Nuclear symmetry potential in the relativistic impulse approximation

Using the relativistic impulse approximation with the Love-Franey $\mathit{NN}$ scattering amplitude developed by Murdock and Horowitz, we investigate the low-energy ($100⩽E_{\mathrm{kin}}⩽400$ MeV) behavior of the nucleon Dirac optical potential, the Schrödinger-equivalent potential, and the nuclear symmetry potential in isospin asymmetric nuclear matter. We find that the nuclear symmetry potential at fixed baryon density decreases with increasing nucleon energy. In particular, the nuclear symmetry potential at saturation density changes from positive to negative values at nucleon kinetic energy of about 200 MeV. Furthermore, the obtained energy and density dependence of the nuclear symmetry potential is consistent with those of the isospin- and momentum-dependent MDI interaction with $x=0$, which has been found to describe reasonably well both the isospin diffusion data from heavy-ion collisions and the empirical neutron-skin thickness of ${}^{208}\mathrm{Pb}$.

Figure 1

The scalar and vector parts of the free $\mathit{NN}$ forward scattering amplitudes $F_{S0}^{\mathit{pp}}$, $F_{S0}^{\mathit{np}}$, $F_{V0}^{\mathit{pp}}$, and $F_{V0}^{\mathit{np}}$ at nucleon kinetic energies $E_{\mathrm{kin}}=135$, 200, 300, and 400 MeV (open squares) from the RIA of MH. Dashed lines show polynomial fits to the energy dependence of the $\mathit{NN}$ scattering amplitude. Corresponding results from the original RIA of MRW are shown by solid squares and lines.

Figure 2

Energy dependence of the real and imaginary parts of the scalar and vector optical potentials in symmetric nuclear matter for different baryon densities ${\rho }_B$, with MH and MRW scattering amplitudes.

Figure 3

Energy dependence of the real part for the nucleon Schrödinger-equivalent potential at normal density in symmetric nuclear matter, from the original RIA of MRW and from the RIA of MH with and without Pauli blocking correction.

Figure 4

Energy dependence of the nuclear symmetry potential from the RIA of MH with isospin-dependent (open squares) and isospin-independent (solid squares) Pauli blocking corrections, as well as the phenomenological MDI interaction with $x=1,0$, and $-1$ at three fixed baryon densities.

Figure 5

Density dependence of the nuclear symmetry potential using RIA with isospin-dependent and isospin-independent Pauli blocking, as well as the results from the phenomenological interaction MDI with $x=-1,0,$ and 1 at four nucleon kinetic energies.