Nucleon-nucleon correlations with quark degrees of freedom

A dynamical equation of two nucleons in a nucleus is formulated in the nonrelativistic quark model including Pauli blocking due to the other nucleons. This equation is solved with a model wave function containing the possiblity of six-quark bags with different radii. It is shown that the Pauli blocking effect is emphasized by the non-nucleonic degrees of freedom represented by six-quark bags. The modification of the quark momentum distribution for correlated nucleons is calculated and probabilities of non-NN components in nuclei are estimated.     

Short range behaviour of the N-N potential within the quark Model

The short range behaviour of the nucleon-nucleon (NN) potential is studied in terms of the quark model, where nucleons are assumed to consist of three colored quarks. By considering the overlap kernel of the wave function of the resonating group method (RGM), it is found that the Pauli effect does not produce a ‘hard core’. Instead, the gluon exchange interaction with the confinement requirement suggests a rather soft one. TheΔ-Δ isobar interaction is also considered. In the (S, T) = (3, 3), (3, 2) and (2, 3) channels we find a ‘hard core’, while calculations in some other cases indicate even strong short range attractions.     

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.     

RGM calculation of the NN spin-orbit interaction in a quark model

A quark-cluster model supplemented by an effective-meson-exchange potential (EMEP) is applied to the NN ³P scattering using the resonating group method (RGM). The repulsive central and the attractive spin-orbit NN interactions are obtained from the quark-exchange interaction including the symmetric spin-orbit term in the one-gluon-exchange potential. When the long- and medium-range central and tensor forces between nucleons are introduced as the EMEP, the results obtained seem to explain a considerable part of the empirical spin-orbit effect in the ³P scattering phase shifts.     

Short-range part of the NN interaction: Lowest-order relativistic corrections to equivalent local potentials from quark exchange kernels

The full Breit hamiltonian, including the Darwin term and relativistic kinetic-energy correction, has been used to construct resonating group kernels in analytic form for the six-quark NN system. The nonlocal kernels have been converted to equivalent local potentials using the WKB approximation based on their Wigner transforms. The equivalent local potentials have been confirmed to be rather insensitive to a choice of parameters and to be fairly accurate by comparing with the phase shifts and the wave functions obtained with the RGM equation. The results indicate the importance of the Darwin term. The term leads to a large reduction of the strong repulsive cores given by the color magnetic interaction and makes the resulting potentials less repulsive than those which neglect this term. The relative importance of the various components in the Breit interaction and of the quark-gluon exchange diagrams is made clear.     

On Possible S-Wave Bound States for an N\bar{N} System Within a Constituent Quark Model

We try to apply a constituent quark model (a variety chiral constituent quark model) and the resonating group approach for the multi-quark problems to compute the effective potential between the N\bar{N} in S-wave (the quarks in the nucleons N and \bar{N}, and the two nucleons relatively as well, are in S wave) so as to see the possibility if there may be a tight bound state of six quarks as indicated by a strong enhancement at threshold of p\bar{p} in J/ψ and B decays. The effective potential which we obtain in terms of the model and approach shows if the experimental enhancement is really caused by a tight S-wave bound state of six quarks, then the quantum number of the bound state is very likely to be I=1, J^PC=0^-+.     

The Pion-Recoil Current and Quark-Cluster Effects of Electromagnetic Form Factors of Deuteron

The electromagnetic form factors of deuteron are investigated on hybrid quarkhadron model, whexe meson exchange and six-quark clusters are taken into account. It is found that pion-recoil current and six-quark clusters have important effects on charge form factor, magnetic structure function and tensor polarization, which are all sensitive to the interaction between nucleons. The theoretical predictions agree well with new experimental data.     

Quark cluster model and the R-matrix theory treatment of NN scattering

A microscopic quark cluster model has been developed for six-quark states consisting of two s³ quark clusters. The consequences of channel nonorthogonality and existence of Pauliforbidden states are investigated explicitly by solving the eigenvalue problem of the resonating group method (RGM) kernel. Since the RGM kernels needed are all available, the form of the six-quark states given in this paper is very suited to detailed RGM calculations. A rigorous treatment based on the R-matrix theory has been carried out to obtain NN phase shifts. The spin-spin term of the quark-quark interaction favors states of higher color-spin symmetry. This explains the larger change caused by the hidden color states in the ³S₁ phase shifts than in the ¹S₀ phase shifts. Phase shifts calculated with inclusion of the delta and hidden color states are still too repulsive. It is pointed out that there arises a subtle problem in adding the one-boson exchange potential by hand to the RGM equation.     

Off-shell behaviour of theN-N interaction in a six-quark resonating group model of the deuteron

Two different 6-quark resonating group models of the deuteron are investigated to study the off-shell property of theN-N interaction. In the first model the quarks interact by a central one-gluon-exchange potential plus confinement potential. The meson-exchange contribution to then-p potential is simulated by a central GaussianN-N potential. In the second model the quarks interact by one-gluon-and one-pion-exchange potentials (central and noncentral) plus confinement potential. A small additional -exchange potential between neutron and proton binds the deuteron at the correct energy.Several off-shell variants of the two resonating group models are compared with each other by analyzing their elastic electron scattering cross sections. It is found that the standard renormalized version of the resonating group model yields potentials and wave functions that may be considered physical within the limitations of the model. Unitary off-shell transformations, which modify potentials and wave functions in any sizeable way, lead to a disagreement between the charge distribution predicted by the model via analysis of electron scattering and the charge distribution following from the microscopic quark distribution.Both of the 6-quark models support a soft repulsive core of the tripletn-p potential with a core height of around 900 MeV.     

