Properties of collective flow and pion production in intermediate-energy heavy-ion collisions with a relativistic quantum molecular dynamics model

he relativistic mean-field approach was implemented in the Lanzhou quantum molecular dynamics transport model (LQMD.RMF). Using the LQMD.RMF, the properties of collective flow and pion production were investigated systematically for nuclear reactions with various isospin asymmetries. The structure of the directed and elliptic flows of the LQMD.RMF is able to describe the experimental data of STAR Collaboration. The directed flow difference between free neutrons and protons was associated with the stiffness of the symmetry energy, that is, a softer symmetry energy led to a larger flow difference. For various collision energies, the  ratio between the $ pi^-$  and $ pi^+$ yields increased with a decrease  in the slope parameter of the symmetry energy. When the collision energy was 270 MeV/nucleon,  the single ratio of the pion transverse momentum spectra also increased with decreasing  slope parameter of the symmetry energy in both nearly symmetric and neutron-rich systems. However, it remained difficult to determine the dependence of the double ratio on the stiffness of the symmetry energy.