Thermal properties of asymmetric nuclear matter with an improved isospin- and momentum-dependent interaction

Thermal properties of asymmetric nuclear matter, including the temperature dependence of the symmetry energy, single-particle properties, and differential isospin fractionation, are investigated with different neutron-proton effective mass splittings by using an improved isospin- and momentum-dependent interaction. In this improved interaction, the momentum dependence of the isoscalar single-particle potential at saturation density is well fit to that extracted from optical-model analyses of proton-nucleus scattering data up to the nucleon kinetic energy of 1 GeV, and the isovector properties, i.e., the slope of the nuclear symmetry energy, the momentum dependence of the symmetry potential, and the symmetry energy at saturation density, can be flexibly adjusted via three parameters: $x,y$, and $z$, respectively. Our results indicate that the nucleon phase-space distribution in equilibrium, the temperature dependence of the symmetry energy, and the differential isospin fractionation can be significantly affected by the isospin splitting of the nucleon effective mass.

Figure 1

The ImMDI prediction for the single-particle potential in symmetric nuclear matter at ${\rho }_0$ as a function of nucleon total energy with its rest mass subtracted. The results of the MDI and the optical potential by Hama et al. [16, 17] are also shown for comparison.

Figure 2

The symmetry energy from the ImMDI by (a) adjusting the value of parameter $x$ at $y=-115$ MeV and $z=0$ MeV or (b) parameter $z$ at $x=0$ and $y=-115$ MeV.

Figure 3

(a) The symmetry potential at saturation density and (b) symmetry energy from the ImMDI by adjusting the value of parameter $y$ at $x=1$ and $z=0$ MeV.

Figure 4

The equilibrated phase-space distribution functions (normalized by the spin degeneracy) of (a) neutrons and (b) protons from the ImMDI for [($x=0$), ($y=-115$ MeV)] and [($x=1$), ($y=115$ MeV)] in neutron-rich nuclear matter of isospin asymmetry $\delta =0.5$ at saturation density and temperature $T=30$ MeV.

Figure 5

The nuclear symmetry energy from the ImMDI for (a) [($x=0$), ($y=-115$ MeV)] and (b) [($x=1$), ($y=115$ MeV)] at temperatures of $0,10,30$, and 50 MeV.

Figure 6

Same as Fig. 5 but only for the kinetic contribution of the symmetry energy.

Figure 7

Same as Fig. 5 but only for the potential contribution of the symmetry energy.

Figure 8

The momentum dependence of the symmetry potential from the ImMDI for (a) [($x=0$), ($y=-115$ MeV)] and (b) [($x=1$), ($y=115$ MeV)] at different densities and temperatures.

Figure 9

The relative neutron-proton effective mass splitting from the ImMDI for (a) [($x=0$), ($y=-115$ MeV)] and (b) [($x=1$), ($y=115$ MeV)] in neutron-rich nuclear matter of isospin asymmetry $\delta =0.5$ at different densities and temperatures.

Figure 10

Left panel shows the section of binodal surface from the ImMDI for [($x=0$), ($y=-115$ MeV)] and [($x=1$), ($y=115$ MeV)] at a temperature $T=10$ MeV. $L,G$, and $M$ represent the liquid phase, the gas phase, and the mixed phase, respectively. Right panel shows the double neutron/proton ratio in gas and liquid phases ${(n/p)}_G/{(n/p)}_L$ at the pressure of $0.10$ ${\mathrm{MeV}/\mathrm{fm}}^3$ as a function of nucleon momentum.