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A t low vacancy concentrations in crystals it is possible to define an encounter of a given pair of atoms and a vacancy as the set of displacements of the pair of atoms caused by a randomly walking vacancy. The relative displacement probability of a pair of atoms caused by an encounter with a vacancy is calculated from random walk theory applied to the vacancy motion. The resulting displacement probability is used to calculate the high-frequency limit of the correlation functions relevant in nuclear spin relaxation by translational diffusion due to the vacancy mechanism in cubic crystals.

In this paper we present a calculation of the effects of bottom mixing with new exotic quarks on the Z −→ bb branching ratio and asymmetries and on the QCD coupling constant. A global fit to these quantities as recently measured in e − e + annihilation at the Z peak is done and stringent bounds are obtained. We discuss the effects of different isospin signatures for the possible new exotic quarks. The consequences for superstring-inspired E 6 models are discussed. Constraints on the bottom mixing angles with the isosinglet quarks of the fundamental 27-plet are presented.

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