The spin up-down splitting of collective flows in intermediate-energyheavy-ion collisions as a result of the nuclear spin-orbit interaction isinvestigated within a spin- and isospin-dependent Boltzmann-Uehing-Uhlenbecktransport model SIBUU12. Using a Skyrme-type spin-orbit coupling quadratic inmomentum, we found that the spin splittings of the directed flow and ellipticflow are largest in peripheral Au+Au collisions at beam energies of about100-200 MeV/nucleon, and the effect is considerable even in smaller systemsespecially for nucleons with high transverse momenta. The collective flows oflight clusters of different spin states are also investigated using an improveddynamical coalescence model with spin. Our study can be important inunderstanding the properties of in-medium nuclear spin-orbit interactions oncethe spin-dependent observables proposed in this work can be measured.
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