A Systematic Study on Nonrelativistic Quarkonium Interaction

recently proposed strictly phenomenological static quark-antiquark potential belonging to the generality $V(r)=-Ar^{-\alpha}+\kappa r^{\beta}+V_{0}$ is tested with heavy quarkonia in the context of the shifted large N-expansion method. This nonrelativistic potential model fits the spin-averaged mass spectra of the $c\bar{c},$ $b\bar{b}$ and $c$ quarkonia within a few ${\rm MeV}$ and also the five experimentally known leptonic decay widths of the $c\bar{c}$ and $b$ vector states. Further, we compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittings of the charmonium spectrum. We give predictions for not yet observed $B_{c}$ splittings. The model is then used to predict the masses of the remaining quarkonia and the leptonic decay widths of the two pseudoscalar c\bar{b%} states. Our results are compared with other models to gauge the reliability of the predictions and point out differences.Comment: 24 page

Bound Energy Masses of Mesons Containing the Fourth Generation and Iso-singlet Quarks

The fourth Standard Model (SM) family quarks and weak iso-singlet quarks The fourth Standard Model (SM) family quarks and weak iso-singlet quarks predicted by ${\rm E}_{6\text{}}$ GUT are considered. The spin-average of the pseudoscalar $\eta_{4}(n^{1}S_{0})$ and vector $\psi_{4}(n^{3}S_{1})$ quarkonium binding masses of the new mesons formed by the fourth Standard Model (SM) family and iso-singlet ${\rm E}_{6\text{}}$ with their mixings to ordinary quarks are investigated. Further, the fine and hyperfine mass splittings of the these states are also calculated. We solved the Schr\"{o}dinger equation with logarithmic and Martin potentials using the Shifted large-${\rm N}$ expansion technique. Our results are compared with other models to gauge the reliability of the predictions and point out differences.Comment: 13 page

New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case

We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically.Comment: Version to match the one which has been accepted for publication by J. Phys. A: Math. Theor. Added one figure, several comments and few references. (24 pages and 7 figures

Exact solution of Schrodinger equation for modified Kratzer's molecular potential with the position-dependent mass

Exact solutions of Schrodinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied. PACS numbers: 03.65.-w; 03.65.Ge; 12.39.Fd Keywords: Morse potential, Kratzer potential, Position-dependent mass, Point canonical transformation, Effective mass Schr\"{o}dinger equation.Comment: 9 page