Effects of momentum-dependent symmetry potential on heavy-ion collisions induced by neutron-rich nuclei

Using an isospin- and momentum-dependent transport model we study effects of the momentum-dependent symmetry potential on heavy-ion collisions induced by neutron-rich nuclei. It is found that symmetry potentials with and without the momentum-dependence but corresponding to the same density-dependent symmetry energy $E_{sym}(\rho)$ lead to significantly different predictions on several $E_{sym}(\rho)$-sensitive experimental observables especially for energetic nucleons. The momentum- and density-dependence of the symmetry potential have to be determined simultaneously in order to extract the $E_{sym}(\rho)$ accurately. The isospin asymmetry of midrapidity nucleons at high transverse momenta is particularly sensitive to the momentum-dependence of the symmetry potential. It is thus very useful for investigating accurately the equation of state of dense neutron-rich matter.