Application of the constituent quark nucleon - nucleon interaction to nuclear matter

Constituent quark model of the nucleon-nucleon interaction. 1. general formalism

Abstract: We use the semirelativistic constituent quark model in conjunction with the resonating group method to obtain a nonlocal Schroedinger equation for the two-nucleon system. As the quark-quark color exchange potential we use the lattice gauge theory result; the sum of the Breit potential and a linearly rising confining potential. Both the Breit potential and the quark kinetic energies are treated consistently to order ({ital v}/{ital c}){sup 2} in the quark speeds; however, we ignore relativistic corrections to the confining potential and to the kinetic energy of relative motion of the nucleons. We distinguish carefully between the exact formulation and the approximations we use to make the calculations tractable. We present the resulting nonlocal nucleon-nucleon Schroedinger equation explicitly and analytically.

Short Range Part of Baryon-Baryon Interaction in a Quark Model. I —Formulation—

Abstract: The short range part of the interaction between non-strange baryons (N and Δ) is studied in a nonrelativistic quark model. The mass of a quark is assumed to be about one-third of the nucleon mass and the quark-quark interaction consists of a confinement term and the one gluon exchange potential. Baryons are described as clusters of three quarks and the resonating group method, which has been extensively developed in the nuclear cluster model, is used to treat the bound state and scattering problems of two baryons. This paper discusses the formal aspects of the present approach, while the numerical results will be given in the subsequent paper.

Nuclear Force in a Quark Model

Abstract: The problem of the nuclear force in a nonrelativistic quark model is studied by the resonating group method which has been extensively used in treating the interaction between composite particles. The calculated phase shifts for the 3 S 1 and 1 S 0 states of two nucleons indicate the presence of a strong repulsive force at short distance, while an attractive force is predicted for the 7 S 3 (( S , T )=(3,0)) state of two Δ's. These features are due to an interplay between the Pauli principle and the spin-spin interaction between quarks.

On the Fractional Parentage Expansions of Color Singlet Six Quark States in a Cluster Model

Abstract: The classification is given of observable (color-singlet) antisymmetric six-quark states in a cluster model with definite orbital and isospin-spin symmetries (“symmetry basis”). A number of “hidden color” states that cannot be represented in terms of free baryons is deduced. Tables of coefficients of fractional parentage (cfp) are recorded which allow the determination of an effective baryon-baryon interaction from a given non-relativistic quark-quark interaction. It is shown that the cfp method can be used to calculate the transformation between the states of the symmetry basis and those of the “physical” basis of di-baryons (N 2 , NΔ and Δ 2 ) and hidden-olor states.

Effective nuclear forces in the quark model with Delta and hidden color channel coupling

Abstract: Adiabatic potentials are calculated in a six-quark cluster model corresponding to having NN, ΔΔ and CC (hidden color) channel coupling. Color-dependent quark interactions are used that yield the N and Δ positive- and negative-parity resonances up to 2 GeV. Channel coupling is found to be large (especially with the CC state) and yields an effective NN potential having none of the characteristics of phenomenological potentials extracted from phase shifts.