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

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 H-3 and He-3 clusters emitted from central Ca-40 + Ca-40, Zr-96 + Zr-96, Ru-96 + Ru-96, and Au-197 + Au-197 collisions in the beam energy range from 0.12 to 1 GeV/nucleon is studied. The recent FOPI data for the H-3/He-3 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 H-3/He-3 ratio is sensitive to the nuclear symmetry energy at sub-saturation densities. Model calculations with moderately soft to linear symmetry energies are in qualitatively agreement with the H-3/He-3 ratio data of the FOPI Collaboration. 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.