Nuclear Saturation Density Research Articles

Quark and gluon condensates in nuclear matter.

Quark and gluon condensates in nuclear matter are studied. These in-medium condensates may be linked to a wide range of nuclear phenomena and are important inputs to QCD sum-rule calculations at finite density. The Hellmann-Feynman theorem yields a prediction of the quark condensate that is model independent to first order in the nucleon density. This linear density dependence, with slope determined by the nucleon \ensuremath{\sigma} term, implies that the quark condensate is reduced considerably at nuclear matter saturation density---it is roughly 25--50 % smaller than the vacuum value. The trace anomaly and the Hellmann-Feynman theorem lead to a prediction of the gluon condensate that is model independent to first order in the nucleon density. At nuclear matter saturation density, the gluon condensate is about 5% smaller than the vacuum value. Contributions to the in-medium quark condensate that are of higher order in the nucleon density are estimated with mean-field quark-matter calculations using the Nambu--Jona-Lasinio and Gell-Mann--L\'evy models. Treatments of nuclear matter based on hadronic degrees of freedom are also considered, and the uncertainties are discussed.

Chiral phase transition and dynamical properties of quarks at finite temperature and density: Application of the “thermo-field dynamics” to the SU(3) Nambu-Jona-Lasinio model with instanton effects

The properties of quarks in hot and/or dense matter are studied using the Nambu-Jona-Lasinio model with instanton effects. Thermo-field dynamics is applied to this model as a useful framework to present the unified description of quarks and nuclear matters at zero and non-zero temperatures. Especially, a four-dimensional cut-off parameter can be introduced transparently. The framework of this thermo-field dynamics is also discussed. We study the chiral symmetry in a finite temperature and/or density system. The dynamical quark masses are obtained up to a temperature of T = 400 MeV and a density of 10 times of the nuclear saturation density for nuclear and neutron matters. Furthermore, we examine the instanton effects in the nuclear medium and discuss s s content in the nucleon for nuclear and neutron matters.

A modified relativistic Hartree approximation to the nuclear matter equation of state

We reconsider the vacuum correction term for the Walecka σ- ω model in the relativistic Hartree approximation retaining explicit dependence on the renormalization scale. The usual Chin-Walecka prescription is recovered by setting the renormalization scale equal to the nucleon mass. We find that when the renormalization scale is set to the effective nucleon mass at nuclear saturation density the model gives a dramatically lower compression modulus. The behavior of the effective nucleon mass at saturation and the compression modulus are examined as a function of the renormalization scale.

Quark matter with pion condensate in an effective chiral model

We study the chirally broken phase of quark matter with static pion condensates. We use the framework of the sigma model with quark and meson degrees of freedom and mean-field approximation. For commonly used parameters, the pion-condensed phase is the ground state of the system already at densities of the order of nuclear saturation density. We find that for the pion-condensed phase the chiral symmetry restoration takes place at much higher densities than for the normal phase. In the case of the neutral pion condensate the up and down quark Fermi seas are oppositely polarized along the direction of the pion field wave vector. We calculate the net spin density of the up and down Fermi seas and we estimate the magnetization of the system. We obtain the equation of state and study the phase transition from nucleon matter to pion-condensed quark matter.

Quark matter in a chiral chromodielectric model.

Zero- and finite-temperature quark matter is studied in a chiral chromodielectric model with quark, meson, and chromodielectric degrees of freedom. The mean-field approximation is used. Two cases are considered: two-flavor and three-flavor quark matter. It is found that at sufficiently low densities and temperatures the system is in a chirally broken phase, with quarks acquiring effective masses of the order of 100 MeV. At higher densities and/or temperatures a chiral phase transition occurs and the quarks become massless. A comparison with traditional nuclear physics suggests that the chirally broken phase with massive quark gas may be the ground state of matter at densities of the order of a few nuclear saturation densities.

