Numerical phase shift analysis of nucleon-nucleon systems with Hellmann plus spin dependence
DOI:
https://doi.org/10.31349/RevMexFis.71.031202Keywords:
Phase function method, Hellmann plus spin-orbit interaction, scattering phase shifts, nucleon–nucleon systemsAbstract
The scattering phase shifts for quantum mechanical potential scattering by local interaction can be computed without solving the Schrödinger equation. This can be done by numerically solving the phase equation from the origin to the asymptotic region. Phase Function Method (PFM) is regarded as a resourceful method for calculating scattering phase shifts in quantum mechanics. We utilize the PFM to handle the Hellmann plus spin-orbit interaction. Our approach uses a five-parameter potential model to compute the scattering phase shift. Our results for nucleon-nucleon systems closely match previous findings.
References
M. G. Mayer, On closed shells in nuclei, Physical Review 74 (1948) 235, https://doi.org/10.1103/PhysRev.74.235
O. Haxel, J. H. D. Jensen, and H. E. Suess, On the “magic numbers” in nuclear structure, Physical Review 75 (1949) 1766, https://doi.org/10.1103/PhysRev.75.1766.2
K. S. Krane, Introductory nuclear physics (John-Wiley & Sons, 1991)
H. Hong-Xia et al., Influence of Spin-Orbit Force on NucleonNucleon Scattering in the Quark Delocalization Colour Screening Model, Chinese Physics Letters 25 (2008) 1617, https://doi.org/10.1088/0256-307X/25/5/026
N. Kaiser, Nuclear spin-orbit interaction from chiral pionnucleon dynamics, Nuclear Physics A 709 (2002) 251, https://doi.org/10.1016/S0375-9474(02)01044-8
M. Sajedi and Z. Kargar, Shifted Deng-Fan potential and cluster structure in 19Ne, Nuclear Physics A 1015 (2021) 122314, https://doi.org/10.1016/j.nuclphysa.2021.122314
L. Kumar, A. Khachi, and O. Sastri, Phase Shift Analysis for Neutron-Alpha Elastic Scattering Using Phase Function Method with Local Gaussian Potential, Journal of Nuclear Physics, Material Sciences, Radiation and Applications 9 (2022) 215, https://doi.org/10.15415/jnp.2022.92032
F. Brieva and J. Rook, Nucleon-nucleus optical model potential:(III). The spin-orbit component, Nuclear Physics A 297 (1978) 206, https://doi.org/10.1016/0375-9474(78)90272-5
P. Signell and R. E. Marshak, Semiphenomenological twonucleon potential, Physical Review 109 (1958) 1229, https://doi.org/10.1103/PhysRev.109.1229
J. Gammel and R. Thaler, Spin-orbit coupling in the protonproton interaction, Physical Review 107 (1957) 291, https://doi.org/10.1103/PhysRev.107.291
H. Hellmann, A combined approximation procedure for calculation of energies in the problem of many electrons, Acta Physicochim URSS 1 (1935) 913
H. Hellmann, A new approximation method in the problem of many electrons, The Journal of Chemical Physics 3 (1935) 61, https://doi.org/10.1063/1.1749559
H. Hellmann and W. Kassatotschkin, Metallic binding according to the combined approximation procedure, The Journal of Chemical Physics 4 (1936) 324, https://doi.org/10.1063/1.1749851
G. Koc¸ak, O. Bayrak, and I. Boztosun, Arbitrary -state solution of the Hellmann potential, Journal of Theoretical and Computational Chemistry 6 (2007) 893, https://doi.org/10.1142/S0219633607003313
A. K. Roy, A. F. Jalbout, and E. I. Proynov, Accurate calculation of the bound states of Hellmann potential, Journal of mathematical chemistry 44 (2008) 260, https://doi.org/10.1007/s10910-007-9308-9
