Heine and Henry have introduced a theory for the isotope shift for zero-phonon optical transition at defects in semiconductors. They remarked that substitutional Cu in ZnO was an anomalous case with an isotope shift opposite in sign to that expected for their model. Here the model is modified slightly to take account of the effect of the excess or deficit charge on the impurity nucleus, which is not discussed in the original. The first explicit calculation within their model is presented and it is shown that both the sign and the magnitude of the shift at Cu in ZnO agree with experiment within experimental accuracy. The point is that Cu is a very deep acceptor and not a shallow donor. © 1976 The American Physical Society.