slater potential is probably a better starting point of perturbative calculations for the rare earth elements.