Nucleon Self-energy In Nuclear Matter Research Articles

Relativistic mean-field approach in nuclear systems

A new scheme to study the properties of finite nuclei is proposed based on the Dirac-Brueckner-Hartree-Fock (DBHF) approach starting from a bare nucleon-nucleon interaction. The relativistic structure of the nucleon self-energies in nuclear matter depending on density, momentum and isospin asymmetry are determined through a subtracted T-matrix technique and parameterized, which makes them easily accessible for general use. The scalar and vector potentials of a single particle in nuclei are generated via a local density approximation (LDA). The surface effect of finite nuclei can be taken into account by an improved LDA (ILDA), which has successfully been applied in microscopic derivations of the optical model potential for nucleon-nucleus scattering. The bulk properties of nuclei can be determined in a self-consistent scheme for nuclei all over the nuclear mass table. Calculated binding energies agree very well with the empirical data, while the predicted values for radii and spin-orbit splitting of single-particle energies are about 10 \% smaller than the experimental data. Basic features of more sophisticated DBHF calculations for finite nuclei are reproduced.

Global analysis of isospin dependent microscopic nucleon-nucleus optical potentials in a Dirac-Brueckner-Hartree-Fock approach

The Microscopic Otical Model Potential is evaluated within a relativistic scheme which provides a natural and consistent relation between the spin-orbit part and the central part of the potential. The Dirac-Brueckner-Hartree-Fock (DBHF) approach provides such a microscopic relativistic scheme, which is based on a realistic nucleon-nucleon interaction and reproduce the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T-matrix (STM) representation provides a reliable extension to asymmetric nuclear matter, which is important to describe the features of the isospin asymmetric nuclei. Therefore, the present work aims to perform a global analysis of the isospin-dependent nucleon-nucleus MOP based on the DBHF calculation in symmetric and asymmetric nuclear matter. The DBHF is used to evaluate the relativistic structure of the nucleon self-energies in nuclear matter at various densities and asymmetries. The Schr\"odinger equivalent potentials of finite nuclei are derived from these Dirac components by a local density approximation (LDA). The nucleon-nucleus scattering calculations are carried out for a broad spectrum $n$ and $p$ scattering experiments below 200 MeV with targets ranging from $^{12}$C to $^{208}$Pb.

Role of the in-medium four-quark condensates reexamined

We calculate the nucleon self-energies in nuclear matter in the QCD sum rules approach, taking into account the contributions of the four-quark condensates. We analyze the dependence of the results on the model employed for the calculation of the condensates and demonstrate that the relativistic character of the models is important. The condensates are calculated with inclusion of the most important terms beyond the gas approximation. This corresponds to inclusion of the two-body nucleon forces and of the most important three-body forces. The results are consistent with the convergence of the operator product expansion. The density dependence of the nucleon self-energies is obtained. The results are consistent with those obtained by the standard nuclear physics methods, thus inspiring further development of the approach.

Relativistic spectral function of nucleons in hot nuclear matter

We present a simple calculation of the nucleon self-energy in nuclear matter at finite temperature in a relativistic framework, using the real time thermal field theory. The imaginary parts of one-loop graphs are identified with discontinuities across the unitary and the Landau cuts. We find that in general both the cuts contribute significantly to the spectral function in the region of (virtual) nucleon mass usually considered, even though the unitary cut is ignored in the literature. Also our relativistic spectral function differs from the one in non-relativistic approximation, used in some earlier calculations.

Relativistic nuclear energy density functionals: Adjusting parameters to binding energies

We study a particular class of relativistic nuclear energy density functionals in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance (high-momentum) correlations, as well as intermediate- and long-range dynamics, are encoded in the medium (nucleon-density) dependence of the strength functionals of an effective interaction Lagrangian. Guided by the density dependence of microscopic nucleon self-energies in nuclear matter, a phenomenological ansatz for the density-dependent coupling functionals is accurately determined in self-consistent mean-field calculations of binding energies of a large set of axially deformed nuclei. The relationship between the nuclear matter volume, surface, and symmetry energies and the corresponding predictions for nuclear masses is analyzed in detail. The resulting best-fit parametrization of the nuclear energy density functional is further tested in calculations of properties of spherical and deformed medium-heavy and heavy nuclei, including binding energies, charge radii, deformation parameters, neutron skin thickness, and excitation energies of giant multipole resonances.

