Comparative Study of the Mass Spectra of Heavy Quarkonium System with an Interacting Potential Model

Abstract

In this work, the comparison of the mass spectra of heavy quarkonium system with an interacting potential (Class of Yukawa potential) was studied. The Schrodinger equation is analytically solved using Nikiforov- Uvarov (NU) method and series expansion method (SEM). The approximate solutions of the eigen energy equation and corresponding eigenfunction in terms of Laguerre polynomials were obtained using the NU method and the solutions of the eigen energy equation were also obtained with the SEM. The mass spectra for heavy quarkonium system (HQS) for the potential under study were obtained for bottomonium  and charmonium  HQS. We compared the results obtained between NU and SEM. It was noticed that SEM solutions yield mass spectra very close to experimental data compared to solutions with NU method. The obtained results were also compared with works by some other authors and were found to be improved. This study can be extended by using other exponential-type potential models with other analytical approach and a different approximation schemes to obtain the mass spectra of heavy quarkonium system. The relativistic properties using Klein-Gordon or Dirac equations can be explored to obtain the mass spectra of light quarkonia. Finally, the information entailed in the normalized wave-functions can also be studied.