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

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_{rm beam} leq 800 , text{MeV/nucl}$ using pBUU and TDHF models. The symmetric $^text{40}$Ca +$^text{40}$Ca, $^text{48}$Ca +$^text{48}$Ca, $^text{100}$Sn +$^text{100}$Sn and $^text{120}$Sn + $^text{120}$Sn and asymmetric $^text{40}$Ca +$^text{48}$Ca and $^text{100}$Sn +$^text{120}$Sn systems were chosen for the simulations. We find limits on the maximum proton and neutron densities and the related proton-neutron asymmetry $delta$ as a function of the initial state, beam energy, system size and a symmetry energy model. While the maximum densities are almost independent of these parameters, our simulation reveals, for the first time, their subtle impact on the proton-neutron asymmetry. Most importantly, we find that 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 its impact on proton and neutron distributions in the initial state. This result puts to forefront the need of 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.