NUCLEAR PHYSICS α-Cluster Optical Potential Model of 40 Ca Zakaria M. M. Mahmoud 1,2 & Kassem O. Behairy 3 Received: 3 September 2016 /Published online: 18 January 2017 # Sociedade Brasileira de Física 2017 Abstract Elastic scattering of α + 40 Ca is analyzed in the framework of the optical model. We adopted an independent α-cluster model to generate the α-cluster and matter density of 40 Ca. We proposed a parametrized form for the α-cluster den- sity and fixed its parameters according to the available exper- imental data about the α-particle and 40 Ca nuclei. The obtain- ed α-cluster density of 40 Ca is used to generate the real part of the optical potential. The single folding procedure is used to generate this real optical potential with two different effective α–α interactions. The real calculated potential supplied with an imaginary Woods–Saxon squared potential is used to ana- lyze 20 sets of experimental data in the energy range between 18 and 166 MeV. We found that our model is successful in reproducing the data for energies above 40 MeV and still doubtful for lower energies. Keywords Optical potential model . Single folding model . α-cluster and matter density of 40 Ca and Woods-Saxon squared potential 1 Introduction The collision between nuclear species is considered as a pow- erful way to get information about nuclear interaction potential and nuclear density. The elastic scattering is the simplest nu- clear collision process that takes place and is considered as the doorway for other reactions. Usually, for the description of nuclear scattering, the optical model is widely used, especially elastic scattering. The microscopic description of the nucleus– nucleus optical model potential is one of the fundamental tasks in nuclear physics. Good microscopic understanding of this potential allows, understanding the relevant reaction dynamics involved, predicting optical potentials of colliding systems for which the elastic scattering measurement is absent. The fold- ing model is widely used to microscopically calculate the nu- cleus–nucleus interaction potential. Folding formulation of the nucleus–nucleus potential was pioneered by Watanabe [1] in his analysis of deuteron projectiles. Through the last few decades, folding model calculations were used for the analysis of scattering processes for a large number of interacting systems with microscopic and semi- microscopic approaches. Successfully and intensively, Satchler and Love [2] used double folding (DF) model for the analysis of light and heavy composite ion scattering. They used in their analysis DF optical potentials built upon a realistic effective nucleon–nucleon interaction folded with the nuclear matter density distributions of projectile and target nuclei. The esence of the folding model lies in its abilities to relate the nuclear potential to some fundamental quantities, namely nuclear densities and nucleon–nucleon effective inter- actions. More review of this subject can be found in ref. [3]. The DF model based on the point nucleon densities and an effective nucleon–nucleon interaction is widely and successful- ly used to analyze α-nucleus and nucleus–nucleus elastic scat- tering [4–10]. Also, another approach of the folding model based on a α-cluster picture of the nucleus is used. This α- cluster based on folded potential is used to analyze the elastic scattering of α-particle and α-like nuclei from other α-like nuclei [11–14]. The α-cluster picture dated back to the * Kassem O. Behairy kassemomar@aswu.edu.eg 1 Physics Department, Faculty of Science, Assiut University, New Valley, Egypt 2 Physics Department, Philipps University Marburg, D-35032 Marburg, Germany 3 Physics Department, Aswan University, Aswan, Egypt Braz J Phys (2017) 47:189–196 DOI 10.1007/s13538-016-0483-7