APPLICABILITY OF HULTHÉN-HELLMANN POTENTIAL TO PREDICT THE MASS-SPECTRA OF HEAVY MESONS VIA SERIES EXPANSION METHOD

Authors

Keywords:

Hulthén potential, Hellmann potential, Heavy mesons, Series expansion method

Abstract

Hulthén plus Hellmann potential was adopted as the quark-antiquark interaction potential for predicting the mass
spectra of heavy mesons. The adopted potential was made to be temperature-dependent by replacing the screening
parameter with Debye mass  ( ) D m T . The radial Schrödinger equation was analytically solved using the series
expansion method and energy eigenvalues were obtained. The energy eigenvalues was used to predict the mass
spectra of heavy mesons such as charmonium(cc) and bottomonium(bb) . Four special cases were considered
when some of the potential parameters were set to zero, resulting in Hellmann potential, Yukawa potential,
Coulomb potential, and Hulthén potential, respectively. The present potential provides satisfying results in
comparison with experimental data and work of other researchers with a maximum error of 0.034 GeV.

Dimensions

Abu-Shady, M. & Khokha, E. M. (2018).Heavy-Light mesons in the non-relativistic Quark model using Laplace Transformation method with the Generalized Cornell potential. Advances in high energy Physics. 12, pp. 331-345.

Abu-Shady, M. (2016).N-dimensional Schrödinger equation at finite temperature using the Nikiforov-Uvarov method Journal of Egyptian Mathematical Society 23, pp. 1-4.

Abu-Shady, M., Abdel-Karim, T.A. &Khokha, E. M. (2018).Exact solution of the N-dimensional Radial Schrödinger Equation via Laplace Transformation method with the Generalized Cornell potential, Journal of Quantum Physics, 45, pp. 577-587.

Abu-Shady, M., Abdel-Karim, T.A. & Ezz-Alarab, Y. (2019). Masses and thermodynamic properties of heavy mesons in the non-relativistic quark model using the Nikiforov-Uvarov method. Journal of Egyptian Mathematical Society. 27, pp. 137-145.

Abu-Shady, M. &Ikot, A.N. (2019).Analytic solution of multi-dimensional Schrödinger equation in hot and dense QCD media using the SUSYQM method, The European Physical Journal Plus, 134.

Akpan, I.O., Inyang, E.P., Inyang, E.P. & William, E.S. (2021).Approximate solutions of the Schrödinger equation with Hulthen-Hellmann Potentials for a Quarkonium system. Revista Mexicana de Fisica 67(3), pp. 483-490.

Ali, M.S., Hassan, G.S., Abdelmonem, A.M., Elshamndy, S.K., Elmasry, F. & Yasser, A.M. (2020). The spectrum of charmed quarkonium in

non-relativistic quark model using matrix Numerov’s method. Journal of Radiation Research and Applied Sciences, 13, pp. 224-233.

Al-Jamel, A. (2019). The search for fractional order in heavy quarkonia spectra. International Journal of Modern Physics, 34, pp. 234-242.

Allosh, M., Mustafa, Y., Ahmed, N.K. & Mustafa, A.S. (2021). Ground and Excited state mass spectra and properties of heavy-light mesons. Few-Body System, 62, pp. 13-26.

Ciftci, H. &Kisoglu, H.F. (2018). Non-relativistic Arbitary l -states of Quarkonium through Asymptotic interation method, Pramana Journal of Physics, 56, pp. 455-467.

Hellmann, H. (1935). A New Approximation Method in the Problem of Many Electrons, Journal of Chemical Physics, 3, pp. 50-61.

Hulthen, L. (1942). Über die eigenlosunger der Schrodinger-Gleichung des deuterons, Ark. Mat. Astron. Fys. A28, pp. 1-5.

Ibekwe, E.E., Okorie, U.S., Emah, J.B., Inyang, E.P. &Ekong, S.A. (2021). Mass spectrum of heavy quarkonium for screened Kratzer potential (SKP) using series expansion method. European Physical Journal Plus, 87, pp. 136-147.

