High-energy behavior of the nuclear symmetry potential in asymmetric nuclear matter

Using the relativistic impulse approximation with empirical NN scattering amplitude and the nuclear scalar and vector densities from the relativistic mean-field theory, we evaluate the Dirac optical potential for neutrons and protons in asymmetric nuclear matter. From the resulting Schrödinger-equivalent potential, the high-energy behavior of the nuclear symmetry potential is studied. We find that the symmetry potential at fixed baryon density is essentially constant once the nucleon kinetic energy is greater than about 500 MeV. Moreover, for such a high-energy nucleon, the symmetry potential is slightly negative below a baryon density of about $\rho =0.22$ fm${}^{-3}$ and then increases almost linearly to positive values at high densities. Our results thus provide an important constraint on the energy and density dependence of nuclear symmetry potential in asymmetric nuclear matter.

Figure 1

(Color online) Neutron and proton scalar densities as functions of baryon density in nuclear matter with isospin asymmetry $\alpha =0$ and $0.5$ for the parameter sets NL3, Z271v, and HA.

Figure 2

(Color online) Energy dependence of real and imaginary parts of the scalar and vector potentials for neutrons and protons in nuclear matter with isospin asymmetry $\alpha =0$ and $0.5$ for the parameter set HA.

Figure 3

(Color online) Density dependence of the real and imaginary parts of the scalar and vector potentials for neutrons and protons in nuclear matter with isospin asymmetry $\alpha =0$ and $0.5$ for the parameter set HA.

Figure 4

(Color online) Energy dependence of the nuclear symmetry potential using the parameter sets NL3, Z271v, and HA as well as from the phenomenological interaction MDI with $x=-1,0,$ and 1 at fixed baryon densities of ${\rho }_B=0.08$ fm${}^{-3}$ (a), $0.16$ fm${}^{-3}$ (b), and $0.24$ fm${}^{-3}$ (c).

Figure 5

(Color online) Density dependence of the nuclear symmetry potential using the parameter sets NL3, Z271v, and HA as well as from the MDI interaction with $x=-1,0$, and 1 at a fixed nucleon kinetic energy of 800 MeV.