SPECTROSCOPY AND STRUCTURAL PROPERTIES OF HEAVY QUARKONIUM SYSTEMS

Jonathan Eyire Osang; Etido Patrick Inyang; Ndianabasi Henry Valentine; Samuel Eyeh Mopta; Eddy Sunday William; Joseph Amajama; Christopher Chinasa Ekechukwu

doi:10.31489/2026N3/126-138

Authors

Jonathan Eyire Osang Dr. (Sci.), Department of Physics, University of Cross River State, Calabar, Nigeria
Etido Patrick Inyang Dr. (Sci.), Department of Physics, Faculty of Science, National Open University of Nigeria, Abuja, Nigeria
Ndianabasi Henry Valentine Dr. (Sci.), Department of Science Laboratory Technology, University of Calabar, Calabar, Nigeria
Samuel Eyeh Mopta Dr. (Sci.), Department of Physics, Faculty of Physical Science, University of Calabar, Calabar, Nigeria
Eddy Sunday William Dr. (Sci.), Department of Physics, School of Pure and Applied Sciences, Federal University of Technology, Ikot Abasi, Nigeria
Joseph Amajama Dr. (Sci.), Department of Physics, Faculty of Physical Science, University of Calabar, Calabar, Nigeria
Christopher Chinasa Ekechukwu Mr. (Sci.), Department of Physics, Faculty of Physical Science, University of Calabar, Calabar, Nigeria

DOI:

https://doi.org/10.31489/2026N3/126-138

Keywords:

Heavy Mesons, Varshni–Hellmann Potential, Quark–antiquark interactions, Schrödinger Equation, Quarkonium Spectroscopy

Abstract

The spectroscopy and structural properties of heavy quarkonium systems are investigated within the Varshni–Hellmann potential model. The radial Schrödinger equation is solved analytically using the Nikiforov–Uvarov method to obtain the energy eigenvalues and normalized wavefunctions of charmonium and bottomonium states. The calculated mass spectra are compared with available experimental data and results from previous theoretical studies. The present model yields sum of absolute deviations (SADs) of 0.002 GeV and 0.003, with corresponding mean absolute errors of 0.00029 GeV and 0.00038 GeV for bottomonium and charmonium, respectively. The corresponding wavefunctions are examined to characterize the spatial structure of the bound states. In addition, the wavefunctions at the origin are used within the Van Royen–Weisskopf formalism to calculate the leptonic decay widths and vector decay constants of the J/ψ(1S) and Υ(1S) states. The calculated leptonic widths are 4.467 keV for J/ψ(1S) and 1.190 keV for Υ(1S)), compared with the experimental values of 5.55 keV and 1.340 keV, respectively. The results demonstrate that the Varshni–Hellmann potential provides an analytically tractable framework for describing heavy quarkonium mass spectra, wavefunctions, and selected decay properties. The framework may provide a basis for future investigations of exotic hadronic systems and quarkonium behaviour in extreme quantum chromodynamics environments.

Author's detail

Jonathan Eyire Osang, Dr. (Sci.), Department of Physics, University of Cross River State, Calabar, Nigeria

Osang, Jonathan Eyire. – Dr. (Sci.), Department of Physics, University of Cross River State, Calabar, Nigeria,; SCOPUS Author ID: 7221839733; https://orcid.org/0000-0001-6895-3332; jonathanosang@yahoo.com

Etido Patrick Inyang, Dr. (Sci.), Department of Physics, Faculty of Science, National Open University of Nigeria, Abuja, Nigeria

Inyang, Etido Patrick. – Dr. (Sci.), Department of Physics, Faculty of Science, National Open University of Nigeria, Abuja, Nigeria; SCOPUS Author ID: 16175170000; https://orcid.org/0000-0002-5031-3297; etidophysics@gmail.com

Ndianabasi Henry Valentine, Dr. (Sci.), Department of Science Laboratory Technology, University of Calabar, Calabar, Nigeria

Valentine, Ndianabasi Henry. -Dr. (Sci.), Department of Science Laboratory Technology, University of Calabar, Calabar, Nigeria; SCOPUS Author ID: 57224817629, https://orcid.org/0009-0001-8978-9997; ndianabasivalentine@ unical.edu.ng

Samuel Eyeh Mopta, Dr. (Sci.), Department of Physics, Faculty of Physical Science, University of Calabar, Calabar, Nigeria

Mopta, Samuel Eyeh. - Dr. (Sci.), Department of Physics, Faculty of Physical Science, University of Calabar, Calabar, Nigeria; SCOPUS Author ID: 57927014600; https://orcid.org/0009-0007-3114-9843; samuelmopta@unical.edu.ng

Eddy Sunday William, Dr. (Sci.), Department of Physics, School of Pure and Applied Sciences, Federal University of Technology, Ikot Abasi, Nigeria

William, Eddy Sunday- Dr. (Sci.), Department of Physics, School of Pure and Applied Sciences, Federal University of Technology, Ikot Abasi, Nigeria; SCOPUS Author ID: 57221313665, https://orcid.org/0000-0002-5247-5281; williameddyphysics@gmail.com

Joseph Amajama, Dr. (Sci.), Department of Physics, Faculty of Physical Science, University of Calabar, Calabar, Nigeria

Amajama, Joseph - Dr. (Sci.), Department of Physics, Faculty of Physical Science, University of Calabar, Calabar, Nigeria; SCOPUS Author ID: 58091457900, https://orcid.org/0000-0002-8475-9457; joeamajama@unical.edu.ng

Christopher Chinasa Ekechukwu, Mr. (Sci.), Department of Physics, Faculty of Physical Science, University of Calabar, Calabar, Nigeria

Ekechukwu, Christopher Chinasa- Mr. (Sci.), Department of Physics, Faculty of Physical Science, University of Calabar, Calabar, Nigeria; SCOPUS Author ID: 57190218952; https://orcid.org/0000-0001-7559-4112; ekehmore@gmail.com

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SPECTROSCOPY AND STRUCTURAL PROPERTIES OF HEAVY QUARKONIUM SYSTEMS