A semi-empirical theory of radiative transitions of trapped electrons in polar crystals is developed using a model in which the crystal is considered to consist of a large number of harmonic oscillators all having the same frequency co and which are coupled to the impurity centre by a coupling linear in all the coordinates of the oscillators. The influence of this coupling is calculated up to the second order of a perturbation calculation. In this approximation explicit expressions for the first three moments of the absorption line and for the first two moments of the emission line are derived. These expressions contain certain intricate expressions consisting of combinations of matrix elements of the coupling operator which are considered as adjustable parameters. From a comparison of the theoretical expressions for the moments with experimental data of F-centre absorption and fluorescence it is seen that there is good qualitative agreement between theory and experiment. This agreement would not be present without the inclusion of a higher order of approximation. Thus the Condon approximation which is usually made in these sort of problems is certainly not valid for the case considered here.