Isobaric Yield Ratios and The Symmetry Energy In Fermi Energy Heavy Ion Reactions

TL;DR

This study analyzes isobaric yield ratios in heavy ion reactions to determine the symmetry energy coefficient's ratio to temperature, revealing its variation with fragment mass and comparing experimental data with AMD model calculations.

Contribution

It introduces a method to extract the symmetry energy coefficient to temperature ratio from experimental yields and compares it with theoretical models, highlighting differences between primary and final fragments.

Findings

The ratio $a_a/T$ increases from 5 to 16 as A increases from 9 to 37.

Calculated ratios agree well with experimental data, unlike primary fragment ratios.

Final fragment observables may underestimate the symmetry energy coefficient.

Abstract

The relative isobaric yields of fragments produced in a series of heavy ion induced multifragmentation reactions have been analyzed in the framework of a Modified Fisher Model, primarily to determine the ratio of the symmetry energy coefficient to the temperature, $a_a/T$, as a function of fragment mass A. The extracted values increase from 5 to ~16 as A increases from 9 to 37. These values have been compared to the results of calculations using the Antisymmetrized Molecular Dynamics (AMD) model together with the statistical decay code Gemini. The calculated ratios are in good agreement with those extracted from the experiment. In contrast, the ratios determined from fitting the primary fragment distributions from the AMD model calculation are ~ 4 and show little variation with A. This observation indicates that the value of the symmetry energy coefficient derived from final fragment observables may be significantly different than the actual value at the time of fragment formation. The experimentally observed pairing effect is also studied within the same simulations. The Coulomb coefficient is also discussed.