SELF-CONSISTENT TREATMENT OF THE SELF-ENERGY IN NUCLEAR MATTER

The influence of hole–hole propagation in addition to the conventional particle–particle propagation on the energy per nucleon and the momentum distribution is investigated. The results are compared to the Brueckner–Hartree–Fock (BHF) calculations with a continuous choice and a conventional choice for the single-particle spectrum. Also, the structure of nucleon self-energy in nuclear matter is evaluated. All the off-shell self-energies are calculated self-consistently. Using the self-consistent self-energy, the hole and particle self-consistent spectral functions including the particle–particle and hole–hole ladder contributions in nuclear matter are calculated using realistic NN interactions. We found that the hole–hole ladder brought about non-negligible contributions to the nuclear matter binding energy per nucleon.

On the nucleon self-energy in nuclear matter

We consider the nucleon self-energy in nuclear matter in the absence of Pauli blocking. It is evaluated using the partial-wave analysis of NN scattering data. Our results are compared with that of a realistic calculation to estimate the effect of this blocking. It is also possible to use our results as a check on the realistic calculations.

Nuclear self-energy and realistic interactions

The structure of nucleon self-energy in nuclear matter is evaluated for various realistic models of the nucleon-nucleon (NN) interaction. Starting from the Brueckner-Hartree-Fock approximation without the usual angle-average approximation, the effects of hole-hole contributions and a self-consistent treatment within the framework of the Green function approach are investigated. Special attention is paid to the predictions for the spectral function originating from various models of the NN interaction which all yield an accurate fit for the NN phase shifts.

Application of a generalized Nambu–Jona-Lasinio model to the calculation of the properties of scalar mesons and nuclear matter

In this work we demonstrate the range of application of our generalized Nambu\char21{}Jona-Lasinio (NJL) model. We discuss the scalar-isoscalar mesons that are thought to have a $q\overline{q}$ structure and also consider some properties of nuclear matter. The spectrum of scalar-isoscalar mesons provides some insight into the sigma models that may be used to describe the dynamics of pseudoscalar and scalar mesons. Some authors have suggested that the lowest $q\overline{q} {0}^{++}$ state is the ${f}_{0}(1370).$ [The ${f}_{0}(400\char21{}1200)$ that now appears in the data tables may be generated dynamically in \ensuremath{\pi}-\ensuremath{\pi} scattering and is not a ``preexisting'' state of the spectrum.] The ${f}_{0}(980)$ and ${a}_{0}(980)$ are often designated as $K\ensuremath{-}\overline{K}$ molecules. However, recent work does not support that assignment. Since there is no low-lying scalar state, the model of choice in describing pseudoscalar meson dynamics is the nonlinear sigma model. However, there are a number of applications of the Nambu\char21{}Jona-Lasinio model in the study of nuclear matter properties that can be described in terms of the linear sigma model. In the linear sigma model there is a low-mass \ensuremath{\sigma} meson, whose effects would be generated dynamically in the nonlinear model. While it is not necessary to ever introduce a low-mass \ensuremath{\sigma} meson, we describe some calculations which may be interpreted in terms of such a meson. That only represents a formal device, and no low-mass \ensuremath{\sigma} is to be found in experiment. However, the use of the low-mass \ensuremath{\sigma} as an order parameter for partial restoration of chiral symmetry at finite density is quite consistent with the picture obtained in the application of QCD sum rules to the calculation of the nucleon self-energy in nuclear matter. We discuss such sum rules to show that the linear sigma model has some limited application if we consider only spacelike values of the \ensuremath{\sigma} meson momentum. We also use our generalized NJL model to discuss the spectrum of scalar-isoscalar states under the assumption that the ${f}_{0}(1370)$ is the $1{}^{3}{P}_{0}$ $n\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ state and the ${f}_{0}(1710)$ is the $1{}^{3}{P}_{0}$ $s\overline{s}$ state before consideration of quarkonium-glueball mixing. That analysis allows us to provide a microscopic model of the two $q\overline{q}$ states used by Close and Kirk in their recent description of quarkonium-glueball mixing in which they obtain wave functions of the ${f}_{0}(1370),$ ${f}_{0}(1500),$ and ${f}_{0}(1710)$ resonances. However, we also present an argument to show that the configuration assignments implied in the work of Close and Kirk are probably incorrect and that the standard scheme for the discussion of quarkonium-glueball mixing needs modification.

