Symmetry Energy of Nucleonic Matter With Tensor Correlations

TL;DR

This paper presents a new analytical model for the kinetic part of the nuclear symmetry energy considering tensor correlations, significantly differing from the free Fermi gas model, and constrains the total symmetry energy at high densities.

Contribution

The study introduces an approximate analytical expression for the kinetic symmetry energy incorporating tensor correlations, challenging the traditional free Fermi gas approximation.

Findings

E_sym^kin(rho_0) = -10 MeV, contrasting with +12.5 MeV from free Fermi gas model

Model aligns with recent experimental data and microscopic calculations

Provides constraints on potential symmetry energy components at supranuclear densities

Abstract

The nuclear symmetry energy (E_sym(\roh)) is a vital ingredient of our understanding of many processes, from heavy-ion collisions to neutron stars structure. While the total nuclear symmetry energy at nuclear saturation density (\rho_0) is relatively well determined, its value at supranuclear densities is not. The latter can be better constrained by separately examining its kinetic and potential terms and their density dependencies. The kinetic term of the symmetry energy, E_sym^kin(\rho_0), equals the difference in the per-nucleon kinetic energy between pure neutron matter (PNM) and symmetric nuclear matter (SNM), often calculated using a simple Fermi gas model. However, experiments show that tensor force induced short-range correlations (SRC) between proton-neutron pairs shift nucleons to high-momentum in SNM, but have almost no effect in PNM. We present an approximate analytical expression for E_sym^kin(\rho) of correlated nucleonic matter. In our model, E_sym^kin(\rho_0) = -10 MeV, which differs significantly from +12.5 MeV for the widely-used free Fermi gas model. This result is consistent with our analysis of recent data on the free proton-to-neutron ratios measured in intermediate energy nucleus-nucleus collisions as well as with microscopic many-body calculations, and previous phenomenological extractions. We then use our calculated E_sym^kin(\rho) in combination with the known total symmetry energy and its density dependence at saturation density to constrain the value and density dependence of the potential part and to extrapolate the total symmetry energy to supranuclear densities.