Virtual phonon exchange between Kramers ions in a field theoretic formalism

Abstract
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 Ce3+ ions in the lanthanide ethyl sulphates.