Extended Skyrme interactions for transport model simulations of heavy-ion collisions

Based on an extended Skyrme interaction that includes the terms in relative momenta up to sixth order, corresponding to the so-called Skyrme pseudopotential up to next-to-next-to-next-to leading order (N3LO), we derive the expressions of Hamiltonian density and single-nucleon potential under general nonequilibrium conditions which can be applied in transport model simulations of heavy-ion collisions induced by neutron-rich nuclei. While the conventional Skyrme interactions, which include the terms in relative momenta up to second order, predict an incorrect behavior as a function of energy for nucleon optical potential in nuclear matter, the present extended N3LO Skyrme interaction can give a nice description for the empirical nucleon optical potential. We also construct three interaction sets with different high-density behaviors of the symmetry energy by fitting both the empirical nucleon optical potential up to energy of 1 GeV and the empirical properties of isospin asymmetric nuclear matter. These extended N3LO Skyrme interactions will be useful in transport model simulations of heavy-ion collisions induced by neutron-rich nuclei at intermediate and high energies, and they can also be useful in nuclear structure studies within the mean-field model.

Figure 1

Nuclear matter properties with SP6s, SP6m, and SP6h, namely the density dependence of (a) the pressure of symmetric nuclear matter $P_{\mathrm{SNM}}\left(\rho \right)$ and (b) the EOS of pure neutron matter $E_{\mathrm{PNM}}\left(\rho \right)$ and (c) symmetry energy $E_{\mathrm{sym}}\left(\rho \right)$. Also displayed are various constraints on $P_{\mathrm{SNM}}\left(\rho \right),E_{\mathrm{PNM}}\left(\rho \right)$, and $E_{\mathrm{sym}}\left(\rho \right)$ obtained in previous studies. See text for details.

Figure 2

Same as Fig. 1 but extended to suprasaturation density.

Figure 3

The predicted single-nucleon potentials in cold symmetric nuclear matter as a function of nucleon kinetic energy with $\mathrm{SP}6\mathrm{s},\mathrm{SP}6\mathrm{m}$, and $\mathrm{SP}6\mathrm{h}$. The result from three conventional Skyrme interactions, and three $\mathrm{N}3\mathrm{LO}$ Skyrme pseudopotentials obtained in the previous literature, as well as the nucleon optical potential (Schrodinger equivalent potential) in symmetric nuclear matter at saturation density ${\rho }_0$ obtained by Hama et al. [78, 79], are also included for comparison. See the text for details.

Figure 4

The predicted first-order symmetry potential as a function of nucleon momentum with $\mathrm{SP}6\mathrm{s},\mathrm{SP}6\mathrm{m}$, and $\mathrm{SP}6\mathrm{h}$. The corresponding results from three conventional Skyrme interactions and three existing $\mathrm{N}3\mathrm{LO}$ Skyrme pseudopotentials, as well as microscopic results from relativistic impulse approximation and BHF method are also included for comparison.