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

TL;DR: In this paper, a simple Thomas-Fermi method for nuclear matter calculations is used to examine how well the non-local potential derived by Morley, Pursey and Williams from the constituent quark model can represent the actual interaction.

Abstract: A simple Thomas - Fermi method for nuclear matter calculations is used to examine how well the non-local potential derived by Morley, Pursey and Williams from the constituent quark model can represent the actual interaction. A strong net repulsion is found which grows rapidly with the nucleon size.

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01 Jan 1984

TL;DR: The semirelativistic constituent quark model is used in conjunction with the resonating group method to obtain a nonlocal Schroedinger equation for the two-nucleon system and is presented explicitly and analytically.

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.

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TL;DR: In this article, the short range part of the interaction between nonstrange baryons (N and Δ) is studied in a nonrelativistic quark model, where 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.

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.

237 citations

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TL;DR: In this paper, 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, and 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.

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.

216 citations

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TL;DR: In this article, a color-singlet antisymmetric six-quark states in a cluster model with definite orbital and isospin-spin symmetries (symmetry basis) are given.

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.

188 citations

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169 citations

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TL;DR: In this paper, a six-quark cluster model corresponding to having NN, ΔΔ and CC (hidden color) channel coupling was used to calculate adiabatic potentials.

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.

148 citations