Nucleon-Nucleon Elastic Scattering for Motion in The Shifted Deng-Fan Potential
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 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 l = 2 in the low and moderate energy region. For l > 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.
C.L. Pekeris, “The Rotation-Vibration Coupling in Diatomic Molecules”, Phys. Rev. 45, 98(1934), https://doi.org/10.1103/PhysRev.45.98
W.C. Qiang, and S.H. Dong, “Analytical approximations to the solutions of the Manning-Rosen potential with centrifugal term”, Phys. Lett. A, 363, 169 (2007), https://doi.org/10.1016/j.physleta.2007.03.057
B. Khirali, A.K. Behera, J. Bhoi, and U. Laha, “Scattering with Manning-Rosen potential in all partial waves”, Ann. Phys. 412, 168044 (2020), https://doi.org/10.1016/j.aop.2019.168044
L.D. Landau and E.M. Lifshitz, Quantum Mechanics, Non-Relativistic Theory, 3rd ed. (Pergamon, 1977).
R.L. Liboff, Introductory Quantum Mechanics, 4th ed. (Addison Wesley, San Francisco, 2003).
M.M. Nieto, “Hydrogen atom and relativistic pi‐mesic atom in N‐space dimensions”, Am. J. Phys. 47, 1067 (1979), https://doi.org/10.1119/1.11976
Z.H. Deng, and Y.P. Fan, “A Potential Function of Diatomic Molecules”, J. Shandong Univ. (Natural Sci.) 1, 162 (1957)
A.N. Ikot, H. Hassanabadi, B.H. Yazarloo, M.I. Umo, and S. Zarrinkamar, Dirac-Deng-Fan Problem with Coulomb-Hulthen Tensor Interactions, Acta Phys. Polonica A, 126, 656 (2014), https://doi.org/10.12693/APhysPolA.126.656
K.J. Oyewumi, O.J. Oluwadare, K.D. Sen, and O.A. Babalola, “Bound state solutions of the Deng–Fan molecular potential with the Pekeris-type approximation using the Nikiforov-Uvarov (N-U) method”, J. Math. Chem. 51(3), 976-991 (2013), https://doi.org/10.1007/s10910-012-0123-6
E. Maghsoodi, H. Hassanabadi, and S. Zarrinkamar, “Spectrum of Dirac equation under Deng–Fan scalar and vector potentials and a Coulomb tensor interaction by SUSYQM”, Few-Body Syst. 53(3-4), 525-538 (2012), https://doi.org/10.1007/s00601-012-0314-5
S.H. Dong, Factorization method in quantum mechanics Fundamental Theories in Physics.150 (Springer, Netherlands, 2007). pp. 187-213.
O.J. Oluwadare, K.J. Oyewumi, C.O. Akoshile, and O.A. Babalola, “Approximate analytical solutions of the relativistic equations with the Deng-Fan molecular potential including a Pekeris-type approximation to the (pseudo) centrifugal term”, Phys. Scr. 86, 035002 (2012), https://doi.org/10.1088/0031-8949/86/03/035002
A.D.S. Mesa, C. Quesne, and Y.F. Smirnov, “Generalized Morse potential: Symmetry and satellite potentials”, J. Phys. A, 31, 321 (1998), https://doi.org/10.1088/0305-4470/31/1/028