J. Adamowski, Bound eigenstates for the superposition of the Coulomb and the Yukawa potentials, Physical Review A 31 (1985) 43, https://doi.org/10.1103/PhysRevA.31.43
S. M. Ikhdair and R. Sever, A perturbative treatment for the bound states of the Hellmann potential, Journal of Molecular Structure: THEOCHEM 809 (2007) 103, https://doi.org/10.1016/j.theochem.2007.01.019
E. William, E. Inyang, and E. Thompson, Arbitrary l-solutions of the Schrödinger equation interacting with Hulthen-Hellmann potential model, Rev. Mex. Fis 66 (2020) 730, https://doi.org/10.24018/ejphysics.2021.3.3.83
C. Edet et al., Any l-state solutions of the Schrodinger equation interacting with Hellmann-Kratzer potential model, Indian Journal of Physics 94 (2020) 243, https://doi.org/10.1007/s12648-019-01467-x
C. Onate et al., Eigen solutions and entropic system for Hellmann potential in the presence of the Schrödinger equation, The European Physical Journal Plus 132 (2017) 1, https://doi.org/10.1140/epjp/i2017-11729-8
R. L. Hall and Q. D. Katatbeh, Spectral bounds for the Hellmann potential, Physics Letters A 287 (2001) 183, https://doi.org/10.1016/S0375-9601(01)00497-2
A. Arda and R. Sever, Pseudospin and spin symmetric solutions of the Dirac equation: Hellmann potential, Wei-Hua potential, Varshni potential, Zeitschrift für Naturforschung A 69 (2014) 163, https://doi.org/10.5560/ZNA.2014-0007
P. Okoi, C. Edet, and T. Magu, Relativistic treatment of the Hellmann-generalized Morse potential, Rev. Mex. Fis 66 (2020) 1, https://doi.org/10.31349/revmexfis.66.1
S. Hassanababdi et al., Approximate solution of scattering states of the spinless Salpeter equation with the Yukawa potential, Chinese journal of physics 52 (2014) 1194, https://doi.org/10.6122/CJP.52.1194
J. Das and S. Chakraborty, Atomic inner-shell ionization, Physical Review A 32 (1985) 176, https://doi.org/10.1103/physreva.32.176
J. Callaway and P. Laghos, Application of the pseudopotential method to atomic scattering, Physical Review 187 (1969) 192, https://doi.org/10.1103/PhysRev.187.192
A. J. Hughes and J. Callaway, Energy Bands in Body-Centered and Hexagonal Sodium, Physical Review 136 (1964) A1390, https://doi.org/10.1103/PhysRev.136.A1390
Y. P. Varshni and R. C. Shukla, Alkali hydride molecules: Potential energy curves and the nature of their binding, Reviews of Modern Physics 35 (1963) 130, https://doi.org/10.1103/RevModPhys.35.130
F. Calogero, Variable Phase Approach to Potential Scattering, vol. 35 (Elsevier, 1967)
B. Khirali et al., Phase function metod for elastic nucleonnucleon scattering using Hellmann plus Coulomb potential, Rev. Mex. Fis 69 (2023) 061201, https://doi.org/10.31349/RevMexFis.69.061201
P. Sahoo et al., Nuclear Hulthén potentials for F and G Partial waves, Research and Reviews: Journal of Physics 10 (2021) 31, https://doi.org/10.37591/RRJoPHY
A. Behera et al., Study of nucleon-nucleon and alphanucleon elastic scattering by the Manning-Rosen potential, Communications in Theoretical Physics 72 (2020) 075301, https://doi.org/10.1088/1572-9494/ab8a1a
G. N. Watson, A treatise on the theory of Bessel functions, vol. 3 (The University Press, 1922)
R. N. Pérez, J. Amaro, and E. R. Arriola, The low-energy structure of the nucleon-nucleon interaction: statistical versus systematic uncertainties, Journal of Physics G: Nuclear and Particle Physics 43 (2016) 114001, https://doi.org/10.1088/0954-3899/43/11/114001
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 B. Khirali, B. Swain, S. Laha, D. Naik, U. Laha

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.