Thermalization of Nuclear Matter in Heavy-Ion Collisions at Fermi-Energies

We analyze the time evolution of the kinetic properties of nuclear matter produced in heavy-ion collisions at Fermi energies. The collision system is simulated using Constrained Molecular Dynamics (CoMD) transport calculations whose output is the isospin, position, and momentum of the nucleons. Focusing on central 35$\,$A$\cdot$MeV $^{40}$Ca+$^{40}$Ca collisions we utilize this information to extract localized momentum distributions in volume elements of 8$\,$fm$^3$ and time steps of 5$\,$fm/$c$. We then parameterize the single-particle momentum distributions with thermally motivated fit functions in the local rest frame of each cell. While the transverse-momentum distributions are well reproduced by thermal ones, the longitudinal ones carry a marked imprint of the initial nuclear motion which we capture by introducing a centroid motion into our fit functions. In particular, we find that Fermi distributions yield significantly better fits than Boltzmann ones, a consequence of the Pauli blocking implemented in CoMD. From the fits we extract the time dependence of the thermodynamic and collective properties of the excited nuclear medium. We find that the transverse temperature gradually rises to about 6$\,$MeV, which is accompanied by a dissipation of the initial centroid motion of the incoming nuclei which vanishes at about 100$\,$fm/$c$ after initial impact. We are therefore able to track the transition of beam energy into random kinetic energy for nucleons, suggesting a three-dimensional equilibration of energy in the late stages of the collision.