Highly accurate vibration-rotation Franck-Condon factors g a b , for a transition between two diatomic electronic states (a) and (b), are sought. When the potentials of states (a) and (b) are of the RKR type, the computation of gab is reduced to that of Franck-Condon integral P b ( i ) = t+' $a(r)$b(r) dr in an interval r,, T , + ~. By using convenient interpolations for the potentials U" and U b in the considered interval, this integral becomes gab(i) = E ~~= 0 8 ~b ( r , + 1 -rJn+'/(n + I), where the "coupling constants" K b depend uniquely on the eigenvalues E a and E of the considered transition and on the potentials U a and U (the number N of terms depends on the desired accuracy). The method used computes the Franck-Condon factors gab without the explicit use of the wave function and by replacing the integrals by simple summations.
To test the values of qQb obtained by this method, the orthogonality rule ~o,$u.$u,z dr = 0 (for v' # u") is used for one state or the other. This test, along with other tests, show that the Franck-Condon factors computed by the present method are accurate to nine significant figures for high and low levels.