Density dependent hadron field theory

Abstract

A fully covariant approach to a density dependent hadron field theory is presented. The relation between in-medium NN interactions and field-theoretical meson-nucleon vertices is discussed. The medium dependence of nuclear interactions is described by a functional dependence of the meson-nucleon vertices on the baryon field operators. As a consequence, the Euler-Lagrange equations lead to baryon rearrangement self-energies which are not obtained when only a parametric dependence of the vertices on the density is assumed. It is shown that the approach is energy-momentum conserving and thermodynamically consistent. Solutions of the field equations are studied in the mean-field approximation. Descriptions of the medium dependence in terms of the baryon scalar and vector density are investigated. Applications to infinite nuclear matter and finite nuclei are discussed. Density dependent coupling constants obtained from Dirac-Brueckner calculations with the Bonn NN potentials are used, Results from Hartree calculations for energy spectra, binding energies, and charge density distributions of ' 0, ' Ca, and Pb are presented. Comparisons to data strongly support the importance of rearrangement in a relativistic density dependent field theory. Most striking is the simultaneous improvement of charge radii, charge densities, and binding energies. The results indicate the appearance of a new "Coester line" in the nuclear matter equation of state.

Relativistic nuclear energy density functional constrained by low-energy QCD

“…In addition to the usual contributions from the time components of the vector self-energies and the scalar potentials, we must also include the "rearrangement" terms, Σ R , arising from the variation of the vertex functionals with respect to the nucleon fields in the density operatorρ. For a Lagrangian with density dependent couplings, the inclusion of the rearrangement self-energies is essential in order to guarantee energy-momentum conservation and thermodynamical consistency [30,31,32]. It is also required by the Hugenholtz-Van Hove theorem [33].…”

Relativistic nuclear model with point-couplings constrained by QCD and chiral symmetry

“…This Lagrangian (2)-(6) is understood to be formally used in the mean-field approximation [19], with fluctuations encoded in density-dependent couplings G i (ρ) and D i (ρ), to be specified in detail later. In addition to the free nucleon Lagrangian L free and the interaction terms contained in L 4f , when applied to finite nuclei the model must include the coupling L em of the protons to the electromagnetic field A µ , and derivative terms contained in L der 1 .…”

“…For a model with density dependent couplings, the inclusion of the rearrangement self-energies is essential for energy-momentum conservation and thermodynamical consistency (i.e. for the pressure equation derived from the thermodynamic definition and from the energy-momentum tensor) [19,24].…”

“…In the density dependent relativistic hadron field (DDRH) models the medium dependence of the meson-nucleon vertices is expressed as a functional of the baryon field operators. The meson-nucleon vertex functions are determined either by mapping the nuclear matter Dirac-Brueckner nucleon self-energies in the local density approximation [19,22,23], or the parameters of an assumed phenomenological density dependence of the meson-nucleon couplings are adjusted to reproduce properties of symmetric and asymmetric nuclear matter and finite nuclei [24,25]. In practical applications of the DDRH models the meson-nucleon couplings are assumed to be functions of the baryon density ψ † ψ.…”

On the density-dependent hadron field theory at finite temperature and its thermodynamical consistency

“…This term guarantees the thermodynamical consistency and the energy-momentum conservation, i.e., ∂ µ T µν = 0 of the density dependent effective models, where the energymomentum tensor is given by [1]:…”