Improved energy formula for highly excited vibrational states of Kratzer-Fues oscillator

A mixed supersymmetric-algebraic approach is employed to derive an improved Kratzer-Fues energy formula, which describes the highly excited states of vibrating diatomic systems up to the dissociation limit. The approach proposed has been used to reproduce the coherent anti-Stokes Raman spectra generated by the vibrational transitions of the nitrogen molecule 14 N 2 in the ground electronic state X 1 Σ g + and the energy levels of dioxygen 16 O 2 in the ground electronic state X 3 Σ g - . The model includes v -dependence of the potential depth D 0 → D v as well as interatomic equilibrium separation r 0 → r v and can be used to describe vibrations of diatomic molecules in which nonadiabatic vibrational effects play a significant role. Exact analytical formulae relating the vibrational spectroscopic constants ω e , ω e x e and ω e y e to the parameters defining the model proposed are derived. They enable calculation of the spectral parameters or determination of the model parameters from the experimental data using the inverse spectroscopic procedure. It has been proven that the improved Kratzer-Fues oscillator has a finite number of vibrational quantum states, which distinguishes it from the original model, endowed with infinite number of states.