Relativistic many-body studies of high density matter

A fully relativistic quantum many-body theory is applied to the study of a model high-density matter which qualitatively describes known nuclear matter. Results pertaining to the equation of state of neutron matter, neutron star mass, vacuum fluctuation corrections, collective modes, exchange energies, and correlation energies are reported.     

The meson propagator in nuclear matter

We present a formal device for calculation of a meson propagator in infinite nuclear matter, through the calculation of the ground state energy of the system in the presence of external, static meson fields, using a pseudo-Hamiltonian simply related to the actual Hamiltonian. This approach is particularly well adapted for dealing with some effects that are not taken into account at all in multiple scattering approaches, for example, the effects of nuclear forces on the intermediate states which are involved in the meson-single-nucleon scattering. A theorem is proved about limiting conditions under which the charged pion propagator is independent of the nuclear forces. These conditions are nearly enough realized in π-nucleus scattering (sufficiently below the energy of the first resonance) so that we can evaluate the corrections perturbatively. The (virtually unknown) two-body force between the 3-3 resonance and nucleons is shown to be of considerable importance in determining the π-meson propagator.     

Abnormal nuclear matter and many-body forces

Qualitative aspects of quantum corrections to the Lee-Wick abnormal nuclear matter are studied in terms of many-body forces in the normal nuclear matter implied by the σ-model Lagrangian field theory. Using a simplified model for the scalar meson self-energy in the nuclear medium and restricting to a set of graphs which in non-relativistic normal nuclear matter reduces to the well-known random phase approximation (RPA), we have found that an abnormal nuclear state can be bound or unbound depending upon whether strongly attractive multi-body forces are present or absent in the normal matter. This is in support of our previous result obtained heuristically from some general considerations of quantum corrections. A strongly bound abnormal matter with an equilibrium density of a few times the normal nuclear matter density ρ₀ can be formed if large attractive manybody forces can be accommodated in the normal nuclear matter. However if one accepts the present status of theories of nuclear matter binding energy in which no attractive many-body forces are called for, then the abnormal state can occur only at large densities (perhaps 8 to 10 times ρ₀) and is expected to be unbound by several hundred MeV per particle.     

Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

Relativistic Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations.     

A sigma-omega-quark model to saturate nuclear matter

A sigma-omega-quark model is investigated to explain the saturation properties of nuclear matter. The quark structure of the nucleon induces a mechanism for saturation by weakening the attraction due to the sigma meson at high density. The boost of the composite system and some center-of-mass corrections are new sources of repulsion and therefore strongly reduce the need for an omega meson.     

Correlations and the Dirac structure of the nucleon self-energy

The Dirac structure of the nucleon self-energy in symmetric nuclear matter as well as neutron matter is derived from a realistic meson exchange model for the nucleon-nucleon (NN) interaction. It is demonstrated that the effects of correlations on the effective NN interaction in the nuclear medium can be parameterized by means of an effective meson exchange. This analysis leads to a very intuitive interpretation of correlation effects and also provides an efficient parametrization of an effective interaction to be used in relativistic structure calculations for finite nuclei. Received: 29 January 2001 / Accepted: 5 May 2001     

The two-pion exchange NN potential in nuclear matter and nuclear stability

A meson exchange model of the ππ interaction which fits free ππ scattering data is used to calculate the interactions of pions in nuclear matter as a function of nuclear density. Polarization of the nuclear medium by the pions results in a marked increase in the s-wave ππ attraction at low energy. The influence of this effect on the nucleon-nucleon interaction is a corresponding increase with density of the NN central potential due to the exchange of two correlated pions, resulting in an NN interaction which fails to saturate. A possible mechanism for restoring the theoretical stability of nuclear matter is explored and found to be effective.     

