APPLIED JOURNAL OF PHYSICAL SCIENCE
Integrity Research Journals

ISSN: 2756-6684
Model: Open Access/Peer Reviewed
DOI: 10.31248/AJPS
Start Year: 2018
Email: ajps@integrityresjournals.org


Applicability of Varshni potential to predict the mass spectra of heavy mesons and its thermodynamic properties

https://doi.org/10.31248/AJPS2021.057   |   Article Number: 7CDCA96D1   |   Vol.3 (3) - September 2021

Received Date: 21 August 2021   |   Accepted Date: 15 September 2021  |   Published Date: 30 September 2021

Authors:  E. P. Inyang* , J. E. Ntibi , E. P. Inyang , F. Ayedun , E. A. Ibanga , E. E. Ibekwe and E. S. William

Keywords: Heavy quarkonia, Nikiforov-Uvarov method, Schrödinger equation, thermodynamic properties, Varshni potential.

In this present study, the radial Schrödinger equation is solved analytically with Varshni potential model using the Nikiforov-Uvarov method. The energy equation and corresponding wave function were obtained. The analytical energy expression was used to predict the mass spectra of heavy quarkonia such as charmonium and bottomonium. Also, the thermodynamic properties such as free energy, mean energy, entropy, and specific heat were obtained. The results obtained with the present model agree excellently with experimental data and the work of other researchers with a maximum error of 0.0055 GeV.

Abu-Shady, M. (2015). Analytic solution of Dirac equation for extended Cornell potential using the Nikiforov-Uvarov method. Boson Journal of modern Physics, 55, Article Number 789.
 
Abu-Shady, M. (2017). N-dimensional Schrödinger equation at finite temperature using the Nikiforov-Uvarov method. Journal of the Egyptian mathematical society, 25(1), 86-89.
Crossref
 
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(7), 321.
Crossref
 
Abu-Shady, M., Abdel-Karim, T. A., & Ezz-Alarab, S. Y. (2019). Masses and thermodynamic properties of heavy mesons in the non-relativistic quark model using the Nikiforov-Uvarov method. Journal of the Egyptian Mathematical Society, 27, Article Number 145.
Crossref
 
Akpan, I. O., Inyang, E. P., & William, E. S. (2021). Approximate solutions of the Schrodinger equation with Hulthen-Hellmann Potentials for a Quarkonium system. Revista Mexicana Fisica 67(3), Article Number 490.
Crossref
 
Ali, S. M., 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(1), 226-233.
Crossref
 
Al-Oun, A., Al-Jamel, A., & Widyan, H. (2015). Various properties of heavy Quakonium from Flavor-independent coulomb plus quadratic potential. Jordan Journal of Physics, 40, Article Number 453.
 
Anisiu, M. C. (2015). Yukawa: The man and the potential. Didactica Mathematica, 33, 1.
 
Barnett, R. M., Carone,C.D., Groom, D. E., Trippe, T. G., & Wohl, C. G. (2012). Particle data group. Physics Review D 92, pp. 654-656.
 
Ciftci, H., & Kisoglu, H. F. (2018). Non-relativistic arbitary -states of Quarkonium through asymptotic interation method. Advances in High Energy Physics, Volume 2018, Article ID 4549705, 7 pages.
Crossref
 
Edet, C. O., & Okoi, P. O. (2019). Any l-state solutions of the Schrödinger equation for q-deformed Hulthen plus generalized inverse quadratic Yukawa potential in arbitrary dimensions. Revista Mexicana de Física, 65(4), 333-344.
Crossref
 
Ekpo, C. M., Inyang, E. P., Okoi, P. O., Magu, T. O., Agbo, E. P., Okorie, K. O., & Inyang, E. P. (2020). New generalized morse-like potential for studying the atomic interaction in diatomic molecules. arXiv preprint arXiv:2012.02581.
 