Nuclear matter saturation density: From finite nuclei to infinite matter

The accuracy of Hartree-Fock (HF) calculations of the average density\(\bar \rho \) in the core of atomic nuclei is studied by a comparison with selected experimental data. It is shown that the scattering of extrapolated HF values for the saturation densityρ ∞ obtained with various effective forces is largely due to a bad fit of many HF forces to experimental data. However, even after correcting the current parametrisations, an uncertainty remains for the value ofρ ∞, due to a correlation between the trends of\(\bar \rho \)(A) and the compression modulusK, which is reflected in the extrapolation toA=∞.Using a generalised Skyrme functional, we show that this correlation is a particular case of a more general relation between\(\bar \rho \)(A) and the distribution of the binding energy between the inner and outer parts of the nuclear surface. Indications are given on possible improvements of the HF force by the inclusion of density- and momentum-dependent terms, supporting a value of ρ∞≈0.158 fm−3 as well as in improved agreement between HF and droplet core densities.The relation of HF results with macroscopic models is discussed in Sect. 5, showing the rôle played by exponential contributions, but also suggesting that dilation/compression effects exist, which are not taken into account in the usual energy density and droplet models.

Comparison of the Effective Nuclear Interactions in Non-Relativistic and Relativistic Microscopic Calculations

The microscopic calculations of the effective nuclear interactions in the Landau Fermi-Liquid theory were performed in the framework of both the nonrelativistic Brueckner theory and relativistic mean-field theory. The Landau parameters obtained from the relativistic approach exhibit a strong density dependence. In the vicinity of the nuclear saturation density the strong density dependence of the scalar and isoscalar Landau parameter has somewhat eased up by the many-body force of nucleons.

Model-space nuclear matter calculations with the Paris nucleon-nucleon potential.

Using a model-space Brueckner-Hartree-Fock approach, we have carried out nuclear matter calculations using the Paris nucleon-nucleon potential. The self-consistent single particle spectrum from this approach is continuous for momentum up to k/sub M/, where k/sub M/roughly-equal2k/sub F/ is the momentum space boundary of our chosen model space. The nuclear matter average binding energy and saturation Fermi momentum given by our calculations are approx.15.6 MeV and approx.1.56 fm , respectively. When using the conventional Brueckner-Hartree-Fock approach with a spectrum which has a gap at k/sub F/, the corresponding results are approx.11.5 MeV and approx.1.50 fm . The gain of approximately 4 MeV in binding energy between the two calculations comes mainly from the TS1 and S0 partial wave channels. We have investigated the effect of adding an empirical density dependent central potential to the Paris potential. It is found that the addition of such a potential whose strength is approx.10% of the central component of the Paris potential is adequate in making the nuclear matter binding energy and saturation density in simultaneous agreement with the empirical values.

Deconfinement phase transition of hot and dense nuclear matter in the non-topological soliton bag model

We investigate the quark deconfinement phase transition in hot and dense nuclear matter in the non-topological soliton bag model. For this purpose we study the behaviour of the nucleon (soliton) at finite temperature in a spherical Wigner-Seitz cell. We find the deconfinement transition to occur for zero temperature through a rather wide transitional region centered at about five times the nuclear matter saturation density while for zero chemical potential the transition happens rather abruptly at a critical temperature of about 112 MeV.

Structure of Matter below Nuclear Saturation Density

It is found that just below nuclear saturation density more stable forms of dense matter exist than the near-spherical nuclei or bubbles customarily assumed. Because of the large effect of the Coulomb lattice energy, cylindrical and planar geometries can occur, both as nuclei and as bubbles. It is suggested that in order to approximate more complicated kinds of short-range order, the dimensionality should be regarded as a continuous variable ranging from d = 3 (spheres) to d = 1 (planes). The dependence of d on density is illustrated, and its dependence on nuclear models discussed.

