Non-relativistic Quark Cluster Model Research Articles

Study of Nucleon-Nucleon and Hyperon-Nucleon Interaction

In this paper we review recent investigations of nucleon-nucleon andhyperon-nucleon interactions employing a non-relativistic quark cluster model. We concentrate mainly on the short andmed ium-range behavior of the baryon-baryon interaction basedon the onegluon andmeson exchange potentials. The chiral quark mod el basedon pion andsigma exchange between quarks is also discussed. We also review a study of the deuteron and its electromagnetic properties in a quark model with exchange currents. There have been a lot of investigations of single baryon properties using the constituent quark model. The study of Isgur and Karl 1) has shown that the baryon spectra are nicely reproduced using the non-relativistic constituent quark model. The confined quarks interact with each other through residual interactions. Isgur and Karl employed the one-gluon exchange potential (OGEP) 2) as residual interaction. The spin-dependent part of the OGEP, called the color magnetic interaction, can explain the mass difference between octet and decuplet baryons, such as the nucleon and the ∆ resonance. Introducing a flavor SU(3) breaking term due to the strange quark mass, the model can also explain the mass difference between Σ and Λ particles as well as the mass difference between strange baryons and nucleons. A chiral quark model, where the residual interactions among quarks are dominated by Goldstone boson exchange due to the spontaneous chiral symmetry breaking, has been employed to study the baryon spectra. 3) This model has been shown to produce the nucleon and ∆ mass difference due to the pseudoscalar meson exchange interaction in a right direction. The absolute value, however, strongly depends on the model of the baryon. In a model where the baryon size is around 0.6 fm, the contribution from the pseudoscalar (ps) meson exchange is roughly one third of the observed mass difference between the nucleon and ∆. Therefore, the rest of the mass difference must be supplied by another mechanism such as the OGEP. It has been shown that the whole mass difference is given by the ps meson exchange if the nucleon size is about 0.3 fm. 4)

Some new results on the H dibaryon in the quark cluster model

The H dibaryon channel, ( I = 0, J = 0, S = −2), is revisited in the non-relativistic quark cluster model (NRQCM) using a basis extended beyond the usual set of baryon cluster pairs to include an explicit spatially symmetric 6q state, analogous in structure to the MIT bag model H. We find that the binding predicted using the two-baryon basis alone is significantly deepened by the addition of the additional 6q configuration. The NRQCM thus appears, contrary to earlier findings, to be incompatible with the experimental information available for this channel.

Baryon-baryon interaction in a chiral quark model

Nucleon-nucleon scattering phase shifts and deuteron properties are studied in the non-relativistic quark cluster model. The quark cluster model is modified to include chiral symmetry. This reduces the number of parameters. The σ meson is exchanged between quarks and not as in earlier versions between nucleons. The charge monopole, quadrupole and magnetic-dipole form factors of the deuteron in this microscopic meson-quark cluster model are calculated. The deuteron wave function is derived from a microscopic 6-quark Hamiltonian which, in addition to a quadratic confinement potential, includes the one-pion and the one-gluon exchange potentials between quarks. The electromagnetic current operators are constructed on the quark level, i.e., the photon is coupled directly to the quarks. Aside from the one-body impulse current, pionic and gluonic exchange current corrections are included. Due to the Pauli principle on the quark level, new quark interchange terms arise in the one-body and two-body current matrix elements, that are not present on the nucleon level. While these additional quark exchange currents are small for low momentum transfers, we find that they appreciably influence the electromagnetic structure of the deuteron beyond a momentum transfer of q = 5 fm −1.

Microscopic description of the nucleon- Delta interaction in the quark cluster model.

By using a nonrelativistic quark cluster model to describe baryonic systems, we generate a nucleon-\ensuremath{\Delta} potential from the elementary interaction between constituents. The basic quark-quark potential used provides, when applied to the nucleon-nucleon system, an adequate description of the scattering phase shifts, the deuteron properties and the nonstrange baryonic spectroscopy. Special attention is paid to the short-range behavior of the interaction and its connection to the quark Pauli principle. This establishes a conceptual difference with meson-exchange models where the interaction, due to the lack of data, is not even well defined.

