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Generalisations of the two apparently rational eigenvalues found by Thorson and Moffitt for the Jahn-Teller system Gamma 8 (X) tau 2 are studied. Equations of finite order are established for determining the strength D of the Jahn-Teller interaction of which an eigenvalue lies on a baseline. (A baseline is the line that constitutes the asymptote of a sequence of rotational levels that come into existence as D tends to infinity.) The analysis is extended to the system E(X) epsilon and is illustrated by a number of special examples.
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B. R. Judd (1979) studied this question.
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