Relativistic aspects of the nuclear mean field in high-energy nucleus-nucleus collisions

The nuclear mean field as obtained within the Dirac-Brueckner approach is studied concerning its high-energy relativistic aspects. It is demonstrated that due to the different Lorentz character of the scalar and vector self-energies, which are the building blocks of the mean field, additional repulsion arises not present in non-relativistic treatments.     

The nuclear symmetry energy from relativistic Brueckner-Hartree-Fock model

The microscopic mechanisms of the symmetry energy in nuclear matter are investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF) model with a high-precision realistic nuclear potential, pvCDBonn A. The kinetic energy and potential contributions to symmetry energy are decomposed. They are explicitly expressed by the nucleon self-energies, which are obtained through projecting the G-matrices from the RBHF model into the terms of Lorentz covariants. The nuclear medium effects on the nucleon self-energy and nucleon-nucleon interaction in symmetry energy are discussed by comparing the results from the RBHF model and those from Hartree-Fock and relativistic Hartree-Fock models. It is found that the nucleon self-energy including the nuclear medium effect on the single-nucleon wave function provides a largely positive contribution to the symmetry energy, while the nuclear medium effect on the nucleon-nucleon interaction, i.e., the effective G-matrices provides a negative contribution. The tensor force plays an essential role in the symmetry energy around the density. The scalar and vector covariant amplitudes of nucleon-nucleon interaction dominate the potential component of the symmetry energy. Furthermore, the isoscalar and isovector terms in the optical potential are extracted from the RBHF model. The isoscalar part is consistent with the results from the analysis of global optical potential, while the isovector one has obvious differences at higher incident energy due to the relativistic effect.     

Self-consistent hartree description of finite nuclei in a relativistic quantum field theory

Relativistic Hartree equations for spherical nuclei are derived from a relativistic nuclear quantum field theory using a coordinate-space Green function approach. The renormalizable field theory lagrangian includes the interaction of nucleons with σ, ω, ρ and π mesons and the photon. The Hartree equations represent the “mean-field” approximation for a finite nuclear system. Coupling constants and the σ-meson mass are determined from the properties of nuclear matter and the rms charge radius in ⁴⁰Ca, and pionic contributions are absent for static, closed-shell nuclei. Calculated charge densities, neutron densities, rms radii, and single-nucleon energy levels throughout the periodic table are compared with data and with results of non-relativistic calculations. Relativistic Hartree results agree with experiment at a level comparable to that of the most sophisticated non-relativistic calculations to date. It is shown that the Lorentz covariance of the relativistic formalism leads naturally to density-dependent interactions between nucleons. Furthermore, non-relativistic reduction reveals non-central and non-local aspects inherent in the Hartree formalism. The success of this simple relativistic Hartree approach is attributed to these features of the interaction.     

A relativistic quantum field theoretical model for nuclear slab collision dynamics

We treat the dynamics of colliding nuclear slabs in a relativistic quantum field theory by using the relativistic mean field approximation. Starting from Walecka's lagrangian, the nucleons are represented by single-particle spinors determined by a Dirac equation that contains a repulsive mean vector meson field and an attractive mean scalar meson field. Both fields satisfy Klein-Gordon equations whose source terms are again determined by the nucleon spinors. The two equal nuclear slabs are translationally invariant in two transverse dimensions and consist of spin and isospin symmetric nuclear matter. By specification of appropriate initial conditions for the collision, we numerically solve the system of coupled Dirac and Klein-Gordon equations for lab energies per nucleon up to 420 MeV. For small energies the results are similar to TDHF results. The time dependence of the density distribution, the mean meson fields, and the damping of the collision are studied. At the highest bombarding energy retardation effects are taken into account.     

相对论带电费密子Liouville方程

作为密度矩阵一种形式的Wigner函数是量子相空间里的分布。用它描述相对论费密子时,它的通常表达形式为4×4矩阵函数。本文得到相对论带电费密子的2×2矩阵形式的Wigner函数以及它所满足的Liouville方程。这一方程与量子电动力学里带电费密子满足的Dirac方程完全等价。在描述中能核碰撞的Walecka模型里,当只有矢量介子(或标量介于取平均场近似)时,核子满足一定形式的Dirac方程。本文的方程也与之等价。还证明了(2×2)Wigner函数与相对论费密子的波函数在描述量子体系上起着同样的作用。量子体系的可观察量的全部知识都可以通过这里的Wigner函数得到。 关键词：     

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.     

