  We have incorporated the spin-dependent nucleon-nucleon cross sections into a
Boltzmann-Uehling-Uhlenbeck transport model for the first time, using the
spin-singlet and spin-triplet nucleon-nucleon elastic scattering cross sections
extracted from the phase-shift analyses of nucleon-nucleon scatterings in free
space. We found that the spin splitting of the collective flows is not affected
by the spin-dependent cross sections, justifying it as a good probe of the
in-medium nuclear spin-orbit interaction. With the in-medium nuclear spin-orbit
mean-field potential that leads to local spin polarization, we found that the
spin-averaged observables, such as elliptic flows of free nucleons and light
clusters, becomes smaller with the spin-dependent differential nucleon-nucleon
scattering cross sections.
