Medium effect in high-density nuclear matter probed by a systematic analysis of nucleus-nucleus elastic scattering

We investigate the property of the high-density nuclear matter probed by the nucleus-nucleus elastic scattering in the framework of the double-folding model with the complex $G$-matrix interaction. The medium effect including the three-body-force (TBF) effect is investigated with present two methods based on the frozen density approximation. The medium effect is clearly seen on the potential and the elastic cross section for the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ system at $E/A=70\mathrm{MeV}$. The crucial role of the medium effect is also confirmed with other effective nucleon-nucleon ($\mathit{NN}$) interactions. In addition, the present methods are applied to other heavy-ion elastic scattering systems. Again, the medium effect is clearly seen in the heavy-ion elastic cross section. The medium effect on the elastic cross section becomes invisible with the increase of the target mass and the incident energy (up to $E/A=200\mathrm{MeV}$). However, the medium effect is again important to fix the heavy-ion scattering over $E/A=200\mathrm{MeV}$. Finally, we make clear the crucial role of the TBF effect up to $k_F=1.6{\mathrm{fm}}^{-1}$ in the nucleus-nucleus elastic scattering.

Figure 1

The real and imaginary parts of the DF potential by the cutting method (with the $k_{\mathrm{cut}}$ value). The solid curve is obtained by the FDA calculation. The dotted, dashed, dot-dashed, bold-solid, bold-dotted, bold-dashed, and bold-dot-dashed curves are the results with $k_{\mathrm{cut}}=1.70,1.65,1.60,1.55,1.50,1.45,$ and 1.40, respectively.

Figure 2

The elastic cross section with the DF potentials shown in Fig. 1. The meaning of the curves is the same as in Fig. 1. The experimental data are taken from Ref. [34].

Figure 3

The real and imaginary parts of the DF potential by the replacement method (with the $k_{\mathrm{rep}.}$ value). The solid curve is obtained by the FDA calculation. The dotted, dashed, dot-dashed, bold-solid, bold-dotted, bold-dashed, and bold-dot-dashed curves are the results with $k_{\mathrm{rep}.}=1.70,1.65,1.60,1.55,1.50,1.45,$ and 1.40, respectively.

Figure 4

The elastic cross section with the DF potentials shown in Fig. 3. The meaning of the curves is the same as in Fig. 3.

Figure 5

The elastic cross sections by the replace method based on the MPa interaction and the cutting method with the ESC interaction.

Figure 6

Same as Fig. 2 but with the MPb, MPc, CEG07b, and CDM3Y6 interactions.

Figure 7

Same as Fig. 4 but based on the MPb, MPc, and CEG07b interactions.

Figure 8

Elastic cross section for the incident ${}^{16}\mathrm{O}$ particle by the several targets at $E/A=93.9\mathrm{MeV}$. The meaning of the curves is the same as in Fig. 5. It means $N_W=1$ without the $N_W$ value. The experimental data are taken from Ref. [38].

Figure 9

Elastic cross section for the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ system at various incident energies. The meaning of the curves is the same as in Fig. 5. The experimental data are taken from Refs. [35, 39, 40, 41].

Figure 10

The real (upper panel) and imaginary (lower panel) parts of the DF potential at $E/A=300$ and 400 MeV. The meaning of the curves is the same as in Fig. 5.

Figure 11

The elastic cross section with the DF potentials shown in Fig. 10. The meaning of the curves is the same as in Fig. 5.