Spectroscopy and Structural Properties of Heavy Quarkonium Systems

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.