Brueckner correlations following a boson mapping of the two-color delta model

Abstract

We study the application of boson mapping methods to a two-color delta model of interacting quarks, with the purpose of extracting information of relevance to quark-model descriptions of nuclei. In an earlier treatment, the boson Hamiltonian resulting from the mapping was approximately diagonalized at the level of Hartree-Bose approximation. The results differed from those of an exact solution of the model at first order in the density. Furthermore, the results were worse than those arising from a BCS treatment of pair correlations at the quark level. Here we extend the analysis to a Brueckner treatment, so as to properly take into account the short-range repulsion between bosons originating from the quark Pauli principle. The resulting energy per quark reproduces the exact results through first order in the density and is significantly better than the BCS results. At higher densities, deviations appear, reflecting the need for a full cluster expansion in the treatment of short-range correlation effects. The relevance of these results to more realistic three-color quark models of nuclei is discussed. ©1996 American Physical Society