TRANSITIONS OF F CENTER ELECTRONS
temperature dependence of the first moment is obtained without any additional hypothesis if the effect of the polar coupling between the longitudinal optical modes and the center is calculated up to the second order of a perturbation calculation. A consequent treatment of such a calculation implies, that the dependence of the electronic part of the Born-Oppenheimer wave function on the normal coordinates of the lattice can no longer be neglected so that the Condon-approximation is certainly not valid. Calculations show that a relation of the form as given in ( 5) is obtained for the second moment if the dependence of the electronic part of the Born-Oppenheimer wave function on the lattice coordinates is no longer neglected. In this theory all the constants S, B and C can be expressed in terms of (unfortunately rather intricate) combinations of matrix elements of the polar interaction between the lattice motion and the charge distribution.in the F center. As also unexpected properties of the emission spectrum which follow from this more detailed theory find strong support in recent although still somewhat preliminary experiments 8) one may conclude that the use of the Huang-Rhys model without the proposed extensions is indeed not completely justified. A detailed account of this extended theory is in preparation.
In the light of these discussions it is clear that the expression given for the radiationless-transition-probability in ref. 2 which was used in our formula (5) can at best indicate orders of magnitude. Thanks are due toDrs Borden, van Doom and Haven of this laboratory for many stimulating discussions and to Dr D. P o 1 d e r of the University of Bristol for helpful criticism.