Abstract
The relativistic density functional with minimal density dependent nucleon–meson couplings for nuclei and nuclear matter is extended to include tensor couplings of the nucleons to the vector mesons. The dependence of the minimal couplings on either vector or scalar densities is explored. New parametrisations are obtained by a fit to nuclear observables with uncertainties that are determined self-consistently. The corresponding nuclear matter parameters at saturation are determined including their uncertainties. An improvement in the description of nuclear observables, in particular for binding energies and diffraction radii, is found when tensor couplings are considered, accompanied by an increase of the Dirac effective mass. The equations of state for symmetric nuclear matter and pure neutron matter are studied for all models. The density dependence of the nuclear symmetry energy, the Dirac effective masses and scalar densities is explored. Problems at high densities for parametrisations using a scalar density dependence of the couplings are identified due to the rearrangement contributions in the scalar self-energies that lead to vanishing Dirac effective masses.
Highlights
Is determined by the corresponding coupling constants
The coupling strengths between mesons and nucleons in the energy density functionals (EDFs) are usually obtained by fitting the model predictions of nuclear observables to experimental data
Tensor coupling terms were derived from a systematic expansion in an effective approach using chiral symmetry in [25] and two new parametrisations, G1 and G2, were obtained by a fit to nuclear observables with much stronger ρ tensor couplings than ω tensor couplings
Summary
Relativistic EDFs are derived originally in the meanfield or Hartree approximation starting from a covariant Lagrangian density with nucleon and meson fields as degrees of freedom. In calculations of nuclear matter, tensor couplings do not contribute in the conventional mean-field approximation of spatially uniform systems since their effect depends on spatial derivatives of densities. In this work a new set of parametrisations for relativistic EDFs is introduced with a vector or a scalar density dependence of the couplings and the effects of tensor couplings are studied. The model parameters are usually determined by minimising an objective function that depends on the differences between calculated and measured nuclear data weighted by (inverse) uncertainties. The latter are mostly set heuristically to certain fixed values. The derivation of the rearrangement contributions to the scalar and vector potentials of the nucleons is presented in Appendix A and the conversion of model parameters is discussed in Appendix B
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