Symmetry energy from fragment observables in the canonical thermodynamic model

TL;DR

This paper evaluates various formulas used to estimate the symmetry energy of excited nuclei from fragment observables, finding that while they do not precisely reconstruct the symmetry energy, they are well correlated with it.

Contribution

It systematically assesses the accuracy of existing formulas for symmetry energy extraction within the canonical thermodynamic model.

Findings

Formulas do not precisely reconstruct the symmetry energy.

Isotopic widths and isoscaling are well correlated with symmetry energy.

Secondary decay effects are not considered in the idealized analysis.

Abstract

Different formulas relying measurable fragment isotopic observables to the symmetry energy of excited nuclei have been proposed and applied to the analysis of heavy ion collision data in the recent literature. In this paper we examine the quality of the different expressions in the framework of the McGill Canonical Thermodynamic Model. We show that even in the idealized situation of canonical equilibrium and in the absence of secondary decay, these formulas do not give a precise reconstruction of the symmetry energy of the fragmenting source. However, both isotopic widths and isoscaling appear very well correlated to the physical symmetry energy.