Ro-vibrational studies of diatomic molecules in a shifted Deng-Fan oscillator potential

TL;DR

This paper introduces a highly accurate and efficient computational method for analyzing the ro-vibrational energy levels of diatomic molecules within a shifted Deng-Fan oscillator potential, providing new data and insights into molecular spectra.

Contribution

A generalized pseudospectral method is developed for precise calculation of bound states in the shifted Deng-Fan potential, including many states reported for the first time.

Findings

Accurate energy levels for low and high states of diatomic molecules.

Excellent agreement with existing literature data.

Many new ro-vibrational states are identified and reported.

Abstract

Bound-state spectra of shifted Deng-Fan oscillator potential are studied by means of a generalized pseudospectral method. Very accurate results are obtained for \emph{both low as well as high} states by a non-uniform optimal discretization of the radial Schr\"odinger equation. Excellent agreement with literature data is observed in \emph{both $s$-wave and rotational} states. Detailed variation of energies with respect to potential parameters is discussed. Application is made to the ro-vibrational levels of four representative diatomic molecules (H$_2$, LiH, HCl, CO). Nine states having $\{n,\ell\} =0,1,2$ are calculated with good accuracy along with 15 other higher states for each of these molecules. Variation of energies with respect to state indices $n$, $\ell$ show \emph{behavior} similar to that in the Morse potential. Many new states are reported here for the first time. In short, a simple, accurate and efficient method is presented for this and other similar potentials in molecular physics.