Quarks in hadrons and nuclei and electromagnetic probes

Deuteron properties and nuclear magnetic moments are studied in the non-relativistic quark cluster model. The quark cluster model is modified to include chiral symmetry. This reduces the number of parameters. The σ meson is exchanged between quarks and not as in earlier versions between nucleons. The charge monopole, quadrupole and magnetic-dipole form factors and the tensor polarization of the deuteron in this microscopic meson-quark cluster model are calculated. The deuteron wave function is derived from a microscopic 6-quark Hamiltonian which, in addition to a quadratic confinement potential, includes the one-pion and the one-gluon exchange potentials between quarks. The electromagnetic current operators are constructed on the quark level, i.e., the photon is coupled directly to the quarks. Aside from the one-body impulse current, pionic and gluonic exchange current corrections are included. Due to the Pauli principle on the quark level, new quark interchange terms arise in the one-body and two-body current matrix elements, that are not present on the nucleon level. While these additional quark exchange currents are small for low momentum transfers, we find that they appreciably influence the electromagnetic structure of the deuteron beyond a momentum transfer of q = 5 fm −1.

Quark delocalization, color screening, and nuclear intermediate range attraction.

We consider the effect on baryon-baryon potentials and phase shifts of including quark delocalization and color screening in the nonrelativistic quark cluster model. We find that the inclusion of these additional effects allows a good qualitative description of both.

The nucleon-H-particle interaction in the quark model

Employing a non-relativistic quark cluster model, we investigate the interaction between a nucleon and an H-particle. The interaction consists of the short-range repulsion due to the color-magnetic terms and the medium-range attraction due to the meson exchange. For the medium and long-range parts of the interaction, we use a phenomenological approach to simulate meson exchange effects. For a certain choice of parameters we find a loosely bound state with a binding energy of 0.20 MeV. Low-energy S-wave scattering phase shifts show that the interaction is weak and attractive on the average.

Study of hyperon-nucleon and hyperon-hyperon interaction in the flip-flop model

The non-relativistic quark cluster model is employed to study two-baryon systems including hyperons such as Λ,Σ and Ξ. The quark confinement is described in terms of the flip-flop model. For a description of long- and medium-range parts of the baryon-baryon interaction, the exchanges of pseudoscalar mesons and a scalar meson σ are taken into account in the present calculation. Adjusting the parameters so as to fit the nucleon-nucleon scattering data, we obtain a strongly bound state di-hyperon which is about 60–120 MeV lower than the ΛΛ threshold.

Baryon-baryon interaction in the quark model and the H-dibaryon

The non-relativistic quark cluster model has been successfully used for describing the nucleon-nucleon interaction. Here it is extended to describe the hyperon-nucleon (ΛN, ΣN) and hyperon-hyperon (H-dibaryon) interaction. Including central and tensor parts of the one-gluon exchange, pseudoscalar-meson exchange plus an additional phenomenological σ-meson exchange, a very good fit of the experimental hyperon-nucleon cross-sections is achieved. Applying this model to the H-dibaryon, a bound state with a binding energy of (−15 ± 5) MeV below the ΛΛ threshold is found, i.e. the mass of the H-dibaryon is predicted to be around 2216 MeV.

Nucleon-nucleon interaction in the quark cluster model

We calculate the phase shifts and mixing parameters of nucleon-nucleon scattering in l = 0–4 channels employing a non-relativistic quark cluster model which includes the tensor and spin-orbit parts as well as the central part of one-gluon-exchange potential (OGEP) for the interaction for quarks, and the one-pion-exchange potential and medium-range central attraction for the effective interaction between two nucleons. Both the tensor and spin-orbit parts of the OGEP strongly enhance the mixing parameter of 3Si 1- 3D 1 channels in the high-energy region, though it is still smaller than the one given by the phase shift analysis. It is also shown that other experimental data except for l = 3 channel can be reproduced fairly well. It is found that the most part of the medium-range attraction is spin-isospin independent.

