The nucleon spin polarization perpendicular to the reaction plane ($P_y$) and along the beam direction ($P_z$) in $\mathrm{Au}+\mathrm{Au}$ collisions at the beam energy of $100\mathrm{A}\mathrm{MeV}$ with different nuclear spin-orbit interactions has been studied based on a spin- and isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model. While the spin polarization is weaker with a weaker nuclear spin-orbit coupling as intuitively expected, a density-dependent nuclear spin-orbit coupling enhances the $P_y$ at large rapidities and leads to a less negative or large $P_y$ at high transverse momenta. The difference in the $P_y$ of free neutrons and protons at midrapidities and at small transverse momenta is sensitive to the isospin dependence of the nuclear spin-orbit interaction. While the $P_z$ is also affected by the properties of nuclear spin-orbit interaction in some sense, the behavior of the $P_y$ serves as a good probe of the strength, density dependence, and isospin dependence of nuclear spin-orbit interaction.

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• Low & intermediate energy heavy-ion reactions
• Nuclear forces
• Polarization phenomena