Hartree-fock contributions to the effective charge and interaction in the sd shell

Abstract

The second-order perturbation theory diagrams for the effective charge which contain HF insertions have been evaluated — they are sizeable and negative for neutrons and quite state-dependent for protons. The total second-order result is generally about − 1 3 of the first-order value which suggests that the effective charge does not smoothly converge to the required value in terms of the number of interactions. As concerns the effective-interaction expansion ordered according to the number of G-matrices, the inclusion of the HF diagrams is not expected to improve the poor convergence. The bare and first-order perturbation theory diagrams have been evaluated in a HF basis for both the effective charge and interaction. The bare effective-charge diagram is enhanced for protons compared to the oscillator result. For the bare interaction the levels are significantly less bound when the HF basis is used, particularly when the s 1 2 2 configuration is involved. The first-order perturbation corrections are much reduced in a HF basis compared to the oscillator results — the core-polarisation diagram is reduced by factors of roughly 2 and 5 for the effective charge and interaction respectively. In all cases the diagrams containing HF insertions give non-negligible contributions which are as important as those from the other diagrams.