Fermi-liquid properties of nuclear matter in a relativistic mean-field theory

The Fermi-liquid properties of the model nuclear system described by a relativistic quantum field theory are examined in terms of a relativistic extension of Landau's Fermi-liquid theory. The relativistic Landau parameters are derived microscopically from the ground state energy in the mean-field approximation, and are used to describe the thermodynamic properties of the system, such as the compressibility, the symmetry energy and the hydrodynamic sound velocities. We reproduce the previous results at nuclear saturation density ( n 0 = 0.19 fm −3) and extrapolate to all density regions. It is shown that the system exhibits instability against the long wavelength density fluctuations in the low density region ( n B <0.70 n 0) and becomes stable at and above the nuclear saturation density due to the relativistic reduction of the attractive scalar meson component in the quasiparticle interaction. In the extreme high-density region, we reproduce the correct causal results for sound velocities. The existence of collisionless zero-sound oscillation is also examined.

Instanton effects in dense quark matter

The equilibrium statistical mechanics of color neutral quark matter in the gas phase is discussed in QCD. The approach is framed in the grand canonical ensemble starting from the path integral representation of the thermodynamic potential Ω based on the θ-vacuum. The description of instantons is limited to the weak coupling, dilute-gas approximation. We develop the general formalism for the perturbation theory expansion of Ω in the instanton background. An approximate evaluation of the finite-density contribution of the quark determinant is attempted in order to reach a quantitative understanding of the instanton correction to the ideal gas term. We also synthesize the current understanding of the perturbative contributions to Ω, up to fourth order inclusive, drawing a distinction between renormalization schemes based on on-shell and off-shell parametrizations of quark masses. All this information on perturbative as well as instanton corrections is assembled to achieve a realistic discussion of the equilibrium properties of cold quark matter with u, d, s flavors from the nuclear saturation density out to densities an order of magnitude larger. Particular attention is devoted to the sensitivity of predictions on the basic QCD parameters, Λ and quark masses. The phase metastability of quark matter and the implications for a quark-hadron first-order phase transition are addressed from a non-dynamical point of view. A small instanton suppression correction is found with a very weak dependence on baryonic density. We also consider the sensitivity of this correction to some of the known uncertainties in the description of the instanton density.

Hartree-Fock test of overhauser's model with a skyrme force

The Overhauser problem in nuclear matter is re-examined carefully with a modern density-dependent Skyrme interaction. The energy per particle, at each density, is obtained as a function of three “order parameters” (which vanish for the spatially homogeneous plane-wave case) and which are momentum integrals over the K-dependent Overhauser orbital mixture coefficients, which in turn are determined by the three original “order parameters”. Spurious energy minima are eliminated by self-consistently solving the above non-linear problem numerically. The Overhauser Hartree-Fock state is more stable than the plane-wave state only in a density region safely below the nuclear saturation density value. This fact is interpreted as embryonic of alpha-cluster formation at sub-nuclear densities.

Density-dependent effective interactions in finite nuclei (II)

The effect of the density dependence of the effective forces on spherical nuclear calculations is examined. Calculations have been made with forces giving different nuclear matter saturation densities and compressibilities and also with interactions having different long-range density dependence. The results have been compared with experiments.

A quarks-on-springs model of the baryons: J. A. Shapiro. Department of Physics, University of California, Berkeley, California

The Fermi-liquid properties of the model nuclear system described by a relativistic quantum field theory are examined in terms of a relativistic extension of Landau's Fermi-liquid theory. The relativistic Landau parameters are derived microscopically from the ground state energy in the mean-field approximation, and are used to describe the thermodynamic properties of the system, such as the compressibility, the symmetry energy and the hydrodynamic sound velocities. We reproduce the previous results at nuclear saturation density (n0 = 0.19 fm−3) and extrapolate to all density regions. It is shown that the system exhibits instability against the long wavelength density fluctuations in the low density region (nB <0.70 n0) and becomes stable at and above the nuclear saturation density due to the relativistic reduction of the attractive scalar meson component in the quasiparticle interaction. In the extreme high-density region, we reproduce the correct causal results for sound velocities. The existence of collisionless zero-sound oscillation is also examined.