Scalar and vector decomposition of the nucleon self-energy in the relativistic Brueckner approach

We investigate the momentum dependence of the nucleon self-energy in nuclear matter. We apply the relativistic Brueckner-Hartree-Fock approach and adopt the Bonn A potential. A strong momentum dependence of the scalar and vector self-energy components can be observed when a commonly used pseudo-vector choice for the covariant representation of the T-matrix is applied. This momentum dependence is dominated by the pion exchange. We discuss the problems of this choice and its relations to on-shell ambiguities of the T-matrix representation. Starting from a complete pseudo-vector representation of the T-matrix, which reproduces correctly the pseudo-vector pion-exchange contributions at the Hartree-Fock level, we observe a much weaker momentum dependence of the self-energy. This fixes the range of the inherent uncertainty in the determination of the scalar and vector self-energy components. Comparing to other work, we find that extracting the self-energy components by a fit to the single particle potential leads to even more ambiguous results.

On the Dirac structure of the nucleon self-energy in nuclear matter

The relativistic structure of the self-energy of a nucleon in nuclear matter is investigated including the imaginary and real components which arise from the terms of first and second order in the NN interaction. A parameterized form of the Brueckner G-matrix is used for the NN interaction. The effects of the terms beyond the DBHF approximation on quasiparticle energies and the optical potential for nucleon-nucleus scattering are discussed.

The binding energy of nuclear matter with pionic degree of freedom

The renormalization of pion exchange nucleon self-energy in nuclear matter is made by dispersion relation. The exchange and correlation energies (in the ring approximation) of pion, σ and ω mesons, are derived and used to calculate the binding energy of nuclear matter at zero temperature. We find that σ, ω and π mesons cannot saturate the binding energy of nuclear matter in the relativistic RPA approximation, but the saturation can be achieved by making a density-dependent correction to the σNN, ωNN coupling constants. We also verify that the binding energy can saturate in the relativistic Hartree approximation plus the exchange and correlation energies of π meson.

Study of the Binding Energy of Relativistic Nuclear Matter in the Relativistic σ-ω-π Model**The project supported by National Natural Science Foundation of China

A relativistic σ-ω-π model is proposed to calculate the binding energy of relativistic nuclear matter. We put emphasis on the relativistic particle-hole, delta-hole excitation of pion propagator in nuclear matter. The renormalization of the nucleon self-energy in nuclear matter is made for the pseudo-vector πNN and πNΔ couplings by introducing corresponding form factor and by dispersion relation. We find that the density dependence correction to meson-NN coupling constants is very important to saturate the binding energy of nuclear matter. The density dependence correction to πNN and πNΔ coupling constants has the effect of softening the EOS of nuclear matter.

Renormalization of Nucleon Self-Energy in Nuclear Matter by Dispersion Relation Method**The project supported by National Natural Science Foundation of China

Taking -exchange Fock term of nucleon self-energy in nuclear matter as an example, we renormalized the nucleon self-energy by both dimensional regularization method and dispersion relation method in the Walecka model. We compared them numerically and found them identical, independent of the renormalization methods.

