Analytical Solutions of the Schrödinger Equation with Class of Yukawa Potential for a Quarkonium System Via Series Expansion Method



Abstract Views
1118

Downloads
756

Citations

Share

##plugins.themes.bootstrap3.article.sidebar##

Submitted Nov 4, 2020
Published Dec 5, 2020
10.24018/ejphysics.2020.2.6.26

Abstract viewed = 1118 times

Table of Contents

##plugins.themes.bootstrap3.article.main##

A class of Yukawa potential is adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. The potential was made to be temperature-dependent by replacing the screening parameter with Debye mass. We solved the radial Schrödinger equation analytically using the series expansion method and obtained the energy eigenvalues. The present results are applied for calculating the mass spectra of heavy mesons such as charmonium and bottomonium . Two special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, and Coulomb potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

Keywords: Schrödinger equation, series expansion method, class of Yukawa potential, heavy mesons

References

  1. S.M. Kuchin and N. V. Maksimenko, “Characteristics of charged pions in the quark model with potential which is the sum of the Coulomb and Oscillator potential”, Journal of Theoretical and applied Physics.vol. 40, pp. 45-55, 2013.
     Google Scholar
  2. R. Kumar and F. Chand, “Asymptotic study to the N-dimensional Radial Schrodinder Equation for the quark-antiquark system”, Communication in Theoretical Physics, vol. 59, pp. 456-467, 2013.
     Google Scholar
  3. M. Abu-Shady, T. A. Abdel-Karim and E. M. Khokha, “Exact solution of the N-dimensional Radial Schrödinger Equation via Laplace Transformation method with the Generalized Cornell potential”, Journal of theoretical Physics, vol.45, pp. 567-587, 2018.
     Google Scholar
  4. M. Abu-shady, “Heavy Quarkonia and mesons in the Cornell potential with harmonic oscillator potential in the N- dimensional Schrödinger equation”, International Journal of Applied Mathematics and Theoretical Physics, vol. 2(2), pp, 16-20, 2016.
     Google Scholar
  5. M. N. Sergeenko, “Light and Heavy Mesons in the complex mass scheme”, 2019, https://arxiv.org/abs/1909.10511.
     Google Scholar
  6. B. R. Martin and G. G. Shaw, Particle Physics, The Manchester Physics Series, 2nd edition, 1997, pp. 245-263.
     Google Scholar
  7. D. H. Perkins, Introduction to High Energy Physics, Cambridge University Press, Cambridge, UK, 20 2000, pp. 124-134.
     Google Scholar
  8. D. Griffiths, Introduction to Elementary Particles, JohnWiley & Sons, New York, NY, USA, 1987, pp. 564-589.
     Google Scholar
  9. A. Bettini, Introduction to Elementary Particle Physics, Cambridge University Press, 2018, pp. 143-154.
     Google Scholar
  10. A. N. Ikot, U. S. Okorie, A. T. Ngiagian, C. A. Onate, C. O. Edet, I. O. Akpan and P .O. Amadi, “Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via Asymptotic iteration method”,Ecletica Quimica Journal, vol. 45 (1), pp. 66-76, 2020.
     Google Scholar
  11. T. Das, “D-dimensional Schrödinger equation for a square root potential”, Electronic Journal of Theoretical Physics, vol. 13(3), pp. 117-124, 2016.
     Google Scholar
  12. M. Abu-Shady and A. N. Ikot, “Analytic solution of multi-dimensional Schrödinger equation in hot and dense QCD media using the SUSYQM method”, European Physics Journal, vol. 54 (4), pp. 134-140, 2019.
     Google Scholar
