Expressing explicitly the parameters of the standard Skyrme interaction in terms of the macroscopic properties of asymmetric nuclear matter, we show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. We find that existing data on neutron skin thickness $\Delta${}rnp of Sn isotopes give an important constraint on the symmetry energy Esym($\rho${}0) and its density slope L at saturation density $\rho${}0. Combining these constraints with those from recent analyses of isospin diffusion and the double neutron/proton ratio in heavy-ion collisions at intermediate energies leads to a more stringent limit on L approximately independent of Esym($\rho${}0). The implication of these new constraints on the $\Delta${}rnp of Pb208 as well as the core-crust transition density and pressure in neutron stars is discussed.

Analytical expressions for the saturation density of asymmetric nuclear matter as well as its binding energy and incompressibility at saturation density are given up to fourth order in the isospin asymmetry $\delta =({\rho }_n-{\rho }_p)/\rho$ using 11 characteristic parameters defined by the density derivatives of the binding energy per nucleon of symmetric nuclear matter, the symmetry energy $E_{\mathrm{sym}}\hspace{0.5em}(\rho )$, and the fourth-order symmetry energy $E_{\mathrm{sym},4}(\rho )$ at normal nuclear density ${\rho }_0$. Using an isospin- and momentum-dependent modified Gogny interaction (MDI) and the Skyrme-Hartree-Fock (SHF) approach with 63 popular Skyrme interactions, we have systematically studied the isospin dependence of the saturation properties of asymmetric nuclear matter, particularly the incompressibility $K_{\mathrm{sat}}(\delta )=K_0+K_{\mathrm{sat},2}{\delta }^2+K_{\mathrm{sat},4}{\delta }^4+O({\delta }^6)$ at saturation density. Our results show that the magnitude of the higher order $K_{\mathrm{sat},4}$ parameter is generally small compared to that of the $K_{\mathrm{sat},2}$ parameter. The latter essentially characterizes the isospin dependence of the incompressibility at saturation density and can be expressed as $K_{\mathrm{sat},2}=K_{\mathrm{sym}}-6L-\frac{J_0}{K_0}L$, where $L$ and $K_{\mathrm{sym}}$ represent, respectively, the slope and curvature parameters of the symmetry energy at ${\rho }_0$ and $J_0$ is the third-order derivative parameter of symmetric nuclear matter at ${\rho }_0$. Furthermore, we have constructed a phenomenological modified Skyrme-like (MSL) model that can reasonably describe the general properties of symmetric nuclear matter and the symmetry energy predicted by both the MDI model and the SHF approach. The results indicate that the higher order $J_0$ contribution to $K_{\mathrm{sat},2}$ generally cannot be neglected. In addition, it is found that there exists a nicely linear correlation between $K_{\mathrm{sym}}$ and $L$ as well as between $J_0/K_0$ and $K_0$. These correlations together with the empirical constraints on $K_0,L,E_{\mathrm{sym}}\hspace{0.5em}({\rho }_0)$, and the nucleon effective mass lead to an estimate of $K_{\mathrm{sat},2}=-370\pm 120$ MeV.

Within the parameter space of the equation of state (EOS) of dense neutron-rich matter limited by existing constraints mainly from terrestrial nuclear experiments, we investigate how the neutron star maximum mass M _max > 2.01 ± 0.04 M _⊙, radius 10.62 km < R _1.4 < 12.83 km and tidal deformability Λ_1.4 ≤ 800 of canonical neutron stars together constrain the EOS of dense neutron-rich nucleonic matter. While the 3D parameter space of K _sym (curvature of nuclear symmetry energy), J _sym, and J ₀ (skewness of the symmetry energy and EOS of symmetric nuclear matter, respectively) is narrowed down significantly by the observational constraints, more data are needed to pin down the individual values of K _sym, J _sym, and J ₀. The J ₀ largely controls the maximum mass of neutron stars. While the EOS with J ₀ = 0 is sufficiently stiff to support neutron stars as massive as 2.37 M _⊙, supporting the hypothetical ones as massive as 2.74 M _⊙ (composite mass of GW170817) requires J ₀ to be larger than its currently known maximum value of about 400 MeV and beyond the causality limit. The upper limit on the tidal deformability of Λ_1.4 = 800 from the recent observation of GW170817 is found to provide upper limits on some EOS parameters consistent with but far less restrictive than the existing constraints of other observables studied.

Simulations by transport codes are indispensable to extract valuable physical information from heavy-ion collisions. In order to understand the origins of discrepancies among different widely used transport codes, we compare 15 such codes under controlled conditions of a system confined to a box with periodic boundary, initialized with Fermi-Dirac distributions at saturation density and temperatures of either 0 or 5 MeV. In such calculations, one is able to check separately the different ingredients of a transport code. In this second publication of the code evaluation project, we only consider the two-body collision term; i.e., we perform cascade calculations. When the Pauli blocking is artificially suppressed, the collision rates are found to be consistent for most codes (to within $1\%$ or better) with analytical results, or completely controlled results of a basic cascade code. In orderto reach that goal, it was necessary to eliminate correlations within the same pair of colliding particles that can be present depending on the adopted collision prescription. In calculations with active Pauli blocking, the blocking probability was found to deviate from the expected reference values. The reason is found in substantial phase-space fluctuations and smearing tied to numerical algorithms and model assumptions in the representation of phase space. This results in the reduction of the blocking probability in most transport codes, so that the simulated system gradually evolves away from the Fermi-Dirac toward a Boltzmann distribution. Since the numerical fluctuations are weaker in the Boltzmann-Uehling-Uhlenbeck codes, the Fermi-Dirac statistics is maintained there for a longer time than in the quantum molecular dynamics codes. As a result of this investigation, we are able to make judgements about the most effective strategies in transport simulations for determining the collision probabilities and the Pauli blocking. Investigation in a similar vein of other ingredients in transport calculations, like the mean-field propagation or the production of nucleon resonances and mesons, will be discussed in the future publications.