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The spectrum of a system of two ions interacting with each other through a boson reservoir is derived in a field theoretic formalism. The symmetries imposed by time reversal are investigated when the ions are of Kramers type. Virtual phonon exchange is found to give a natural explanation for the strong crystal-field dependence and for the anisotropy of the non-dipolar exchange interaction observed for Ce 3+ ions in the lanthanide ethyl sulphates.
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McKenzie et al. (1979) studied this question.
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