Quark model and equivalent local potential

Abstract

In this paper, we investigate the short-range repulsion given by the quark cluster model employing an inverse scattering problem. We find that the local potential which reproduces the same phase shifts as those given by the quark cluster model has a strong repulsion at short distances in the $\mathrm{NN}{ }^{1}{S}_{0}$ channel. There, however, appears an attractive pocket at very short distances due to a rather weak repulsive behavior at very high energy. This repulsion-attractive-pocket structure becomes more manifest in the channel which has an almost forbidden state, $\ensuremath{\Sigma}N(T=3/2){ }^{3}{S}_{1}.$ In order to see what kinds of effects are important to reproduce the short-range repulsion in the quark cluster model, we investigate the contribution coming from the one-gluon-exchange potential and the normalization separately. It is clarified that the gluon exchange constructs the short-range repulsion in the $\mathrm{NN}{ }^{1}{S}_{0}$ while the quark Pauli-blocking effect governs the feature of the repulsive behavior in the $\ensuremath{\Sigma}N(T=3/2){ }^{3}{S}_{1}$ channel.