Examination of $\alpha$-induced fusion reactions relevant to the production of p-nuclei

The present paper examines the effect of temperature-dependent repulsive core potential on the fusion reactions of the $\alpha$ particle relevant to the production of p-nuclei such as ${}^{154}$Sm, ${}^{162}$Dy, ${}^{166}$Er, and ${}^{197}$Au. For this purpose, the $\alpha$-nucleus potentials making use of the double folding model with the density-dependent CDM3Y3 interaction plus the temperature-dependent repulsion (CDM3Y3+Repulsion) are employed. In addition, three nuclear level density (NLD) models of Fermi-Gas (FG), Hartree-Fock BCS (HFBCS), and exact pairing plus independent-particle model (EP+IPM) are used to describe the temperature-dependent excitation energy of the compound nucleus produced in the fusion reaction. The results obtained show that temperature has a significant effect on the repulsive core potential, and different NLD models predict different fusion potentials, especially at high temperatures and near the center point (origin) of the interaction. Going further away from the origin, the repulsive core potential decreases to approximately zero near the barrier region, while at sufficiently far distances, it is least affected by nuclear temperature. The calculated fusion cross sections using the CDM3Y3+Repulsion potential are only affected by the diffuseness parameter of the repulsive potential $a_{rep.}$ in the region above the Coulomb barrier, and a good agreement with the experimental data is found at $a_{rep.}$ = 0.35 fm. Hence, the effect of repulsive potential on the $\alpha$-induced reactions is only justified as a correction term, which is added to resolve the Pauli principle problem. This conclusion is in line with those reported previously using similar formalism but for other fusion reactions of heavy nuclei.