An exact treatment of localization of electromagnetic plus separable potential

Authors

  • A. K. Behera National Institute of Technology Jamshedpur, India
  • B. Swain National Institute of Technology Jamshedpur, India
  • U. Laha National Institute of Technology Jamshedpur, India
  • J. Bhoi Veer Surendra Sai University of Technology Burla, India

DOI:

https://doi.org/10.31349/RevMexFis.70.051201

Keywords:

Hulthén plus Yamaguchi potential, Phase equivalent potential, Phase parameters, (p-p) and (p-d) systems

Abstract

Equivalent local potential with energy-momentum dependence is developed for the combined interaction of Hulthén modified Yamaguchi potential by developing its exact Jost solution. The generated local potentials are applied to compute scattering phase parameters for (p-p) and (p-d) systems through the phase function method (PFM). The same are also calculated for the nonlocal potential from the expression of the Fredholm determinant. Our obtained data for both the energy-momentum dependent local and the pure nonlocal interactions are in reasonable agreement with the standard data. Reasonable correspondence between the results for the phase equivalent and the nonlocal potentials indicate that our equivalent local analysis is in proper order.

References

P. B. Abraham and H. E. Moses, Changes in potentials due to changes in the point spectrum: Anharmonic oscillators with exact solutions, Phys. Rev. A 22 (1980) 1333, https://doi.org/10.1103/PhysRevA.22.1333

D. L. Pursey, Isometric operators, isospectral Hamiltonians, and supersymmetric quantum mechanics, Phys. Rev. D 33 (1986) 2267, https://doi.org/10.1103/PhysRevD.33.2267

D. Baye, Supersymmetry between deep and shallow nucleusnucleus potentials, Phys. Rev. Lett. 58 (1987) 2738, https://doi.org/10.1103/PhysRevLett.58.2738

R. D. Amado, Phase-equivalent supersymmetric quantummechanical partners of the Coulomb potential, Phys. Rev. A 37 (1988) 2277, https://doi.org/10.1103/PhysRevA.37.2277

A. Khare and U. J. Sukhatme, Phase-equivalent potentials obtained from supersymmetry, J. Phys. A: Math. Gen. 22 (1989) 2847, https://doi.org/10.1088/0305-4470/22/14/031

B. Talukdar, U. Das, C. Bhattacharyya and P. K. Bera, Phaseequivalent potentials from supersymmetric quantum mechanics, J. Phys. A: Math. Gen. 25 (1992) 4073, https://doi.org/10.1088/0305-4470/25/14/021

J. M. Sparenberg and D. Baye, Supersymmetry between Phase-Equivalent Coupled-Channel Potentials, Phys Rev Lett. 79 (1997) 3802, https://doi.org/10.1103/PhysRevLett.79.3802

M. Majumder and U. Laha, Phase-equivalent potentials using SUSY transformations, Pramana-J. Phys. 96, (2022) 145 https://doi.org/10.1007/s12043-022-02390-3

M. Coz, L. D. Arnold and A. D. MacKellar, Nonlocal potentials and their local equivalents, Ann. Phys. (N.Y) 59 (1970) 219, https://doi.org/10.1016/0003-4916(70)90401-X

L. G. Arnold and A. D. MacKellar, Study of Equivalent Local Potentials Obtained from Separable Two-Nucleon Interactions, Phys. Rev. C 3 (1971) 1095, https://link.aps.org/doi/10.1103/PhysRevC.3.1095

J. P. McTavish, Separable potentials and their momentumenergy dependence, J. Phys. G: Nucl. Phys. 8 (1982) 1037, https://doi.org/10.1088/0305-4616/8/8/010

B. Talukdar, G. C. Sett and S. R. Bhattaru, On the localisation of separable non-local potentials, J. Phys. G: Nucl. Phys. 11 (1985) 591, https://doi.org/10.1088/0305-4616/11/5/006

G. C. Sett, U. Laha and B. Talukdar, Equivalent potentials for a nonsymmetric non-local interaction, PramanaJ Phys. 28 (1987) 325, https://doi.org/10.1007/BF02847093

A. K. Behera and U. Laha, Phase equivalent Coulomb-like potential, Pramana J. Phys. 95 (2021) 103, https://doi.org/10.1007/s12043-021-02141-w

