The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications.

Self-consistent mean-field models for nuclear structure

Relativistic mean field theory in finite nuclei

Nowadays it has become customary in nuclear physics to denote by “tradition” the approach that considers nucleons and mesons as the relevant degrees of freedom. It is the purpose of this chapter to review this “traditional” approach in the area of nuclear forces and their applications to nuclear structure.

The Meson Theory of Nuclear Forces and Nuclear Structure

https://www.physi.uni-heidelberg.de/~fschney/2008SS-Preseminar/buballarev.pdf

NJL-model analysis of dense quark matter

Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions

The formalism for the Dirac-Brueckner approach to the nuclear many-body problem is described including its basis in relativistic two-nucleon scattering. A family of relativistic meson-exchange potentials is constructed which (apart from the usual coupling terms for heavy mesons) apply the pseudovector (gradient) coupling for the interaction of pseudoscalar mesons (\ensuremath{\pi},\ensuremath{\eta}) with nucleons. These potentials describe low-energy two-nucleon scattering and the deuteron data accurately. Using these potentials, the properties of nuclear matter are calculated in the Dirac-Brueckner-Hartree-Fock approximation, in which the empirical nuclear matter saturation is explained quantitatively. The effective two-body interaction in the nuclear matter medium (G matrix) is calculated directly in the nuclear matter rest frame. Thus, cumbersome transformations between the two-nucleon center-of-mass frame and the nuclear matter rest frame are avoided. Size and nature of relativistic effects included in the present approach are examined in detail. The formalism, the potentials, and the results of this paper may also serve as a basis and a realistic starting point for systematic relativistic nuclear structure studies as well as for the investigation of further relativistic many-body corrections and of contributions of higher order.

Relativistic nuclear structure. I. Nuclear matter.

Within the framework of the Dirac-Brueckner (DB) approach, the properties of dense nuclear and neutron matter are investigated using realistic nucleon-nucleon (NN) interactions which are derived from relativistic meson-field theory and describe the two-nucleon system quantitatively. Single-particle potentials, equations of state, nucleon effective masses, Landau parameters, and speeds of sound are calculated and analyzed as functions of density, for both nuclear and neutron matter. In the DB approach, the equation of state comes out stiffer than in the most sophisticated nonrelativistic calculation, but softer than in the Walecka model. Possible extensions of the present approach to nucleon-nucleus scattering and nucleus-nucleus collisions are also discussed.

Properties of dense nuclear and neutron matter with relativistic nucleon-nucleon interactions

Relativistic nuclear structure. II. Finite nuclei.

We propose the quark mean field model for nucleons in nuclei, where the meson mean fields created by other nucleons act on quarks in a nucleon and change the nucleon properties in nuclei. We take the constituent quark model for the nucleon, which naturally allows the direct coupling of pions and in turn other mesons as $\ensuremath{\sigma}$ and $\ensuremath{\omega}$ mesons. We find very good nuclear matter properties with the use of the nonlinear self-energy terms in the meson Lagrangian. We expect the spin-orbit splitting in finite nuclei to be large due to the large reduction of the nucleon mass, which is in agreement with experiment. The nucleon size increases by about 7% at the normal matter density.

R. Brockmann

Papers

Relativistic nuclear structure. I. Nuclear matter.

Properties of dense nuclear and neutron matter with relativistic nucleon-nucleon interactions

Relativistic nuclear structure. II. Finite nuclei.

Quark mean field model for nucleons in nuclei

Dirac-Brueckner-Hartree-Fock approach in finite nuclei☆