Orthogonal polynomial solutions to the non-central modified Kratzer potential

We investigate the analytical solution of a new exactly solvable non-central potential of $V(r,\theta) = D({\frac{r - a}{r}})^2+{\frac{\beta}{r^2\sin^2 \theta}}+{\frac{\gamma \cos \theta}{r^2\sin^2 \theta}}$ type, which may be called as the modified non-central Kratzer potential. The energy eigenvalues as well as the corresponding eigenfunctions are calculated for various values of $n$ and $m$ quantum numbers within the framework of the Nikiforov-Uvarov and Asymtotic Iteration Methods for the $CO$ diatomic molecule as an application of this potential. In this paper, we first present the effect of the non-central term on the bound-state energy eigenvalues: this effect is determined explicitly for different $n$ and $m$ quantum numbers with $\beta=\gamma$=0.0, 0.1, 1.0 and 5.0 values and the results are compared with the findings of the modified Kratzer potential for different $n$ and $l$ quantum numbers. Then, we show that the angle-dependent non-central part behaves like a centrifugal barrier and it reduces the depth of the attractive potential pocket, which effects the bound-state energy eigenvalues.