Surface effect in explaining the elastic scattering of the $\alpha +^{12}$C system at low energies

Abstract

In this paper, the elastic scattering angular distributions data of the $\alpha +$12C reaction at an energy range of 13.0 to 172.5 MeV were analyzed within the framework of optical model formalism. A phenomenological deep real potential was used with a phenomenological Woods-Saxon type imaginary potential. Excellent agreement was obtained in the high-energy region. The phenomenological deep potential was unable to explain the experimental data in the low-energy region. The experimental data at both low and high energies could not be explained at the same time. In order to explain the data simultaneously at low energy and high energy, the shape of the deep real potential was modified in the surface region. This work shows the role of the surface region of two nuclei in explaining the elastic scattering data of this system.