The influence of a self-consistent model space on the folded diagram expansion of nuclear effective interactions

Abstract

The modification of the convergence properties of the folded diagram (FD) expansion of the effective interaction is studied in a self-consistent and in an oscillator sd shell model space. The Reid soft-core potential is used as the free N-N interaction. The self-consistent sd shell model space is defined by the Brueckner-Hartree-Fock approach without and with the inclusion of rearrangement terms. The main results are the following : (i) The FD expansion of the effective interaction converges considerably faster for a self-consistent model space, (ii) The core-polarization diagram is reduced by self-consistency, (iii) Shell-model calculations with the effective interaction defined in a self-consistent model space yield too little binding energy relative to 16O and the spectra are too compressed. This may indicate that the agreement found here and elsewhere employing an oscillator model space is accidental. It is argued that contributions as yet not included can improve the situation.