Florkowski, W., Broniowski, W., & Bożek, P. (2004). Production of resonances in a thermal model: invariant-mass spectra and balance functions. Journal of Physics G: Nuclear and Particle Physics, 30(8), S1321.
Crossref
 
Ibekwe, E. E., Ngiangia, A. T., Okorie, U. S., Ikot, A. N., & Abdullah, H. Y. (2020). Bound state solution of Radial Schrodinger equation for the quark-antiquark interaction potential. Iranian Journal of Science and Technology, Transactions A: Science, 44(4), 1191-1204.
Crossref
 
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. The European Physical Journal Plus, 136(1), 1-11.
Crossref
 
Ikot, A. N., Azogor, W., Okorie, U. S., Bazuaye, F. E., Onjeaju, M. C., Onate, C. A., & Chukwuocha, E. O. (2019). Exact and Poisson summation thermodynamic properties for diatomic molecules with shifted Tietz potential. Indian Journal of Physics, 93(9), 1171-1179.
Crossref
 
Ikot, A. N., Chukwuocha, E. O., Onyeaju, M. C., Onate, C. A., Ita, B. I., & Udoh, M. E. (2018). Thermodynamics properties of diatomic molecules with general molecular potential. Pramana, 90, Article number 22
Crossref
 
Ikot, A. N., Lutfuoglu, B. C., Ngwueke, M. I., Udoh, M. E., Zare, S., & Hassanabadi, H. (2016). Klein-Gordon equation particles in exponential-type molecule potentials and their thermodynamic properties in D dimensions. The European Physical Journal Plus, 131, Article Number 419.
Crossref
 
Inyang, E. P., Akpan, I. O., Ntibi, J. E., & William, E. S. (2020a). Analytical solutions of the Schrödinger equation with class of Yukawa potential for a Quarkonium system via series expansion method. European Journal of Applied Physics, 2(6), 1-6.
Crossref
 
Inyang, E. P., Ibanga, E. A., Aiyedun, F., Ntibi, J. E., and William, E. S. (2021c). Non-relativistic study of generalized Yukawa potential to predict the mass-spectra of heavy quarkonium system. Journal of the Nigerian Association of Mathematical Physics, 60, 14.
 
Inyang, E. P., Inyang, E. P., Akpan, I. O., Ntibi, J. E., & William, E. S. (2021h). Masses and Thermodynamic Properties of a Quarkonium System. Canadian Journal of Physics, (ja).
Crossref
 
Inyang, E. P., Inyang, E. P., Ntibi, J. E., & William, E. S. (2021b). Analytical solutions of Schrodinger equation with Kratzer- screened Coulomb potential for a Quarkonium system. Bulletin of Pure and Applied Sciences, 40, Article Number 24.
Crossref
 
Inyang, E. P., Inyang, E. P., Ntibi, J. E., Ibekwe, E. E., & William, E. S. (2021a). Approximate solutions of D-dimensional Klein-Gordon equation with Yukawa potential via Nikiforov-Uvarov method. Indian Journal of Physics, 1-7.
Crossref
 
Inyang, E. P., Inyang, E. P., William, E. S., Ibekwe, E. E., & Akpan, I. O. (2020c). Analytical investigation of Meson spectrum via exact quantization rule approach. arXiv preprint arXiv:2012.10639.
 
Inyang, E. P., Ita, B. I., & Inyang, E. P. (2021g). Relativistic treatment of quantum mechanical gravitational-harmonic oscillator potential. European Journal of Applied Physics, 3(3), 42-47.
Crossref
 
Inyang, E. P., Ntibi, J. E., Ibanga, E. A., Ayedun, F., Inyang, E. P., Ibekwe, E. E., William, E. S., & Akpan, I. O. (2021e). Thermodynamic properties and mass spectra of a quarkonium system with Ultra Generalized Exponential-Hyperbolic Potential. Communication in Physical Sciences, 7(2), Article Number 114.
Crossref
 
Inyang, E. P., Inyang, E. P., Ntibi, J. E., Ibekwe, E. E., & William, E. S. (2021i). Analytical study on the Applicability of Ultra Generalized Exponential Hyperbolic Potential to Predict the Mass Spectra of the Heavy Mesons. arXiv preprint arXiv:2101.06389.
 
Inyang, E. P., Ntibi, J. E., Inyang, E. P., William, E. S., & Ekechukwu, C. C. (2020b). Any l-state solutions of the Schrödinger equation interacting with class of Yukawa-Eckart potentials. International Journal of Innovative & Engineering Technology, 7(11), 1-52.
 
