Nucleon-nucleon interaction in a chiral constituent quark model

Abstract

We study the short-range nucleon-nucleon interaction in a chiral constituent quark model by diagonalizing a Hamiltonian comprising a linear confinement and a Goldstone boson exchange interaction between quarks. The six-quark harmonic oscillator basis contains up to two excitation quanta. We show that the highly dominant configuration is $|{s}^{4}{p}^{2}[42{]}_{O}[51{]}_{\mathrm{FS}}〉$ due to its specific flavor-spin symmetry. Using the Born-Oppenheimer approximation we find a strong effective repulsion at zero separation between nucleons in both ${}^{3}{S}_{1}$ and ${}^{1}{S}_{0}$ channels. The symmetry structure of the highly dominant configuration implies the existence of a node in the $S$-wave relative motion wave function at short distances. The amplitude of the oscillation of the wave function at short range will be, however, strongly suppressed. We discuss the mechanism leading to the effective short-range repulsion within the chiral constituent quark model as compared to that related with the one-gluon exchange interaction.