CROSS-OVER TO INCOHERENT TUNNELING OF SUBSTITUTIONAL DEFECTS IN ALKALI-HALIDE CRYSTALS

The dielectric susceptibility of substitutional defects in alkali hali des shows a surprising dependence on concentration c. In the dilute ca se c < 100 ppm, the susceptibility is proportional to the number of de fects. It reaches a maximum at a concentration where the average dipol e-dipole interaction is equal to the bare tunnelling amplitude of a si ngle defect and for still higher concentrations c > 1000 ppm it strong ly 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 increas ing defect concentration a universal cross-over from coherent tunnelli ng to incoherent relaxation is driven by a novel relaxation mechanism, based on the dipolar interaction.