Low Energy n–p and n–d Scattering with Deng–Fan Potential
DOI:
https://doi.org/10.15407/ujpe69.4.247Keywords:
Deng–Fan potential, variable phase approach, scattering phase parameters, cross-section, analyzing power, n–p and n–d systemsAbstract
In any first approach toward a nuclear structure problem, one presumes the nucleons to be elementary particles. The failure or success of this approach may then instruct us something about the significance of sub-nuclear degrees of freedom. The Deng–Fan potential, although extensively used in molecular dynamics to reproduce several observables for the atomic-atomic and atomic-molecular interactions, is parametrized for nuclear systems to fit low-energy observables. By exploiting the variable phase approach (VPA) to potential scattering, phase parameters, cross-sections and analyzing powers are estimated for the nucleon–nucleon and nucleon–nucleus systems. Our results show good concurrence with the earlier theoretical and experimental data within this simple model of interaction.
References
R.G. Newton. Scattering Theory of Waves and Particles (Springer, 2014) [ISBN: 978-3-642-88130-5].
Z.H. Deng, Y.P. Fan. A potential function of diatomic molecules. J. Shandong Univ. (Natural Sci.) 7, 162 (1957).
A. Del Sol Mesa, C. Quesne, Y.F. Smirnov. Generalized Morse potential: Symmetry and satellite potentials. J. Phys. A: Math. Gen. 31, 321 (1998).
https://doi.org/10.1088/0305-4470/31/1/028
H. Hassanabadi, B. H. Yazarloo, S. Zarrinkamar, 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. Commun. Theor. Phys. 55, 969 (2011).
https://doi.org/10.1088/0253-6102/55/6/05
O.J. Oluwadare, K.J. Oyewumi, O.A. Babalola. Exact s-wave solution of the Klein-Gordon equation with the Deng-Fan molecular potential using the Nikiforov-Uvarov (NU) method. African Rev. Phys. 7, 16 (2012).
B.H. Yazarloo, L. Lu, G. Liu, S. Zarrinkamar, 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, X.Y. Gu. Arbitrary l state solutions of the Schr¨odinger 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, 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, X.-P. Li, 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 к 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
S.H. Dong, J. Garc'ıa-Ravelo. Exact solutions of the swave Schr¨odinger equation with Manning-Rosen potential. Phys. Scr. 75, 307 (2007).
https://doi.org/10.1088/0031-8949/75/3/013
A. Diaf, A. Chouchaoui, R.J. Lombard. Feynman integral treatment of the Bargmann potential. Ann. Phys. (N.Y.) 317, 354 (2005).
https://doi.org/10.1016/j.aop.2004.11.010
W.C. Qiang, K. Li, W.L. Chen. New bound and scattering state solutions of the Manning-Rosen potential with the centrifugal term. J. Phys. A Math. Theor. 42, 205306 (2009).
https://doi.org/10.1088/1751-8113/42/20/205306
X.Y. Gu, S.H. Dong. Energy spectrum of the ManningRosen potential including centrifugal term solved by exact and proper quantization rules. J. Math. Chem. 49, 2053 (2011).
https://doi.org/10.1007/s10910-011-9877-5
M.F. Manning, N. Rosen. A potential function for the vibrations of the diatomic molecules. Phys. Rev. 44, 953 (1933).
L. Hulth'en. On the characteristic solutions of the Schr¨odinger deuteron equation. Ark. Mat. Astron. Fys. A 29B, 1 (1942).
J. Bhoi, U. Laha. Supersymmetry-inspired low-energy α-p elastic scattering phases. Theor. Math. Physics (Russian Fed.) 190, 69 (2017).
https://doi.org/10.1134/S0040577917010056
U. Laha, off-shell jost solution for the Hulth'en potential. Few-Body Syst. 59, 68 (2018).
https://doi.org/10.1007/s00601-018-1380-0
J. Bhoi, U. Laha. Hulth'en potential models for α-α and α-He3 elastic scattering. Pramana - J. Phys. 88, 42 (2017).
https://doi.org/10.1007/s12043-016-1352-1
J. Bhoi, A.K. Behera, U. Laha. Off-shell Jost function for the Hulth'en potential in all partial waves. J. Math. Phys. 60, 083502 (2019).
https://doi.org/10.1063/1.5093115
B. Khirali, A.K. Behera, J. Bhoi, U. Laha. Regular and Jost states for the S-wave Manning-Rosen potential. J. Phys. G Nucl. Part. Phys. 46, 115104 (2019).
https://doi.org/10.1088/1361-6471/ab4118
B. Khirali, A.K. Behera, J. Bhoi, U. Laha. Scattering with Manning-Rosen potential in all partial waves. Ann. Phys. (N.Y.) 412, 168044 (2020).
