Abstract
The investigation of the nucleus-nucleus ($AA$) elastic scattering gives several informations for the nuclear structure, reaction and interaction. The complex $AA$ interaction (potential) to describe the elastic scattering has been investigated by the phenomenological way. From the microscopic view point, the double-folding (DF) model is a powerful tool to construct the $AA$ potential. The effective nucleon-nucleon ($NN$) interaction has been used for the DF model in the embryonic stage. Nowadays, the complex $G$-matrix interaction based on the realistic $NN$ interaction is applied to the DF model potential~[1-3]. The important role of the three body force is discussed and indicated in the references. In this present talk, we will introduce a candidate to obtain the medium effect in the high-density region through the local density approximation in the DF model [4]. Our result is confirmed by the systematic analysis for the dependence of the incident energy, nuclear system and the $NN$ interaction. Finally, the crucial role of the medium effect around $k_F =$ 1.4-1.6 fm$^{-1}$ is made clear by the nucleus-nucleus elastic scattering.

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[2] Y. Yamamoto, T. Furumoto, N. Yasutake, and Th. A. Rijken, Phys. Rev. C 88, 022801(R) (2013).
[3] Y. Yamamoto, T. Furumoto, N. Yasutake, and Th. A. Rijken, Phys. Rev. C 90, 045805 (2014).
[4] T. Furumoto, Y. Sakuragi, and Y. Yamamoto, Phys. Rev. C 90, 041601(R) (2014).