The pion pair current in the quark cluster model

The pion pair current is re-evaluated in the non-relativistic quark cluster model. Its effect on the elastic form factors of the deuteron is studied in a consistent framework in which the wavefunction and the electromagnetic current operators are calculated on the quark level. Due to the Pauli principle on the quark level, new quark interchange terms arise which are not present in a nucleon level calculation. While these additional quark exchange terms are small for low momentum transfers, the authors find that they appreciably modify the total pion pair current contribution to the charge form factors of the deuteron beyond q=5 fm4-1. In the magnetic form factor they find even at q=0 a 25% contribution of the diagrams including both meson and simultaneous quark exchange compared with the diagram with pion exchange only Their calculation is compared with a conventional calculation on the nucleon level and experimental data.

Hyperon-nucleon interaction in the quark cluster model

Abstract The lambda-nucleon and sigma-nucleon interaction is described in the nonrelativistic quark cluster model. The SU(3) flavor symmetry breaking due to the different quark masses is taken into account, i.e. different wavefunctions for the light (up, down) and heavy (strange) quarks are used in flavor and orbital space. The six-quark wavefunction is fully antisymmetrized. The model hamiltonian contains gluon exchange, pseudoscalar meson exchange and a phenomenological σ-meson exchange. The six-quark scattering problem is solved within the resonating group method. The experimental lambda-nucleon and sigma-nucleon cross sections are well reproduced.

Binding energy of the dihyperon in the quark cluster model

The dihyperon is described in the non-relativistic quark cluster model. The SU(3) flavor symmetry breaking due to the different quark masses is taken into account not only in the hamiltonian, but also in the quark wave functions. The interaction contains the one-gluon-exchange potential, pseudoscalar-meson exchange between quarks plus an additional phenomenological σ-meson exchange. The mass of the dihyperon is predicted to be (2211 ± 5) MeV, i.e. a binding energy of the dihyperon of (−20 ± 5) MeV below the ΛΛ threshold is found.

Hyperon-nucleon and hyperon-hyperon interaction in a quark model

The non-relativistic quark cluster model is employed to describe the two-baryon systems including hyperons such as Λ, Σ and Ξ. Qualitative discussions about the role of the Pauli principle for quarks and the color magnetic interaction in the baryon-baryon scattering are given. Results of the resonating group method (RGM) calculation show a repulsive interaction at short distances in most of the two-baryon systems with strangeness S = −1 and −2. There appears, however, a sharp resonance in the 1S 0ΛΛ scattering at E = 26.3 MeV, which may correspond to the di-hyperon state.

The effect of quark degrees of freedom on nuclear properties

Employing a simplified non-relativistic quark cluster model for deuteron and α-particle, we investigate the effects of quark exchange and modification of nucleon size on nuclear form factors, quark momentum distributions and nucleon quasifree scattering. We find that the size modification affects all the above quantities and that the quark exchange has an appreciable influence on the quasifree scattering.

Non-relativistic quark cluster model of the isospin-violating two-nucleon interaction

The violations of isospin symmetry induced in the two-nucleon system at the quark level by the mass difference between up and down quarks are studied in a quark cluster model. Quark dynamics are treated by means of the standard non-relativistic quark model with a quark hamiltonian consisting of a confining harmonic potential, eventually corrected for anharmonicities, and a spin-dependent potential truncated to the contact-gluon-exchange hyperfine interaction. The resonating group method is adopted to treat the six-quark system and we restrict ourselves to configurations of two three-quark clusters with nucléon quantum numbers. π- and σ-meson-mediated quark interactions are tentatively considered in an attempt to achieve a good matching to the empirical strong NN potentials. We supply explicit formulas for the various kernels. Equivalent adiabatic potentials are calculated for the pp, np and nn systems in low partial waves. We also solve the resonating group scattering equations for these systems and give predictions for phase observables and low-energy parameters.

The di-hyperon state in the quark cluster model

The di-hyperon state (DH) predicted by Jaffe in the MIT bag model is studied in the non-relativistic quark cluster model. The resonating group method is applied to the ΛΛ, NΞ and ΣΣ coupled channels problem. No stable bound state is found below the lowest ΛΛ threshold but a sharp resonance with spin-parity 0 + is predicted just below the NΞ threshold. The structure of the state is similar to that of the flavour SU 3 singlet state and the attractive nature of the color magnetic interaction in this state is responsible for the appearance of the resonance. The difference between the present model and the bag model which predicted a strongly bound state is attributed to the difference in the mechanism of confinement for these two models.