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Based on an isospin and momentum-dependent transport model, we studied theeffect of momentum-dependent symmetry potential on the free neutron to protonratio of preequilibrium nucleon emission. It is found that for$^{132}Sn+^{124}Sn$ reaction at 400 MeV/nucleon incident beam energy, free n/pratio of preequilibrium nucleon emission mainly probe the momentum-dependenceof symmetry potential at nucleon momentum around 400 $\sim$ 600 MeV/c. Whereasfor 200 MeV/nucleon incident beam energy, this observable mainly probe themomentum-dependence of symmetry potential at nucleon momentum around 200 $\sim$400 MeV/c. To probe the symmetry energy/potential using free n/p ratio, not allthe details of the momentum-dependence of the symmetry potential are important,the values of symmetry potential at only certain momentum range are crucial foran observable. It is important to input reasonable density- andmomentum-dependence of the symmetry potential according to the magnitude ofincident beam energy of heavy-ion collisions. The present experimental data onthe symmetry potential are not enough for probing the density-dependentsymmetry energy. More experimental data (such as nucleon and nuclei'sscattering experiments at different nucleonic momenta and densities) on thesymmetry potential are therefore needed to pin down the density-dependentsymmetry energy.

Probing the momentum-dependence of the symmetry potential by the free n/p ratio of preequilibrium emission