Asymmetric nuclear matter in a Hartree-Fock approach to nonlinear quantum hadrodynamics

Abstract

The Equation of State (EOS) for asymmetric nuclear matter is discussed starting from a phenomenological hadronic field theory of Serot-Walecka type including exchange terms. In a model with self interactions of the scalar sigma-meson we show that the Fock terms naturally lead to isospin effects in the nuclear EOS. These effects are quite large and dominate over the contribution due to isovector mesons. We obtain a potential symmetry term of "stiff" type, i.e. increasing with baryon density and an interesting behaviour of neutron/proton effective masses of relevance for transport properties of asymmetric dense matter.Phenomenological hadronic field theories (Quantum Hadrodynamics, QHD) are widely used in dense nuclear matter studies since relativistic effects are expected to increase with baryon density [1]. In most of the previous works on the subject, the Relativistic Mean Field (RMF ) approximation of QHD has been followed. In the RMF the meson fields are treated as classical fields and consequently a Hartree reduction of one body density matrices is used.Although the model has driven a large amount of results on relativistic effects in nuclear structure and dynamics [2-6], the lack of exchange terms has implied some non satisfying features of the theory and some efforts have been done to try to cure this problem [7][8][9][10]. In the RMF theory each meson field is introduced, with appropriated readjusted couplings, just to describe the dynamics of a corresponding degree of freedom, without mixing due to many-body effects. Neutral σ and ω mesons are in charge of saturation properties, isospin effects are carried by isovector δ [a 0 (980)] and ρ mesons and finally spin terms are coming from pseudoscalar π and η fields. In a sense the model represents a straightforward extension of the One-Boson-Exchange (OBE) description of nucleon-nucleon scattering.The aim of this letter is to introduce explicit many-body effects just evaluating exchange term contributions. We will get qualitative new features of equilibrium (EOS) and dynamical properties of asymmetric nuclear matter. In particular a new density dependence of the symmetry term is expected, at variance with the simple linear increase predicted by the ρ−exchange mechanism in the Hartree scheme.

A new approach to physics of nuclei

“…Our results for the difference of the effective masses of neutron and proton m * np = m * n − m * p appears to be twice smaller than the result of [129], but only 30% smaller than that of [130]. However, a discrepancy from the relativistic Brueckner-Hartree-Fock (RHFB) calculations [130] is smaller.…”

Asymmetric nuclear matter in the relativistic mean-field approach with vector cross interaction

“…dom used (see Table III and is similar as consequences of density dependence of the isovector couplings due to Fock contributions, which was calculated in [23]. Above 0.13 fm −3 it slowers symmetry energy rise thus implicating an impact on higher density behavior of matter (high energy beam collisions, supernovae explosions, neutron stars properties), and it is also in agreement with recent Hartree calculations [24], where similar high-density influence of cross-interactions was concluded.…”

Neutron-proton mass difference in isospin-asymmetric nuclear matter

“…The result of our work is also consistent with the findings of Refs. [23,24,25,26,27,28,29] that utilize a relativistic approach and with the nonrelativistic calculation [21] based on Skyrme-like effective interactions.…”

“…Furthermore, it is also important for the description of the properties of mirror nuclei [6], the stability of drip-line nuclei [7] and the transport in neutron-rich matter induced by heavy-ion collisions [8]. Although there exist various publications dealing directly with the density dependence of the neutron-proton mass difference [9,10,11,12,13,14,15,16,17] and its implications for asymmetric nuclear matter and finite nuclei properties [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32], this quantity is still not well understood. Quantitatively and even qualitatively the predictions about the behavior of the neutron-proton mass difference in nuclear matter change from model to model.…”