Mass spectra of quarkonium systems in the shifted generalized Cornell–inverse quadratic potential model

Etido P Inyang

Abstract

In this study, we present an application of the Shifted Generalized Cornell–Inverse Quadratic Potential (SG-CIQP) to heavy quarkonium systems. By solving the radial Schrödinger equation with the Pekeris-type approximation within the Nikiforov–Uvarov method, we derive closed-form expressions for both the energy eigenvalues and wave functions. This approach is applied to charmonium and bottomonium mesons, yielding mass spectra in excellent agreement with experimental data and established theoretical predictions. Notably, the S-wave states are reproduced with high precision, while the P-wave states are captured with quantitatively reliable accuracy, with minor deviations in the charmonium sector attributable to relativistic and coupled-channel effects. These results not only confirm the robustness of the SG-CIQP framework but also establish its potential as a versatile tool for extending quarkonium studies to spin-dependent interactions, relativistic corrections, and the spectroscopy of exotic hadronic states.

Keywords

Schrödinger equation; Quarkonium spectroscopy; Shifted Generalized Cornell–Inverse Quadratic Potential; Nikiforov–Uvarov method; Pekeris-type approximation

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References

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DOI: https://doi.org/10.20961/jphystheor-appl.v9i2.109207

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