Density dependence of nucleon radius and mass in the global color symmetry model of QCD with a sophisticated effective gluon propagator

Making use of the global color symmetry model (GCM) at finite chemical potential and with a sophisticated effective gluon propagator, the density dependence of the bag constant, the total energy and the radius of a nucleon in nuclear matter is investigated. A maximal nuclear matter density for the existence of the bag with three quarks confined within is given as about 8 times the normal nuclear matter density. The calculated results indicate that, before the maximal density is reached, the bag constant and the total energy of a nucleon decrease, and the radius of a nucleon increases, with the increasing of the nuclear matter density. As the maximal nuclear matter density is reached, the mass and the bag constant of the nucleon vanish and the radius becomes infinite suddenly. It manifests that a phase transition from nucleons to quarks takes place. Meanwhile, shortening the interaction range among quarks can induce the phase transition to happen easier.     

Medium dependence of the bag constant in the quark-meson coupling model

Possible variations of the quark-meson coupling (QMC) model are examined in which the bag constant decreases in the nuclear medium. The reduction is supposed to depend on either the mean scalar field or the effective mass of the nucleon. It is shown that the electric and magnetic radii of the bound nucleon are almost linearly correlated with the bag constant. Using the fact that the size of the bound nucleon inside a nucleus is strongly constrained by y-scaling data in quasi-elastic, electron-nucleus scattering, we set a limit for the reduction allowed in the bag constant for these two models. The present study implies that the bag constant can decrease up to 10–17% at average nuclear density, depending on the details of the model.     

ρ-Meson coupling to the nucleon in the chiral bag model

The vector and tensor couplings of the ρ-meson to the nucleon are calculated by assuming the indirect coupling of the ρ-meson to the nucleon, through the pion cloud of the chiral bag model. Qualitative agreement with experiment is found at reasonable bag radii for both versions of the model: the cloudy bag model with pions in the interior, and the standard model with pions excluded from the bag.     

The fuzzy bag and baryonic properties with center of mass and recoil corrections

The fuzzy bag is a hadronic model which has features both of the bag model (energy-momentum conservation, QCD vacuum energy) and of relativistic potential models (confinement achieved through a potential). It is also a chiral model, with the unique property that the pion field is suppressed in the interior of the bag by means of a scalar potential, and yet chiral symmetry is preserved. This scalar potential allows one to control how far the pion field can penetrate in the interior of the bag. We calculate the masses of the fundamental baryon octet taking into account the center of mass, one-gluon exchange and one-pion exchange corrections. We also calculate the nucleon axial charge, charge radii and magnetic moments including center of mass and recoil corrections. The agreement with experiment is excellent, and the results indicate that the pion field is suppressed only very close to the center of the bag. Received: 14 January 2003 / Published online: 5 May 2003 RID="a" ID="a" e-mail: pilotto@if.ufrgs.br     

NUCLEON PROPERTIES IN A QUARK BAG MODEL WITH WOODS-SAXON TYPE CONFINING POTENTIAL

A quark bag model with Woods-Saxon type confining potential is suggested. This model is used to examine three well-nown characteristic quantities of the nucleon and the proton electromagnetic form factors are evaluated by considering the quark core contributions. It is found that our model employing a confinement of W-S potential can improve the fit with the experimental values and can give good results for the form factors.     

Quark models of nuclear isobaric energy differences

We study the energy differences between mirror nuclei in both nonrelativistic (NR) and relativistic quark models based on the one-gluon exchange interaction. Both six-quark (6q) and resonating-group (RG) methods are used to treat the effects of overlapping nucleons in nuclei. The 6q method is simple and useful, but it can give only qualitative results because of a lack of precision and the neglect of non-(1s)⁶ configurations. It is used here to compare bag and potential models of quarks and to study the effects of kinetic energy, quark-quark interaction and nucleon size. Six-quark results show that the usual Breit-Fermi NR reduction has serious limitations in treating quark masses and nucleon sizes. In contrast, the RG method is much more complete, but it is also much harder to use. It is used here with simple NR potential models to study the effects of complicated 6q configurations, nucleon size and nucleon-nucleon short-range correlations. We find that NR potential models tend to give Nolan-Schiffer anomalies larger than experimental results, while bag models give too small results, especially if the bag radius is as small as 0.6 fm.     