Temperature and density dependence of the nucleon mean free path in the relativistic mean field model

The nucleon mean free path is obtained based on the relativistic $\ensuremath{\sigma}$-$\ensuremath{\omega}$ model, the thermofield dynamics and the relativistic Dirac-Brueckner-Hartree-Fock results which includes the important medium effects at finite temperature in nuclear matter. The temperature and density dependence of the nucleon self-energy in nuclear matter is derived from the effective Lagrangian taking diagrams up to fourth order into account. The calculated results of the nucleon mean free path at zero temperature are in good agreement with the experimental data in normal nuclear matter.

The imaginary part of the nucleon self-energy in hot nuclear matter

A semiphenomenological approach to the nucleon self-energy in nuclear matter at finite temperatures is followed. It combines elements of Thermo Field Dynamics for the treatment of finite temperature with a model for the self-energy, which evaluates the second order diagrams taking the needed dynamics of the NN interaction from experiment. The approach proved to be accurate at zero temperature to reproduce Im(Sigma) and other properties of nucleons in matter. In the present case we apply it to determine Im(Sigma) at finite temperatures. An effective NN cross section is deduced which can be easily used in analyses of heavy ion reactions.

Relation of QCD sum rules in matter and the nuclear many-body problem.

The method of QCD sum rules provides a powerful technique for the calculation of properties of hadrons in terms of a number of parameters that specify various condensate matrix elements. One may hope that it will be possible to calculate some of the condensate matrix elements using effective Lagrangians. If we concentrate on quark condensates, the Nambu--Jona-Lasinio model may provide a useful model. In this work we study the relation between relativistic nuclear many-body theory and the analysis of the nucleon self-energy in nuclear matter made using QCD sum rules. This is done by introducing the fields of a bosonized version of the Nambu--Jona-Lasinio (NJL) model. Using the simplest version of the QCD sum-rule analysis, we replace the QCD order parameters in matter with related order parameters describing a Lorentz scalar and a vector field. In our mean-field analysis we find that the many-body theory, based upon the bosonization of the NJL model, is consistent with the simplest version of the QCD sum-rule calculation of the nucleon self-energy in matter.

Parity violation in heavy nuclei in a relativistic Hartree-Fock approximation.

The parity violating (PV) nucleon self-energy in nuclear matter is calculated in a relativistic Hartree-Fock approximation. Omega meson contributions are enhanced 63% by relativistic effects. However, the total PV self-energy is dominated by [pi] and [rho] contributions, which are relatively insensitive to relativistic effects. These results are used to estimate the 2[ital d][sub 5/2] to 2[ital f][sub 5/2] PV matrix element in [sup 207]Pb.

From QCD sum rules to relativistic nuclear physics.

Nucleon self-energies in nuclear matter are studied by analyzing the correlator of nucleon interpolating fields using QCD sum-rule methods. Large Lorentz scalar and vector self-energies arise naturally, and are comparable to the optical potentials of Dirac phenomenology. The key phenomenological inputs are the baryon density and the value of the nucleon \ensuremath{\sigma} term.

Effective interaction for relativistic mean-field theories of nuclear structure.

We construct an effective interaction, which when treated in a relativistic Hartree-Fock approximation, reproduces rather accurately the nucleon self-energy in nuclear matter and the Migdal parameters obtained via relativistic Brueckner-Hartree-Fock calculations. This effective interaction is constructed by adding Born terms, describing the exchange of pseudoparticles, to the Born terms of the Dirac-Hartree-Fock analysis. The pseudoparticles have relatively large masses and either real or imaginary coupling constants. (For example, exchange of a pseudo-sigma with an imaginary coupling constant has the effect of reducing the scalar attraction arising from sigma exchange while exchange of a pseudo-omega with an imaginary coupling constant has the effect of reducing the repulsion arising from omega exchange. The terms beyond the Born term in the case of pion exchange are well simulated by pseudo-sigma exchange with a real coupling constant.) The effective interaction constructed here may be used for calculations of the properties of finite nuclei in a relativistic Hartree-Fock approximation.