Derivation of closed analytical expressions for Rosen-Morse Franck-Condon factors (Q1272669)

Analytical expressions are derived for matrix elements including those which correspond to energy regions near the molecule dissociation barrier, and for Rosen-Morse Franck-Condon factors. In previous works numerical difficulties in computing the double summation were encountered. The solutions presented here allow to avoid the double summations. The summation with respect to very high quantum numbers is presented in closed form. The analytic expressions can be easily examined with respect to the dependence on the parameters of the potential. Closed form solutions for the case of different anharmonicities in the wave functions of the integrand are also derived.