The Effect of Debye Mass on the Mass Spectra of Heavy Quarkonium System and Its Thermal Properties with Class of Yukawa Potential

Abstract: In this research, we first solve the radial Schrödinger equation analytically using the Nikiforov–Uvarov method with the class of Yukawa potential by replacing the screening parameter with Debye mass and the energy eigenvalues and Then, the corresponding wave functions are obtained in closed form. The obtained energy equation is used to predict the mass spectra of heavy quarkonium systems, namely, charmonium ( ) and bottomonium ( ). Thermal properties such as mean energy, free energy, entropy, and specific heat capacity are also studied. It is found that the presence of Debye mass removes degeneracy in the newly predicted quantum states. Three particular cases are examined, yielding Hellmann potential, inversely quadratic Yukawa potential, and Coulomb potential. The research provides satisfying results in comparison with experimental data and some works in literature with a maximum error of 0.0045 GeV. Keywords: Schrödinger equation, Nikiforov–Uvarov method, Class of Yukawa potential, Heavy quarkonium system, Thermal properties.