Relativistic Mean Field Models and Nucleon-Nucleon Interactions

Abstract

We investigate the connection between relativistic mean field models and the bare nucleon-nucleon interaction by using a realistic interaction in the nuclear medium. Starting from a nonrelativistic bare potential and by employing a G-matrix formalism we derive an effective interaction in the nuclear medium that depends on its density. We show that its medium-and long-range components can be described to a good extent by an effective density-dependent one-boson-exchange (OBE) potential. For a good fit of the OBE to the G-matrix potential the following degrees of freedom have been found to be necessary: an isoscalar scalar S (σ-meson), an isoscalar vector V (ω-meson), an isovector scalar T S (δmeson), an isovector vector T V (ρ-meson), and an isovector pseudoscalar P S (π-meson) Yukawa field. This allows us to extract the mass and the coupling strength of the various mesons at different densities of nuclear matter. In such a way, we investigate the densitydependence of these parameters and the influence of many-body and multi-scattering effects. We find that with increasing density of the nuclear medium m σ is constant to a good approximation, m δ decreases quite strongly, while m ω and m ρ decrease rather weakly. The coupling strengths of the fields also show a rather weak decreasing tendency. Furthermore it turns out that the extracted values of the meson fields masses and couplings are rather consistent with the parameters of effective mesons of recent RMF phenomenologies. Finally, we find that the tensor force of the bare nucleon-nucleon interaction is essential to explain the dominance of the σ-field for the attraction. This makes RMF models more consistent with ab initio calculations. † deceased

Relativistic mean-field interaction with density-dependent meson-nucleon vertices based on microscopical calculations

“…However, to reproduce nucleon-nucleon scattering measurements in vacuum, one needs to incorporate a scalar-isovector meson into the parametrization of the two-body nuclear interaction [72]. Microscopic derivations of the nuclear fields using relativistic Brueckner theory [42,52,53,65,[73][74][75] or nonrelativistic Brueckner theory [43,44] show clearly that the scalar field in the nuclear interior has an isovector part. These reasons motivate one to incorporate the δ meson also in models of covariant density functional theory and to study its influence on properties such as the symmetry energy, the effective mass splitting between protons and neutrons in asymmetric matter, the isospin dependence of the spin-orbit potential, and the spin-orbit splittings far from stability.…”

“…On the other hand, it is very complicated to deduce Dirac masses from a nonrelativistic calculation which does not distinguish between Lorentz scalars and vectors. This is in principle possible [43,44], but it is difficult and connected with additional uncertainties. With this caveat in mind, we decided to use a reliable relativistic Brueckner calculation [65] Keeping this in mind, we determine 10 of the 14 parameters in the Lagrangian of DD-MEδ by these pseudo-data obtained from ab initio calculations of nuclear matter.…”

“…These models have shown considerable improvements with respect to previous relativistic mean-field (RMF) models in the description of asymmetric nuclear matter, neutron matter, and nuclei far from the stability valley. On the other hand, attempts have been made to derive this density dependence in a microscopic way from Brueckner calculations in nuclear matter at various densities [41][42][43][44]. An example is density-dependent relativistic hadron field theory [42] in which the specific density dependence of the meson-nucleon vertices is mapped from Dirac-Brueckner calculations where the in-medium interaction is obtained from nucleon-nucleon potentials consistent with scattering experiments.…”

Simplified method to include the tensor contribution in α-cluster model

“…Because of this difference, the relative wave function between nucleons does not have a large amplitude, where the contribution of the tensor interaction becomes maximum. However, the effective interaction derived from the realistic one by solving the G matrix [26,27] shows the optimal distance between nucleons at around 1 fm, when multiplied by r 2 . Therefore, to compare the tensor contribution with the calculations using the realistic nucleon-nucleon interactions, it is also necessary to modify the central part of the interaction completely.…”

“…To quantitatively estimate this effect, we apply SMSO to 8 Be: One α cluster with the (0s) 4 configuration is centered at the origin and the other one is centered at R on the x axis. Next, the Gaussian centers of nucleons in the second α cluster are changed from R e x to R ( e x + i e y ) for the spin-up (27) and to R ( e x − i e y ) for the spin-down nucleons as…”