Comparative folding-model study of low-energy elastic scattering and fusion of the ${}^{12}$C+${}^{12}$C and ${}^{16}$O+${}^{16}$O systems

Abstract

A density dependent nucleon-nucleon interaction (CDM3YR) has been parametrized based on the original M3Y-Reid interaction, to properly reproduce the saturation properties of symmetric nuclear matter (NM) in the nonrelativistic Hartree-Fock calculation, with the energy of NM in a good agreement with the microscopic \emph{ab-initio} results over densities up to three times the saturation density. The real optical potential (OP) of symmetric ${}^{12}$C+${}^{12}$C and ${}^{16}$O+${}^{16}$O systems is then calculated within the double-folding model (DFM), using the realistic densities of ${}^{12}$C and ${}^{16}$O nuclei and CDM3YR interaction, for the optical model analysis of elastic scattering at low energies and determination of the astrophysical $S$ factor of ${}^{12}$C+${}^{12}$C and ${}^{16}$O+${}^{16}$O fusion in the barrier penetration model. The DFM calculation of the real OP for these two symmetric systems was also done using the original (density independent) M3Y-Reid interaction, and that added by a repulsive core suggested by Esbensen {\it et al.} to explore the impact of medium effects that are effectively encoded in the density dependence of the CDM3YR interaction.