THE PROPERTIES OF NUCLEAR MATTER AT LOW TEMPERATURE IN A POSSIBLE QUARK MECHANISM

In this paper,the nucleon is described by the MIT bag model,and the internal quark motion in the nucleon is modified by the scalar and vector meson fields.The Fermi motion of nucleon in nuclear matter is considered.The changes for intrinsic properties of nucleon in nuclear matter at different temperature are calculated as a function of the density.The binding energy per nucleon for different temperature is given.     

A compressible bag model and equation of state for high density nuclear matter

We propose a compressible bag model, in which a nucleon bag responds microscopic thermal pressure of the other bags. The volume exclusion effect and the particle exchange type interaction ensure the saturation property of the nucleus at normal density and bring about the deconfinement transition in high density region. The critical values of chemical potential and baryon number density for nuclear/neutron matter are estimated. Our equation of state is applied to neutron stars, and shown to be consistent with the observed rotation periods of millisecond pulsars.     

Effects of bag surface motion with relativistic kinematics

Radial surface motion of the baryon bag is carried out in a model with relativistic kinematics, with confinement the result of volume energy and surface tension and the pion field coupled to the bag surface. We calculate radial wave functions for the nucleon, the Δ(1233) and the Roper resonance N^*(1450), which is identified as the first radial excitation of the nucleon.

Results are used to calculate form factors and pionic decay widths of the baryons examined. The approximations made in these calculations are discussed in extensio.     

Magnetic moments of the nucleon octet calculated in the cloudy bag model

The formalism of the cloudy bag model is used to calculate the pion coupling to the strange members of the nucleon octet (and delta decuplet). We then calculate the magnetic moments of all members of the octet, including lowest-order pionic corrections. Results are presented as a function of the radius of the bag, R, which is the only true free parameter of the model. Excellent agreement is obtained with experiment for bag radii ranging from 0.8 to 1.1 fm.     

Excluded volume,bag constant and hadron-quark phase transition

The model of hadron-quark phase transitions proposed by Cleymans et al. is modified by taking into account the fact that the nuclear repulsive force is operative between a pair of nucleons or a pair of antinucleons but not between a nucleon and an antinucleon. The phase boundary in the temperature (T)-chemical potential (μ) plane is calculated for some values of the bag constantB and the hard core radiusR. Stability of the normal nuclear matter together with the bag picture for the nucleon yields rather stringent bounds forB as functions ofR. The most probable range of values is estimated to beB ^1/4?150～200 MeV being consistent with the estimate from hadron spectroscopy. For this range ofB, it is improbable to realize the broken chiral phase with deconfining constituent quarks and Goldstone pions at someT and μ.     

Critical analysis of quark-meson coupling models for nuclear matter and finite nuclei

Three versions of the quark-meson coupling (QMC) model are applied to describe properties of nuclear matter and finite nuclei. The models differ in the treatment of the bag constant and in terms of non-linear scalar self-interactions. In two versions of the model the bag constant is held fixed at its free-space value whereas in the third model it depends on the density of the nuclear environment. As a consequence opposite predictions for the medium modifications of the internal nucleon structure arise. After calibrating the model parameters at equilibrium nuclear matter density, binding energies, charge radii, single-particle spectra and density distributions of spherical nuclei are analyzed and compared with QHD calculations. For the models which predict a decreasing size of the nucleon in the nuclear environment, unrealistic features of the nuclear shapes arise.     

Zero-point motion in the bag description of the nucleon

In the bag model, confinement of quarks is accomplished by introduction of a boundary condition at some definite radius $\text{R}$, where the energy of the total system is a minimum. This minimum is, however, realtively shallow and energies for substantially different bag radii are not much larger than this minimum value. This indicates that the zero-point motion of the bag surface may be important.In this paper, quantization of the bag surface motion is carried out in a somewhat ad hoc fashion, modelled after the generator coordinate theory in nuclear physics. This procedure unifies a number of ideas previously in the literature; it stresses the anharmonicity of the collective motion. As in earlier treatments, the Roper resonance emerges as a breathing-mode type of excitation of the nucleon.The one- and two-pion decays of the Roper resonance are calculated and the widths are found to fall short of the empirical ones. It is pointed out, however, that decays involving intermediate states containing virtual ρ-mesons will enhance the widths. Pion-nucleon scattering in the P₁₁ channel is constructed in our model and found to agree roughly with experiment. A crucial term in the driving force involves the pion coupling to the nucleon through a virtual ρ-meson.With introduction of zero-point motion of the bag surface, the notion of “bag radius” becomes dependent on precisely which moment of the radius is measured. Our development gives a model for cutting off smoothly the pion-exchange term in the nucleon-nucleon interaction.     