The study of the binding energy of nuclear matter in the relativistic σ− ω− π model with Δ isobar degree of freedom

The relativistic σ?ω?π model is proposed and used to calculate the binding energy of relativistic nuclear matter. By coupling Δ isobar to the σ meson, the zero-point fluctuation energy of the Δ isobar in the one loop approximation is derived. We calculate the effective mass of nucleon and Δ isobar, exchange and correlation energies, pressure and incompressibility of nuclear matter. The density dependence correction to σNN ωNN coupling constants is a very important mechanism to saturate the binding energy. The pion propagator is nuclear matter is constructed by the relativistic particle-hole, delta-hole and short-range correlation. The pion dispersion relation is calculated we find it’s very sensitive to the effective mass of nucleon and Δ isobar.     

OBEP and eikonal form factor: (II). Nuclear matter results

Nuclear matter properties are calculated in a first-order Brueckner-Bethe calculation using a one-boson exchange potential recently proposed by the authors, in which the phenomenological cutoff of dipole type used so far has been replaced by a form factor obtained from an eikonal approximation to multiple vector meson exchange processes. We find ?23.5 MeV saturation energy at a Fermi momentum k_F = 1.77 fm^?1, i.e. about 12 MeV more binding than realistic OBEP using dipole-type cutoffs and about 8 MeV overbinding compared to the empirical value of 16 MeV. On the other hand, estimates suggest that, compared to the Reid soft-core potential, this new OBEP predicts about 1.5 MeV more binding in the case of the triton and about 4 MeV more binding in the case of ¹⁶O, i.e. gives nearly the correct empirical result. The additional binding is traced back to the small deuteron D-state probability of 4.32% predicted by this OBEP, which is a consequence of the special structure of the eikonal form factor. However, taking the effect of the Δ-resonance into account recently given by Green and Niskanen, one arrives at ?14 MeV saturation energy for nuclear matter at k_F = 1.36 fm^?1, whereas the results for the triton and ¹⁶O are changed to a negligible extent only.     

A variational approach to dense relativistic matter using functional techniques

The zero temperature ground state of an infinite system of baryons interacting with each other through the exchange of scalar and vector mesons is studied by means of a variational principle appropriate to relativistic systems. A trial wavefunctional is constructed which represents the fluctuation of the quantum fields about their mean values. The renormalized ground-state energy is subsequently calculated at a point where the vacuum is stable. Renormalization to all orders in the strong coupling constants is thereby obtained. A simple expression for the binding energy per particle with three free parameters is found. These parameters are fixed by fitting to the observed nucleon mass and to the values of the fermi momentum and binding energy of nuclear matter. A prediction for the binding energy and equation of state of nuclear and neutron matter is obtained for densities far away from the density of normal nuclei. Finally, a comparison is made with results obtained by other authors who have used classical-perturbative methods for the same system.     

Hadron masses in medium and neutron star properties

We investigate the properties of the neutron star with relativistic mean-field models. We incorporate in the quantum hadrodynamics and in the quark-meson coupling models a possible reduction of meson masses in nuclear matter. The equation of state for neutron star matter is obtained and is employed in Oppenheimer-Volkov equation to extract the maximum mass of the stable neutron star. We find that the equation of state, the composition and the properties of the neutron stars are sensitive to the values of the meson masses in medium.     

Abnormal phase in dense neutron star matter

The possibility that neutron stars may possess an “abnormal” central region of the Lee-Wick type is discussed. It is found that when the abnormal equation of state includes quantum corrections and short-range repulsion as required in normal nuclear matter, the gravitational pressure in stable neutron stars is insufficient to induce a phase transition to abnormal matter.     

Neutrino-nucleon scattering rate in proto-neutron star matter

We present a calculation of the neutrino-nucleon scattering cross-section which takes into account the nuclear correlations in the relativistic random phase approximation (RPA). Our approach is based on a quantum-hadrodynamics model with exchange of σ, ω, π, ρ and δ mesons. In view of applications to neutrino transport in the final stages of supernova explosion and proto-neutron star cooling, we study the evolution of the neutrino mean free path as a function of density, proton-neutron asymmetry and temperature. Special attention was paid to the issues of renormalization of the Dirac sea, residual interactions in the tensor channel, coupling to the delta-meson and meson mixing. In contrast with the results of other authors, we find that the neutral-current process is not sensitive to the strength g' of the residual contact interaction. As a consequence, it is found that RPA corrections with respect to the mean-field approximation amount to only 10% to 15% at high density. Received: 27 June 2001 / Accepted: 14 January 2002     