  13. C. O. Edet and P. O. Okoi, “Any l-state solutions of the Schrödinger equation for q-deformed Hulthen plus generalized inverse quadratic Yukawa potential in arbitrary dimensions”, Revista Mexicana Fisica, vol. 65, pp. 333-344, 2019.
     Google Scholar
  14. J. E. Ntibi, E. P. Inyang, E. P. Inyang, and E.S.William, “Relativistic Treatment of D-Dimensional Klien-Gordon equation with Yukawa potential”, International Journal of Innovative Science, Engineering Technology, vol. 11(7), pp. 2348-7968, 2020.
     Google Scholar
  15. C. O. Edet, K. O. Okorie, H. Louis and N. A. Nzeata-Ibe, “Any l-state solutions of the Schrödinger equation interacting with Hellmann-Kratzer potential model”, Indian Journal of Physics, vol. 94(2), pp.241- 251, 2019.
     Google Scholar
  16. C. O. Edet, U. S. Okorie, G. Osobonye, A. N. Ikot, G.J.Rampho and R. Sever, “Thermal properties of Deng-Fan-Eckart potential model using Poisson summation approach”,Journal of Mathematical Chemistry pp.18- 25, 2020.
     Google Scholar
  17. C. O. Edet,U. S. Okorie, A. T. Ngiangia, and A. N. Ikot, “Bound state solutions of the Schrödinger equation for the modified Kratzer plus screened Coulomb potential”, Indian Journal of Physics, vol. 94, pp. 423- 433, 2020.
     Google Scholar
  18. P. O. Okoi, C. O. Edet and T. O. Magu, “Relativistic Treatment of the Hellmann-generalized Morse potential”, Revista Mexicana de Fisica, vol. 66(1), pp.1-13, 2020.
     Google Scholar
  19. C. O. Edet, P. O. Okoi, and S. O. Chima, “Analytic solutions of the Schrödinger equation with non-central generalized inverse quadratic Yukawa potential”, Revista Brasileira de Ensino de Fisica, pp.1-9, 2019.
     Google Scholar
  20. A. N. Ikot, C. O. Edet, P. O. Amadi,U. S. Okorie, G. J. Rampho and H. Y. Abdullah, “Thermodynamic properties of Aharanov-Bohm(AB) AND magnetic fields with screened Kratzer potential”, European Physical Journal D, vol.74(159), pp.1-13, 2020.
     Google Scholar
  21. A. N. Ikot, C. O. Edet, P. O. Amadi, U. S. Okorie, G. J. Rampho and H. Y. Abdullah, “Thermodynamic function for diatomic molecules with modified Kratzer plus screened Coulomb potential”,Indian Journal of Physics, pp.1-11, 2020.
     Google Scholar
  22. C. O. Edet, P. O. Okoi, A. S. Yusuf, P. O. Ushie and P. O. Amadi, “Bound state solutions of the generalized shifted Hulthen potential”, Indian Journal of physics, pp. 1-10, 2020.
     Google Scholar
  23. E. S. William, E. P. Inyang, and E. A. Thompson,”Arbitrary -solutions of the Schrödinger equation interacting with Hulthén-Hellmann potential model”. Revista Mexicana de Fisica, vol.66(6), pp.730-741, Nov. 2020.
     Google Scholar
  24. E. P. Inyang, E. P. Inyang, E. S. William, P. O. Ushie, and G. A. Oteikwu, “Measurement of Electric Field Radiation from 11KVA high tension power line and its environmental effects in Calabar Metropolis,Nigeria”, Physical Science International Journal, pp. 1-6, 2018.
     Google Scholar
  25. E. P. Inyang, E. P. Inyang, and M. B. Latif,”A Correlation: TL response of synthetic fused quartz with 60Co gamma (high dose) source and 90Sr/90Y Beta (low dose) source” Bulletin of Pure and applied Sciences-Physics, vol.38(1), pp.6-12, 2019.
     Google Scholar
  26. C. O. Edet, P. O. Amadi, M. C. Onyeaju, U. S. Okorie, R. Sever, and G.J. Rampho, “Thermal properties and magnetic susceptibility of Hellmann potential in Aharonov-Bohm(AB) Flux and magnetic fields at Zero and Finite temperature”, Journal of Low Temperature Physics, pp.1- 23, 2020.
     Google Scholar
