562 EAST EUROPEAN JOURNAL OF PHYSICS. 3. 562-569 (2023) DOI:10.26565/2312-4334-2023-3-66 ISSN 2312-4334 NUCLEON-NUCLEON ELASTIC SCATTERING FOR MOTION IN THE SHIFTED DENG-FAN POTENTIAL † Bidhan Khirali*, S. Laha † , Biswanath Swain § , Ujjwal Laha # Department of Physics, National Institute of Technology, Jamshedpur, 831014, India *Corresponding author:b.khirali720@gmail.com § e-mail: lahas.bol@gmail.com; § e-mail: biswanathswain73@gmail.com; # e-mail: ujjwal.laha@gmail.com Received July, 5, 2023; revised July 22, 2023; accepted July 26, 2023 The scattering theory's main objective is to comprehend an object by hurling something at it. One can learn details about an object by observing how it bounces off other objects. The potential that exists between the two particles is the thing that one seeks to comprehend. In a time-independent approach to scattering, one assumes that the incident beam has been activated for a very long time and that the entire system is in a stationary state. For short-range local potentials, the variable phase methodology is highly useful in solving quantum mechanical scattering problems. Variable phase methodology/phase-function technique has been explicitly utilized for non- relativistic nucleon-nucleon scattering phenomenon with the fundamental central local potential term and without spin-orbit force. Working under this methodology, scattering phase shifts, total scattering cross section, and Differential cross section have been investigated for a new nuclear potential model “Shifted Deng-Fan potential”. Real nucleon-nucleon scattering systems (n-p) and (p-p) have been treated for this purpose with partial waves up to 2 =  in the low and moderate energy region. For 0 >  waves, interacting repulsive barrier potential has been incorporated with the existing central part. Our results for the considered potential model show a close contest with that of the experimental data. Keywords: Shifted Deng-Fan Potential; Phase function method; Scattering Phase shifts; Scattering cross sections; (n-p) and (p-p) systems PACS: 03.65.Nk; 21.30.Fe; 13.75.Cs; 24.10.-i INTRODUCTION It is a well-known fact that the exact solution of the Schrödinger equation is significant in quantum mechanics as they enclose all necessary information regarding the quantum system under consideration. Most of the quantum systems can only be treated by approximation methodologies [1,2,3], as exact analytic solutions are feasible only for a few simple cases such as the hydrogen atom, the harmonic oscillator and others [4,5,6] in all partial waves and all energies. In a quest to find a suitable potential for diatomic interaction to describe the vibrational spectrum, Deng and Fan, in 1957, proposed a new molecular potential model [7] that is exponential in nature and was called Generalized Morse potential [8]. This potential is a modification of the Morse potential also known as Deng-Fan molecular potential (DF). Numerous studies were performed for this potential by researchers in various applications [9]. This potential has been adequately utilized in describing the nucleons’ mobility in the mean field produced from the interactions of the nuclei [10]. Dong treated the Deng-fan potential as a pertinent alternative to the Morse potential for vibrational spectrum and electromagnetic transitions [11,12] of the diatomic molecules. Mesa [13] applied this potential for energy spectra studies of the diatomic molecules. Oyewumi [14] utilized the Nikiforov–Uvarov method to obtain bound state solutions of the Deng–Fan molecular potential for several diatomic molecules like HCl, LiH, H2 and so on. Many of the other works have been accomplished with this potential via different quantum mechanical wave equations [15-22] by utilizing several standard approximation prescriptions to the solution in both relativistic and non-relativistic domains. A modified form of the DF called Shifted Deng-Fan potential (SDF)was proposed by Hamzavi et al. in 2012[23] for the calculation of ro-vibrational energy levels for few of the diatomic molecules. In the modified form, the DF potential is shifted by the dissociation energy (D). Ref. [23] also demonstrated that DF and Morse potential are qualitatively similar but SDF and Morse potentials are very much similar for large values of r i.e in the regions r ≈ re and r >r e , however, they differ at r ≈ 0. Here, r e is the equilibrium diatomic separation. Louis [24] solved the Dirac equation for the Manning- Rosen plus shifted Deng-Fan (MRSDF) potential in the presence of spin and pseudospin (pspin) symmetries and by including a Coulomb-like tensor potential. All of above works [7-24] pertains to molecular spectroscopy and molecular dynamics. Within the framework of the shifted Deng Fan potential (SDF), Sajedi [25] studied the cluster structure of astrophysically important 19 Ne nucleus. In recent past, working with the exponential class of potentials, our group obtained exact analytical solution of the elastic Deng Fan potential [26] scattering of a particle in S-wave and obtained the phase parameters using the Jost function methodology for the systems under consideration in the nuclear realm. In this article, we present the study of the non-relativistic nuclear scattering treatment of the SDF potential in terms of the fundamental nucleon-nucleon scattering both charged and uncharged. In support of our justification, we present phase shift observables, total scattering cross section for proton-neutron (p-n) and proton-proton (p-p) scattering & differential cross section studies for proton-proton (p-p) scattering. A comparison is drawn for the obtained data against † Cite as: B. Khirali, S. Laha, B. Swain, U. Laha, East Eur. J. Phys. 3, 562 (2023), https://doi.org/10.26565/2312-4334-2023-3-66 © B. Khirali, S. Laha, B. Swain, U. Laha, 2023