Gohar Fractional Effect on the Diatomic structure and Ro-vibrational Spectroscopy in the Molecular Kratzer Model

Solving Schrödinger equation (SE) for the wavefunction and binding energy levels of the diatomic molecular system is essential for modeling its structure and analyzing its spectral properties, as the complete wave function inherently involves all the necessary information to analyze its physical properties, while the obtained energy levels reveal its spectroscopic characteristics. In this work, the Nikiforov-Uvarov (NU) analytical method is brought into the domain of Gohar fractional calculus (GFC). We use the Gohar fractional NU (GFNU) method to solve the fractional hyper-radial SE for the binding ro-vibrational energy spectra of some homo-nuclear and hetero-nuclear diatomic molecules (DMs) in the molecular Kratzer model for arbitrary values of the vibrational and rotational quantum numbers. Graphical analysis is used to explore the effect of the fractional parameter on the obtained diatomic energy levels and their corresponding normalized hyper-radial wave functions. Interestingly, the fractional parameter was found to have a significant effect on the diatomic structure and spectral properties. The graphical behavior of the Kratzer potential (KP) model and its modified version was analyzed for various DMs. It was observed that the characteristic features of both potential models were affected by the variation of the fractional parameter. We also investigated the dependence of the diatomic energies in both potentials on dimensionality, equilibrium inter-nuclear distance, reduced mass, and quantum numbers. This study provided entirely new results for the energy levels of HCL, LiH, ScH, H2, O2, and I2 DMs in the modified Kratzer potential (MKP) that had not been previously reported in the literature.