Effects of medium-induced $\rho-\omega$ meson mixing on the equation of state in isospin-asymmetric nuclear matter

TL;DR

This paper investigates how medium-induced $ ho- ext{omega}$ meson mixing influences the symmetry energy in isospin-asymmetric nuclear matter, revealing significant softening at various densities and introducing a novel evaluation method within relativistic models.

Contribution

It introduces a new approach to evaluate $ ho- ext{omega}$ mixing angles considering rearrangement effects and extends the analysis beyond lowest-order calculations using RPA.

Findings

Symmetry energy is significantly softened at high densities.

RPA calculations show softening at both supra- and subsaturation densities.

Nonlinear $\sigma$ meson self-interaction can partly suppress the softening.

Abstract

We reexamine effects of the $\rho-\omega$ meson mixing mediated by nucleon polarizations on the symmetry energy in isospin-asymmetric nuclear matter. Taking into account the rearrangement term neglected in previous studies by others, we evaluate the $\rho-\omega$ mixing angle in a novel way within the Relativistic Mean-Field Models with and without chiral limits. It is found that the symmetry energy is significantly softened at high densities contrary to the finding in earlier studies. As the first step of going beyond the lowest-order calculations, we also solve the RPA equation for the $\rho-\omega$ mixing. In this case, it is found that the symmetry energy is not only significantly softened by the $\rho-\omega$ mixing at supra-saturation densities, similar to the lowest-order $\rho-\omega$ mixing, but interestingly also softened at subsaturation densities. In addition, the softening of the symmetry energy at subsaturation densities can be partly suppressed by the nonlinear self-interaction of the $\sigma$ meson.