K.J. Oyewumi, O.J. Oluwadare, K. D. Sen, and O.A. Babalola, “Bound state solutions of the Deng-Fan molecular potential with the Pekeris-type approximation using the Nikiforov-Uvarov (N-U) method”, J. Math. Chem. 51, (2012) 976, https://doi.org/10.1007/s10910-012-0123-6
H. Hassanabadi, B.H. Yazarloo, S. Zarrinkamar, and H. Rahimov, “Deng-Fan potential for relativistic spinless particles - An ansatz solution”, Commun. Theor. Phys. 57 339 (2012), https://doi.org/10.1088/0253-6102/57/3/02
S.H. Dong, “Relativistic Treatment of Spinless Particles Subject to a Rotating Deng-Fan Oscillator Relativistic Treatment of Spinless Particles Subject to a Rotating Deng-Fan Oscillator”, Commun. Theor. Phys. 55, 969 (2011), https://doi.org/10.1088/0253-6102/55/6/05
J. Oluwadare, K.J. Oyewumi, and O.A. Babalola, “Exact s-wave solution of the Klein-Gordon equation with the Deng-Fan molecular potential using the Nikiforov-Uvarov (NU) Method”, Afr. Rev. Phys. 7, 16 (2012). http://aphysrev.ictp.it/index.php/aphysrev/article/download/543/236
B.H. Yazarloo, L. Lu, G. Liu, S. Zarrinkamar, and H. Hassanabadi, “The nonrelativistic scattering states of the Deng-Fan potential”, Adv. High Energy Phys. 2013, 317605 (2013), https://doi.org/10.1155/2013/317605
S.H. Dong, and X.Y. Gu, “Arbitrary l state solutions of the Schrödinger equation with the Deng-Fan molecular potential”, J. Phys. Conf. Ser. 96, 012109 (2008), https://doi.org/10.1088/1742-6596/96/1/012109
Z. Rong, H.G. Kjaergaard, and M.L. Sage, “Comparison of the Morse and Deng-Fan potentials for X-H bonds in small molecules”, Mol. Phys. 101 2285 (2003), https://doi.org/10.1080/0026897031000137706
L.H. Zhang, P. Li, and C.S. Jia, “Approximate analytical solutions of the Dirac equation with the generalized Morse potential model in the presence of the spin symmetry and pseudo-spin symmetry”, Phys. Scr. 80, 035003 (2009), https://doi.org/10.1088/0031-8949/80/03/035003
S.M. Ikhdair, “An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry”, J. Math. Phys. 52 052303 (2011), https://doi.org/10.1063/1.3583553
M. Hamzavi, S.M. Ikhdair, and K.E. Thylwe, “Equivalence of the empirical shifted Deng–Fan oscillator potential for diatomic molecules”, J. Math. Chem. 51(1), 227-238 (2013), https://doi.org/10.1007/s10910-012-0075-x
H. Louis, B.I. Ita, P.I. Amos, O.U. Akakuru, M.M. Orosun, N.A. Nzeata-Ibe, and M. Philip, “Solutions to the Dirac Equation for Manning-Rosen Plus Shifted Deng-Fan Potential and Coulomb-Like Tensor Interaction Using Nikiforov-Uvarov Method”, Int. J. Chem.10, 3(2018), https://doi.org/10.5539/ijc.v10n3p99
M. Sajedi, and Z. Kargar, “Shifted Deng-Fan potential and cluster structure in 19Ne”, Nucl. Phys. A, 1015, 122314 (2021), https://doi.org/10.1016/j.nuclphysa.2021.122314
D. Saha, B. Khirali, B. Swain, and J. Bhoi, “Jost states for the Deng-Fan potential”, Phys. Scr. 98, 015303 (2023), https://doi.org/10.1088/1402-4896/aca1e6
