$^3$H/$^3$He ratio as a probe of the nuclear symmetry energy at sub-saturation densities

TL;DR

This study uses an updated UrQMD model to analyze the $^3$H/$^3$He ratio in heavy-ion collisions, demonstrating its sensitivity to the nuclear symmetry energy at sub-saturation densities and aligning with recent experimental constraints.

Contribution

It introduces an improved UrQMD model with Skyrme functional to connect $^3$H/$^3$He ratios with the density dependence of nuclear symmetry energy.

Findings

$^3$H/$^3$He ratio is sensitive to symmetry energy at sub-saturation densities.

Model results agree with experimental FOPI data for various Skyrme interactions.

Moderately soft to linear symmetry energies match the observed ratios.

Abstract

Within the newly updated version of the Ultra-relativistic quantum molecular dynamics (UrQMD) model in which the Skyrme potential energy-density functional is introduced, the yield ratio between $^3$H and $^3$He clusters emitted from central $^{40}$Ca+$^{40}$Ca, $^{96}$Zr+$^{96}$Zr, $^{96}$Ru+$^{96}$Ru, and $^{197}$Au+$^{197}$Au collisions in the beam energy range from 0.12 to 1 GeV$/$nucleon is studied. The recent FOPI data for the $^3$H$/$$^3$He ratio are compared with UrQMD calculations using 13 Skyrme interactions (all exhibiting similar values of iso-scalar incompressibility but very different density dependences of the symmetry energy). It is found that the $^3$H$/$$^3$He ratio is sensitive to the nuclear symmetry energy at sub-saturation densities. Model calculations with moderately soft to linear symmetry energies are in agreement with the experimental FOPI data. This result is in line with both, the recent constraints on the low-density symmetry energy available in the literature and our previous results for the high-density symmetry energy obtained with the elliptic flow of free nucleons and hydrogen isotopes as a sensitive probe.