Shifted Tietz-Wei oscillator for simulating the atomic interaction in diatomic molecules

The shifted Tietz-Wei (sTW) oscillator is as good as traditional Morse potential in simulating the atomic interaction in diatomic molecules. By using the Pekeris-type approximation to deal with the centrifugal term, we obtain the bound-state solutions of the radial Schr"odinger equation with this typical molecular model via the exact quantization rule (EQR). The energy spectrum for a set of diatomic molecules ($NO\left(a^4{\mathrm{\Pi }}_i\right)$, $NO \left(B^2\Pi_r\right)$,$NO \left(L’^2\phi\right)$,$NO \left(b^4\Sigma^{-}\right)$,$ICl\left(X^1\Sigma_g^{+}\right)$,$ICl\left(A^3\Pi_1\right)$and$ICl\left(A’^3\Pi_2\right)$ for arbitrary values of $n$ and $\mathrm{\ell }$ quantum numbers are obtained. For the sake of completeness, we study the corresponding wavefunctions using the formula method.