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

Abstract

AbstractA 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 $$^{14}$$ 14 N$$_2$$ 2 in the ground electronic state $$X^1\Sigma _g^+$$ X 1 Σ g + and the energy levels of dioxygen $$^{16}$$ 16 O$$_2$$ 2 in the ground electronic state $$X^3\Sigma _g^-$$ X 3 Σ g - . The model includes v-dependence of the potential depth $$D_0\rightarrow D_v$$ D 0 → D v as well as interatomic equilibrium separation $$r_0\rightarrow r_v$$ 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 $$\omega _e$$ ω e , $$\omega _ex_e$$ ω e x e and $$\omega _ey_e$$ 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.