Partial summations and ESR line shapes in the slow tumbling region

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Abstract
Beginning with the results of Hwang, Anderson, and Friedman we derive an expression for the line shape of a spin‐one system having an axially symmetrical isotropically tumbling g‐tensor and a zero‐field splitting term. The expression is in the form of a continued fraction and is obtained by a series of partial summations of subsets of an infinite set of graphs appropriate to the problem. We are able to vary the relative strengths of the g and D tensors, thereby obtaining any mixture of the two. The expression allows us to go to arbitrarily slow tumbling rates with a minimum of computation.