Primary Isotope Yields and Characteristic Properties of the Fragmenting Source in Heavy-ion Reactions near the Fermi Energies

TL;DR

This study uses isotope yield ratios from AMD simulations to determine the density and temperature of a fragmenting source in heavy-ion collisions near the Fermi energy, revealing a formation density of about 0.67 times nuclear saturation density.

Contribution

It introduces an improved method based on the Modified Fisher Model to extract symmetry energy ratios from isotope yields in AMD simulations, enabling density and temperature determination of the fragmenting source.

Findings

Fragment formation density is approximately 0.67 times nuclear saturation density.

Temperature values derived from isotope yields are consistent with fluctuation thermometer estimates.

The method correlates symmetry energy at formation density with isotope yield ratios.

Abstract

For central collisions of $^{40}$Ca $+ ^{40}$Ca at 35 MeV/nucleon, the density and temperature of a fragmenting source have been evaluated in a self-consistent manner using the ratio of the symmetry energy coefficient relative to the temperature, $a_{sym}/T$, extracted from the yields of primary isotopes produced in antisymmetrized molecular dynamics (AMD) simulations. The $a_{sym}/T$ values are extracted from all isotope yields using an improved method based on the Modified Fisher Model (MFM). The values of $a_{sym}/T$ obtained, using different interactions with different density dependencies of the symmetry energy term, are correlated with the values of the symmetry energies at the density of fragment formation. Using this correlation, the fragment formation density is found to be $\rho/\rho_0 = 0.67 \pm 0.02$. Using the input symmetry energy value for each interaction temperature values are extracted as a function of isotope mass $A$. The extracted temperature values are compared with those evaluated from the fluctuation thermometer with a radial flow correction.