Influence of the symmetry energy on the cone-azimuthal emission

Abstract

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, effects of the symmetry energy on the evolutions of the free $n/p$ ratio and the charged pion ratio in the semicentral collision of ${}^{197}$Au+${}^{197}$Au at an incident beam energy of 400 MeV/nucleon are studied. At the beginning of the reaction (before 11 fm/$c$) they are both affected by the low-density behavior of the symmetry energy but soon after are affected by the high-density behavior of the symmetry energy after nuclei are compressed (after 11 fm/$c$), and the effects of the symmetry energy are generally smaller compared with the central collision case. Interestingly, their dependences on the symmetry energy are shown to rise with an increase of the cone-azimuthal angle of the emitted particles. In the direction perpendicular to the reaction plane, the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio or the free $n/p$ ratio, especially at high kinetic energies, exhibits significant sensitivity to the symmetry energy.