https://doi.org/10.1016/j.aop.2019.168044
B. Khirali, U. Laha, P. Sahoo. Off-shell solutions and Halfshell T-matrix for the Manning-Rosen potential. Few-Body Syst. 62, 20 (2021).
https://doi.org/10.1007/s00601-021-01603-6
B. Khirali, U. Laha, P. Sahoo. Analytic transition matrix for the Manning-Rosen potential in all partial waves. Chin. J. Phys. 77 (23), 2355 (2022).
https://doi.org/10.1016/j.cjph.2022.04.021
F. Calogero. Variable Phase Approach to Potential Scattering (Academic Press, 1967).
U. Laha, 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, U. Laha. Parameterization of nuclear hulth'en potential for nucleus-nucleus elastic scattering. Commun. Theor. Phys. 69, 203 (2018).
https://doi.org/10.1088/0253-6102/69/2/203
U. Laha, J. Bhoi. Parameterization of the nuclear Hulth'en potentials. Phys. At. Nucl. 79, 62 (2016).
https://doi.org/10.1134/S1063778816010129
A.K. Behera, U. Laha, M. Majumder, J. Bhoi. Energymomentum dependent potentials and np scattering. Research and Reviews: J. Phys. 8, 2265 (2019).
A.K. Behera, J. Bhoi, U. Laha, 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, U. Laha. Nuclear Hulth'en potentials for F and G partial waves. Research & Reviews: J. Phys. 10, 31 (2021).
A.K. Behera, U. Laha, M. Majumder, J. Bhoi. Applicability of phase- equivalent energy-dependent potential. Case Studies. Phys. At. Nucl. 85, 124 (2020).
https://doi.org/10.1134/S1063778822010057
B. Talukdar, D. Chattarji, P. Banerjee. A generalized approach to the phase-amplitude method. J. Phys. G Nucl. Phys. 3, 813 (1977).
https://doi.org/10.1088/0305-4616/3/6/012
G.C. Sett, L. Laha, B. Talukdar. Phase-function method for Coulomb-distorted nuclear scattering. J. Phys. A: Math. Gen. 21, 3643 (1988).
https://doi.org/10.1088/0305-4470/21/18/017
G.N. Watson. A Treatise on the Theory of Bessel Functions (Cambridge University Press, 1922) [ISBN-13:9781330302774].
R. Navarro P'erez, J.E. Amaro, E. Ruiz Arriola. The lowenergy structure of the nucleon-nucleon interaction: Statistical versus systematic uncertainties. J. Phys. G: Nucl. Part. Phys. 43, 114001 (2016).
https://doi.org/10.1088/0954-3899/43/11/114001
D. H¨uber, J. Golak, H. Witala, W. Gl¨ockle, H. Kamada. Phase shifts and mixing parameters for elastic neutrondeuteron scattering above breakup threshold. Few-Body Syst. 19, 175 (1995).
https://doi.org/10.1007/s006010050025
C.L. Bailey, W.E. Bennett, T. Bergstralth, R.G. Nuckolls, H.T. Richards, 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
A.L. Latter, R. Latter. A phase shift analysis of neutrondeuteron scattering. Phys. Rev. 86, 727 (1952).
https://doi.org/10.1103/PhysRev.86.727
F.F. Chen, C.P. Leavitt, 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
R.O. Lane, A.J. Elwyn, A. Langsdorf. Polarization and differential cross section for neutron scattering from silicon. Phys. Rev. 126, 1105 (1962).
https://doi.org/10.1103/PhysRev.126.1105
J.M. Clement, P. Stoler, C.A. Goulding, R.W. Fairchild. Hydrogen and deuterium total neutron cross sections in the MeV region. Nucl. Physics, Sect. A 183, 51 (1972).
https://doi.org/10.1016/0375-9474(72)90930-X
R.A. Arndt, W.J. Briscoe, A.B. Laptev, I.I. Strakovsky, R.L. Workman. Absolute total np and pp cross-section determinations. Nucl. Sci. Eng. 162, 312 (2009).
https://doi.org/10.13182/NSE162-312
P. Schwarz, H.O. Klages, P. Doll, B. Haesner, J. Wilczynski, Z. Zeitnitz, J. Kecskemeti. Elastic neutron-deuteron scattering in the energy range from 2.5 MeV to 30 MeV. Nucl. Phys. A 398, 1 (1983).
https://doi.org/10.1016/0375-9474(83)90645-0
J.E. McAninch, W. Haeberli, H. Wita la, W. Gl¨ockle, J. Golak. Analyzing power in nd elastic scattering at Elab = 3 MeV. Measurement and calculation. Phys. Lett. B 307, 13 (1993).
https://doi.org/10.1016/0370-2693(93)90185-K
J.L. Friar, G.L. Payne, W. Gl¨ockle, D. H¨uber, H. Wita la. Benchmark solutions for n-d breakup amplitudes. Phys. Rev. C 51, 2356 (1995).
