Short range part of theNNinteraction: Equivalent local potentials from quark exchange kernels

Abstract

To focus on the nature of the short range part of the $\mathrm{NN}$ interaction, the intrinsically nonlocal interaction among the quark constituents of colorless nucleons is converted to an equivalent local potential using resonating group kernels which can be evaluated in analytic form. The WKB approximation based on the Wigner transform of the nonlocal kernels has been used to construct the equivalent potentials without recourse to the long range part of the $\mathrm{NN}$ interaction. The relative importance of the various components of the exchange kernels can be examined: The results indicate the importance of the color magnetic part of the exchange kernel for the repulsive part in the $(\mathrm{ST})=(10), (01)$ channels, in particular since the energy dependence of the effective local potentials seems to be set by this term. Large cancellations of color Coulombic and quark confining contributions, together with the kinetic energy and norm exchange terms, indicate that the exact nature of the equivalent local potential may be sensitive to the details of the parametrization of the underlying quark-quark interaction. The equivalent local potentials show some of the characteristics of the phenomenological short range terms of the Paris potential.NUCLEAR REACTIONS Short range part of $\mathrm{NN}$ interaction, six-quark model, RGM quark exchange kernels, equivalent local potentials via WKB and Wigner transforms.