F. Calogero, Variable Phase Approach to Potential Scattering (New York: Academic1967).
U. Laha, and J. Bhoi, “Higher partial-wave potentials from supersymmetry-inspired factorization and nucleon-nucleus elastic scattering”, Phys. Rev. C - Nucl. Phys.91,034614(2015), https://doi.org/10.1103/PhysRevC.91.034614
J. Bhoi, R. Upadhyay, and U. Laha, “Parameterization of Nuclear Hulthén Potential for Nucleus-Nucleus Elastic Scattering”, Commun. Theor. Phys.69, 203–210 (2018),https://doi.org/10.1088/0253-6102/69/2/203
 U. Laha, and J. Bhoi, “Parameterization of the nuclear Hulthén potentials”, Phys. At. Nucl. 79, 62-66 (2016), https://doi.org/10.1134/S1063778816010129
A.K. Behera, U. Laha, M. Majumder, and J. Bhoi, “Energy-Momentum Dependent Potential sand np Scattering”, Research and Reviews: J. Phys. 8, 2265 (2019).https://sciencejournals.stmjournals.in/index.php/RRJoPHY/article/view/2139
A. K. Behera, J. Bhoi, U. Laha, and B. Khirali, “Study of nucleon – nucleon and alpha-nucleon elastic scattering by the Manning-Rosen potential”, Commun. Theor. Phys. 72, 075301 (2020), https://doi.org/10.1088/1572-9494/ab8a1a
P. Sahoo, A. K. Behera, B. Khirali, and U. Laha, “Nuclear Hulthén potentials for F and G partial Waves”, Research & Reviews: J. Phys. 10, 31-37 (2021),https://doi.org/10.37591/RRJoPHY
A.K. Behera, U. Laha, M. Majumder, and J. Bhoi, “Applicability of Phase-Equivalent Energy-Dependent Potential. Case Studies”, Phys. At. Nucl. 85, 124-138 (2020), https://doi.org/10.1134/S1063778822010057
B. Talukdar, D. Chattarji, and P. Banerjee, “A generalized approach to the phase amplitude Method”, J. Phys. G: Nucl. Phys. 3, 813–820 (1977), https://doi.org/10.1088/0305-4616/3/6/012
G.C. Sett, U. Laha, and B. Talukdar, “Phase function method for Coulomb -distorted nuclear Scattering”, J. Phys. A: Math. Gen. 21, 3643-3657 (1999), https://doi.org/10.1088/03054470/21/18/017
U. Laha, A.K. Jana, and T.K. Nandi, “Phase-function method for Hulthén -modified Separable potentials”, Pramana - J. Phys. 37(5), 387-393 (1991), https://doi.org/10.1007/BF02848506
J.M. Watson, A Treatise on the Theory of Bessel Functions, (Cambridge University Press, London, 1922).
F. Gross, and A. Stadler, “Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV”, Phys. Rev. C, 78, 014005 (2008), https://doi.org/10.1103/PhysRevC.78.014005
R.B. Wiringa, V.G.J. Stoks, and R. Schiavilla, “Accurate nucleon-nucleon potential with charge-independence breaking”, Phys. Rev. C, 51, 38 (1995). https://doi.org/10.1103/PhysRevC.51.38
J.R Taylor, Scattering Theory: The Quantum Theory of Nonrelativistic Collisions (Dover Publications INC, New York, 2006).
R.G. Newton, Scattering theory of Waves and Particles (McGraw-Hill, New York, 1982).
C.L. Bailey, W.E. Bennett, T. Bergstralth, R.G. Nuckolls, H.T. Richards, and J.H. Williams, “The neutron-proton and neutron-carbon scattering cross sections for fast Neutrons”, Phys. Rev. 70, 583 (1946), https://doi.org/10.1103/PhysRev.70.583
F.F. Chen, C.P. Leavitt, and A.M. Shapiro, “Total p-p and “p-n” cross sections at cosmotron Energies”, Phys. Rev. 103, 211 (1956), https://doi.org/10.1103/PhysRev.103.211
B.H. Daub, V. Henzl, M.A. Kovash, J.L. Matthews, Z.W. Miller, K. Shoniyozov, and H. Yang, “Measurements of the neutron-proton and neutron-carbon total cross sectionfrom150 to 800 keV”, Phys. Rev. C, 87, 014005 (2013), https://doi.org/10.1103/PhysRevC.87.014005
J.D. Jackson, and J.M. Blatt, “The interpretation of low energy proton-proton scattering”, Rev. Mod. Phys, 22, 77 (1950), https://doi.org/10.1103/RevModPhys.22.77
R. J. Slobodrian, H.E. Conzett, E. Shield, and W.F. Tivol, “Proton-proton elastic scattering between 6 and 10 MeV”, Phys. Rev. 174, 1122 (1968), https://doi.org/10.1103/PhysRev.174.1122
R.A. Arndt, W.J. Briscoe, A.B. Laptev, I.I. Strakovskyt, and R.L. Workman, “Absolute total np and pp cross-section determinations”, Nucl. Sci. Eng. 162, 312 (2009), https://doi.org/10.13182/NSE162-312
Copyright (c) 2023 Bidhan Khirali, S. Laha, Biswanath Swain, Ujjwal Laha
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).