Exact analytic formula for calculating Franck–Condon factors using the Kratzer potential

Abstract

To calculate Franck–Condon factors (i.e., squares of the vibrational overlap integrals for two electronic states of a diatomic molecule), the potential energy curve in each state is approximated by the function proposed originally by Kratzer. The resulting factors q(v′,v″) are compared with experimental data for the following band systems: CN(A 2Π–X 2Σ+), N2(B 3Πg–A 3Σ+u; a 1Πg–X 1Σ+g; C 3Πu–X 1Σ+g), and CO(A 1Π–X 1Σ+). Very satisfactory agreement between theory and experiment is observed for low values of the vibrational quantum numbers v′ and v″ (v′,v″≤3).