Spin–orbit effect in low-energy heavy-ion collisions

The spin–orbit (SO) coupling is fundamental to the description of the nuclear shell structure. However, its dynamical role in heavy-ion collisions remains a crucial, but not fully understood, aspect of nuclear physics. While static properties are well-constrained, the influence of the SO force on energy dissipation and collective motion during collisions requires deeper investigation. We address this using microscopic three-dimensional Time-Dependent Hartree–Fock (TDHF) calculations with the SKY3D code, employing the SLy4, Sv-bas, and SkM* interactions. This study performs a systematic survey of central collisions across a broad mass range (Z = 6–36), covering isotopes with neutron numbers from Z - 4 to Z + 4, at center-of-mass energies defined slightly above the Coulomb barrier. We focus on the collective density oscillations of the forming dinuclear system. By analyzing the time evolution of the relative distance R, we extract the oscillation period T and the corresponding restoring force coefficient k via the relation k = 4π²μ / T². Our analysis reveals that k is strongly correlated with the total nucleon number A. Interestingly, the impact of the SO coupling is clearly mass-dependent: for lighter systems, the SO interaction enhances the restoring force, whereas for heavier systems, the restoring force is stronger when the SO interaction is excluded. Notably, results with the SLy4, Sv-bas, and SkM* interactions exhibit a distinct peak in k around A ≈ 60 in the absence of SO coupling, reflecting significant structural variations. These findings clarify the signatures of spin-dependent dynamics and offer critical constraints for improving the time-odd components of nuclear energy density functionals.