Application of extended Cornell potential with spin-spin interaction to diatomic molecules and mass spectra of heavy mesons

Abstract

In this work, the study of mass spectra of mesons with extended Cornell potential coupled with spin-spin interaction has been carried out. This involves approximating the Gaussian function to harmonic term in radial Schrodinger wave equation with the help of Greene-Aldrich approximation to centrifugal term using parametric Nikiforov-Uvarov (NU) method. The addition of spin-spin interaction to the extended Cornell potential helped in determining the singlet (s = 0) and triplet (s = 1) state of mesons which cannot be determined with the absence of the spin. Using the minimization approach implemented using the Mathematica package, the potential free parameters (a,b,c,σ and a_s) ere obtained by fitting the mesons mass spectra states with experimentally observed values of the Particle Data Group (PGD). The potential model was reduced to Pseudoharmonic, Kratzer and extended Cornell potential as special cases. The numerical energies of the Kratzer potential for selected diatomic molecules and for extended Cornell potential as applied to mass spectra of charmonium and bottomonium were in excellent agreement when compared to the work of existing literature. The total wave function for the proposed potential model was expressed in term of Jacobi polynomial. The wave function and probability density plots for charmonium were obtained using Mathematica package.