The Nucleon-nucleon potential in the chromodielectric soliton model: Statics

We study the nucleon-nucleon interaction in the framework of the chromodielectric soliton model (CDM). Here, the long range parts of the non-abelian gluon self-interactions are assumed to give rise to a color dielectric function which is parametrized in terms of an effective scalar background. The six-quark system is confined in a deformed mean field through an effective nonlinear interaction between the quarks and the scalar field. The CDM is covariant, respects chiral invariance, leads to absolute color confinement and is free of the spurious van der Waals forces which trouble the nonrelativistic investigations employing a confinement potential. Six-quark molecular type configurations are generated as a function of deformation and their energies are evaluated in a coupled channel analysis. By using molecular states instead of cluster model wave functions, all important six-quark configurations are properly taken into account. The corresponding Hamiltonian includes the effective interaction between the quarks and the scalar background field and quark-quark interactions generated through one gluon exchange treated in the Coulomb gauge. When evaluating the gluon propagators, the inhomogeneity and deformation of the electric medium are taken into account. Results for the adiabatic nucleon-nucleon potential are presented, and the various contributions are discussed. Finally, an outlook is given on how, in the next stage of our investigation, dynamical effects will be incorporated by employing the generator coordinate method.