Mixing of scalar meson and baryon-baryon interaction

At quark level,we study the effect of ideal mixing of singlet σ 0 and octet σ 8 scalar mesons on baryon-baryon interaction in the chiral SU(3) quark model.We solve the resonating group method equation for scattering process and bound state.The results show that the binding energy of deuteron and nucleonnucleon and hyperon-nucleon scattering data can be reasonably described for ideal mixing.Taking the same parameters we used in the scattering calculation,we further investigate the possible dibaryons and find the binding energy of (ΩΩ) ST =00 and (Ξ *Ω) ST =0 1 2 can be reduced a lot for ideal mixing.     

Microscopic calculation of the repulsive core in the elastic nucleon-nucleon scattering

The resonating group method is used to study the effective potential between two nucleons, due to the confining potential between quarks taken together with the Pauli principle for quarks. The potential used has harmonic form, unitary spin factor λ(1)·λ(2), and both ordinary and spin-spin components. Its parameters are determined by appeal to experimental data, and phase shifts are calculated for the¹ S ₀ and³ S ₁ states of the nuncleon-nucleon (NN) system. The results indicate that the repulsive core in theNN potential may arise from quark antisymmetrization required if nucleons are composed of quarks.     

Simulation of the Pauli-principle effects in the description of light ion scattering and bound states

A simple model which takes care phenomenologically of the effects of the Pauli principle is proposed to calculate, in the framework of the resonating group method, bound and scattering states of nuclear systems comprised of two light nuclei (n, t and α-particles) without performing a complete antisymmetrization of the wave functions. Retaining only the antisymmetrization between the nucleons belonging to a given cluster, the contributions of the terms corresponding to the exchange of two nucleons belonging to two different clusters are simulated by the matrix elements of an effective central, local, l-dependent, energy-independent nucleon-nucleon potential. The lowenergy levels of ⁸Be and ⁷Li as well as the phase shifts for l = 0 to 4 for energies below 10 MeV (c.m.) have been calculated with this effective potential (added to the regular nucleon-nucleon potential). Good agreement between exact and model calculations is achieved.     

Allowance for the Coulomb interaction in the framework of an algebraic version of the resonating group method

The Coulomb proton interaction is taken into account in the problem of light atomic nucleus scattering using an algebraic version of the resonating group method. Specific formulas are obtained for calculating the elastic scattering phases. The elastic pα scattering phases, the positions of resonances and their widths are calculated for some NN potentials. Theoretical values of the quantities under consideration adequately describe experimental data.     

Three-nucleon interaction in a quark cluster model

Taking into account the quark structure of the nucleons, a new three-nucleon potential is derived. It contains two parts: the pairwise interactions and a three-nucleon force. The pairwise interactions are described by the NN potentials of the quark-compound-bag model in the off-shell generalized form. The three-body force has the form of a separable potential which has a pole singularity on the energy axis. The residue at the pole is determined by the three-nucleon vertex given explicitly through all possible intermediate states formed by the 6q and 9q bags. The solution of the three-nucleon problem is obtained in an analytical form by means of the known solution of the problem with ordinary pairwise interaction. It is shown that: (i) the 9q bag is an additional source of an attractive interaction between three nucleons; (ii) the pole singularity of the three-nucleon force exhibits a resonance structure of the three-nucleon scattering amplitude; (iii) the total and partial widths of the quasi-discrete level are defined by the three-nucleon vertex. Some consequences of the new potential are discussed.     

N-N INTERACTION IN THE DEFORMED CHIRAL BAG I

Using the hybrid chiral bag a formulation is developed for discussing the short range behaviour of the nuclear force. Quarks interact with each other via exchange gluons inside the bag and exchange "pion field" quanta on the bag surface. In terms of the Green's functions for the confined quarks, gluons in the bag and pions outside the bag the second order perturbation interaction energy of the sixquark state is derived. In principle, it can be used for any configurations. To compare with the result without the pion field outside the bag the DeTar's six-quark states are used for the numerical calculation. As estimated, the streagth of the repulsion core will increase. The numerical result will be shown in the succeeding paper.     

The short-range nucleon-nucleon repulsion

The short-range repulsion (0.2–0.4 fm) between nucleons is investigated. The opposing effects of ω-meson exchange and ε-meson (J^p = 0⁺) exchange are investigated, and the relation to Regge behaviour is demonstrated using fixed-s dispersion relations. The energy dependence of the short-range interaction is emphasized, and experimental data on polarization in elastic NN scattering at high energy are used to give the necessary coupling constant.     

Analysis of α-7Li elastic and inelastic scattering at low energy with a simple model of the pauli principle effects

The elastic and inelastic scattering of α on ⁷Li are calculated at different low energies in the framework of the resonating group method in which the ⁷Li is supposed to be comprised of two clusters, α and t. To reduce the time of calculation, the effects of the Pauli principle due to the exchange of two nucleons belonging to two different clusters are approximated with an effective nucleon-nucleon potential which has been determined previously in order to reproduce correctly the scattering and bound states of the nuclear systems comprised of two particles, 2α or α + t. This calculation takes into account the exchange of the incoming a with the a belonging to ⁷Li as well as the coupling with the ⁸Be + t channel. Without any free parameter, the model calculation reproduces correctly the main features of the experimental data when the projectile energy is less than 5 MeV (lab). It appears that the coupling with the ⁸Be + t channel cannot be neglected.     

NN potential with a six-quark core from the constituent quark model

A mesonic nucleon-nucleon potential from an effective quark interchange mechanism for non-overlapping nucleons is obtained from the constituent quark model. This is supplemented at short range by a phenomenological, non-mesonic potential describing the transition to a six-quark core with a discrete energy spectrum. NN phase shifts and low energy parameters are calculated and compared with data and phase shift analyses. Core parameters are extracted from the fits.