Cross-checking the symmetry energy at high densities

By considering both the effects of the nucleon-nucleon short-range correlations and the isospin-dependent in-medium inelastic baryon-baryon scattering cross section in the transport model, two unrelated Au + Au experimental measurements at 400 MeV/nucleon beam energy are simultaneously analyzed, and a mildly soft symmetry energy ($L\left({\rho }_0\right)=37$ MeV) at supra-saturation densities is obtained. This result is compatible with recent result [Phys. Rev. C 92, 064304 (2015)] shown by comparing the available data on the electric dipole polarizability with the theoretical predictions.

Figure 1

Momentum distributions of neutron and proton in nucleus ${}^{197}\mathrm{Au}$ calculated with the BHF with Av18 + TBF. Taken from Ref. [43].

Figure 2

Evolution of the momentum distribution of nucleon in nucleus ${}^{197}\mathrm{Au}$. The upper panel (a) is for the case of initial nucleon distribution with HMT while the lower panel (b) is a simple Fermi-Dirac initial distribution. Both cases are under the interaction given by Eq. (2).

Figure 3

Time dependence of the number of evaporated nucleons by the nucleus in the ground state using two initial distributions with and without high momentum tail as shown in Fig. 2.

Figure 4

Time dependence of the asymmetry ${\delta }_{\mathrm{bound}}=({\rho }_n-{\rho }_p)/({\rho }_n+{\rho }_p)$ of bound nucleons in the nucleus in the ground state using two initial distributions with and without high-momentum tail as shown in Figs. 2 and 3.

Figure 5

Kinetic symmetry energy and density-dependent symmetry energy with different $x$ parameters. Note here that in heavy-ion collisions at 400 MeV/nucleon beam energy, the high-density part of the symmetry energy plays a major role.

Figure 6

Reduced factor $R_{\mathrm{medium}}^{\mathrm{np}}$ of neutron-proton scattering cross section as a function of density and nucleonic momentum in asymmetric medium $\delta$ = 0.2. The red shadow region and label “0.5–0.7” denote experimental density and momentum region and the corresponding value of reduced factor $R_{\mathrm{medium}}^{\mathrm{np}}$.

Figure 7

Multiplicity of charged pion meson produced in Au + Au reaction at 400 MeV/nucleon with different symmetry energies. The shadow region denotes the FOPI data [50]. The dashed lines show the cases without SRC.

Figure 8

${\pi }^{-}/{\pi }^{+}$ ratio in Au + Au reaction at 400 MeV/nucleon with different symmetry energies. Also shown are the effects of the SRC of nucleon-nucleon and the in-medium inelastic cross section on the ${\pi }^{-}/{\pi }^{+}$ ratio with same $x$ parameters.

Figure 9

The effects of in-medium inelastic cross section on the productions of different $\mathrm{\Delta }$ resonance in Au + Au reaction at 400 MeV/nucleon with the symmetry energy parameter $x=1$.

Figure 10

Elliptic flow of emitting nucleons in Au + Au collision at 400 MeV per nucleon incident beam energy with different symmetry energies. The shadow region denotes the experimental FOPI-LAND data [20]. The dashed lines show the cases without SRC.

Figure 11

Same as Fig. 10, but for the ratio of $V_2^n/V_2^p$. The effects of the SRC of nucleon-nucleon on the $V_2^n/V_2^p$ with same $x$ parameters are also shown.