Effects of the momentum-dependence of the symmetry potential in nuclear reactions induced by neutron-rich nuclei at RIA energies are studied using an isospin-and momentum-dependent transport model. It is found that symmetry potentials with and without the momentum-dependence but corresponding to the same density-dependent symmetry energy Esym(ρ) lead to significantly different predictions on several Esym(ρ)-sensitive experimental observables. The momentum-dependence of the symmetry potential is thus critically important for investigating accurately the equation of state (EOS) and novel properties of dense neutron-rich matter at RIA. The rapid advance in technologies to accelerate radioactive beams has opened up several new frontiers in nuclear sciences [1,2]. Particularly, the high energy radioactive beams to be available at the planned Rare Isotope Accelerator (RIA) and the new accelerator facility at GSI provide a great opportunity to explore the EOS and novel properties of dense neutronrich matter [3,4,5,6]. The energy per particle E(ρ, δ) in asymmetric nuclear matter of density ρ and relative, where E sym (ρ) is the density-dependent nuclear symmetry energy. The latter is among the most important and yet very poorly known properties of dense neutron-rich matter [7,8]. For instance, it is important for Type II supernova explosions, for neutron-star mergers, and for the stability of neutron stars. It also determines the proton fraction and electron chemical potential in neutron stars at β equilibrium. These quantities consequently determine the cooling rate and neutrino emission flux of protoneutron stars and the possibility of kaon condensation in dense stellar matter [7,8]. In nuclear reactions induced by neutron-rich nuclei, the E sym (ρ) reveals itself through dynamical effects of the corresponding symmetry potentials acting differently on neutrons and protons. Based on isospin-dependent transport model calculations, several experimental observables have been identified as promising probes of the E sym (ρ), such as, the neutron/proton ratio [9,10,11], the neutronproton differential flow [12,13], the neutron-proton correlation function [14] and the isobaric yield ratios of light clusters [15]. However, in all existing transport models the momentum-dependence of the symmetry (isovector) potential has never been taken into account. Effects of the momentum-dependence of the symmetry potential in nuclear reactions are thus completely unknown, although effects of the momentum-dependence of the isoscalar potential are well-known [16,17,18,19]. This is mainly because only very recently was the momentum-dependence of the symmetry potential given in a form practically usable in transport model calculations [20]. In this work, we study for the very first time effects of the momentumdependence of the symmetry potential within an isospinand momentum-dependent transport model for nuclear reactions induced by neutron-rich nuclei at RIA energies. It is found that symmetry potentials with and without the momentum-dependenc...
