Understanding the symmetry energy using data from the ALADIN-2000 Collaboration taken at the GSI Large Neutron Detector

Abstract

The present study deals with the extraction of the symmetry energy from heavy-ion collisions at intermediate energies. Using the isospin quantum molecular dynamical (IQMD) model, the dependence of the sum of the charge number for fragments with $Z\ge2$ ($Z_\textrm{bound}$) on the multiplicity of neutrons ($M_n$) from the projectile spectator fragmentation of $^{124}$Sn and $^{124}$La at 600 MeV/nucleon is compared with the experimental results of the ALADIN-2000 Collaboration. The comparison suggest a soft symmetry energy. In addition, the sensitivities of the symmetry energy towards the $Z_\textrm{bound}$ dependence on proton multiplicity ($M_p$), neutron-to-proton single [$R(n/p)$] and double ratio [$R_D(n/p)$] are also examined. The $Z_\textrm{bound}$ dependence of $R(n/p)$ is found to be the most sensitive observable towards the symmetry energy. The ALADIN Collaboration should extend the results for $R(n/p)$ in the near future.