# How tightly is nuclear symmetry energy constrained by unitary Fermi gas?

## TL;DR

This paper investigates how the universal equation of state of the unitary Fermi gas constrains the density dependence of nuclear symmetry energy, highlighting the limitations imposed by uncertainties in higher order parameters.

## Contribution

It critically assesses the extent to which the unitary Fermi gas EOS constrains the nuclear symmetry energy and emphasizes the importance of precise higher order parameter measurements.

## Key findings

- $E_{UG}(
ho)$ provides a lower boundary for $E_{sym}$.
- Uncertainties in $K_{sym}$ and skewness parameters significantly affect the $E_{sym}$ and $L$ correlation.
- Constraints are limited without precise knowledge of curvature and skewness parameters.

## Abstract

We examine critically how tightly the density dependence of nuclear symmetry energy \esym is constrained by the universal equation of state (EOS) of the unitary Fermi gas $E_{\rm{UG}}(\rho)$ considering currently known uncertainties of higher order parameters describing the density dependence of the Equation of State of isospin-asymmetric nuclear matter. We found that $E_{\rm{UG}}(\rho)$ does provide a useful lower boundary for the \esym. However, it does not tightly constrain the correlation between the magnitude $E_{\rm{sym}}(\rho_0)$ and slope $L$ unless the curvature $K_{\rm{sym}}$ of the symmetry energy at saturation density $\rho_0$ is more precisely known. The large uncertainty in the skewness parameters affects the $E_{\rm{sym}}(\rho_0)$ versus $L$ correlation by the same almost as significantly as the uncertainty in $K_{\rm{sym}}$.