* Corresponding author e-mail: kass_phys@aswu.edu.eg © 2016 NSP Natural Sciences Publishing Cor. Quant. Phys. Lett. 5, No. 2, 19-25 (2016) 19 http://dx.doi.org/10.18576/qpl/050202 Real Cluster Folding Potential for α+ 40 Ca Elastic Scattering Zakaria M. M. Mahmoud 1,2 and Kassem. O. Behairy 3,* 1 Physics Department, Faculty of Science, Assiut University, New Valley Branch, Egypt. 2 Physics Department, Philipps University Marburg, D-35032 Marburg, Germany 3 Physics Department, Aswan University, Aswan, Egypt. Received: 21 Jun. 2016, Revised: 22 Jul. 2016, Accepted: 24 Jul. 2016. Published online: 1 Aug. 2016. Abstract: elastic scattering of α+ 40 Ca are analyzed in the framework of optical model based on the α-cluster model of 40 Ca. We adopted an independent α-cluster model to generate the α-cluster and matter densities of 40 Ca. we pre-suggested the functional form of α-cluster density and fixed its parameters according to the available experimental data about the α- particle and 40 Ca nuclei. The obtained 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 squared Woods Saxon potential are used to analyze 20 sets of experimental data on 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, cluster model, α+40Ca elastic scattering. 1 Introduction Collision between nuclear species is considered as a powerful way to get information about nuclear interaction potential and nuclear density. The simplest nuclear collision process which is considered as the doorway for other reactions is the elastic scattering. Optical model is one of the mostly used models for the description of nuclear scattering especially elastic scattering. The microscopic description of the nucleus–nucleus optical model potential is considered as one of the fundamental tasks in nuclear physics. Good microscopic understanding of this potential allows, besides understanding the relevant reaction dynamics involved, predicting optical potentials of colliding systems for which the elastic scattering measurement is absent. One of the mostly used methods to calculate the nucleus-nucleus interaction potential is the folding model. 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 was 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 ions 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. It is appeared that the beauty of the folding model lies in its abilities to relate the nuclear potential to some fundamental quantities, namely nuclear densities and nucleon-nucleon effective interactions. 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 successfully used to analyze α-nucleus and nucleus-nucleus elastic scattering [4-9]. Also another approach of the folding model based on α-cluster picture of the nucleus is used. This α-cluster based folded potential is used to analyze the elastic scattering of α-particle and α-like nuclei from other α-like nuclei [10-13]. This α-cluster picture dated back to the beginning of nuclear physics through the explanation of nuclear α-decay from heavy nuclei. For more details and review about α-clustering in light nuclei from both experimental and theoretical point of view see ref. [14,15] and references therein. Previously, the present α-cluster folding model was used successfully to describe the α-nucleus [16] and nucleus– nucleus scattering [17]. The interaction potentials between Quantum Physics Letters An International Journal