Three-nucleon interaction in a quark cluster model

Abstract

Taking into account the quark structure of the nucleons, a new three-nucleon potential is derived. It contains two parts: the pairwise interactions and a three-nucleon force. The pairwise interactions are described by the NN potentials of the quark-compound-bag model in the off-shell generalized form. The three-body force has the form of a separable potential which has a pole singularity on the energy axis. The residue at the pole is determined by the three-nucleon vertex given explicitly through all possible intermediate states formed by the 6q and 9q bags. The solution of the three-nucleon problem is obtained in an analytical form by means of the known solution of the problem with ordinary pairwise interaction. It is shown that: (i) the 9q bag is an additional source of an attractive interaction between three nucleons; (ii) the pole singularity of the three-nucleon force exhibits a resonance structure of the three-nucleon scattering amplitude; (iii) the total and partial widths of the quasi-discrete level are defined by the three-nucleon vertex. Some consequences of the new potential are discussed.