An analytic formula of one-dimensional Franck-Condon factors for linear harmonic oscillators

With the aid of an addition theorem for harmonic oscillator wave functions, the Franck-Condon factors between two displaced linear oscillators with unequal vibrational frequencies are transformed into an analytic form which is programmable for numerical evaluations. Franck-Condon factors for the A¹Σ_u⁺-X¹Σ_g⁺ system and the B¹Π_u-X¹Σ_g⁺ system of ⁷Li₂ are calculated via this analytic formula.