Inyang, E.P., Inyang, E. P., William, E. S. & Ibekwe, E. E. (2021). 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(4), pp. 337-345.

Inyang, E.P., Inyang, E.P., Ntibi, J.E. & William, E.S. (2021).Analytical solutions of Schrodinger equation with Kratzer-screened Coulomb potential for a Quarkonium system. Bulletin of Pure and Applied Sciences, 40(D). pp. 14-24.

Inyang, E.P., Inyang, E.P., Ntibi, J.E., Ibekwe, E.E. & William, E.S. (2021).Approximate solutions of D dimensional Klein-Gordon equation with Yukawa potential via Nikiforov-Uvarov method. Indian Journal of Physics, 23, pp. 1-7.

Inyang, E.P., Ibekwe, E.E., William E.S. & Akpan, I.O. (2021). Thermodynamic properties and mass spectra of a quarkonium system with Ultra Generalized Exponential-Hyperbolic potential, Communication in Physical Science, 7, pp. 97-114.

Inyang, E.P., Inyang, E.P., Akpan, I.O., Ntibi, J.E., & William, E.S. (2021). Masses and thermodynamic properties of a Quarkonium system, Canadian Journal Physics, 99, pp 976-990.

Khokha, E.M., Abushady, M., & Abdel-Karim, T.A. (2016). Quarkonium masses in the N-dimensional space using the Analytical Exact Iteration method, International Journal of heoretical and Applied. Mathematics,2, pp. 76-86.

Olive, R., Groom, D. E. & Trippe, T. G. (2014). Particle Data Group. Chinine Physics. C,38(9).

Omugbe, E. O., O.E. Inyang, E.P. & Jahanshir, A.(2022). Bound state solutions of the hyper-radial Klein-Gordon equation under the Deng-Fan poten-tial by WKB and SWKB methods. Physicacripta , 96(12), pp. 125-136.

Oyewumi, K .J. & Oluwadare, O.J. (2016). The scattering phase shifts of the Hulthen-type potential plus Yukawa potential, European Physical Journal Plus,131, pp. 280-295.

Rani, S.B. Bhardwaj, & Chand, F. (2018).Bound state solutions to the Schrodinger equation for some diatomic molecules. Pramana-Journal of Physical, 91, pp. 1-8.

Tanabashi, M., Carone C. D., Trippe, T. G. &Wohl, C. G. (2018). Particle Data Group. Physical Review D, 98, pp. 546-548.

William, E.S., Inyang, E.P. &Thompson, E.A. (2020). Arbitrary -solutions of the Schrödinger equation interacting with Hulthén-Hellmann potential model. Revista Mexicana de Fisica.66 (6), pp. 730-741.

Published

2021-11-30

How to Cite

Inyang, E. P., Ntibi, J. E., Ayedun, F., Ibanga, E. A., & William, E. S. (2021). APPLICABILITY OF HULTHÉN-HELLMANN POTENTIAL TO PREDICT THE MASS-SPECTRA OF HEAVY MESONS VIA SERIES EXPANSION METHOD. Nigerian Journal of Physics, 30(2), 140-145. https://njp.nipngr.org/index.php/njp/article/view/105

Issue

Vol. 30 No. 2 (2021): Nigerian Journal of Physics - Vol. 30 No. 2

Section

Articles
Copyright & Licensing

How to Cite

Inyang, E. P., Ntibi, J. E., Ayedun, F., Ibanga, E. A., & William, E. S. (2021). APPLICABILITY OF HULTHÉN-HELLMANN POTENTIAL TO PREDICT THE MASS-SPECTRA OF HEAVY MESONS VIA SERIES EXPANSION METHOD. Nigerian Journal of Physics, 30(2), 140-145. https://njp.nipngr.org/index.php/njp/article/view/105