A new deformed Schioberg-type potential and ro-vibrational energies for some diatomic molecules

TL;DR

This paper introduces a new deformed Schioberg-type potential for diatomic molecules, demonstrating its equivalence to the Tietz-Hua oscillator and deriving accurate analytical ro-vibrational energy levels.

Contribution

It presents a novel deformed Schioberg potential, relates it to existing models, and provides an analytical solution for ro-vibrational energies with high accuracy.

Findings

Excellent agreement with numerical methods for selected molecules

Analytical solutions applicable over wide quantum number ranges

Potential equivalence to Tietz-Hua oscillator confirmed

Abstract

We suggest a new deformed Schioberg-type potential for diatomic molecules. We show that it is equivalent to Tietz-Hua oscillator potential. We discuss how to relate our deformed Schi\"oberg potential to Morse, to Deng-Fan , to the improved Manning-Rosen, and to the deformed modified Rosen-Morse potential models. We transform our potential into a proper form and use the supersymmetric quantization to find a closed form analytical solution for the ro-vibrational energy levels that are highly accurate over a wide range of vibrational and rotational quantum numbers. We discuss our results using 4-diatomic molecules NO, O2, O2+, and N2. Our results turn out to compare excellently with those from a generalized pseudospectral numerical method.