  Ab initio Perturbed Ion cluster-in-the-lattice calculations of the impurity
centers NaI:Tl+ and CsI:Tl+ are pressented. We study several active clusters of
increasing complexity and show that the lattice relaxation around the Tl+
impurity implies the concerted movement of several shells of neighbors. The
results also reveal the importance of considering a set of ions that can
respond to the geometrical displacements of the inner shells by adapting
selfconsistently their wave functions. Comparison with other calculations
involving comparatively small active clusters serves to assert the significance
of our conclusions. Contact with experiment is made by calculating absorption
energies. These are in excellent agreement with the experimental data for the
most realistic active clusters considered.
