Longitudinal muon spin relaxation in muonium-like systems

Nuclear spin-lattice relaxation in paramagnetic systems is treated using the classic expression for transition probability between the coupled electron and nuclear spin states. The rate equations governing the incoherent occupancies of these states are solved analytically (where possible) and numerically (where not) to construct the relaxation function for the nuclear spin. The method is illustrated for muonium, and the muonium-substituted molecular radicals, for the case of perturbation due to fluctuation of the local field,i.e. modulation of the interaction with a third spin. A slight departure from single exponential behaviour is demonstrated for slow fluctuations.