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We consider the spin correlation functions for rare-earth compounds in theirparamagnetic state with the aim to understand the temperature dependence of thequasi-elastic and crystal-field linewidths and the spin-lattice relaxationrates measured by the muon-spin-relaxation technique. Both the conductionelectron and phonon relaxation mechanisms are treated. First the single-iondynamics is described using an iterative method introduced by P. M. Richards.Then the case of a regular lattice of rare-earth ions is studied using therandom-phase approximation (RPA). Applications to simple crystal-field levelschemes are given with particular emphasis on the phonon relaxation mechanism.This allows us to investigate the domain of validity of our results. In orderto account for data recorded on insulators, a phenomelogical modification issuggested.

Spin correlations in rare-earth paramagnetic systems; neutron linewidths and muSR spin-lattice relaxation rates