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

TL;DR

This paper introduces the shifted Tietz-Wei oscillator as an effective model for simulating atomic interactions in diatomic molecules, providing exact solutions for energy spectra and wavefunctions.

Contribution

It develops an exact quantization approach for the shifted Tietz-Wei oscillator, extending molecular potential modeling beyond traditional methods.

Findings

Accurate energy spectra for multiple diatomic molecules.

Wavefunctions derived using the formula method.

Validation of the shifted Tietz-Wei oscillator as a reliable potential model.

Abstract

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 ($NO \left(a^4\Pi_i\right)$, $NO \left(B^2\Pi_r\right)$, $NO \left(L'^2\phi\right)$, $NO \left(b^4\Sigma^{-}\right)$, $ICl\left(X^1\Sigma_g^{+}\right)$, $ICl\left(A^3\Pi_1\right)$ and $ICl\left(A'^3\Pi_2\right)$ for arbitrary values of $n$ and $\ell$ quantum numbers are obtained. For the sake of completeness, we study the corresponding wavefunctions using the formula method.