Density dependence of the single-particle potential in nuclear matter

The single-particle potential in infinite nuclear matter is computed as a function of density and energy in a variety of relativistic mean-field models of nuclear matter. A comparison of this potential is made with that computed by Friedman and Pandharipande using the variational method. We also show that the self-consistent mean-field Hartree approximation satisfies the Hugenholtz-van Hove theorem. High-density behavior of the single-particle potential is considered.     

Pion tensor force and nuclear binding energy in the relativistic Hartree-Fock formalism

The binding energies of several isotopic families are studied within the relativistic Hartree-Fock approximation with the pseudovector coupling for the πN vertex, to find out a suitable strength for the effective pion tensor force (EPTF). An approximation for determining separately the contributions of the central and tensor forces generated by pion is considered. The results for heavy nuclei indicate that a realistic strength for the EPTF is smaller than a half of that appearing in the OPEP. This conclusion also applies to the results for the single-particle energies. Besides, it has been found that there is a genuine relativistic contribution of the EPTF in nuclear matter which is small but significant.     

Dependence of the density distribution of 208Pb on the occupation probabilities of shell-model orbits

An independent-particle model for the proton density distribution of ²⁰⁸Pb is constructed; it closely approximates the Hartree-Fock calculation of Dechargé and Gogny. We investigate the modifications which arise when one introduces a depletion of the Fermi sea of the amount suggested by analyses of recent electron scattering data and by nuclear-matter calculations. The main effect of the depletion is to flatten the density distribution in the nuclear interior. The calculated density is in good agreement with the empirical one near the nuclear centre but is too small in the vicinity of 5 fm. The main consequences of the depletion are shown to be largely independent of the details of the model. It is concluded that Hartree-Fock single-particle wave functions which yield good agreement with empirical density distributions are rather different from the natural orbitals. Accordingly they should not be expected to yield a good approximation to the off-diagonal elements of the one-body density matrix, e.g. to the momentum distribution.     

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition.     

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition.     

Saturating chiral field theory for the study of nuclear matter in the relativistic Hartree approximation

The bulk properties of nuclear matter are studied by considering a chirally invariant lagrangian which contains an interaction term involving scalar and vector mesons, of the form (apart from a numerical factor) used by Boguta. The calculation is performed in the relativistic Hartree approximation which includes the baryon vacuum fluctuation correction.     

A treatment of renormalization,potential energy of intermediate states and re-arrangement effects in brueckner calculations of closed shell nuclei

In the Brueckner-Hartree-Fock theory of finite nuclei, the problems of renormalization, potential energy of intermediate states and re-arrangement effects are examined. For practical calculations it is shown that satisfactory solutions to them can be obtained if the parametrization chosen for the single-particle potential in finite nuclei is linked closely to nuclear matter results. We make the link with similar problems in the density dependent Hartree-Fock theory and emphasize the possibility of such a parametrization by recalling the existence of a formal solution for the Hartree-Fock single-particle potential if the effective interaction is of the δ-function type. A method of solution of the Bethe-Goldstone equation is then presented which separates the intermediate states into those of an “open shell” and of a “continuum”. Finally results of model calculations of ¹⁶O and ⁴⁰Ca with harmonic oscillator functions are presented in which the parametrization chosen for the BHF single-particle potential is taken from the Skyrme-Vautherin δ-function force. A self-consistent determination of certain parameters of this form of force leads to values in close agreement with the empirical estimate made by Vautherin and Brink in ¹⁶O, with the exception of the spin-orbit splittings. Limitations and possible improvements of this type of approach are discussed for ⁴⁰Ca.     

Nuclear relativistic Hartree-Fock approximation with weakened pion tensor force

Properties linked to the single-particle energies, as nuclear spectra, spin-orbit splittings and shell gaps are investigated in the framework of the relativistic Hartree-Fock approximation with pseudovector coupling for the πN vertex. The role of an effective mass of pions moving in the nuclear medium and its relationship with the strength of pion tensor force is discussed. A simple method to reduce the contribution of this tensor force that considerably improves the single-particle spectrum of nuclei is proposed.     

Landau theory of relativistic Fermi liquids

A relativistic extension of the Landau Fermi liquid theory, applicable to the study of high density matter, is developed. Consequences of Lorentz invariance in the theory are explored. The formalism is illustrated by a study of relativistic Fermi systems weakly interacting via scalar and vector meson exchange. Second order exchange energies for both massless scalar and massless vector interactions are calculated in terms of Landau parameters on the Fermi surface. Zero sound and “color-plasma oscillations” are studied in quark matter with SU(3) color gluon coupling.