Third-order spin-orbit contributions to two-photon absorption rates were introduced by Judd and Pooler when the second-order theory was found to be inadequate to explain the experimental data for Gd3+ ions in LaF3. However, only one of the two perturbation terms that arise in thrid order was considered. When the omitted term is added, ‘‘unlinked’’ parts are canceled and the good agreement with experiment is lost. Inclusion of previously overlooked scalar two-electron contributions can restore the agreement between theory and experiment.