Isoscalar and isovector nuclear matter properties and neutron skin thickness

Isoscalar and isovector nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and the isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. We also discovered that the correlations between the isovector properties and the incompressibility K show a singularity at the critical incompressibility K_c=306 MeV. It is shown that the neutron skin thickness gives crucial information about not only for the neutron EOS but also about the isovector nuclear matter properties and about the parameterization of Skyrme interaction. Charge exchange spin-dipole (SD) excitations are proposed to determine the neutron skin thickness model independently.     

Mean field model of nuclear matter

Phenomenological models of nuclear matter based on meson theory in the mean field approximation are investigated. In particular, the vector meson mean field function is studied in detail. It is shown that the low experimental compression modulus of nuclear matter places severe constraint on the form of the vector meson mean field function. Meson mean field functions taking into account nuclear correlation effects are discussed.     

Hyperon coupling dependence of hadron matter properties in relativistic mean field model

The properties of hadronic matter at β equilibrium in a wide range of densities are described by appropriate equations of state in the framework of the relativistic mean field model. Strange meson fields, namely the scalar meson field σ＊（975） and the vector meson field φ（1020）, are included in the present work. We discuss and compare the results of the equation of state, nucleon effective mass, and strangeness fraction obtained by adopting the TM1, TMA, and GL parameter sets for nuclear sector and three different choices for the hypcron couplings. We find that the parameter set TM1 favours the onset of hyperons most, while at high densities the GL parameter set leads to the most hyperon-rich matter. For a certain parameter set （e.g. TM1）, the most hyperon-rich matter is obtained for the hyperon potential model. The influence of the hyperon couplings on the effective mass of nucleon, is much weaker than that on the nucleon parameter set. The nonstrange mesons dominate essentially the global properties of dense hyperon matter. The hyperon potential model predicts the lowest value of the neutron star maximum mass of about 1.45 Msun to be 0.4--0.5 Msun lower than the prediction by using the other choices for hyperon couplings.[第一段]     

Neutron skin thickness and nuclear matter properties

Linear correlations are found among the isovector nuclear matter properties in both the Skyrme-Hartree-Fock (SHF) and the relativistic mean-field (RMF) models. In addition, we found a kind of correlation between the isovector nuclear matter properties and the incompressibility in the SHF model. The Skyrme parameters are related analytically to nuclear matter properties with the Thomas—Fermi approximation. By using a linear correlation between the neutron skin thickness and the pressure of the neutron matter in the SHF model, we show that the neutron skin thickness of ²⁰⁸Pb gives crucial information about not only the neutron equation of state but also the isovector nuclear matter properties and the parametrization of Skyrme interaction. The text was submitted by the authors in English.     

Relativistic Mean-Field Approach to Infinite Nuclear Matter and Neutron Star

The properties of infinite nuclear matter and neutron star are studied theoretically in relativistic mean-field (RMF) approach with three typical parameter sets NL1, NL-SH and TM1. It is found that all these new RMF parameter sets can very satisfactorily reproduce the properties of high density matter. Among these parameter sets, TM1, with a nonlinear ω term, reproduces a slightly smaller energy, piessure and neutron star mass than NL-SH and NL1. The ρ meson field has a large influence on the properties of neutron star and infinite nuclear matter. A detailed discussion for the significance of numerical results is also given.     

Static properties of nuclear matter within the Boson Loop Expansion

The use of the Boson Loop Expansion is proposed for investigating the static properties of nuclear matter. We explicitly consider a schematic dynamical model in which nucleons interact with the scalar–isoscalar σ meson. The suggested approximation scheme is examined in detail at the mean field level and at the one- and two-loop orders. The relevant formulas are provided to derive the binding energy per nucleon, the pressure and the compressibility of nuclear matter. Numerical results of the binding energy at the one-loop order are presented for Walecka’s σ-ω model in order to discuss the degree of convergence of the Boson Loop Expansion.