A. K. Behera, U. Laha and J. Bhoi, Generating velocitydependent potential in all partial waves, Turk. J Phys. 44 (2020) 229, https://doi.org/10.3906/fiz-1909-16

A. K. Behera, B. Khirali, U. Laha and J. Bhoi, Construction of an equivalent energy-dependent potential by a Taylor series expansion, Theor. Math. Phys. 205 (2020) 1353, https://doi.org/10.1134/S0040577920100086

A. K. Behera, U. Laha, M. Majumder and J. Bhoi, Applicability of Phase-Equivalent Energy-Dependent Potential. Case Studies, Phys. Atom Nuclei. 85 (2022) 124, https://doi.org/10.1134/S1063778822010057

M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964).

M. Gell-Mann and M. L. Goldberger, The Formal Theory of Scattering, Phys. Rev. 91 (1953) 398, https://doi.org/10.1103/PhysRev.91.398

L. Hulthen, On the characteristic solutions of the Schrödinger deuteron equation, Ark. Mat. Astron. Fys. A. 28 (1942) 5

Y. Yamaguchi, Two-Nucleon Problem When the Potential Is Nonlocal but Separable. I, Phys. Rev. 95 (1954) 1628, https://doi.org/10.1103/PhysRev.95.1628

R. G. Newton, Scattering Theory of Waves and particles, 2nd. ed. (Springer- Verlag, New York, 1982)

J. R. Taylor, Scattering theory: The quantum theory of nonrelativistic collisions, (John Wiley & Sons, New York, 1972)

U. Laha, C. Bhattacharyya, K. Roy and B. Talukdar, Hamiltonian hierarchy and the Hulthen potential, ´ Phys. Rev. C 38 (1988) 558, https://doi.org/10.1103/PhysRevC.38.558

A. Erdeyli, Higher Transcendental Functions, Vol. 1 (McGrawHill, New York, 1953)

L. J. Slater, Generalized Hypergeometric Functions, (Cambridge University Press, London, 1966)

W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics, (Chelsea, New York, 1949)

A. W. Babister, Transcendental Functions satisfying Nonhomogeneous Linear Differential Equations, (The MacMillan Company, New York, 1967)

W. N. Bailey, Generalised hypergeometric series, (Cambridge University Press, London, 1935)

F. Calogero, Variable Phase Approach to Potential Scattering, (Academic, New York, 1967)

A. K. Behera, P. Sahoo, B. Khirali and U. Laha, Fredholm determinants for the Hulthen-distorted separable potential, Pramana J. Phys. 95 (2021) 100, https://doi.org/10.1007/s12043-021-02119-8

R. A. Arndt, L. D. Roper, R. A. Bryan, R. B. Clark, B. J. VerWest and P. Signell, Nucleon-nucleon partial-wave analysis to 1 GeV, Phys. Rev. D 28 (1983) 97, https://doi.org/10.1103/PhysRevD.28.97

F. Gross and A. Stadler, Covariant spectator theory of scattering: Phase shifts obtained from precision fits to data below 350 MeV, Phys. Rev. C 78 (2008) 014005, https://doi.org/10.1103/PhysRevC.78.014005

H. van Haeringen, Scattering length and effective range in closed form for the Coulomb plus Yamaguchi potential, Nucl. Phys. A 253 (1975) 355, https://doi.org/10.1016/0375-9474(75)90486-8

E. Huttel, W. Arnold, H. Baumgart, H. Berg and G. Clausnitzer, Phase-shift analysis of pd elastic scattering below breakup threshold, Nucl. Phys. A 406 (1983) 443, https://doi.org/10.1016/0375-9474(83)90369-X

S. Ishikawa, Low-energy proton-deuteron scattering with a Coulomb-modified Faddeev equation, Few-Body Systems 32 (2003) 229, https://doi.org/10.1007/s00601-003-0001-7

Downloads

Published

2024-09-01

How to Cite

[1]
A. K. BEHERA, B. Swain, U. Laha, and J. Bhoi, “An exact treatment of localization of electromagnetic plus separable potential”, Rev. Mex. Fís., vol. 70, no. 5 Sep-Oct, pp. 051201 1–, Sep. 2024.