EXPLICIT FORM OF THE EFFECTIVE N-N POTENTIAL FROM THE QUARK CLUSTER MODEL

We derive an effective N-N potential from a microscopic quark Hamiltonian using the quark cluster model. We construct it in an explicit analytical form, which is expressed only by nuclear variables and which can be used in nuclear structure calculations. To this end we first solve the equation of motion for the six-quark system with a microscopic quark Hamiltonian that includes the quadratic-confinement, one-gluon-, and one-pion-exchange potentials. We then eliminate the quark (internal) degrees of freedom explicitly and express them implicitly in terms of an effective N-N potential. The equation of motion for the two-nucleon system is then described by a Schrodinger equation with an effective N-N potential. In addition to the one-pion-exchange potential, this effective N-N potential contains the quark-exchange potential, which represents the quark-exchange processes associated with a gluon or a pion exchange. This quark-exchange potential is incorporated into the effective N-N potential through nonlocal and isospin-dependent terms, which produce a short-range repulsion in the N-N interaction. We give the explicit analytical form of this quark-exchange potential so that it can be used in the nuclear structure calculations.