Estimates and error distribution of EPR g-factors and hyperfine coupling constants

The least-squares method yields well-known estimates which will be called /b G/ macr /sup 2/ and /b K/ macr /sup 2/ for the /b G//sup 2/ and /b K//sup 2/ tensors related to the hyperfine tensor /b T//sup 2/ by /b T//sup 2/=/b G/ /sup -1/ /b K//sup 2/ /b G//sup -1/. However, very little is known about how to estimate the eigenvalues of /b G//sup 2 / and /b T//sup 2/, which are the important EPR parameters. The common procedure used in estimating these EPR parameters consists in computing the eigenvalues of /b G/ macr /sup 2/ and /b T/ macr /sup 2/. The statistical characteristics of these eigenvalue estimators are studied by stimulation. An empirical description of the joint distribution of the eigenvalue estimators is generated. The authors show that a good experimental design is necessary to prevent biased and highly correlated eigenvalue estimators.