Cross-over to incoherent tunnelling of substitutional defects in alkali halide crystals

The dielectric susceptibility of substitutional defects in alkali halides shows a surprising dependence on concentration c. In the dilute case $c<100$ ppm, the susceptibility is proportional to the number of defects. It reaches a maximum at a concentration where the average dipole-dipole interaction is equal to the bare tunnelling amplitude of a single defect and for still higher concentrations $c>1000$ ppm it strongly decreases. The data for various defect systems are in quantitative agreement with a parameter-free master curve derived from a continued fraction expansion for the relevant correlation function. With increasing defect concentration a universal cross-over from coherent tunnelling to incoherent relaxation is driven by a novel relaxation mechanism, based on the dipolar interaction