https://doi.org/10.1103/PhysRevC.51.2356
A. Kievsky, M. Viviani, S. Rosati. Cross section, polarization observables, and phase-shift parameters in p-d and n-d elastic scattering. Phys. Rev. C 52, 1 (1995).
https://doi.org/10.1103/PhysRevC.52.R15
A. Kievsky, M. Viviani, S. Rosati. n-d scattering above the deuteron breakup threshold. Phys. Rev. C 56, 2987 (1997).
https://doi.org/10.1103/PhysRevC.56.2987
B.H. Daub, V. Henzl, M.A. Kovash. Measurements of the neutron-proton and neutron-carbon total cross section from 150 to 800 keV. Phys. Rev. C - Nucl. Phys. 87, 014005 (2013).
https://doi.org/10.1103/PhysRevC.87.014005
M. Lacombe, B. Loiseau, J.M. Richard, R. Vinh Mau, J. Cˆot'e, P. Pir'es, R. de Tourreil. Parametrization of the Paris N-N potential. Phys. Rev. C 21, 861 (1980).
https://doi.org/10.1103/PhysRevC.21.861
R.A. Arndt, L.D. Roper, R.A. Brayan, R.B. Clark, B.J. VerWest, P. Signell. Nucleon-nucleon partial-wave analysis to 1 GeV. Phys. Rev. D 28, 97 (1983).
https://doi.org/10.1103/PhysRevD.28.97
W. Schwinger, W. Plessas, L.P. Kok, H. Van Haeringen. Separable representation of the nuclear proton proton interaction. Phys. Rev. C 27, 515 (1983).
https://doi.org/10.1103/PhysRevC.27.515
R. Machleidt, K. Holinde, Ch. Elster. The bonn mesonexchange model for the nucleon-nucleon interaction. Phys. Rep. 149, 1 (1987).
https://doi.org/10.1016/S0370-1573(87)80002-9
J. Bystrick'y, C. Lechanoine-LeLuc, F. Lehar. Direct reconstruction of pp elastic scattering amplitudes and phase shift analyses at fixed energies from 1.80 to 2.70 GeV. Eur. Phys. J. C 4, 607 (1987).
https://doi.org/10.1007/s100529800946
V. Mau R, C. Semay, B. Loiseau, M. Lacombe. Nuclear forces and quark degrees of freedom. Phys. Rev. Lett. 67, 1392 (1991).
https://doi.org/10.1103/PhysRevLett.67.1392
F. Gross, J.W. Van Orden, K. Holinde. Relativistic oneboson-exchange model for the nucleon-nucleon interaction. Phys. Rev. C 45, 2094 (1992).
https://doi.org/10.1103/PhysRevC.45.2094
V.G.J. Stoks, R.A.M. Klomp, C. Terheggen, J.J. de Swart. Construction of high-quality NN potential models. Phys. Rev. C 49, 2950 (1994).
https://doi.org/10.1103/PhysRevC.49.2950
R.B. Wiringa, V.G.J. Stoks, R. Schiavilla. Accurate nucleon-nucleon potential with charge-independence breaking. Phys. Rev. C 51, 38 (1995).
https://doi.org/10.1103/PhysRevC.51.38
R. Machleidt. High-precision, charge-dependent Bonn nucleon-nucleon potential. Phys. Rev. C 63, 024001 (2001).
https://doi.org/10.1103/PhysRevC.63.024001
F. Gross, 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
U. Laha, J. Bhoi. Two-nucleon Hulthen-type interactions for few higher partial waves. Pramana-J. Phys. 84, 555 (2015).
https://doi.org/10.1007/s12043-014-0845-z
J.P, Scanlon, G.H. Stafford, J.J. Thresher, A. Langsford. Angular distributions for n-p scattering in the energy range 22.5 to 110 MeV. Nucl. Phys. 41, 401 (1963).
https://doi.org/10.1016/0029-5582(63)90519-4
E.D. Cooper, C.J. Horowitz. Vector analyzing power in elastic electron-nucleus scattering. Phys. Rev. C 72, 034602 (2005).
https://doi.org/10.1103/PhysRevC.72.034602
Wilczynski, J. Hansmeyer, F.P. Brady, P. Doll, W. Heeringa, J.C. Hiebert, H.O. Klages, P. Plischke. Measurements of the neutron-proton analyzing power in the energy range from 17 to 50 MeV. Nucl. Phys. A 425, 458 (1984).
https://doi.org/10.1016/0375-9474(84)90019-8
W. Tornow, C.R. Howell, M. Alohali, Z.P. Chen, P.D. Felsher, J.M. Hanly, R.L. Walter, G. Weisel. The low-energy neutron-deuteron analyzing power and the 3P0,1,2 interactions of nucleon-nucleon potentials. Phys. Letts. B 257, 273 (1991).
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