Stochastic theory of spin relaxation in liquids

A stochastic theory of line shape is considered for describing molecular reorientational processes in liquids. The theory takes into account both secular and nonsecular terms in the interaction Hamiltonian. A general solution for the line shape is given in a matrix form by assuming a Markovian modulation for the random process. The usefulness of the theory is demonstrated by doing perturbation theory calculations in the motionally narrowed limit. A resolvent-operator technique is employed for collecting higher-order terms in perturbation theory. Two models for molecular motion, (i) rotational diffusion and (ii) strong-collision approximation, are treated and their predictions compared. In the case of the rotational-diffusion model, the results are illustrated by considering a $g$-tensor interaction in liquids. Expressions for line width and shift are given up to fourth order in perturbation theory, and a detailed comparison is made with the existing theories.