  27. E. P. Inyang, E. S. William and J. A. Obu, “Eigensolutions of the N-dimensional Schrödinger equation interacting with Varshni-Hulthen potential” Revista Mexicana de Fisica.66 (2020) (Accepted).
     Google Scholar
  28. E. E. Ibekwe, T. N. Alalibo, S. O. Uduakobong , A. N. Ikot, and N. Y. Abdullah, “Bound state solution of radial Schrödinger equation for the quark-antiquark interaction potential”, Iran Journal of Science Technology,vol.20, pp. 913,2020.
     Google Scholar
  29. A. Vega and J. Flores, “Heavy quarkonium properties from Cornell potential using variational method and Supersymmetric quantum mechanics”, Pramana-Journal of Physics, vol.56, pp.456-467,2016.
     Google Scholar
  30. H. Ciftci and H. F. Kisoglu, “Schrödinger equation for the Cornell potential by the Asymptotic Iteration method”, Pramana Journal of Physics, vol. 57 pp.458- 467, 2018.
     Google Scholar
  31. M. Abu-Shady, “Analytic solution of Dirac Equation for extended Cornell Potential using the Nikiforov-Uvarov method”, Boson Journal of modern Physics. Vol.55(1), pp.789-799, 2015.
     Google Scholar
  32. A. Al-Jamel and H. Widyan, “Heavy quarkonium mass spectra in a Coulomb field plus Quadratic potential using Nikiforov-Uvarov method” Canadian center of Science and Education.vol.4, pp.18-29, 2012.
     Google Scholar
  33. A. Al-Oun, A. Al-Jamel, and H. Widyan, “Various properties of Heavy Quakonium from Flavor-independent Coulomb plus Quadratic potential. Jordan Journal of Physics, vol.40, pp.453-464, 2015.
     Google Scholar
  34. E. Omuge, O. E. Osafile and M. C. Onyeajh, “Mass spectrum of mesons via WKB Approximation method”, Advance in High Energy. Phys.vol.10, pp.1143-1155, 2020.
     Google Scholar
  35. C. Cari, A, Suparmi, M. Yunianto and B. N. Pratiwi, “Supersymmetric approach for Killingbeck radial potential plus non-central potential in Schrödinger equation”, Journal of physics conference series, pp.769-776, 2016.
     Google Scholar
  36. E. P. Inyang, E. P. Inyang, J. E. Ntibi, E. E. Ibekwe, and E. S. William,”Approximate solutions of D-dimensional Klein-Gordon equation with Yukawa potential via Nikiforov-Uvarov method”, Indian Journal of Physics 20 : 00097R2,Sept.2020.(accepted paper)
     Google Scholar
  37. C. A. Onate and J. O. Ojonubah, “Eigensolutions of the Schrödinger equation with a class of Yukawa potentials via supersymmetric approach”, Journal of Theoretical and Applied Physics, vol.10(1), pp. 21-26, 2016.
     Google Scholar
  38. R. Rani, S. B. Bhardwaj, and F. Chand, “Bound state solutions to the Schrödinger equation for some diatomic molecules”, Pramana Journal of Physics, vol.91, pp. 1602-1615, 2018.
     Google Scholar
  39. E. P. Inyang, E. P.Inyang, E. S.William, and E. E. Ibekwe, “Study on the applicability of Varshni potential to predict the mass-spectra of the Quark-antiquark systems in a non-relativistic framework”, Jordan Journal of Physics, 14-11-10-020 (2020)(Accepted).
     Google Scholar
  40. M. Abu-Shady, “N-dimensional Schrödinger equation at finite temperature using the Nikiforov-Uvarov method”, Journal of the Egyptian mathematical society, vol.23, pp. 1-4, 2016.
     Google Scholar
  41. R. M. Barnett, C. D. Carone, D. E. Groom, T. G. Trippe, and C. G. Wohl, “Particle Data Group” Physics Review D vol.92, pp. 654-656, 2012.
     Google Scholar
  42. M. Tanabashi, C. D. Carone, T. G. Trippe, and C. G. Wohl, “Particle Data Group”, Physics Review D vol.98, pp. 546-548, 2018.
     Google Scholar