Knowledge Bank

The simple expression is offered to approximate sums of the form where f and g are some operators which couple the vibrational levels $\nu \prime$ and $\nu \prime \prime$ of two interacting electronic states and $\Delta U=U\prime U\prime \prime$ is the difference of the corresponding internuclear $potentials1$. The rigorous quantum proofs as well as semiclassical justification of this formula are presented. The approximate sum rule is numerically tested for radiative lifetimes, electronic polarizabilities, fine-structure constants and Lande factors for the vibronic states of the NaK $molecule2$ and its absolute accuracy is estimated in a closed functional forms:- . The approximation is demonstrated to have high accuracy and efficiency for non-diagonal systems, especially for those with significant continuum contributions.