We have calculated electron-phonon matrix elements relevant for indirect optical absorption, intervalley matrix elements and intravalley deformation potentials as well as splitting parameters for the k = 0 states in silicon and germanium within the rigid quasi-ion model. In contrast to the “atomic” potentials in conventional rigid-ion models the quasi-ion potentials are well-defined. The agreement with experiment and with other theoretical results is satisfactory in most cases. We have also studied the role of distortion corrections to the rigid quasi-ion approximation. We find that the influence of distortions is small, indicating that the rigid quasi-ion model is an adequate description - at least in case of these two materials.