# Limiting symmetry energy elements from empirical evidence

## TL;DR

This paper investigates the symmetry energy elements of infinite nuclear matter using a finite-range effective interaction, aligning results with empirical data and exploring higher-order coefficients at various densities.

## Contribution

It provides a comprehensive analysis of symmetry energy parameters using a specific effective interaction model and compares results with a Skyrme-inspired functional, highlighting the significance of higher-order terms.

## Key findings

- Symmetry energy coefficient $a_2$ and slope $L_0$ agree with other methods.
- Higher order symmetry coefficients $a_4, a_6$ are negligible at normal densities.
- Results are consistent across different theoretical frameworks.

## Abstract

In the framework of an equation of state (EoS) constructed from a momentum and density-dependent finite-range two-body effective interaction, the quantitative magnitudes of the different symmetry elements of infinite nuclear matter are explored. The parameters of this interaction are determined from well-accepted characteristic constants associated with homogeneous nuclear matter. The symmetry energy coefficient $a_2$, its density slope $L_0$, the symmetry incompressibility $K_\delta $ as well as the density dependent incompressibility $K(\rho )$ evaluated with this EoS are seen to be in good harmony with those obtained from other diverse perspectives. The higher order symmetry energy coefficients $a_4,~a_6$ etc are seen to be not very significant in the domain of densities relevant to finite nuclei, but gradually build up at supra-normal densities. The analysis carried with a Skyrme-inspired energy density functional obtained with the same input values for the empirical bulk data associated with nuclear matter yields nearly the same results.