Inyang, E. P., William, E. S., & Obu, J. A. (2021d). Eigensolutions of the N-dimensional Schr\" odinger equation interacting with Varshni-Hulth\'en potential model. Revista Mexicana Fisica, 67(2), Article Number 193.
Crossref
 
Inyang, E. P., William, E. S., Obu, J. A., Ita, B. I., Inyang, E. P., & Akpan, I. O. (2021f). Energy spectra and expectation values of selected diatomic molecules through the solutions of Klein-Gordon equation with Eckart-Hellmann potential model. Molecular Physics, e1956615.
Crossref
 
Jia, C. S., Zhang, L. H., & Wang, C. W. (2017). Thermodynamic properties for the lithium dimer. Chemical Physics Letters, 667, 211-215.
Crossref
 
Lim, T. C., & Udyavara, R. A. (2009). Relations between Varshni and Morse potential energy parameters. Central European Journal of Physics, 7, 193-197.
Crossref
 
Lütfüoğlu, B. C. (2018). Surface interaction effects to a Klein-Gordon particle embedded in a Woods-Saxon potential well in terms of thermodynamic functions. Canadian Journal of Physics, 96(7), 843-850.
Crossref
 
Mansour, H., & Gamal, A. (2018). Bound state of heavy quarks using a general polynomial potential. Advances in High Energy Physics, Volume 2018, Article ID 7269657.
Crossref
 
Mocsy, A. (2009). Potential models for quarkonia. The European Physical Journal C, 61(4), 705-710.
Crossref
 
Modarres, M., & Mohamadnejad, A. (2013). The thermodynamic properties of weakly interacting quark-gluon plasma via the one-gluon exchange interaction. Physics of Particles and Nuclei Letters, 10(2), 99-104.
Crossref
 
Mutuk, H. (2018). Mass spectra and decay constants of heavy-light mesons: A case study of QCD sum Rules and Quark model. Advances in High Energy Physics, 20, Article Number 5653.
Crossref
 
Nikiforov, A. F., & Uvarov, V. B. (1988). Special functions of mathematical physics (Vol. 205). Basel: Birkhäuser.
Crossref
 
Ntibi, J. E., Inyang, E. P., Inyang, E. P., & William, E. S. (2020). Relativistic Treatment of D-Dimensional Klien-Gordon equation with Yukawa potential. International Journal of Innovative Science, Engineering Technology, 11(7), 2348-7968.
 
Nwabuzor, P., Edet, C., Ndem Ikot, A., Okorie, U., Ramantswana, M., Horchani, R., ... & Rampho, G. (2021). Analyzing the Effects of Topological Defect (TD) on the Energy Spectra and Thermal Properties of LiH, TiC and I2 Diatomic Molecules. Entropy, 23(8), Article Number 1060.
Crossref
 
Obu, J. A., William, E. S., Akpan, I. O., Thompson, E. A., & Inyang, E. P. (2020). Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of 56Ni and 116Sn. European Journal of Applied Physics, 2(6), 1-6.
Crossref
 
Okoi, P. O., Edet, C. O., & Magu, T. O. (2020). Relativistic treatment of the Hellmann-generalized Morse potential. Revista mexicana de física, 66(1), 1-13.
Crossref
 
Okorie, U. S., Ibekwe, E. E., Ikot, A. N., Onyeaju, M. C., & Chukwuocha, E. O. (2018). Thermodynamic properties of the modified Yukawa potential. Journal of the Korean Physical Society, 73(9), 1211-1218.
Crossref
 
Oluwadare, O. J., & Oyewumi, K. J. (2017). The semi-relativistic scattering states of the two-body spinless Salpeter equation with the Varshni potential model. The European Physical Journal Plus, 132, Article Number 277.
Crossref
 
Oyewumi, K. J., Falaye, B. J., Onate, C. A., Oluwadare, O. J., & Yahya, W. A. (2014). Thermodynamic properties and the approximate solutions of the Schrödinger equation with the shifted Deng-Fan potential model. Molecular Physics, 112(1), 127-141.
Crossref
 
Song, X. Q., Wang, C. W., & Jia, C. S. (2017). Thermodynamic properties for the sodium dimer. Chemical physics letters, 673, 50-55.
Crossref
 
Tanabashi, M., Carone, C. D., Trippe, T. G., & Wohl, C. G. (2018). Particle Data Group. Physics Review D 98, Article Number 546.
 
Varshni, Y. P. (1957). Comparative study of potential energy functions for diatomic molecules. Reviews of Modern Physics, 29(4), Article Number 664.
Crossref
 
Vega, A., & Flores, J. (2016). Heavy quarkonium properties from Cornell potential using variational method and supersymmetric quantum mechanics. Pramana Journal of Physics, 87(5), 1-7.
Crossref
 
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), 730-741.
Crossref