Approximate sum rule for diatomic vibronic states

The simple expression 〈v’‖fΔ${\mathit{U}}^{\mathit{n}}$g‖v’〉 is offered tg are some operators which couple the vibrational levels v’ and v’’ of two interacting electronic states and ΔU=U’-U’’ is the difference of the corresponding internuclear potentials. The rigorous quantum proofs as well as semiclassical justification of this formula are presented and its absolute accuracy is estimated in a closed functional form. Invariant properties and spectroscopic applications of the sum rule, including the evaluation of lifetimes, fine-structure (Λ-doubling) constants, and Landé factors, are discussed.