A chiral bag model with a soft surface : structure and solutions of the Fuzzy and the modified Fuzzy Bag Model

In the present work we propose a new bag model for hadrons, called the modified fuzzy bag model (MFBM). The distinguishing feature of this model is the suppression of the pion field, as it enters the bag, by means of a scalar potential for the pions, while still preserving chiral symmetry. The mechanism of pion suppression in the MFBM is similar to the mechanism of quark suppression in the fuzzy bag model (FBM). The standard chiral transformation for the pion field suffers a natural alteration in the MFBM, and as a result the model is chiral invariant. We present also a discussion of the FBM and study, in the quark sector, the implications of the soft surface of the bag on the expectation value of the mass operator. In the pion-quark sector, we study the effects of the suppression of the pion field on the form factor for the pion-nucleon interaction, on the pion-nucleon coupling constant and on the nucleon axial charge . Calculations of the pion-nucleon form factor exhibit, in particular, an improvement over previous results. The pionic axial current induces, in the MFBM, a nonvanishing and orientation dependent contribution to axial charge. An analysis of the asymptotic behaviour of the axial charge shows that the role of the surface is to increase the difference of the contributions associated to different orientations. Received: 10 March 1997 / Revised version: 14 October 1997     

Kaon cloud and baryon magnetic moments

The kaon cloud correction to the magnetic moments of the octet baryons that arises when chiral SU(2) × SU(2) symmetry is enlarged to SU(3) × SU(3) is calculated in the chiral bag model. The effect is considerably smaller than the pion cloud effect provided the bag radius is R ? 1 fm. We discuss the implications of this result on our ongoing attempt to incorporate chiral symmetry into the bag model of the nucleon and on the scale sizes associated with (nearly) massless quarks and massive quarks.     

Electric and magnetic polarizabilities of nucleon and QCD quark models

The experimental and theoretical work carried out on electric and magnetic polarizabilities of a nucleon is reviewed. The results of an exactly solvable one-dimensional chiral bag model predicts correct signs and order of magnitudes of polarizabilities supporting the approximations used in their realistic calculations.     

A new approach to centre-of-mass motion in relativistic quark models and electroweak properties of hadrons

It is assumed that independent quark models describe hadrons bound in a fictitious external potential well. Hadron properties in such models are only calculable after the effects of this binding (CM effects) have been removed. Our procedure for removing these CM effects is applied to the MIT bag model results for nucleon properties. We find very reasonable values for electroweak matrix elements (μ, g_A and r²) with previously fixed parameters.     

A METHOD OF COMPUTING THE EFFECTIVE COLOR DIELECTRIC CONSTANT AND THE BAG RADIUS OF NUCLEONS IN NUCLEI

Using the parabolic Fermi distribution of the nucleon number density instead of the average density, a new method of computing the effective color dielectric constant and the nucleon bag radius in nuclei is presented, so that the physical picture is made more realistic, and the results thus obtained are better consistent with the data and have two new features.     

Nucleon photoabsorption and quark structure

The electromagnetic excitation of nucleon resonances is stidied discussing retardation effects and relativistic corrections in the integrated photo-absorption cross sections. The retardation effects are calculated using the constituent quark model (CQM), while the relativistic corrections are evaluated in the framework of a bag model with massless quarks. The influence of three-body forces on the theoretical strength is also analyzed.     

Quark-Meson Bag Model and Hadron Structure

Based on the assumption that quarks (e.g. up, down quarks) couple with σ, ω and π mesons directly, a quark-meson bag model is-proposed. By adjusting the quark effective mass and quark-meson coupling constants, the nucleon, Δ baryon masses and some observables of proton are calculated.