Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions

Background: The distribution of protons and neutrons in the matter created in heavy-ion collisions is one of the main points of interest for the collision physics, especially at supranormal densities. These distributions are the basis for predictions of the density dependence of the symmetry energy and the density range that can be achieved in a given colliding system. We report results of the first systematic simulation of proton and neutron density distributions in central heavy-ion collisions within the beam energy range of E-beam <= 800 MeV/nucl. The symmetric Ca-40 + Ca-40, Ca-48 + Ca-48, Sn-100 + Sn-100, and Sn-120 + Sn-120 and asymmetric Ca-40 + Ca-48 and Sn-100 + Sn-120 systems were chosen for the simulations. Purpose: We simulate development of proton and neutron densities and asymmetries as a function of initial state, beam energy, and system size in the selected collisions in order to guide further experiments pursuing the density dependence of the symmetry energy. Methods: The Boltzmann-Uhlenbeck-Uehling (pBUU) transport model with four empirical models for the density dependence of the symmetry energy was employed. Results of simulations using pure Vlasov dynamics were added for completeness. In addition, the time-dependent Hartree-Fock (TDHF) model, with the SV-bas Skyrme interaction, was used to model the heavy-ion collisions at E-beam <= 40 MeV/nucl. Maximum proton and neutron densities rho(max)(p) and rho(max)(n) n, reached in the course of a collision, were determined from the time evolution of rho(p) and rho(n). Results: The highest total densities predicted at E-beam = 800 MeV/nucl. were of the order of similar to 2.5 rho(0) (rho(0) = 0.16 fm(-3)) for both Sn and Ca systems. They were found to be only weakly dependent on the initial conditions, beam energy, system size, and a model of the symmetry energy. The proton-neutron asymmetry delta = (rho(max)(n) . rho(max)(p))/(rho(max)(n) + rho(max)(p)) at maximum density does depend, though, on these parameters. The highest value of d found in all systems and at all investigated beam energies was similar to 0.17. Conclusions: We find that the initial state, beam energy, system size, and a symmetry energy model affect very little the maximum proton and neutron densities, but have a subtle impact on the proton-neutron asymmetry. Most importantly, the variations in the proton-neutron asymmetry at maximum densities are related at most at 50% level to the details in the symmetry energy at supranormal density. The reminder is due to the details in the symmetry energy at subnormal densities and proton and neutron distributions in the initial state. This result brings to the forefront the need for a proper initialization of the nuclei in the simulation, but also brings up the question of microscopy, such as shell effects, that affect initial proton and neutron densities, but cannot be consistently incorporated into semiclassical transport models.